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Add Dgebrd, Dgebd2, and Dlabrd and tests

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This commit is contained in:
btracey
2015-10-28 00:24:32 -06:00
parent d6fe31a937
commit bd71f87f5f
57 changed files with 17917 additions and 44 deletions
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6
cgo/lapack.go
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@@ -14,8 +14,10 @@ import (
// Copied from lapack/native. Keep in sync.
const (
absIncNotOne = "lapack: increment not one or negative one"
badD = "lapack: d has insufficient length"
badDiag = "lapack: bad diag"
badDirect = "lapack: bad direct"
badE = "lapack: e has insufficient length"
badIpiv = "lapack: insufficient permutation length"
badLdA = "lapack: index of a out of range"
badNorm = "lapack: bad norm"
@@ -24,15 +26,19 @@ const (
badSlice = "lapack: bad input slice length"
badStore = "lapack: bad store"
badTau = "lapack: tau has insufficient length"
badTauQ = "lapack: tauQ has insufficient length"
badTauP = "lapack: tauP has insufficient length"
badTrans = "lapack: bad trans"
badUplo = "lapack: illegal triangle"
badWork = "lapack: insufficient working memory"
badWorkStride = "lapack: insufficient working array stride"
badZ = "lapack: insufficient z length"
kGTM = "lapack: k > m"
kGTN = "lapack: k > n"
kLT0 = "lapack: k < 0"
mLTN = "lapack: m < n"
negDimension = "lapack: negative matrix dimension"
negZ = "lapack: negative z value"
nLT0 = "lapack: n < 0"
nLTM = "lapack: n < m"
shortWork = "lapack: working array shorter than declared"

27
internal/testdata/dlasqtest/Makefile vendored Normal file
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@@ -0,0 +1,27 @@
FC = gfortran
FFLAGS = -O2
targets = testdlasq1 testdlasq2 testdlasq3 testdlasq4
objects = dlamch.o lsame.o xerbla.o ieeeck.o iparmq.o ilaenv.o dlasrt.o \
dlaisnan.o disnan.o dlasq6.o dlasq5.o dlasq4.o dlasq3.o dlasq2.o
default : $(targets)
.PHONY : default
testdlasq1 : testdlasq1.o $(objects) dcopy.o dlas2.o dlascl.o dlasq1.o
testdlasq2 : testdlasq2.o $(objects)
testdlasq3 : testdlasq3.o $(objects)
testdlasq4 : testdlasq4.o $(objects)
% : %.o
$(FC) $(FFLAGS) $^ -o $@
%.o : %.f90
$(FC) $(FFLAGS) -c -o $@ $<
clean :
rm -f *.o $(targets) *.txt
.PHONY : clean

23
internal/testdata/dlasqtest/Readme.md vendored Normal file
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@@ -0,0 +1,23 @@
This set of codes generates tests for the dlasq* routines.
The high level routines are testdlasq*.f90. The testdlasq*.f90 routines are intended in combination with the routines in gonum/lapack/testlapack.
During execution, these high-level routines record the inputs and outputs
to the executed subroutines. For example, testdlasq3, when executed,
generates files gen4tests.txt and gen5tests.txt that record the inputs
and outputs to the evaluation of dlasq4 and dlasq5 respectively. The output
format in gen*tests.txt is the struct literal that matches the respective test
in gonum/lapack/testlapack/dlasq*.go. Thus, these generated tests can be copied
into the testing routine to test the native implementation.
The testing routines in testlapack have code for generating inputs for these
fortran routines. Typically, one would isolate the particular failing test,
and modify the testlapack routine to print it to the terminal, for example
in testlapack/dlasq3.go one might add
printDlasq3FortranInput(test)
os.Exit(1)
This prints variable initialization for dlasq3 routine to the terminal, which
can be copied and pasted into testdlasq3.f90. Please note that this process
is not completely automated. Some of the other initialization may need to
change, particularly the size allocation of the data array(s).

115
internal/testdata/dlasqtest/dcopy.f vendored Normal file
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@@ -0,0 +1,115 @@
*> \brief \b DCOPY
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
*
* .. Scalar Arguments ..
* INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION DX(*),DY(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DCOPY copies a vector, x, to a vector, y.
*> uses unrolled loops for increments equal to one.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup double_blas_level1
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
*
* -- Reference BLAS level1 routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
DOUBLE PRECISION DX(*),DY(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I,IX,IY,M,MP1
* ..
* .. Intrinsic Functions ..
INTRINSIC MOD
* ..
IF (N.LE.0) RETURN
IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN
*
* code for both increments equal to 1
*
*
* clean-up loop
*
M = MOD(N,7)
IF (M.NE.0) THEN
DO I = 1,M
DY(I) = DX(I)
END DO
IF (N.LT.7) RETURN
END IF
MP1 = M + 1
DO I = MP1,N,7
DY(I) = DX(I)
DY(I+1) = DX(I+1)
DY(I+2) = DX(I+2)
DY(I+3) = DX(I+3)
DY(I+4) = DX(I+4)
DY(I+5) = DX(I+5)
DY(I+6) = DX(I+6)
END DO
ELSE
*
* code for unequal increments or equal increments
* not equal to 1
*
IX = 1
IY = 1
IF (INCX.LT.0) IX = (-N+1)*INCX + 1
IF (INCY.LT.0) IY = (-N+1)*INCY + 1
DO I = 1,N
DY(IY) = DX(IX)
IX = IX + INCX
IY = IY + INCY
END DO
END IF
RETURN
END

80
internal/testdata/dlasqtest/disnan.f vendored Normal file
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@@ -0,0 +1,80 @@
*> \brief \b DISNAN tests input for NaN.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DISNAN + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/disnan.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/disnan.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/disnan.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* LOGICAL FUNCTION DISNAN( DIN )
*
* .. Scalar Arguments ..
* DOUBLE PRECISION DIN
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DISNAN returns .TRUE. if its argument is NaN, and .FALSE.
*> otherwise. To be replaced by the Fortran 2003 intrinsic in the
*> future.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] DIN
*> \verbatim
*> DIN is DOUBLE PRECISION
*> Input to test for NaN.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
* =====================================================================
LOGICAL FUNCTION DISNAN( DIN )
*
* -- LAPACK auxiliary routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
DOUBLE PRECISION DIN
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL DLAISNAN
EXTERNAL DLAISNAN
* ..
* .. Executable Statements ..
DISNAN = DLAISNAN(DIN,DIN)
RETURN
END

91
internal/testdata/dlasqtest/dlaisnan.f vendored Normal file
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@@ -0,0 +1,91 @@
*> \brief \b DLAISNAN tests input for NaN by comparing two arguments for inequality.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLAISNAN + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaisnan.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaisnan.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaisnan.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 )
*
* .. Scalar Arguments ..
* DOUBLE PRECISION DIN1, DIN2
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> This routine is not for general use. It exists solely to avoid
*> over-optimization in DISNAN.
*>
*> DLAISNAN checks for NaNs by comparing its two arguments for
*> inequality. NaN is the only floating-point value where NaN != NaN
*> returns .TRUE. To check for NaNs, pass the same variable as both
*> arguments.
*>
*> A compiler must assume that the two arguments are
*> not the same variable, and the test will not be optimized away.
*> Interprocedural or whole-program optimization may delete this
*> test. The ISNAN functions will be replaced by the correct
*> Fortran 03 intrinsic once the intrinsic is widely available.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] DIN1
*> \verbatim
*> DIN1 is DOUBLE PRECISION
*> \endverbatim
*>
*> \param[in] DIN2
*> \verbatim
*> DIN2 is DOUBLE PRECISION
*> Two numbers to compare for inequality.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
* =====================================================================
LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 )
*
* -- LAPACK auxiliary routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
DOUBLE PRECISION DIN1, DIN2
* ..
*
* =====================================================================
*
* .. Executable Statements ..
DLAISNAN = (DIN1.NE.DIN2)
RETURN
END

193
internal/testdata/dlasqtest/dlamch.f vendored Normal file
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@@ -0,0 +1,193 @@
*> \brief \b DLAMCH
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION DLAMCH( CMACH )
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLAMCH determines double precision machine parameters.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] CMACH
*> \verbatim
*> Specifies the value to be returned by DLAMCH:
*> = 'E' or 'e', DLAMCH := eps
*> = 'S' or 's , DLAMCH := sfmin
*> = 'B' or 'b', DLAMCH := base
*> = 'P' or 'p', DLAMCH := eps*base
*> = 'N' or 'n', DLAMCH := t
*> = 'R' or 'r', DLAMCH := rnd
*> = 'M' or 'm', DLAMCH := emin
*> = 'U' or 'u', DLAMCH := rmin
*> = 'L' or 'l', DLAMCH := emax
*> = 'O' or 'o', DLAMCH := rmax
*> where
*> eps = relative machine precision
*> sfmin = safe minimum, such that 1/sfmin does not overflow
*> base = base of the machine
*> prec = eps*base
*> t = number of (base) digits in the mantissa
*> rnd = 1.0 when rounding occurs in addition, 0.0 otherwise
*> emin = minimum exponent before (gradual) underflow
*> rmin = underflow threshold - base**(emin-1)
*> emax = largest exponent before overflow
*> rmax = overflow threshold - (base**emax)*(1-eps)
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup auxOTHERauxiliary
*
* =====================================================================
DOUBLE PRECISION FUNCTION DLAMCH( CMACH )
*
* -- LAPACK auxiliary routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER CMACH
* ..
*
* .. Scalar Arguments ..
DOUBLE PRECISION A, B
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
DOUBLE PRECISION RND, EPS, SFMIN, SMALL, RMACH
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. Intrinsic Functions ..
INTRINSIC DIGITS, EPSILON, HUGE, MAXEXPONENT,
$ MINEXPONENT, RADIX, TINY
* ..
* .. Executable Statements ..
*
*
* Assume rounding, not chopping. Always.
*
RND = ONE
*
IF( ONE.EQ.RND ) THEN
EPS = EPSILON(ZERO) * 0.5
ELSE
EPS = EPSILON(ZERO)
END IF
*
IF( LSAME( CMACH, 'E' ) ) THEN
RMACH = EPS
ELSE IF( LSAME( CMACH, 'S' ) ) THEN
SFMIN = TINY(ZERO)
SMALL = ONE / HUGE(ZERO)
IF( SMALL.GE.SFMIN ) THEN
*
* Use SMALL plus a bit, to avoid the possibility of rounding
* causing overflow when computing 1/sfmin.
*
SFMIN = SMALL*( ONE+EPS )
END IF
RMACH = SFMIN
ELSE IF( LSAME( CMACH, 'B' ) ) THEN
RMACH = RADIX(ZERO)
ELSE IF( LSAME( CMACH, 'P' ) ) THEN
RMACH = EPS * RADIX(ZERO)
ELSE IF( LSAME( CMACH, 'N' ) ) THEN
RMACH = DIGITS(ZERO)
ELSE IF( LSAME( CMACH, 'R' ) ) THEN
RMACH = RND
ELSE IF( LSAME( CMACH, 'M' ) ) THEN
RMACH = MINEXPONENT(ZERO)
ELSE IF( LSAME( CMACH, 'U' ) ) THEN
RMACH = tiny(zero)
ELSE IF( LSAME( CMACH, 'L' ) ) THEN
RMACH = MAXEXPONENT(ZERO)
ELSE IF( LSAME( CMACH, 'O' ) ) THEN
RMACH = HUGE(ZERO)
ELSE
RMACH = ZERO
END IF
*
DLAMCH = RMACH
RETURN
*
* End of DLAMCH
*
END
************************************************************************
*> \brief \b DLAMC3
*> \details
*> \b Purpose:
*> \verbatim
*> DLAMC3 is intended to force A and B to be stored prior to doing
*> the addition of A and B , for use in situations where optimizers
*> might hold one of these in a register.
*> \endverbatim
*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..
*> \date November 2011
*> \ingroup auxOTHERauxiliary
*>
*> \param[in] A
*> \verbatim
*> A is a DOUBLE PRECISION
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is a DOUBLE PRECISION
*> The values A and B.
*> \endverbatim
*>
DOUBLE PRECISION FUNCTION DLAMC3( A, B )
*
* -- LAPACK auxiliary routine (version 3.4.0) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2010
*
* .. Scalar Arguments ..
DOUBLE PRECISION A, B
* ..
* =====================================================================
*
* .. Executable Statements ..
*
DLAMC3 = A + B
*
RETURN
*
* End of DLAMC3
*
END
*
************************************************************************

183
internal/testdata/dlasqtest/dlas2.f vendored Normal file
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*> \brief \b DLAS2 computes singular values of a 2-by-2 triangular matrix.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLAS2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlas2.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlas2.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlas2.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX )
*
* .. Scalar Arguments ..
* DOUBLE PRECISION F, G, H, SSMAX, SSMIN
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLAS2 computes the singular values of the 2-by-2 matrix
*> [ F G ]
*> [ 0 H ].
*> On return, SSMIN is the smaller singular value and SSMAX is the
*> larger singular value.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] F
*> \verbatim
*> F is DOUBLE PRECISION
*> The (1,1) element of the 2-by-2 matrix.
*> \endverbatim
*>
*> \param[in] G
*> \verbatim
*> G is DOUBLE PRECISION
*> The (1,2) element of the 2-by-2 matrix.
*> \endverbatim
*>
*> \param[in] H
*> \verbatim
*> H is DOUBLE PRECISION
*> The (2,2) element of the 2-by-2 matrix.
*> \endverbatim
*>
*> \param[out] SSMIN
*> \verbatim
*> SSMIN is DOUBLE PRECISION
*> The smaller singular value.
*> \endverbatim
*>
*> \param[out] SSMAX
*> \verbatim
*> SSMAX is DOUBLE PRECISION
*> The larger singular value.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Barring over/underflow, all output quantities are correct to within
*> a few units in the last place (ulps), even in the absence of a guard
*> digit in addition/subtraction.
*>
*> In IEEE arithmetic, the code works correctly if one matrix element is
*> infinite.
*>
*> Overflow will not occur unless the largest singular value itself
*> overflows, or is within a few ulps of overflow. (On machines with
*> partial overflow, like the Cray, overflow may occur if the largest
*> singular value is within a factor of 2 of overflow.)
*>
*> Underflow is harmless if underflow is gradual. Otherwise, results
*> may correspond to a matrix modified by perturbations of size near
*> the underflow threshold.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX )
*
* -- LAPACK auxiliary routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
DOUBLE PRECISION F, G, H, SSMAX, SSMIN
* ..
*
* ====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D0 )
DOUBLE PRECISION TWO
PARAMETER ( TWO = 2.0D0 )
* ..
* .. Local Scalars ..
DOUBLE PRECISION AS, AT, AU, C, FA, FHMN, FHMX, GA, HA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, SQRT
* ..
* .. Executable Statements ..
*
FA = ABS( F )
GA = ABS( G )
HA = ABS( H )
FHMN = MIN( FA, HA )
FHMX = MAX( FA, HA )
IF( FHMN.EQ.ZERO ) THEN
SSMIN = ZERO
IF( FHMX.EQ.ZERO ) THEN
SSMAX = GA
ELSE
SSMAX = MAX( FHMX, GA )*SQRT( ONE+
$ ( MIN( FHMX, GA ) / MAX( FHMX, GA ) )**2 )
END IF
ELSE
IF( GA.LT.FHMX ) THEN
AS = ONE + FHMN / FHMX
AT = ( FHMX-FHMN ) / FHMX
AU = ( GA / FHMX )**2
C = TWO / ( SQRT( AS*AS+AU )+SQRT( AT*AT+AU ) )
SSMIN = FHMN*C
SSMAX = FHMX / C
ELSE
AU = FHMX / GA
IF( AU.EQ.ZERO ) THEN
*
* Avoid possible harmful underflow if exponent range
* asymmetric (true SSMIN may not underflow even if
* AU underflows)
*
SSMIN = ( FHMN*FHMX ) / GA
SSMAX = GA
ELSE
AS = ONE + FHMN / FHMX
AT = ( FHMX-FHMN ) / FHMX
C = ONE / ( SQRT( ONE+( AS*AU )**2 )+
$ SQRT( ONE+( AT*AU )**2 ) )
SSMIN = ( FHMN*C )*AU
SSMIN = SSMIN + SSMIN
SSMAX = GA / ( C+C )
END IF
END IF
END IF
RETURN
*
* End of DLAS2
*
END

364
internal/testdata/dlasqtest/dlascl.f vendored Normal file
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*> \brief \b DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLASCL + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlascl.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlascl.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlascl.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO )
*
* .. Scalar Arguments ..
* CHARACTER TYPE
* INTEGER INFO, KL, KU, LDA, M, N
* DOUBLE PRECISION CFROM, CTO
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLASCL multiplies the M by N real matrix A by the real scalar
*> CTO/CFROM. This is done without over/underflow as long as the final
*> result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that
*> A may be full, upper triangular, lower triangular, upper Hessenberg,
*> or banded.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TYPE
*> \verbatim
*> TYPE is CHARACTER*1
*> TYPE indices the storage type of the input matrix.
*> = 'G': A is a full matrix.
*> = 'L': A is a lower triangular matrix.
*> = 'U': A is an upper triangular matrix.
*> = 'H': A is an upper Hessenberg matrix.
*> = 'B': A is a symmetric band matrix with lower bandwidth KL
*> and upper bandwidth KU and with the only the lower
*> half stored.
*> = 'Q': A is a symmetric band matrix with lower bandwidth KL
*> and upper bandwidth KU and with the only the upper
*> half stored.
*> = 'Z': A is a band matrix with lower bandwidth KL and upper
*> bandwidth KU. See DGBTRF for storage details.
*> \endverbatim
*>
*> \param[in] KL
*> \verbatim
*> KL is INTEGER
*> The lower bandwidth of A. Referenced only if TYPE = 'B',
*> 'Q' or 'Z'.
*> \endverbatim
*>
*> \param[in] KU
*> \verbatim
*> KU is INTEGER
*> The upper bandwidth of A. Referenced only if TYPE = 'B',
*> 'Q' or 'Z'.
*> \endverbatim
*>
*> \param[in] CFROM
*> \verbatim
*> CFROM is DOUBLE PRECISION
*> \endverbatim
*>
*> \param[in] CTO
*> \verbatim
*> CTO is DOUBLE PRECISION
*>
*> The matrix A is multiplied by CTO/CFROM. A(I,J) is computed
*> without over/underflow if the final result CTO*A(I,J)/CFROM
*> can be represented without over/underflow. CFROM must be
*> nonzero.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> The matrix to be multiplied by CTO/CFROM. See TYPE for the
*> storage type.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> 0 - successful exit
*> <0 - if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
* =====================================================================
SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO )
*
* -- LAPACK auxiliary routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
CHARACTER TYPE
INTEGER INFO, KL, KU, LDA, M, N
DOUBLE PRECISION CFROM, CTO
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
* ..
* .. Local Scalars ..
LOGICAL DONE
INTEGER I, ITYPE, J, K1, K2, K3, K4
DOUBLE PRECISION BIGNUM, CFROM1, CFROMC, CTO1, CTOC, MUL, SMLNUM
* ..
* .. External Functions ..
LOGICAL LSAME, DISNAN
DOUBLE PRECISION DLAMCH
EXTERNAL LSAME, DLAMCH, DISNAN
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
*
IF( LSAME( TYPE, 'G' ) ) THEN
ITYPE = 0
ELSE IF( LSAME( TYPE, 'L' ) ) THEN
ITYPE = 1
ELSE IF( LSAME( TYPE, 'U' ) ) THEN
ITYPE = 2
ELSE IF( LSAME( TYPE, 'H' ) ) THEN
ITYPE = 3
ELSE IF( LSAME( TYPE, 'B' ) ) THEN
ITYPE = 4
ELSE IF( LSAME( TYPE, 'Q' ) ) THEN
ITYPE = 5
ELSE IF( LSAME( TYPE, 'Z' ) ) THEN
ITYPE = 6
ELSE
ITYPE = -1
END IF
*
IF( ITYPE.EQ.-1 ) THEN
INFO = -1
ELSE IF( CFROM.EQ.ZERO .OR. DISNAN(CFROM) ) THEN
INFO = -4
ELSE IF( DISNAN(CTO) ) THEN
INFO = -5
ELSE IF( M.LT.0 ) THEN
INFO = -6
ELSE IF( N.LT.0 .OR. ( ITYPE.EQ.4 .AND. N.NE.M ) .OR.
$ ( ITYPE.EQ.5 .AND. N.NE.M ) ) THEN
INFO = -7
ELSE IF( ITYPE.LE.3 .AND. LDA.LT.MAX( 1, M ) ) THEN
INFO = -9
ELSE IF( ITYPE.GE.4 ) THEN
IF( KL.LT.0 .OR. KL.GT.MAX( M-1, 0 ) ) THEN
INFO = -2
ELSE IF( KU.LT.0 .OR. KU.GT.MAX( N-1, 0 ) .OR.
$ ( ( ITYPE.EQ.4 .OR. ITYPE.EQ.5 ) .AND. KL.NE.KU ) )
$ THEN
INFO = -3
ELSE IF( ( ITYPE.EQ.4 .AND. LDA.LT.KL+1 ) .OR.
$ ( ITYPE.EQ.5 .AND. LDA.LT.KU+1 ) .OR.
$ ( ITYPE.EQ.6 .AND. LDA.LT.2*KL+KU+1 ) ) THEN
INFO = -9
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DLASCL', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. M.EQ.0 )
$ RETURN
*
* Get machine parameters
*
SMLNUM = DLAMCH( 'S' )
BIGNUM = ONE / SMLNUM
*
CFROMC = CFROM
CTOC = CTO
*
10 CONTINUE
CFROM1 = CFROMC*SMLNUM
IF( CFROM1.EQ.CFROMC ) THEN
! CFROMC is an inf. Multiply by a correctly signed zero for
! finite CTOC, or a NaN if CTOC is infinite.
MUL = CTOC / CFROMC
DONE = .TRUE.
CTO1 = CTOC
ELSE
CTO1 = CTOC / BIGNUM
IF( CTO1.EQ.CTOC ) THEN
! CTOC is either 0 or an inf. In both cases, CTOC itself
! serves as the correct multiplication factor.
MUL = CTOC
DONE = .TRUE.
CFROMC = ONE
ELSE IF( ABS( CFROM1 ).GT.ABS( CTOC ) .AND. CTOC.NE.ZERO ) THEN
MUL = SMLNUM
DONE = .FALSE.
CFROMC = CFROM1
ELSE IF( ABS( CTO1 ).GT.ABS( CFROMC ) ) THEN
MUL = BIGNUM
DONE = .FALSE.
CTOC = CTO1
ELSE
MUL = CTOC / CFROMC
DONE = .TRUE.
END IF
END IF
*
IF( ITYPE.EQ.0 ) THEN
*
* Full matrix
*
DO 30 J = 1, N
DO 20 I = 1, M
A( I, J ) = A( I, J )*MUL
20 CONTINUE
30 CONTINUE
*
ELSE IF( ITYPE.EQ.1 ) THEN
*
* Lower triangular matrix
*
DO 50 J = 1, N
DO 40 I = J, M
A( I, J ) = A( I, J )*MUL
40 CONTINUE
50 CONTINUE
*
ELSE IF( ITYPE.EQ.2 ) THEN
*
* Upper triangular matrix
*
DO 70 J = 1, N
DO 60 I = 1, MIN( J, M )
A( I, J ) = A( I, J )*MUL
60 CONTINUE
70 CONTINUE
*
ELSE IF( ITYPE.EQ.3 ) THEN
*
* Upper Hessenberg matrix
*
DO 90 J = 1, N
DO 80 I = 1, MIN( J+1, M )
A( I, J ) = A( I, J )*MUL
80 CONTINUE
90 CONTINUE
*
ELSE IF( ITYPE.EQ.4 ) THEN
*
* Lower half of a symmetric band matrix
*
K3 = KL + 1
K4 = N + 1
DO 110 J = 1, N
DO 100 I = 1, MIN( K3, K4-J )
A( I, J ) = A( I, J )*MUL
100 CONTINUE
110 CONTINUE
*
ELSE IF( ITYPE.EQ.5 ) THEN
*
* Upper half of a symmetric band matrix
*
K1 = KU + 2
K3 = KU + 1
DO 130 J = 1, N
DO 120 I = MAX( K1-J, 1 ), K3
A( I, J ) = A( I, J )*MUL
120 CONTINUE
130 CONTINUE
*
ELSE IF( ITYPE.EQ.6 ) THEN
*
* Band matrix
*
K1 = KL + KU + 2
K2 = KL + 1
K3 = 2*KL + KU + 1
K4 = KL + KU + 1 + M
DO 150 J = 1, N
DO 140 I = MAX( K1-J, K2 ), MIN( K3, K4-J )
A( I, J ) = A( I, J )*MUL
140 CONTINUE
150 CONTINUE
*
END IF
*
IF( .NOT.DONE )
$ GO TO 10
*
RETURN
*
* End of DLASCL
*
END

226
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*> \brief \b DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLASQ1 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq1.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq1.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq1.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLASQ1( N, D, E, WORK, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION D( * ), E( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLASQ1 computes the singular values of a real N-by-N bidiagonal
*> matrix with diagonal D and off-diagonal E. The singular values
*> are computed to high relative accuracy, in the absence of
*> denormalization, underflow and overflow. The algorithm was first
*> presented in
*>
*> "Accurate singular values and differential qd algorithms" by K. V.
*> Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230,
*> 1994,
*>
*> and the present implementation is described in "An implementation of
*> the dqds Algorithm (Positive Case)", LAPACK Working Note.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of rows and columns in the matrix. N >= 0.
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*> D is DOUBLE PRECISION array, dimension (N)
*> On entry, D contains the diagonal elements of the
*> bidiagonal matrix whose SVD is desired. On normal exit,
*> D contains the singular values in decreasing order.
*> \endverbatim
*>
*> \param[in,out] E
*> \verbatim
*> E is DOUBLE PRECISION array, dimension (N)
*> On entry, elements E(1:N-1) contain the off-diagonal elements
*> of the bidiagonal matrix whose SVD is desired.
*> On exit, E is overwritten.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (4*N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: the algorithm failed
*> = 1, a split was marked by a positive value in E
*> = 2, current block of Z not diagonalized after 100*N
*> iterations (in inner while loop) On exit D and E
*> represent a matrix with the same singular values
*> which the calling subroutine could use to finish the
*> computation, or even feed back into DLASQ1
*> = 3, termination criterion of outer while loop not met
*> (program created more than N unreduced blocks)
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
* =====================================================================
SUBROUTINE DLASQ1( N, D, E, WORK, INFO )
*
* -- LAPACK computational routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
INTEGER INFO, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION D( * ), E( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
* ..
* .. Local Scalars ..
INTEGER I, IINFO
DOUBLE PRECISION EPS, SCALE, SAFMIN, SIGMN, SIGMX
* ..
* .. External Subroutines ..
EXTERNAL DCOPY, DLAS2, DLASCL, DLASQ2, DLASRT, XERBLA
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, SQRT
* ..
* .. Executable Statements ..
*
INFO = 0
IF( N.LT.0 ) THEN
INFO = -2
CALL XERBLA( 'DLASQ1', -INFO )
RETURN
ELSE IF( N.EQ.0 ) THEN
RETURN
ELSE IF( N.EQ.1 ) THEN
D( 1 ) = ABS( D( 1 ) )
RETURN
ELSE IF( N.EQ.2 ) THEN
CALL DLAS2( D( 1 ), E( 1 ), D( 2 ), SIGMN, SIGMX )
D( 1 ) = SIGMX
D( 2 ) = SIGMN
RETURN
END IF
*
* Estimate the largest singular value.
*
SIGMX = ZERO
DO 10 I = 1, N - 1
D( I ) = ABS( D( I ) )
SIGMX = MAX( SIGMX, ABS( E( I ) ) )
10 CONTINUE
D( N ) = ABS( D( N ) )
*
* Early return if SIGMX is zero (matrix is already diagonal).
*
IF( SIGMX.EQ.ZERO ) THEN
CALL DLASRT( 'D', N, D, IINFO )
RETURN
END IF
*
DO 20 I = 1, N
SIGMX = MAX( SIGMX, D( I ) )
20 CONTINUE
*
* Copy D and E into WORK (in the Z format) and scale (squaring the
* input data makes scaling by a power of the radix pointless).
*
EPS = DLAMCH( 'Precision' )
SAFMIN = DLAMCH( 'Safe minimum' )
SCALE = SQRT( EPS / SAFMIN )
CALL DCOPY( N, D, 1, WORK( 1 ), 2 )
CALL DCOPY( N-1, E, 1, WORK( 2 ), 2 )
CALL DLASCL( 'G', 0, 0, SIGMX, SCALE, 2*N-1, 1, WORK, 2*N-1,
$ IINFO )
*
* Compute the q's and e's.
*
DO 30 I = 1, 2*N - 1
WORK( I ) = WORK( I )**2
30 CONTINUE
WORK( 2*N ) = ZERO
*
CALL DLASQ2( N, WORK, INFO )
*
IF( INFO.EQ.0 ) THEN
DO 40 I = 1, N
D( I ) = SQRT( WORK( I ) )
40 CONTINUE
CALL DLASCL( 'G', 0, 0, SCALE, SIGMX, N, 1, D, N, IINFO )
ELSE IF( INFO.EQ.2 ) THEN
*
* Maximum number of iterations exceeded. Move data from WORK
* into D and E so the calling subroutine can try to finish
*
DO I = 1, N
D( I ) = SQRT( WORK( 2*I-1 ) )
E( I ) = SQRT( WORK( 2*I ) )
END DO
CALL DLASCL( 'G', 0, 0, SCALE, SIGMX, N, 1, D, N, IINFO )
CALL DLASCL( 'G', 0, 0, SCALE, SIGMX, N, 1, E, N, IINFO )
END IF
*
RETURN
*
* End of DLASQ1
*
END

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*> \brief \b DLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLASQ2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq2.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq2.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq2.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLASQ2( N, Z, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION Z( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLASQ2 computes all the eigenvalues of the symmetric positive
*> definite tridiagonal matrix associated with the qd array Z to high
*> relative accuracy are computed to high relative accuracy, in the
*> absence of denormalization, underflow and overflow.
*>
*> To see the relation of Z to the tridiagonal matrix, let L be a
*> unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and
*> let U be an upper bidiagonal matrix with 1's above and diagonal
*> Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the
*> symmetric tridiagonal to which it is similar.
*>
*> Note : DLASQ2 defines a logical variable, IEEE, which is true
*> on machines which follow ieee-754 floating-point standard in their
*> handling of infinities and NaNs, and false otherwise. This variable
*> is passed to DLASQ3.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of rows and columns in the matrix. N >= 0.
*> \endverbatim
*>
*> \param[in,out] Z
*> \verbatim
*> Z is DOUBLE PRECISION array, dimension ( 4*N )
*> On entry Z holds the qd array. On exit, entries 1 to N hold
*> the eigenvalues in decreasing order, Z( 2*N+1 ) holds the
*> trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If
*> N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 )
*> holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of
*> shifts that failed.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if the i-th argument is a scalar and had an illegal
*> value, then INFO = -i, if the i-th argument is an
*> array and the j-entry had an illegal value, then
*> INFO = -(i*100+j)
*> > 0: the algorithm failed
*> = 1, a split was marked by a positive value in E
*> = 2, current block of Z not diagonalized after 100*N
*> iterations (in inner while loop). On exit Z holds
*> a qd array with the same eigenvalues as the given Z.
*> = 3, termination criterion of outer while loop not met
*> (program created more than N unreduced blocks)
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Local Variables: I0:N0 defines a current unreduced segment of Z.
*> The shifts are accumulated in SIGMA. Iteration count is in ITER.
*> Ping-pong is controlled by PP (alternates between 0 and 1).
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DLASQ2( N, Z, INFO )
*
* -- LAPACK computational routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
INTEGER INFO, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION Z( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION CBIAS
PARAMETER ( CBIAS = 1.50D0 )
DOUBLE PRECISION ZERO, HALF, ONE, TWO, FOUR, HUNDRD
PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0,
$ TWO = 2.0D0, FOUR = 4.0D0, HUNDRD = 100.0D0 )
* ..
* .. Local Scalars ..
LOGICAL IEEE
INTEGER I0, I1, I4, IINFO, IPN4, ITER, IWHILA, IWHILB,
$ K, KMIN, N0, N1, NBIG, NDIV, NFAIL, PP, SPLT,
$ TTYPE
DOUBLE PRECISION D, DEE, DEEMIN, DESIG, DMIN, DMIN1, DMIN2, DN,
$ DN1, DN2, E, EMAX, EMIN, EPS, G, OLDEMN, QMAX,
$ QMIN, S, SAFMIN, SIGMA, T, TAU, TEMP, TOL,
$ TOL2, TRACE, ZMAX, TEMPE, TEMPQ
* ..
* .. External Subroutines ..
EXTERNAL DLASQ3, DLASRT, XERBLA
* ..
* .. External Functions ..
INTEGER ILAENV
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH, ILAENV
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, MAX, MIN, SQRT
* ..
* .. Executable Statements ..
*
* Test the input arguments.
* (in case DLASQ2 is not called by DLASQ1)
*
INFO = 0
EPS = DLAMCH( 'Precision' )
SAFMIN = DLAMCH( 'Safe minimum' )
TOL = EPS*HUNDRD
TOL2 = TOL**2
*
IF( N.LT.0 ) THEN
INFO = -1
CALL XERBLA( 'DLASQ2', 1 )
RETURN
ELSE IF( N.EQ.0 ) THEN
RETURN
ELSE IF( N.EQ.1 ) THEN
*
* 1-by-1 case.
*
IF( Z( 1 ).LT.ZERO ) THEN
INFO = -201
CALL XERBLA( 'DLASQ2', 2 )
END IF
RETURN
ELSE IF( N.EQ.2 ) THEN
*
* 2-by-2 case.
*
IF( Z( 2 ).LT.ZERO .OR. Z( 3 ).LT.ZERO ) THEN
INFO = -2
CALL XERBLA( 'DLASQ2', 2 )
RETURN
ELSE IF( Z( 3 ).GT.Z( 1 ) ) THEN
D = Z( 3 )
Z( 3 ) = Z( 1 )
Z( 1 ) = D
END IF
Z( 5 ) = Z( 1 ) + Z( 2 ) + Z( 3 )
IF( Z( 2 ).GT.Z( 3 )*TOL2 ) THEN
T = HALF*( ( Z( 1 )-Z( 3 ) )+Z( 2 ) )
S = Z( 3 )*( Z( 2 ) / T )
IF( S.LE.T ) THEN
S = Z( 3 )*( Z( 2 ) / ( T*( ONE+SQRT( ONE+S / T ) ) ) )
ELSE
S = Z( 3 )*( Z( 2 ) / ( T+SQRT( T )*SQRT( T+S ) ) )
END IF
T = Z( 1 ) + ( S+Z( 2 ) )
Z( 3 ) = Z( 3 )*( Z( 1 ) / T )
Z( 1 ) = T
END IF
Z( 2 ) = Z( 3 )
Z( 6 ) = Z( 2 ) + Z( 1 )
RETURN
END IF
*
* Check for negative data and compute sums of q's and e's.
*
Z( 2*N ) = ZERO
EMIN = Z( 2 )
QMAX = ZERO
ZMAX = ZERO
D = ZERO
E = ZERO
*
DO 10 K = 1, 2*( N-1 ), 2
IF( Z( K ).LT.ZERO ) THEN
INFO = -( 200+K )
CALL XERBLA( 'DLASQ2', 2 )
RETURN
ELSE IF( Z( K+1 ).LT.ZERO ) THEN
INFO = -( 200+K+1 )
CALL XERBLA( 'DLASQ2', 2 )
RETURN
END IF
D = D + Z( K )
E = E + Z( K+1 )
QMAX = MAX( QMAX, Z( K ) )
EMIN = MIN( EMIN, Z( K+1 ) )
ZMAX = MAX( QMAX, ZMAX, Z( K+1 ) )
10 CONTINUE
IF( Z( 2*N-1 ).LT.ZERO ) THEN
INFO = -( 200+2*N-1 )
CALL XERBLA( 'DLASQ2', 2 )
RETURN
END IF
D = D + Z( 2*N-1 )
QMAX = MAX( QMAX, Z( 2*N-1 ) )
ZMAX = MAX( QMAX, ZMAX )
*
* Check for diagonality.
*
IF( E.EQ.ZERO ) THEN
DO 20 K = 2, N
Z( K ) = Z( 2*K-1 )
20 CONTINUE
CALL DLASRT( 'D', N, Z, IINFO )
Z( 2*N-1 ) = D
RETURN
END IF
*
TRACE = D + E
*
* Check for zero data.
*
IF( TRACE.EQ.ZERO ) THEN
Z( 2*N-1 ) = ZERO
RETURN
END IF
*
* Check whether the machine is IEEE conformable.
*
IEEE = ILAENV( 10, 'DLASQ2', 'N', 1, 2, 3, 4 ).EQ.1 .AND.
$ ILAENV( 11, 'DLASQ2', 'N', 1, 2, 3, 4 ).EQ.1
*
* Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...).
*
DO 30 K = 2*N, 2, -2
Z( 2*K ) = ZERO
Z( 2*K-1 ) = Z( K )
Z( 2*K-2 ) = ZERO
Z( 2*K-3 ) = Z( K-1 )
30 CONTINUE
*
I0 = 1
N0 = N
*
* Reverse the qd-array, if warranted.
*
IF( CBIAS*Z( 4*I0-3 ).LT.Z( 4*N0-3 ) ) THEN
IPN4 = 4*( I0+N0 )
DO 40 I4 = 4*I0, 2*( I0+N0-1 ), 4
TEMP = Z( I4-3 )
Z( I4-3 ) = Z( IPN4-I4-3 )
Z( IPN4-I4-3 ) = TEMP
TEMP = Z( I4-1 )
Z( I4-1 ) = Z( IPN4-I4-5 )
Z( IPN4-I4-5 ) = TEMP
40 CONTINUE
END IF
*
* Initial split checking via dqd and Li's test.
*
PP = 0
*
DO 80 K = 1, 2
*
D = Z( 4*N0+PP-3 )
DO 50 I4 = 4*( N0-1 ) + PP, 4*I0 + PP, -4
IF( Z( I4-1 ).LE.TOL2*D ) THEN
Z( I4-1 ) = -ZERO
D = Z( I4-3 )
ELSE
D = Z( I4-3 )*( D / ( D+Z( I4-1 ) ) )
END IF
50 CONTINUE
*
* dqd maps Z to ZZ plus Li's test.
*
EMIN = Z( 4*I0+PP+1 )
D = Z( 4*I0+PP-3 )
DO 60 I4 = 4*I0 + PP, 4*( N0-1 ) + PP, 4
Z( I4-2*PP-2 ) = D + Z( I4-1 )
IF( Z( I4-1 ).LE.TOL2*D ) THEN
Z( I4-1 ) = -ZERO
Z( I4-2*PP-2 ) = D
Z( I4-2*PP ) = ZERO
D = Z( I4+1 )
ELSE IF( SAFMIN*Z( I4+1 ).LT.Z( I4-2*PP-2 ) .AND.
$ SAFMIN*Z( I4-2*PP-2 ).LT.Z( I4+1 ) ) THEN
TEMP = Z( I4+1 ) / Z( I4-2*PP-2 )
Z( I4-2*PP ) = Z( I4-1 )*TEMP
D = D*TEMP
ELSE
Z( I4-2*PP ) = Z( I4+1 )*( Z( I4-1 ) / Z( I4-2*PP-2 ) )
D = Z( I4+1 )*( D / Z( I4-2*PP-2 ) )
END IF
EMIN = MIN( EMIN, Z( I4-2*PP ) )
60 CONTINUE
Z( 4*N0-PP-2 ) = D
*
* Now find qmax.
*
QMAX = Z( 4*I0-PP-2 )
DO 70 I4 = 4*I0 - PP + 2, 4*N0 - PP - 2, 4
QMAX = MAX( QMAX, Z( I4 ) )
70 CONTINUE
*
* Prepare for the next iteration on K.
*
PP = 1 - PP
80 CONTINUE
*
* Initialise variables to pass to DLASQ3.
*
TTYPE = 0
DMIN1 = ZERO
DMIN2 = ZERO
DN = ZERO
DN1 = ZERO
DN2 = ZERO
G = ZERO
TAU = ZERO
*
ITER = 2
NFAIL = 0
NDIV = 2*( N0-I0 )
*
DO 160 IWHILA = 1, N + 1
IF( N0.LT.1 ) THEN
GO TO 170
END IF
*
* While array unfinished do
*
* E(N0) holds the value of SIGMA when submatrix in I0:N0
* splits from the rest of the array, but is negated.
*
DESIG = ZERO
IF( N0.EQ.N ) THEN
SIGMA = ZERO
ELSE
SIGMA = -Z( 4*N0-1 )
END IF
IF( SIGMA.LT.ZERO ) THEN
INFO = 1
RETURN
END IF
*
* Find last unreduced submatrix's top index I0, find QMAX and
* EMIN. Find Gershgorin-type bound if Q's much greater than E's.
*
EMAX = ZERO
IF( N0.GT.I0 ) THEN
EMIN = ABS( Z( 4*N0-5 ) )
ELSE
EMIN = ZERO
END IF
QMIN = Z( 4*N0-3 )
QMAX = QMIN
DO 90 I4 = 4*N0, 8, -4
IF( Z( I4-5 ).LE.ZERO )
$ GO TO 100
IF( QMIN.GE.FOUR*EMAX ) THEN
QMIN = MIN( QMIN, Z( I4-3 ) )
EMAX = MAX( EMAX, Z( I4-5 ) )
END IF
QMAX = MAX( QMAX, Z( I4-7 )+Z( I4-5 ) )
EMIN = MIN( EMIN, Z( I4-5 ) )
90 CONTINUE
I4 = 4
*
100 CONTINUE
I0 = I4 / 4
PP = 0
*
IF( N0-I0.GT.1 ) THEN
DEE = Z( 4*I0-3 )
DEEMIN = DEE
KMIN = I0
DO 110 I4 = 4*I0+1, 4*N0-3, 4
DEE = Z( I4 )*( DEE /( DEE+Z( I4-2 ) ) )
IF( DEE.LE.DEEMIN ) THEN
DEEMIN = DEE
KMIN = ( I4+3 )/4
END IF
110 CONTINUE
IF( (KMIN-I0)*2.LT.N0-KMIN .AND.
$ DEEMIN.LE.HALF*Z(4*N0-3) ) THEN
IPN4 = 4*( I0+N0 )
PP = 2
DO 120 I4 = 4*I0, 2*( I0+N0-1 ), 4
TEMP = Z( I4-3 )
Z( I4-3 ) = Z( IPN4-I4-3 )
Z( IPN4-I4-3 ) = TEMP
TEMP = Z( I4-2 )
Z( I4-2 ) = Z( IPN4-I4-2 )
Z( IPN4-I4-2 ) = TEMP
TEMP = Z( I4-1 )
Z( I4-1 ) = Z( IPN4-I4-5 )
Z( IPN4-I4-5 ) = TEMP
TEMP = Z( I4 )
Z( I4 ) = Z( IPN4-I4-4 )
Z( IPN4-I4-4 ) = TEMP
120 CONTINUE
END IF
END IF
*
* Put -(initial shift) into DMIN.
*
DMIN = -MAX( ZERO, QMIN-TWO*SQRT( QMIN )*SQRT( EMAX ) )
*
* Now I0:N0 is unreduced.
* PP = 0 for ping, PP = 1 for pong.
* PP = 2 indicates that flipping was applied to the Z array and
* and that the tests for deflation upon entry in DLASQ3
* should not be performed.
*
NBIG = 100*( N0-I0+1 )
DO 140 IWHILB = 1, NBIG
IF( I0.GT.N0 )
$ GO TO 150
*
! Print out test cases
write(3,*) "{"
write(3,*) "i0: ", I0, ","
write(3,*) "n0: ", N0, ","
write(3,'(9999(g0))',advance="no") "z: []float64{"
do i = 1, 4*n
write (3,'(99999(e24.16,a))',advance="no") z(i), ","
end do
write (3,*) "},"
write (3,*) "pp: ", PP, ","
write (3,*) "dmin: ", DMIN, ","
write (3,*) "desig:", DESIG, ","
write (3,*) "qmax: ", QMAX, ","
write (3,*) "ttype:", TTYPE, ","
write (3,*) "dmin1:", DMIN1, ","
write (3,*) "dmin2:", DMIN2, ","
write (3,*) "dn: ", DN, ","
write (3,*) "dn1: ", DN1, ","
write (3,*) "dn2: ", DN2, ","
write (3,*) "g: ", G, ","
write (3,*) "tau: ", TAU, ","
write (3,*) "nFail:", NFAIL, ","
write (3,*) "iter: ", ITER, ","
write (3,*) "sigma:", SIGMA, ","
write (3,*) "nDiv: ", NDIV, ","
* While submatrix unfinished take a good dqds step.
*
CALL DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL,
$ ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1,
$ DN2, G, TAU )
! Write the outputs
write(3,'(9999(g0))',advance="no") "zOut: []float64{"
do i = 1, 4*n
write (3,'(99999(e24.16,a))',advance="no") z(i), ","
end do
write (3,*) "},"
write (3,*) "i0Out:",I0, ","
write (3,*) "n0Out:", N0, ","
write (3,*) "ppOut:", PP, ","
write (3,*) "dminOut:", DMIN, ","
write (3,*) "desigOut:", DESIG, ","
write (3,*) "sigmaOut:", SIGMA, ","
write (3,*) "qmaxOut:", QMAX, ","
write (3,*) "nFailOut:", NFAIL, ","
write (3,*) "iterOut:", ITER, ","
write (3,*) "nDivOut:", NDIV, ","
write (3,*) "ttypeOut:", TTYPE, ","
write (3,*) "dmin1Out:", DMIN1, ","
write (3,*) "dmin2Out:", DMIN2, ","
write (3,*) "dnOut:", DN, ","
write (3,*) "dn1Out:", DN1, ","
write (3,*) "dn2Out:", DN2, ","
write (3,*) "gOut:", G, ","
write (3,*) "tauOut:", TAU, ","
write (3,*) "},"
PP = 1 - PP
*
* When EMIN is very small check for splits.
*
IF( PP.EQ.0 .AND. N0-I0.GE.3 ) THEN
IF( Z( 4*N0 ).LE.TOL2*QMAX .OR.
$ Z( 4*N0-1 ).LE.TOL2*SIGMA ) THEN
SPLT = I0 - 1
QMAX = Z( 4*I0-3 )
EMIN = Z( 4*I0-1 )
OLDEMN = Z( 4*I0 )
DO 130 I4 = 4*I0, 4*( N0-3 ), 4
IF( Z( I4 ).LE.TOL2*Z( I4-3 ) .OR.
$ Z( I4-1 ).LE.TOL2*SIGMA ) THEN
Z( I4-1 ) = -SIGMA
SPLT = I4 / 4
QMAX = ZERO
EMIN = Z( I4+3 )
OLDEMN = Z( I4+4 )
ELSE
QMAX = MAX( QMAX, Z( I4+1 ) )
EMIN = MIN( EMIN, Z( I4-1 ) )
OLDEMN = MIN( OLDEMN, Z( I4 ) )
END IF
130 CONTINUE
Z( 4*N0-1 ) = EMIN
Z( 4*N0 ) = OLDEMN
I0 = SPLT + 1
END IF
END IF
*
140 CONTINUE
*
INFO = 2
*
* Maximum number of iterations exceeded, restore the shift
* SIGMA and place the new d's and e's in a qd array.
* This might need to be done for several blocks
*
I1 = I0
N1 = N0
145 CONTINUE
TEMPQ = Z( 4*I0-3 )
Z( 4*I0-3 ) = Z( 4*I0-3 ) + SIGMA
DO K = I0+1, N0
TEMPE = Z( 4*K-5 )
Z( 4*K-5 ) = Z( 4*K-5 ) * (TEMPQ / Z( 4*K-7 ))
TEMPQ = Z( 4*K-3 )
Z( 4*K-3 ) = Z( 4*K-3 ) + SIGMA + TEMPE - Z( 4*K-5 )
END DO
*
* Prepare to do this on the previous block if there is one
*
IF( I1.GT.1 ) THEN
N1 = I1-1
DO WHILE( ( I1.GE.2 ) .AND. ( Z(4*I1-5).GE.ZERO ) )
I1 = I1 - 1
END DO
SIGMA = -Z(4*N1-1)
GO TO 145
END IF
DO K = 1, N
Z( 2*K-1 ) = Z( 4*K-3 )
*
* Only the block 1..N0 is unfinished. The rest of the e's
* must be essentially zero, although sometimes other data
* has been stored in them.
*
IF( K.LT.N0 ) THEN
Z( 2*K ) = Z( 4*K-1 )
ELSE
Z( 2*K ) = 0
END IF
END DO
RETURN
*
* end IWHILB
*
150 CONTINUE
*
160 CONTINUE
*
INFO = 3
RETURN
*
* end IWHILA
*
170 CONTINUE
*
* Move q's to the front.
*
DO 180 K = 2, N
Z( K ) = Z( 4*K-3 )
180 CONTINUE
*
* Sort and compute sum of eigenvalues.
*
CALL DLASRT( 'D', N, Z, IINFO )
*
E = ZERO
DO 190 K = N, 1, -1
E = E + Z( K )
190 CONTINUE
*
* Store trace, sum(eigenvalues) and information on performance.
*
Z( 2*N+1 ) = TRACE
Z( 2*N+2 ) = E
Z( 2*N+3 ) = DBLE( ITER )
Z( 2*N+4 ) = DBLE( NDIV ) / DBLE( N**2 )
Z( 2*N+5 ) = HUNDRD*NFAIL / DBLE( ITER )
RETURN
*
* End of DLASQ2
*
END

498
internal/testdata/dlasqtest/dlasq3.f vendored Normal file
View File

@@ -0,0 +1,498 @@
*> \brief \b DLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLASQ3 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq3.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq3.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq3.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL,
* ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1,
* DN2, G, TAU )
*
* .. Scalar Arguments ..
* LOGICAL IEEE
* INTEGER I0, ITER, N0, NDIV, NFAIL, PP
* DOUBLE PRECISION DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G,
* $ QMAX, SIGMA, TAU
* ..
* .. Array Arguments ..
* DOUBLE PRECISION Z( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds.
*> In case of failure it changes shifts, and tries again until output
*> is positive.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] I0
*> \verbatim
*> I0 is INTEGER
*> First index.
*> \endverbatim
*>
*> \param[in,out] N0
*> \verbatim
*> N0 is INTEGER
*> Last index.
*> \endverbatim
*>
*> \param[in] Z
*> \verbatim
*> Z is DOUBLE PRECISION array, dimension ( 4*N )
*> Z holds the qd array.
*> \endverbatim
*>
*> \param[in,out] PP
*> \verbatim
*> PP is INTEGER
*> PP=0 for ping, PP=1 for pong.
*> PP=2 indicates that flipping was applied to the Z array
*> and that the initial tests for deflation should not be
*> performed.
*> \endverbatim
*>
*> \param[out] DMIN
*> \verbatim
*> DMIN is DOUBLE PRECISION
*> Minimum value of d.
*> \endverbatim
*>
*> \param[out] SIGMA
*> \verbatim
*> SIGMA is DOUBLE PRECISION
*> Sum of shifts used in current segment.
*> \endverbatim
*>
*> \param[in,out] DESIG
*> \verbatim
*> DESIG is DOUBLE PRECISION
*> Lower order part of SIGMA
*> \endverbatim
*>
*> \param[in] QMAX
*> \verbatim
*> QMAX is DOUBLE PRECISION
*> Maximum value of q.
*> \endverbatim
*>
*> \param[out] NFAIL
*> \verbatim
*> NFAIL is INTEGER
*> Number of times shift was too big.
*> \endverbatim
*>
*> \param[out] ITER
*> \verbatim
*> ITER is INTEGER
*> Number of iterations.
*> \endverbatim
*>
*> \param[out] NDIV
*> \verbatim
*> NDIV is INTEGER
*> Number of divisions.
*> \endverbatim
*>
*> \param[in] IEEE
*> \verbatim
*> IEEE is LOGICAL
*> Flag for IEEE or non IEEE arithmetic (passed to DLASQ5).
*> \endverbatim
*>
*> \param[in,out] TTYPE
*> \verbatim
*> TTYPE is INTEGER
*> Shift type.
*> \endverbatim
*>
*> \param[in,out] DMIN1
*> \verbatim
*> DMIN1 is DOUBLE PRECISION
*> \endverbatim
*>
*> \param[in,out] DMIN2
*> \verbatim
*> DMIN2 is DOUBLE PRECISION
*> \endverbatim
*>
*> \param[in,out] DN
*> \verbatim
*> DN is DOUBLE PRECISION
*> \endverbatim
*>
*> \param[in,out] DN1
*> \verbatim
*> DN1 is DOUBLE PRECISION
*> \endverbatim
*>
*> \param[in,out] DN2
*> \verbatim
*> DN2 is DOUBLE PRECISION
*> \endverbatim
*>
*> \param[in,out] G
*> \verbatim
*> G is DOUBLE PRECISION
*> \endverbatim
*>
*> \param[in,out] TAU
*> \verbatim
*> TAU is DOUBLE PRECISION
*>
*> These are passed as arguments in order to save their values
*> between calls to DLASQ3.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
* =====================================================================
SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL,
$ ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1,
$ DN2, G, TAU )
*
* -- LAPACK computational routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
LOGICAL IEEE
INTEGER I0, ITER, N0, NDIV, NFAIL, PP
DOUBLE PRECISION DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G,
$ QMAX, SIGMA, TAU
* ..
* .. Array Arguments ..
DOUBLE PRECISION Z( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION CBIAS
PARAMETER ( CBIAS = 1.50D0 )
DOUBLE PRECISION ZERO, QURTR, HALF, ONE, TWO, HUNDRD
PARAMETER ( ZERO = 0.0D0, QURTR = 0.250D0, HALF = 0.5D0,
$ ONE = 1.0D0, TWO = 2.0D0, HUNDRD = 100.0D0 )
* ..
* .. Local Scalars ..
INTEGER IPN4, J4, N0IN, NN, TTYPE
DOUBLE PRECISION EPS, S, T, TEMP, TOL, TOL2
* ..
* .. External Subroutines ..
EXTERNAL DLASQ4, DLASQ5, DLASQ6
* ..
* .. External Function ..
DOUBLE PRECISION DLAMCH
LOGICAL DISNAN
EXTERNAL DISNAN, DLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, SQRT
* ..
* .. Executable Statements ..
*
N0IN = N0
EPS = DLAMCH( 'Precision' )
TOL = EPS*HUNDRD
TOL2 = TOL**2
*
* Check for deflation.
*
10 CONTINUE
*
IF( N0.LT.I0 )
$ RETURN
IF( N0.EQ.I0 )
$ GO TO 20
NN = 4*N0 + PP
IF( N0.EQ.( I0+1 ) )
$ GO TO 40
*
* Check whether E(N0-1) is negligible, 1 eigenvalue.
*
IF( Z( NN-5 ).GT.TOL2*( SIGMA+Z( NN-3 ) ) .AND.
$ Z( NN-2*PP-4 ).GT.TOL2*Z( NN-7 ) )
$ GO TO 30
*
20 CONTINUE
*
Z( 4*N0-3 ) = Z( 4*N0+PP-3 ) + SIGMA
N0 = N0 - 1
GO TO 10
*
* Check whether E(N0-2) is negligible, 2 eigenvalues.
*
30 CONTINUE
*
IF( Z( NN-9 ).GT.TOL2*SIGMA .AND.
$ Z( NN-2*PP-8 ).GT.TOL2*Z( NN-11 ) )
$ GO TO 50
*
40 CONTINUE
*
IF( Z( NN-3 ).GT.Z( NN-7 ) ) THEN
S = Z( NN-3 )
Z( NN-3 ) = Z( NN-7 )
Z( NN-7 ) = S
END IF
T = HALF*( ( Z( NN-7 )-Z( NN-3 ) )+Z( NN-5 ) )
IF( Z( NN-5 ).GT.Z( NN-3 )*TOL2.AND.T.NE.ZERO ) THEN
S = Z( NN-3 )*( Z( NN-5 ) / T )
IF( S.LE.T ) THEN
S = Z( NN-3 )*( Z( NN-5 ) /
$ ( T*( ONE+SQRT( ONE+S / T ) ) ) )
ELSE
S = Z( NN-3 )*( Z( NN-5 ) / ( T+SQRT( T )*SQRT( T+S ) ) )
END IF
T = Z( NN-7 ) + ( S+Z( NN-5 ) )
Z( NN-3 ) = Z( NN-3 )*( Z( NN-7 ) / T )
Z( NN-7 ) = T
END IF
Z( 4*N0-7 ) = Z( NN-7 ) + SIGMA
Z( 4*N0-3 ) = Z( NN-3 ) + SIGMA
N0 = N0 - 2
GO TO 10
*
50 CONTINUE
IF( PP.EQ.2 )
$ PP = 0
*
* Reverse the qd-array, if warranted.
*
IF( DMIN.LE.ZERO .OR. N0.LT.N0IN ) THEN
IF( CBIAS*Z( 4*I0+PP-3 ).LT.Z( 4*N0+PP-3 ) ) THEN
IPN4 = 4*( I0+N0 )
DO 60 J4 = 4*I0, 2*( I0+N0-1 ), 4
TEMP = Z( J4-3 )
Z( J4-3 ) = Z( IPN4-J4-3 )
Z( IPN4-J4-3 ) = TEMP
TEMP = Z( J4-2 )
Z( J4-2 ) = Z( IPN4-J4-2 )
Z( IPN4-J4-2 ) = TEMP
TEMP = Z( J4-1 )
Z( J4-1 ) = Z( IPN4-J4-5 )
Z( IPN4-J4-5 ) = TEMP
TEMP = Z( J4 )
Z( J4 ) = Z( IPN4-J4-4 )
Z( IPN4-J4-4 ) = TEMP
60 CONTINUE
IF( N0-I0.LE.4 ) THEN
Z( 4*N0+PP-1 ) = Z( 4*I0+PP-1 )
Z( 4*N0-PP ) = Z( 4*I0-PP )
END IF
DMIN2 = MIN( DMIN2, Z( 4*N0+PP-1 ) )
Z( 4*N0+PP-1 ) = MIN( Z( 4*N0+PP-1 ), Z( 4*I0+PP-1 ),
$ Z( 4*I0+PP+3 ) )
Z( 4*N0-PP ) = MIN( Z( 4*N0-PP ), Z( 4*I0-PP ),
$ Z( 4*I0-PP+4 ) )
QMAX = MAX( QMAX, Z( 4*I0+PP-3 ), Z( 4*I0+PP+1 ) )
DMIN = -ZERO
END IF
END IF
*
* Choose a shift.
*
! Print out DLASQ4 test cases
write(4,*) "{"
write(4,'(9999(g0))',advance="no") "z: []float64{"
do i = 1, NN
write (4,'(99999(e24.16,a))',advance="no") z(i), ","
end do
write (4,*) "},"
write (4,*) "i0: ", I0, ","
write (4,*) "n0: ", N0, ","
write (4,*) "pp: ", PP, ","
write (4,*) "n0in: ", N0IN, ","
write (4,*) "dmin: ", DMIN, ","
write (4,*) "dmin1:", DMIN1, ","
write (4,*) "dmin2:", DMIN2, ","
write (4,*) "dn: ", DN, ","
write (4,*) "dn1: ", DN1, ","
write (4,*) "dn2: ", DN2, ","
write (4,*) "tau: ", TAU, ","
write (4,*) "ttype: ", TTYPE, ","
write (4,*) "g: ", G, ","
CALL DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, DN1,
$ DN2, TAU, TTYPE, G )
write(4,'(9999(g0))',advance="no") "zOut: []float64{"
do i = 1, NN
write (4,'(99999(e24.16,a))',advance="no") z(i), ","
end do
write (4,*) "},"
write (4,*) "tauOut: ", TAU, ","
write (4,*) "ttypeOut: ", TTYPE, ","
write (4,*) "gOut: ", G, ","
write (4,*) "},"
*
* Call dqds until DMIN > 0.
*
70 CONTINUE
*
write(5,*) "{"
write(5,'(9999(g0))',advance="no") "z: []float64{"
do i = 1, NN
write (5,'(99999(e24.16,a))',advance="no") z(i), ","
end do
write (5,*) "},"
write (5,*) "i0: ", I0, ","
write (5,*) "n0: ", N0, ","
write (5,*) "pp: ", PP, ","
write (5,*) "tau: ", TAU, ","
write (5,*) "sigma: ", SIGMA, ","
write (5,*) "dmin: ", DMIN, ","
write (5,*) "dmin1:", DMIN1, ","
write (5,*) "dmin2:", DMIN2, ","
write (5,*) "dn: ", DN, ","
write (5,*) "dnm1: ", DN1, ","
write (5,*) "dnm2: ", DN2, ","
CALL DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, DN,
$ DN1, DN2, IEEE, EPS )
write (5,*) "i0Out: ", I0, ","
write (5,*) "n0Out: ", N0, ","
write (5,*) "ppOut: ", PP, ","
write (5,*) "tauOut: ", TAU, ","
write (5,*) "sigmaOut: ", SIGMA, ","
write (5,*) "dminOut: ", DMIN, ","
write (5,*) "dmin1Out:", DMIN1, ","
write (5,*) "dmin2Out:", DMIN2, ","
write (5,*) "dnOut: ", DN, ","
write (5,*) "dnm1Out: ", DN1, ","
write (5,*) "dnm2Out: ", DN2, ","
write (5,*) "},"
*
NDIV = NDIV + ( N0-I0+2 )
ITER = ITER + 1
*
* Check status.
*
IF( DMIN.GE.ZERO .AND. DMIN1.GE.ZERO ) THEN
*
* Success.
*
GO TO 90
*
ELSE IF( DMIN.LT.ZERO .AND. DMIN1.GT.ZERO .AND.
$ Z( 4*( N0-1 )-PP ).LT.TOL*( SIGMA+DN1 ) .AND.
$ ABS( DN ).LT.TOL*SIGMA ) THEN
*
* Convergence hidden by negative DN.
*
Z( 4*( N0-1 )-PP+2 ) = ZERO
DMIN = ZERO
GO TO 90
ELSE IF( DMIN.LT.ZERO ) THEN
*
* TAU too big. Select new TAU and try again.
*
NFAIL = NFAIL + 1
IF( TTYPE.LT.-22 ) THEN
*
* Failed twice. Play it safe.
*
TAU = ZERO
ELSE IF( DMIN1.GT.ZERO ) THEN
*
* Late failure. Gives excellent shift.
*
TAU = ( TAU+DMIN )*( ONE-TWO*EPS )
TTYPE = TTYPE - 11
ELSE
*
* Early failure. Divide by 4.
*
TAU = QURTR*TAU
TTYPE = TTYPE - 12
END IF
GO TO 70
ELSE IF( DISNAN( DMIN ) ) THEN
*
* NaN.
*
IF( TAU.EQ.ZERO ) THEN
GO TO 80
ELSE
TAU = ZERO
GO TO 70
END IF
ELSE
*
* Possible underflow. Play it safe.
*
GO TO 80
END IF
*
* Risk of underflow.
*
80 CONTINUE
CALL DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, DN1, DN2 )
NDIV = NDIV + ( N0-I0+2 )
ITER = ITER + 1
TAU = ZERO
*
90 CONTINUE
IF( TAU.LT.SIGMA ) THEN
DESIG = DESIG + TAU
T = SIGMA + DESIG
DESIG = DESIG - ( T-SIGMA )
ELSE
T = SIGMA + TAU
DESIG = SIGMA - ( T-TAU ) + DESIG
END IF
SIGMA = T
*
RETURN
*
* End of DLASQ3
*
END

427
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@@ -0,0 +1,427 @@
*> \brief \b DLASQ4 computes an approximation to the smallest eigenvalue using values of d from the previous transform. Used by sbdsqr.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLASQ4 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq4.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq4.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq4.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN,
* DN1, DN2, TAU, TTYPE, G )
*
* .. Scalar Arguments ..
* INTEGER I0, N0, N0IN, PP, TTYPE
* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU
* ..
* .. Array Arguments ..
* DOUBLE PRECISION Z( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLASQ4 computes an approximation TAU to the smallest eigenvalue
*> using values of d from the previous transform.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] I0
*> \verbatim
*> I0 is INTEGER
*> First index.
*> \endverbatim
*>
*> \param[in] N0
*> \verbatim
*> N0 is INTEGER
*> Last index.
*> \endverbatim
*>
*> \param[in] Z
*> \verbatim
*> Z is DOUBLE PRECISION array, dimension ( 4*N )
*> Z holds the qd array.
*> \endverbatim
*>
*> \param[in] PP
*> \verbatim
*> PP is INTEGER
*> PP=0 for ping, PP=1 for pong.
*> \endverbatim
*>
*> \param[in] N0IN
*> \verbatim
*> N0IN is INTEGER
*> The value of N0 at start of EIGTEST.
*> \endverbatim
*>
*> \param[in] DMIN
*> \verbatim
*> DMIN is DOUBLE PRECISION
*> Minimum value of d.
*> \endverbatim
*>
*> \param[in] DMIN1
*> \verbatim
*> DMIN1 is DOUBLE PRECISION
*> Minimum value of d, excluding D( N0 ).
*> \endverbatim
*>
*> \param[in] DMIN2
*> \verbatim
*> DMIN2 is DOUBLE PRECISION
*> Minimum value of d, excluding D( N0 ) and D( N0-1 ).
*> \endverbatim
*>
*> \param[in] DN
*> \verbatim
*> DN is DOUBLE PRECISION
*> d(N)
*> \endverbatim
*>
*> \param[in] DN1
*> \verbatim
*> DN1 is DOUBLE PRECISION
*> d(N-1)
*> \endverbatim
*>
*> \param[in] DN2
*> \verbatim
*> DN2 is DOUBLE PRECISION
*> d(N-2)
*> \endverbatim
*>
*> \param[out] TAU
*> \verbatim
*> TAU is DOUBLE PRECISION
*> This is the shift.
*> \endverbatim
*>
*> \param[out] TTYPE
*> \verbatim
*> TTYPE is INTEGER
*> Shift type.
*> \endverbatim
*>
*> \param[in,out] G
*> \verbatim
*> G is REAL
*> G is passed as an argument in order to save its value between
*> calls to DLASQ4.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> CNST1 = 9/16
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN,
$ DN1, DN2, TAU, TTYPE, G )
*
* -- LAPACK computational routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
INTEGER I0, N0, N0IN, PP, TTYPE
DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU
* ..
* .. Array Arguments ..
DOUBLE PRECISION Z( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION CNST1, CNST2, CNST3
PARAMETER ( CNST1 = 0.5630D0, CNST2 = 1.010D0,
$ CNST3 = 1.050D0 )
DOUBLE PRECISION QURTR, THIRD, HALF, ZERO, ONE, TWO, HUNDRD
PARAMETER ( QURTR = 0.250D0, THIRD = 0.3330D0,
$ HALF = 0.50D0, ZERO = 0.0D0, ONE = 1.0D0,
$ TWO = 2.0D0, HUNDRD = 100.0D0 )
* ..
* .. Local Scalars ..
INTEGER I4, NN, NP
DOUBLE PRECISION A2, B1, B2, GAM, GAP1, GAP2, S
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, SQRT
* ..
* .. Executable Statements ..
*
* A negative DMIN forces the shift to take that absolute value
* TTYPE records the type of shift.
*
IF( DMIN.LE.ZERO ) THEN
TAU = -DMIN
TTYPE = -1
RETURN
END IF
*
NN = 4*N0 + PP
IF( N0IN.EQ.N0 ) THEN
*
* No eigenvalues deflated.
*
IF( DMIN.EQ.DN .OR. DMIN.EQ.DN1 ) THEN
*
B1 = SQRT( Z( NN-3 ) )*SQRT( Z( NN-5 ) )
B2 = SQRT( Z( NN-7 ) )*SQRT( Z( NN-9 ) )
A2 = Z( NN-7 ) + Z( NN-5 )
*
* Cases 2 and 3.
*
IF( DMIN.EQ.DN .AND. DMIN1.EQ.DN1 ) THEN
GAP2 = DMIN2 - A2 - DMIN2*QURTR
IF( GAP2.GT.ZERO .AND. GAP2.GT.B2 ) THEN
GAP1 = A2 - DN - ( B2 / GAP2 )*B2
ELSE
GAP1 = A2 - DN - ( B1+B2 )
END IF
IF( GAP1.GT.ZERO .AND. GAP1.GT.B1 ) THEN
S = MAX( DN-( B1 / GAP1 )*B1, HALF*DMIN )
TTYPE = -2
ELSE
S = ZERO
IF( DN.GT.B1 )
$ S = DN - B1
IF( A2.GT.( B1+B2 ) )
$ S = MIN( S, A2-( B1+B2 ) )
S = MAX( S, THIRD*DMIN )
TTYPE = -3
END IF
ELSE
*
* Case 4.
*
TTYPE = -4
S = QURTR*DMIN
IF( DMIN.EQ.DN ) THEN
GAM = DN
A2 = ZERO
IF( Z( NN-5 ) .GT. Z( NN-7 ) )
$ RETURN
B2 = Z( NN-5 ) / Z( NN-7 )
NP = NN - 9
ELSE
NP = NN - 2*PP
B2 = Z( NP-2 )
GAM = DN1
IF( Z( NP-4 ) .GT. Z( NP-2 ) )
$ RETURN
A2 = Z( NP-4 ) / Z( NP-2 )
IF( Z( NN-9 ) .GT. Z( NN-11 ) )
$ RETURN
B2 = Z( NN-9 ) / Z( NN-11 )
NP = NN - 13
END IF
*
* Approximate contribution to norm squared from I < NN-1.
*
A2 = A2 + B2
DO 10 I4 = NP, 4*I0 - 1 + PP, -4
IF( B2.EQ.ZERO )
$ GO TO 20
B1 = B2
IF( Z( I4 ) .GT. Z( I4-2 ) )
$ RETURN
B2 = B2*( Z( I4 ) / Z( I4-2 ) )
A2 = A2 + B2
IF( HUNDRD*MAX( B2, B1 ).LT.A2 .OR. CNST1.LT.A2 )
$ GO TO 20
10 CONTINUE
20 CONTINUE
A2 = CNST3*A2
*
* Rayleigh quotient residual bound.
*
IF( A2.LT.CNST1 )
$ S = GAM*( ONE-SQRT( A2 ) ) / ( ONE+A2 )
END IF
ELSE IF( DMIN.EQ.DN2 ) THEN
*
* Case 5.
*
TTYPE = -5
S = QURTR*DMIN
*
* Compute contribution to norm squared from I > NN-2.
*
NP = NN - 2*PP
B1 = Z( NP-2 )
B2 = Z( NP-6 )
GAM = DN2
IF( Z( NP-8 ).GT.B2 .OR. Z( NP-4 ).GT.B1 )
$ RETURN
A2 = ( Z( NP-8 ) / B2 )*( ONE+Z( NP-4 ) / B1 )
*
* Approximate contribution to norm squared from I < NN-2.
*
IF( N0-I0.GT.2 ) THEN
B2 = Z( NN-13 ) / Z( NN-15 )
A2 = A2 + B2
DO 30 I4 = NN - 17, 4*I0 - 1 + PP, -4
IF( B2.EQ.ZERO )
$ GO TO 40
B1 = B2
IF( Z( I4 ) .GT. Z( I4-2 ) )
$ RETURN
B2 = B2*( Z( I4 ) / Z( I4-2 ) )
A2 = A2 + B2
IF( HUNDRD*MAX( B2, B1 ).LT.A2 .OR. CNST1.LT.A2 )
$ GO TO 40
30 CONTINUE
40 CONTINUE
A2 = CNST3*A2
END IF
*
IF( A2.LT.CNST1 )
$ S = GAM*( ONE-SQRT( A2 ) ) / ( ONE+A2 )
ELSE
*
* Case 6, no information to guide us.
*
IF( TTYPE.EQ.-6 ) THEN
G = G + THIRD*( ONE-G )
ELSE IF( TTYPE.EQ.-18 ) THEN
G = QURTR*THIRD
ELSE
G = QURTR
END IF
S = G*DMIN
TTYPE = -6
END IF
*
ELSE IF( N0IN.EQ.( N0+1 ) ) THEN
*
* One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN.
*
IF( DMIN1.EQ.DN1 .AND. DMIN2.EQ.DN2 ) THEN
*
* Cases 7 and 8.
*
TTYPE = -7
S = THIRD*DMIN1
IF( Z( NN-5 ).GT.Z( NN-7 ) )
$ RETURN
B1 = Z( NN-5 ) / Z( NN-7 )
B2 = B1
IF( B2.EQ.ZERO )
$ GO TO 60
DO 50 I4 = 4*N0 - 9 + PP, 4*I0 - 1 + PP, -4
A2 = B1
IF( Z( I4 ).GT.Z( I4-2 ) )
$ RETURN
B1 = B1*( Z( I4 ) / Z( I4-2 ) )
B2 = B2 + B1
IF( HUNDRD*MAX( B1, A2 ).LT.B2 )
$ GO TO 60
50 CONTINUE
60 CONTINUE
B2 = SQRT( CNST3*B2 )
A2 = DMIN1 / ( ONE+B2**2 )
GAP2 = HALF*DMIN2 - A2
IF( GAP2.GT.ZERO .AND. GAP2.GT.B2*A2 ) THEN
S = MAX( S, A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ) )
ELSE
S = MAX( S, A2*( ONE-CNST2*B2 ) )
TTYPE = -8
END IF
ELSE
*
* Case 9.
*
S = QURTR*DMIN1
IF( DMIN1.EQ.DN1 )
$ S = HALF*DMIN1
TTYPE = -9
END IF
*
ELSE IF( N0IN.EQ.( N0+2 ) ) THEN
*
* Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN.
*
* Cases 10 and 11.
*
IF( DMIN2.EQ.DN2 .AND. TWO*Z( NN-5 ).LT.Z( NN-7 ) ) THEN
TTYPE = -10
S = THIRD*DMIN2
IF( Z( NN-5 ).GT.Z( NN-7 ) )
$ RETURN
B1 = Z( NN-5 ) / Z( NN-7 )
B2 = B1
IF( B2.EQ.ZERO )
$ GO TO 80
DO 70 I4 = 4*N0 - 9 + PP, 4*I0 - 1 + PP, -4
IF( Z( I4 ).GT.Z( I4-2 ) )
$ RETURN
B1 = B1*( Z( I4 ) / Z( I4-2 ) )
B2 = B2 + B1
IF( HUNDRD*B1.LT.B2 )
$ GO TO 80
70 CONTINUE
80 CONTINUE
B2 = SQRT( CNST3*B2 )
A2 = DMIN2 / ( ONE+B2**2 )
GAP2 = Z( NN-7 ) + Z( NN-9 ) -
$ SQRT( Z( NN-11 ) )*SQRT( Z( NN-9 ) ) - A2
IF( GAP2.GT.ZERO .AND. GAP2.GT.B2*A2 ) THEN
S = MAX( S, A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ) )
ELSE
S = MAX( S, A2*( ONE-CNST2*B2 ) )
END IF
ELSE
S = QURTR*DMIN2
TTYPE = -11
END IF
ELSE IF( N0IN.GT.( N0+2 ) ) THEN
*
* Case 12, more than two eigenvalues deflated. No information.
*
S = ZERO
TTYPE = -12
END IF
*
TAU = S
RETURN
*
* End of DLASQ4
*
END

413
internal/testdata/dlasqtest/dlasq5.f vendored Normal file
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@@ -0,0 +1,413 @@
*> \brief \b DLASQ5 computes one dqds transform in ping-pong form. Used by sbdsqr and sstegr.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLASQ5 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq5.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq5.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq5.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, DN,
* DNM1, DNM2, IEEE, EPS )
*
* .. Scalar Arguments ..
* LOGICAL IEEE
* INTEGER I0, N0, PP
* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU, SIGMA, EPS
* ..
* .. Array Arguments ..
* DOUBLE PRECISION Z( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLASQ5 computes one dqds transform in ping-pong form, one
*> version for IEEE machines another for non IEEE machines.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] I0
*> \verbatim
*> I0 is INTEGER
*> First index.
*> \endverbatim
*>
*> \param[in] N0
*> \verbatim
*> N0 is INTEGER
*> Last index.
*> \endverbatim
*>
*> \param[in] Z
*> \verbatim
*> Z is DOUBLE PRECISION array, dimension ( 4*N )
*> Z holds the qd array. EMIN is stored in Z(4*N0) to avoid
*> an extra argument.
*> \endverbatim
*>
*> \param[in] PP
*> \verbatim
*> PP is INTEGER
*> PP=0 for ping, PP=1 for pong.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is DOUBLE PRECISION
*> This is the shift.
*> \endverbatim
*>
*> \param[in] SIGMA
*> \verbatim
*> SIGMA is DOUBLE PRECISION
*> This is the accumulated shift up to this step.
*> \endverbatim
*>
*> \param[out] DMIN
*> \verbatim
*> DMIN is DOUBLE PRECISION
*> Minimum value of d.
*> \endverbatim
*>
*> \param[out] DMIN1
*> \verbatim
*> DMIN1 is DOUBLE PRECISION
*> Minimum value of d, excluding D( N0 ).
*> \endverbatim
*>
*> \param[out] DMIN2
*> \verbatim
*> DMIN2 is DOUBLE PRECISION
*> Minimum value of d, excluding D( N0 ) and D( N0-1 ).
*> \endverbatim
*>
*> \param[out] DN
*> \verbatim
*> DN is DOUBLE PRECISION
*> d(N0), the last value of d.
*> \endverbatim
*>
*> \param[out] DNM1
*> \verbatim
*> DNM1 is DOUBLE PRECISION
*> d(N0-1).
*> \endverbatim
*>
*> \param[out] DNM2
*> \verbatim
*> DNM2 is DOUBLE PRECISION
*> d(N0-2).
*> \endverbatim
*>
*> \param[in] IEEE
*> \verbatim
*> IEEE is LOGICAL
*> Flag for IEEE or non IEEE arithmetic.
*> \endverbatim
*
*> \param[in] EPS
*> \verbatim
*> EPS is DOUBLE PRECISION
*> This is the value of epsilon used.
*> \endverbatim
*>
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
* =====================================================================
SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2,
$ DN, DNM1, DNM2, IEEE, EPS )
*
* -- LAPACK computational routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
LOGICAL IEEE
INTEGER I0, N0, PP
DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU,
$ SIGMA, EPS
* ..
* .. Array Arguments ..
DOUBLE PRECISION Z( * )
* ..
*
* =====================================================================
*
* .. Parameter ..
DOUBLE PRECISION ZERO, HALF
PARAMETER ( ZERO = 0.0D0, HALF = 0.5 )
* ..
* .. Local Scalars ..
INTEGER J4, J4P2
DOUBLE PRECISION D, EMIN, TEMP, DTHRESH
* ..
* .. Intrinsic Functions ..
INTRINSIC MIN
* ..
* .. Executable Statements ..
*
IF( ( N0-I0-1 ).LE.0 )
$ RETURN
*
DTHRESH = EPS*(SIGMA+TAU)
IF( TAU.LT.DTHRESH*HALF ) TAU = ZERO
IF( TAU.NE.ZERO ) THEN
J4 = 4*I0 + PP - 3
EMIN = Z( J4+4 )
D = Z( J4 ) - TAU
DMIN = D
DMIN1 = -Z( J4 )
*
IF( IEEE ) THEN
*
* Code for IEEE arithmetic.
*
IF( PP.EQ.0 ) THEN
DO 10 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-2 ) = D + Z( J4-1 )
TEMP = Z( J4+1 ) / Z( J4-2 )
D = D*TEMP - TAU
DMIN = MIN( DMIN, D )
Z( J4 ) = Z( J4-1 )*TEMP
EMIN = MIN( Z( J4 ), EMIN )
10 CONTINUE
ELSE
DO 20 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-3 ) = D + Z( J4 )
TEMP = Z( J4+2 ) / Z( J4-3 )
D = D*TEMP - TAU
DMIN = MIN( DMIN, D )
Z( J4-1 ) = Z( J4 )*TEMP
EMIN = MIN( Z( J4-1 ), EMIN )
20 CONTINUE
END IF
*
* Unroll last two steps.
*
DNM2 = D
DMIN2 = DMIN
J4 = 4*( N0-2 ) - PP
J4P2 = J4 + 2*PP - 1
Z( J4-2 ) = DNM2 + Z( J4P2 )
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
DMIN = MIN( DMIN, DNM1 )
*
DMIN1 = DMIN
J4 = J4 + 4
J4P2 = J4 + 2*PP - 1
Z( J4-2 ) = DNM1 + Z( J4P2 )
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
DMIN = MIN( DMIN, DN )
*
ELSE
*
* Code for non IEEE arithmetic.
*
IF( PP.EQ.0 ) THEN
DO 30 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-2 ) = D + Z( J4-1 )
IF( D.LT.ZERO ) THEN
RETURN
ELSE
Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) )
D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU
END IF
DMIN = MIN( DMIN, D )
EMIN = MIN( EMIN, Z( J4 ) )
30 CONTINUE
ELSE
DO 40 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-3 ) = D + Z( J4 )
IF( D.LT.ZERO ) THEN
RETURN
ELSE
Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) )
D = Z( J4+2 )*( D / Z( J4-3 ) ) - TAU
END IF
DMIN = MIN( DMIN, D )
EMIN = MIN( EMIN, Z( J4-1 ) )
40 CONTINUE
END IF
*
* Unroll last two steps.
*
DNM2 = D
DMIN2 = DMIN
J4 = 4*( N0-2 ) - PP
J4P2 = J4 + 2*PP - 1
Z( J4-2 ) = DNM2 + Z( J4P2 )
IF( DNM2.LT.ZERO ) THEN
RETURN
ELSE
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
END IF
DMIN = MIN( DMIN, DNM1 )
*
DMIN1 = DMIN
J4 = J4 + 4
J4P2 = J4 + 2*PP - 1
Z( J4-2 ) = DNM1 + Z( J4P2 )
IF( DNM1.LT.ZERO ) THEN
RETURN
ELSE
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
END IF
DMIN = MIN( DMIN, DN )
*
END IF
ELSE
* This is the version that sets d's to zero if they are small enough
J4 = 4*I0 + PP - 3
EMIN = Z( J4+4 )
D = Z( J4 ) - TAU
DMIN = D
DMIN1 = -Z( J4 )
IF( IEEE ) THEN
*
* Code for IEEE arithmetic.
*
IF( PP.EQ.0 ) THEN
DO 50 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-2 ) = D + Z( J4-1 )
TEMP = Z( J4+1 ) / Z( J4-2 )
D = D*TEMP - TAU
IF( D.LT.DTHRESH ) D = ZERO
DMIN = MIN( DMIN, D )
Z( J4 ) = Z( J4-1 )*TEMP
EMIN = MIN( Z( J4 ), EMIN )
50 CONTINUE
ELSE
DO 60 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-3 ) = D + Z( J4 )
TEMP = Z( J4+2 ) / Z( J4-3 )
D = D*TEMP - TAU
IF( D.LT.DTHRESH ) D = ZERO
DMIN = MIN( DMIN, D )
Z( J4-1 ) = Z( J4 )*TEMP
EMIN = MIN( Z( J4-1 ), EMIN )
60 CONTINUE
END IF
*
* Unroll last two steps.
*
DNM2 = D
DMIN2 = DMIN
J4 = 4*( N0-2 ) - PP
J4P2 = J4 + 2*PP - 1
Z( J4-2 ) = DNM2 + Z( J4P2 )
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
DMIN = MIN( DMIN, DNM1 )
*
DMIN1 = DMIN
J4 = J4 + 4
J4P2 = J4 + 2*PP - 1
Z( J4-2 ) = DNM1 + Z( J4P2 )
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
DMIN = MIN( DMIN, DN )
*
ELSE
*
* Code for non IEEE arithmetic.
*
IF( PP.EQ.0 ) THEN
DO 70 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-2 ) = D + Z( J4-1 )
IF( D.LT.ZERO ) THEN
RETURN
ELSE
Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) )
D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU
END IF
IF( D.LT.DTHRESH) D = ZERO
DMIN = MIN( DMIN, D )
EMIN = MIN( EMIN, Z( J4 ) )
70 CONTINUE
ELSE
DO 80 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-3 ) = D + Z( J4 )
IF( D.LT.ZERO ) THEN
RETURN
ELSE
Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) )
D = Z( J4+2 )*( D / Z( J4-3 ) ) - TAU
END IF
IF( D.LT.DTHRESH) D = ZERO
DMIN = MIN( DMIN, D )
EMIN = MIN( EMIN, Z( J4-1 ) )
80 CONTINUE
END IF
*
* Unroll last two steps.
*
DNM2 = D
DMIN2 = DMIN
J4 = 4*( N0-2 ) - PP
J4P2 = J4 + 2*PP - 1
Z( J4-2 ) = DNM2 + Z( J4P2 )
IF( DNM2.LT.ZERO ) THEN
RETURN
ELSE
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
END IF
DMIN = MIN( DMIN, DNM1 )
*
DMIN1 = DMIN
J4 = J4 + 4
J4P2 = J4 + 2*PP - 1
Z( J4-2 ) = DNM1 + Z( J4P2 )
IF( DNM1.LT.ZERO ) THEN
RETURN
ELSE
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
END IF
DMIN = MIN( DMIN, DN )
*
END IF
END IF
*
Z( J4+2 ) = DN
Z( 4*N0-PP ) = EMIN
RETURN
*
* End of DLASQ5
*
END

258
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*> \brief \b DLASQ6 computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLASQ6 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq6.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq6.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq6.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN,
* DNM1, DNM2 )
*
* .. Scalar Arguments ..
* INTEGER I0, N0, PP
* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2
* ..
* .. Array Arguments ..
* DOUBLE PRECISION Z( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLASQ6 computes one dqd (shift equal to zero) transform in
*> ping-pong form, with protection against underflow and overflow.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] I0
*> \verbatim
*> I0 is INTEGER
*> First index.
*> \endverbatim
*>
*> \param[in] N0
*> \verbatim
*> N0 is INTEGER
*> Last index.
*> \endverbatim
*>
*> \param[in] Z
*> \verbatim
*> Z is DOUBLE PRECISION array, dimension ( 4*N )
*> Z holds the qd array. EMIN is stored in Z(4*N0) to avoid
*> an extra argument.
*> \endverbatim
*>
*> \param[in] PP
*> \verbatim
*> PP is INTEGER
*> PP=0 for ping, PP=1 for pong.
*> \endverbatim
*>
*> \param[out] DMIN
*> \verbatim
*> DMIN is DOUBLE PRECISION
*> Minimum value of d.
*> \endverbatim
*>
*> \param[out] DMIN1
*> \verbatim
*> DMIN1 is DOUBLE PRECISION
*> Minimum value of d, excluding D( N0 ).
*> \endverbatim
*>
*> \param[out] DMIN2
*> \verbatim
*> DMIN2 is DOUBLE PRECISION
*> Minimum value of d, excluding D( N0 ) and D( N0-1 ).
*> \endverbatim
*>
*> \param[out] DN
*> \verbatim
*> DN is DOUBLE PRECISION
*> d(N0), the last value of d.
*> \endverbatim
*>
*> \param[out] DNM1
*> \verbatim
*> DNM1 is DOUBLE PRECISION
*> d(N0-1).
*> \endverbatim
*>
*> \param[out] DNM2
*> \verbatim
*> DNM2 is DOUBLE PRECISION
*> d(N0-2).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
* =====================================================================
SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN,
$ DNM1, DNM2 )
*
* -- LAPACK computational routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
INTEGER I0, N0, PP
DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2
* ..
* .. Array Arguments ..
DOUBLE PRECISION Z( * )
* ..
*
* =====================================================================
*
* .. Parameter ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
* ..
* .. Local Scalars ..
INTEGER J4, J4P2
DOUBLE PRECISION D, EMIN, SAFMIN, TEMP
* ..
* .. External Function ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC MIN
* ..
* .. Executable Statements ..
*
IF( ( N0-I0-1 ).LE.0 )
$ RETURN
*
print *, "In dlasq6"
STOP
SAFMIN = DLAMCH( 'Safe minimum' )
J4 = 4*I0 + PP - 3
EMIN = Z( J4+4 )
D = Z( J4 )
DMIN = D
*
IF( PP.EQ.0 ) THEN
DO 10 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-2 ) = D + Z( J4-1 )
IF( Z( J4-2 ).EQ.ZERO ) THEN
Z( J4 ) = ZERO
D = Z( J4+1 )
DMIN = D
EMIN = ZERO
ELSE IF( SAFMIN*Z( J4+1 ).LT.Z( J4-2 ) .AND.
$ SAFMIN*Z( J4-2 ).LT.Z( J4+1 ) ) THEN
TEMP = Z( J4+1 ) / Z( J4-2 )
Z( J4 ) = Z( J4-1 )*TEMP
D = D*TEMP
ELSE
Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) )
D = Z( J4+1 )*( D / Z( J4-2 ) )
END IF
DMIN = MIN( DMIN, D )
EMIN = MIN( EMIN, Z( J4 ) )
10 CONTINUE
ELSE
DO 20 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-3 ) = D + Z( J4 )
IF( Z( J4-3 ).EQ.ZERO ) THEN
Z( J4-1 ) = ZERO
D = Z( J4+2 )
DMIN = D
EMIN = ZERO
ELSE IF( SAFMIN*Z( J4+2 ).LT.Z( J4-3 ) .AND.
$ SAFMIN*Z( J4-3 ).LT.Z( J4+2 ) ) THEN
TEMP = Z( J4+2 ) / Z( J4-3 )
Z( J4-1 ) = Z( J4 )*TEMP
D = D*TEMP
ELSE
Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) )
D = Z( J4+2 )*( D / Z( J4-3 ) )
END IF
DMIN = MIN( DMIN, D )
EMIN = MIN( EMIN, Z( J4-1 ) )
20 CONTINUE
END IF
*
* Unroll last two steps.
*
DNM2 = D
DMIN2 = DMIN
J4 = 4*( N0-2 ) - PP
J4P2 = J4 + 2*PP - 1
Z( J4-2 ) = DNM2 + Z( J4P2 )
IF( Z( J4-2 ).EQ.ZERO ) THEN
Z( J4 ) = ZERO
DNM1 = Z( J4P2+2 )
DMIN = DNM1
EMIN = ZERO
ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND.
$ SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN
TEMP = Z( J4P2+2 ) / Z( J4-2 )
Z( J4 ) = Z( J4P2 )*TEMP
DNM1 = DNM2*TEMP
ELSE
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) )
END IF
DMIN = MIN( DMIN, DNM1 )
*
DMIN1 = DMIN
J4 = J4 + 4
J4P2 = J4 + 2*PP - 1
Z( J4-2 ) = DNM1 + Z( J4P2 )
IF( Z( J4-2 ).EQ.ZERO ) THEN
Z( J4 ) = ZERO
DN = Z( J4P2+2 )
DMIN = DN
EMIN = ZERO
ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND.
$ SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN
TEMP = Z( J4P2+2 ) / Z( J4-2 )
Z( J4 ) = Z( J4P2 )*TEMP
DN = DNM1*TEMP
ELSE
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) )
END IF
DMIN = MIN( DMIN, DN )
*
Z( J4+2 ) = DN
Z( 4*N0-PP ) = EMIN
RETURN
*
* End of DLASQ6
*
END

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*> \brief \b DLASRT sorts numbers in increasing or decreasing order.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLASRT + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasrt.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasrt.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasrt.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLASRT( ID, N, D, INFO )
*
* .. Scalar Arguments ..
* CHARACTER ID
* INTEGER INFO, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION D( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> Sort the numbers in D in increasing order (if ID = 'I') or
*> in decreasing order (if ID = 'D' ).
*>
*> Use Quick Sort, reverting to Insertion sort on arrays of
*> size <= 20. Dimension of STACK limits N to about 2**32.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] ID
*> \verbatim
*> ID is CHARACTER*1
*> = 'I': sort D in increasing order;
*> = 'D': sort D in decreasing order.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The length of the array D.
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*> D is DOUBLE PRECISION array, dimension (N)
*> On entry, the array to be sorted.
*> On exit, D has been sorted into increasing order
*> (D(1) <= ... <= D(N) ) or into decreasing order
*> (D(1) >= ... >= D(N) ), depending on ID.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
* =====================================================================
SUBROUTINE DLASRT( ID, N, D, INFO )
*
* -- LAPACK computational routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
CHARACTER ID
INTEGER INFO, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION D( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
INTEGER SELECT
PARAMETER ( SELECT = 20 )
* ..
* .. Local Scalars ..
INTEGER DIR, ENDD, I, J, START, STKPNT
DOUBLE PRECISION D1, D2, D3, DMNMX, TMP
* ..
* .. Local Arrays ..
INTEGER STACK( 2, 32 )
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Executable Statements ..
*
* Test the input paramters.
*
INFO = 0
DIR = -1
IF( LSAME( ID, 'D' ) ) THEN
DIR = 0
ELSE IF( LSAME( ID, 'I' ) ) THEN
DIR = 1
END IF
IF( DIR.EQ.-1 ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DLASRT', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.LE.1 )
$ RETURN
*
STKPNT = 1
STACK( 1, 1 ) = 1
STACK( 2, 1 ) = N
10 CONTINUE
START = STACK( 1, STKPNT )
ENDD = STACK( 2, STKPNT )
STKPNT = STKPNT - 1
IF( ENDD-START.LE.SELECT .AND. ENDD-START.GT.0 ) THEN
*
* Do Insertion sort on D( START:ENDD )
*
IF( DIR.EQ.0 ) THEN
*
* Sort into decreasing order
*
DO 30 I = START + 1, ENDD
DO 20 J = I, START + 1, -1
IF( D( J ).GT.D( J-1 ) ) THEN
DMNMX = D( J )
D( J ) = D( J-1 )
D( J-1 ) = DMNMX
ELSE
GO TO 30
END IF
20 CONTINUE
30 CONTINUE
*
ELSE
*
* Sort into increasing order
*
DO 50 I = START + 1, ENDD
DO 40 J = I, START + 1, -1
IF( D( J ).LT.D( J-1 ) ) THEN
DMNMX = D( J )
D( J ) = D( J-1 )
D( J-1 ) = DMNMX
ELSE
GO TO 50
END IF
40 CONTINUE
50 CONTINUE
*
END IF
*
ELSE IF( ENDD-START.GT.SELECT ) THEN
*
* Partition D( START:ENDD ) and stack parts, largest one first
*
* Choose partition entry as median of 3
*
D1 = D( START )
D2 = D( ENDD )
I = ( START+ENDD ) / 2
D3 = D( I )
IF( D1.LT.D2 ) THEN
IF( D3.LT.D1 ) THEN
DMNMX = D1
ELSE IF( D3.LT.D2 ) THEN
DMNMX = D3
ELSE
DMNMX = D2
END IF
ELSE
IF( D3.LT.D2 ) THEN
DMNMX = D2
ELSE IF( D3.LT.D1 ) THEN
DMNMX = D3
ELSE
DMNMX = D1
END IF
END IF
*
IF( DIR.EQ.0 ) THEN
*
* Sort into decreasing order
*
I = START - 1
J = ENDD + 1
60 CONTINUE
70 CONTINUE
J = J - 1
IF( D( J ).LT.DMNMX )
$ GO TO 70
80 CONTINUE
I = I + 1
IF( D( I ).GT.DMNMX )
$ GO TO 80
IF( I.LT.J ) THEN
TMP = D( I )
D( I ) = D( J )
D( J ) = TMP
GO TO 60
END IF
IF( J-START.GT.ENDD-J-1 ) THEN
STKPNT = STKPNT + 1
STACK( 1, STKPNT ) = START
STACK( 2, STKPNT ) = J
STKPNT = STKPNT + 1
STACK( 1, STKPNT ) = J + 1
STACK( 2, STKPNT ) = ENDD
ELSE
STKPNT = STKPNT + 1
STACK( 1, STKPNT ) = J + 1
STACK( 2, STKPNT ) = ENDD
STKPNT = STKPNT + 1
STACK( 1, STKPNT ) = START
STACK( 2, STKPNT ) = J
END IF
ELSE
*
* Sort into increasing order
*
I = START - 1
J = ENDD + 1
90 CONTINUE
100 CONTINUE
J = J - 1
IF( D( J ).GT.DMNMX )
$ GO TO 100
110 CONTINUE
I = I + 1
IF( D( I ).LT.DMNMX )
$ GO TO 110
IF( I.LT.J ) THEN
TMP = D( I )
D( I ) = D( J )
D( J ) = TMP
GO TO 90
END IF
IF( J-START.GT.ENDD-J-1 ) THEN
STKPNT = STKPNT + 1
STACK( 1, STKPNT ) = START
STACK( 2, STKPNT ) = J
STKPNT = STKPNT + 1
STACK( 1, STKPNT ) = J + 1
STACK( 2, STKPNT ) = ENDD
ELSE
STKPNT = STKPNT + 1
STACK( 1, STKPNT ) = J + 1
STACK( 2, STKPNT ) = ENDD
STKPNT = STKPNT + 1
STACK( 1, STKPNT ) = START
STACK( 2, STKPNT ) = J
END IF
END IF
END IF
IF( STKPNT.GT.0 )
$ GO TO 10
RETURN
*
* End of DLASRT
*
END

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*> \brief \b IEEECK
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download IEEECK + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ieeeck.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ieeeck.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ieeeck.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* INTEGER FUNCTION IEEECK( ISPEC, ZERO, ONE )
*
* .. Scalar Arguments ..
* INTEGER ISPEC
* REAL ONE, ZERO
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> IEEECK is called from the ILAENV to verify that Infinity and
*> possibly NaN arithmetic is safe (i.e. will not trap).
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] ISPEC
*> \verbatim
*> ISPEC is INTEGER
*> Specifies whether to test just for inifinity arithmetic
*> or whether to test for infinity and NaN arithmetic.
*> = 0: Verify infinity arithmetic only.
*> = 1: Verify infinity and NaN arithmetic.
*> \endverbatim
*>
*> \param[in] ZERO
*> \verbatim
*> ZERO is REAL
*> Must contain the value 0.0
*> This is passed to prevent the compiler from optimizing
*> away this code.
*> \endverbatim
*>
*> \param[in] ONE
*> \verbatim
*> ONE is REAL
*> Must contain the value 1.0
*> This is passed to prevent the compiler from optimizing
*> away this code.
*>
*> RETURN VALUE: INTEGER
*> = 0: Arithmetic failed to produce the correct answers
*> = 1: Arithmetic produced the correct answers
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup auxOTHERauxiliary
*
* =====================================================================
INTEGER FUNCTION IEEECK( ISPEC, ZERO, ONE )
*
* -- LAPACK auxiliary routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER ISPEC
REAL ONE, ZERO
* ..
*
* =====================================================================
*
* .. Local Scalars ..
REAL NAN1, NAN2, NAN3, NAN4, NAN5, NAN6, NEGINF,
$ NEGZRO, NEWZRO, POSINF
* ..
* .. Executable Statements ..
IEEECK = 1
*
POSINF = ONE / ZERO
IF( POSINF.LE.ONE ) THEN
IEEECK = 0
RETURN
END IF
*
NEGINF = -ONE / ZERO
IF( NEGINF.GE.ZERO ) THEN
IEEECK = 0
RETURN
END IF
*
NEGZRO = ONE / ( NEGINF+ONE )
IF( NEGZRO.NE.ZERO ) THEN
IEEECK = 0
RETURN
END IF
*
NEGINF = ONE / NEGZRO
IF( NEGINF.GE.ZERO ) THEN
IEEECK = 0
RETURN
END IF
*
NEWZRO = NEGZRO + ZERO
IF( NEWZRO.NE.ZERO ) THEN
IEEECK = 0
RETURN
END IF
*
POSINF = ONE / NEWZRO
IF( POSINF.LE.ONE ) THEN
IEEECK = 0
RETURN
END IF
*
NEGINF = NEGINF*POSINF
IF( NEGINF.GE.ZERO ) THEN
IEEECK = 0
RETURN
END IF
*
POSINF = POSINF*POSINF
IF( POSINF.LE.ONE ) THEN
IEEECK = 0
RETURN
END IF
*
*
*
*
* Return if we were only asked to check infinity arithmetic
*
IF( ISPEC.EQ.0 )
$ RETURN
*
NAN1 = POSINF + NEGINF
*
NAN2 = POSINF / NEGINF
*
NAN3 = POSINF / POSINF
*
NAN4 = POSINF*ZERO
*
NAN5 = NEGINF*NEGZRO
*
NAN6 = NAN5*ZERO
*
IF( NAN1.EQ.NAN1 ) THEN
IEEECK = 0
RETURN
END IF
*
IF( NAN2.EQ.NAN2 ) THEN
IEEECK = 0
RETURN
END IF
*
IF( NAN3.EQ.NAN3 ) THEN
IEEECK = 0
RETURN
END IF
*
IF( NAN4.EQ.NAN4 ) THEN
IEEECK = 0
RETURN
END IF
*
IF( NAN5.EQ.NAN5 ) THEN
IEEECK = 0
RETURN
END IF
*
IF( NAN6.EQ.NAN6 ) THEN
IEEECK = 0
RETURN
END IF
*
RETURN
END

624
internal/testdata/dlasqtest/ilaenv.f vendored Normal file
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@@ -0,0 +1,624 @@
*> \brief \b ILAENV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ILAENV + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ilaenv.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ilaenv.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ilaenv.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, N4 )
*
* .. Scalar Arguments ..
* CHARACTER*( * ) NAME, OPTS
* INTEGER ISPEC, N1, N2, N3, N4
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ILAENV is called from the LAPACK routines to choose problem-dependent
*> parameters for the local environment. See ISPEC for a description of
*> the parameters.
*>
*> ILAENV returns an INTEGER
*> if ILAENV >= 0: ILAENV returns the value of the parameter specified by ISPEC
*> if ILAENV < 0: if ILAENV = -k, the k-th argument had an illegal value.
*>
*> This version provides a set of parameters which should give good,
*> but not optimal, performance on many of the currently available
*> computers. Users are encouraged to modify this subroutine to set
*> the tuning parameters for their particular machine using the option
*> and problem size information in the arguments.
*>
*> This routine will not function correctly if it is converted to all
*> lower case. Converting it to all upper case is allowed.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] ISPEC
*> \verbatim
*> ISPEC is INTEGER
*> Specifies the parameter to be returned as the value of
*> ILAENV.
*> = 1: the optimal blocksize; if this value is 1, an unblocked
*> algorithm will give the best performance.
*> = 2: the minimum block size for which the block routine
*> should be used; if the usable block size is less than
*> this value, an unblocked routine should be used.
*> = 3: the crossover point (in a block routine, for N less
*> than this value, an unblocked routine should be used)
*> = 4: the number of shifts, used in the nonsymmetric
*> eigenvalue routines (DEPRECATED)
*> = 5: the minimum column dimension for blocking to be used;
*> rectangular blocks must have dimension at least k by m,
*> where k is given by ILAENV(2,...) and m by ILAENV(5,...)
*> = 6: the crossover point for the SVD (when reducing an m by n
*> matrix to bidiagonal form, if max(m,n)/min(m,n) exceeds
*> this value, a QR factorization is used first to reduce
*> the matrix to a triangular form.)
*> = 7: the number of processors
*> = 8: the crossover point for the multishift QR method
*> for nonsymmetric eigenvalue problems (DEPRECATED)
*> = 9: maximum size of the subproblems at the bottom of the
*> computation tree in the divide-and-conquer algorithm
*> (used by xGELSD and xGESDD)
*> =10: ieee NaN arithmetic can be trusted not to trap
*> =11: infinity arithmetic can be trusted not to trap
*> 12 <= ISPEC <= 16:
*> xHSEQR or one of its subroutines,
*> see IPARMQ for detailed explanation
*> \endverbatim
*>
*> \param[in] NAME
*> \verbatim
*> NAME is CHARACTER*(*)
*> The name of the calling subroutine, in either upper case or
*> lower case.
*> \endverbatim
*>
*> \param[in] OPTS
*> \verbatim
*> OPTS is CHARACTER*(*)
*> The character options to the subroutine NAME, concatenated
*> into a single character string. For example, UPLO = 'U',
*> TRANS = 'T', and DIAG = 'N' for a triangular routine would
*> be specified as OPTS = 'UTN'.
*> \endverbatim
*>
*> \param[in] N1
*> \verbatim
*> N1 is INTEGER
*> \endverbatim
*>
*> \param[in] N2
*> \verbatim
*> N2 is INTEGER
*> \endverbatim
*>
*> \param[in] N3
*> \verbatim
*> N3 is INTEGER
*> \endverbatim
*>
*> \param[in] N4
*> \verbatim
*> N4 is INTEGER
*> Problem dimensions for the subroutine NAME; these may not all
*> be required.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup auxOTHERauxiliary
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> The following conventions have been used when calling ILAENV from the
*> LAPACK routines:
*> 1) OPTS is a concatenation of all of the character options to
*> subroutine NAME, in the same order that they appear in the
*> argument list for NAME, even if they are not used in determining
*> the value of the parameter specified by ISPEC.
*> 2) The problem dimensions N1, N2, N3, N4 are specified in the order
*> that they appear in the argument list for NAME. N1 is used
*> first, N2 second, and so on, and unused problem dimensions are
*> passed a value of -1.
*> 3) The parameter value returned by ILAENV is checked for validity in
*> the calling subroutine. For example, ILAENV is used to retrieve
*> the optimal blocksize for STRTRI as follows:
*>
*> NB = ILAENV( 1, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 )
*> IF( NB.LE.1 ) NB = MAX( 1, N )
*> \endverbatim
*>
* =====================================================================
INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, N4 )
*
* -- LAPACK auxiliary routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER*( * ) NAME, OPTS
INTEGER ISPEC, N1, N2, N3, N4
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I, IC, IZ, NB, NBMIN, NX
LOGICAL CNAME, SNAME
CHARACTER C1*1, C2*2, C4*2, C3*3, SUBNAM*6
* ..
* .. Intrinsic Functions ..
INTRINSIC CHAR, ICHAR, INT, MIN, REAL
* ..
* .. External Functions ..
INTEGER IEEECK, IPARMQ
EXTERNAL IEEECK, IPARMQ
* ..
* .. Executable Statements ..
*
GO TO ( 10, 10, 10, 80, 90, 100, 110, 120,
$ 130, 140, 150, 160, 160, 160, 160, 160 )ISPEC
*
* Invalid value for ISPEC
*
ILAENV = -1
RETURN
*
10 CONTINUE
*
* Convert NAME to upper case if the first character is lower case.
*
ILAENV = 1
SUBNAM = NAME
IC = ICHAR( SUBNAM( 1: 1 ) )
IZ = ICHAR( 'Z' )
IF( IZ.EQ.90 .OR. IZ.EQ.122 ) THEN
*
* ASCII character set
*
IF( IC.GE.97 .AND. IC.LE.122 ) THEN
SUBNAM( 1: 1 ) = CHAR( IC-32 )
DO 20 I = 2, 6
IC = ICHAR( SUBNAM( I: I ) )
IF( IC.GE.97 .AND. IC.LE.122 )
$ SUBNAM( I: I ) = CHAR( IC-32 )
20 CONTINUE
END IF
*
ELSE IF( IZ.EQ.233 .OR. IZ.EQ.169 ) THEN
*
* EBCDIC character set
*
IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR.
$ ( IC.GE.145 .AND. IC.LE.153 ) .OR.
$ ( IC.GE.162 .AND. IC.LE.169 ) ) THEN
SUBNAM( 1: 1 ) = CHAR( IC+64 )
DO 30 I = 2, 6
IC = ICHAR( SUBNAM( I: I ) )
IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR.
$ ( IC.GE.145 .AND. IC.LE.153 ) .OR.
$ ( IC.GE.162 .AND. IC.LE.169 ) )SUBNAM( I:
$ I ) = CHAR( IC+64 )
30 CONTINUE
END IF
*
ELSE IF( IZ.EQ.218 .OR. IZ.EQ.250 ) THEN
*
* Prime machines: ASCII+128
*
IF( IC.GE.225 .AND. IC.LE.250 ) THEN
SUBNAM( 1: 1 ) = CHAR( IC-32 )
DO 40 I = 2, 6
IC = ICHAR( SUBNAM( I: I ) )
IF( IC.GE.225 .AND. IC.LE.250 )
$ SUBNAM( I: I ) = CHAR( IC-32 )
40 CONTINUE
END IF
END IF
*
C1 = SUBNAM( 1: 1 )
SNAME = C1.EQ.'S' .OR. C1.EQ.'D'
CNAME = C1.EQ.'C' .OR. C1.EQ.'Z'
IF( .NOT.( CNAME .OR. SNAME ) )
$ RETURN
C2 = SUBNAM( 2: 3 )
C3 = SUBNAM( 4: 6 )
C4 = C3( 2: 3 )
*
GO TO ( 50, 60, 70 )ISPEC
*
50 CONTINUE
*
* ISPEC = 1: block size
*
* In these examples, separate code is provided for setting NB for
* real and complex. We assume that NB will take the same value in
* single or double precision.
*
NB = 1
*
IF( C2.EQ.'GE' ) THEN
IF( C3.EQ.'TRF' ) THEN
IF( SNAME ) THEN
NB = 64
ELSE
NB = 64
END IF
ELSE IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR.
$ C3.EQ.'QLF' ) THEN
IF( SNAME ) THEN
NB = 32
ELSE
NB = 32
END IF
ELSE IF( C3.EQ.'HRD' ) THEN
IF( SNAME ) THEN
NB = 32
ELSE
NB = 32
END IF
ELSE IF( C3.EQ.'BRD' ) THEN
IF( SNAME ) THEN
NB = 32
ELSE
NB = 32
END IF
ELSE IF( C3.EQ.'TRI' ) THEN
IF( SNAME ) THEN
NB = 64
ELSE
NB = 64
END IF
END IF
ELSE IF( C2.EQ.'PO' ) THEN
IF( C3.EQ.'TRF' ) THEN
IF( SNAME ) THEN
NB = 64
ELSE
NB = 64
END IF
END IF
ELSE IF( C2.EQ.'SY' ) THEN
IF( C3.EQ.'TRF' ) THEN
IF( SNAME ) THEN
NB = 64
ELSE
NB = 64
END IF
ELSE IF( SNAME .AND. C3.EQ.'TRD' ) THEN
NB = 32
ELSE IF( SNAME .AND. C3.EQ.'GST' ) THEN
NB = 64
END IF
ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN
IF( C3.EQ.'TRF' ) THEN
NB = 64
ELSE IF( C3.EQ.'TRD' ) THEN
NB = 32
ELSE IF( C3.EQ.'GST' ) THEN
NB = 64
END IF
ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN
IF( C3( 1: 1 ).EQ.'G' ) THEN
IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
$ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
$ THEN
NB = 32
END IF
ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN
IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
$ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
$ THEN
NB = 32
END IF
END IF
ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN
IF( C3( 1: 1 ).EQ.'G' ) THEN
IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
$ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
$ THEN
NB = 32
END IF
ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN
IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
$ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
$ THEN
NB = 32
END IF
END IF
ELSE IF( C2.EQ.'GB' ) THEN
IF( C3.EQ.'TRF' ) THEN
IF( SNAME ) THEN
IF( N4.LE.64 ) THEN
NB = 1
ELSE
NB = 32
END IF
ELSE
IF( N4.LE.64 ) THEN
NB = 1
ELSE
NB = 32
END IF
END IF
END IF
ELSE IF( C2.EQ.'PB' ) THEN
IF( C3.EQ.'TRF' ) THEN
IF( SNAME ) THEN
IF( N2.LE.64 ) THEN
NB = 1
ELSE
NB = 32
END IF
ELSE
IF( N2.LE.64 ) THEN
NB = 1
ELSE
NB = 32
END IF
END IF
END IF
ELSE IF( C2.EQ.'TR' ) THEN
IF( C3.EQ.'TRI' ) THEN
IF( SNAME ) THEN
NB = 64
ELSE
NB = 64
END IF
END IF
ELSE IF( C2.EQ.'LA' ) THEN
IF( C3.EQ.'UUM' ) THEN
IF( SNAME ) THEN
NB = 64
ELSE
NB = 64
END IF
END IF
ELSE IF( SNAME .AND. C2.EQ.'ST' ) THEN
IF( C3.EQ.'EBZ' ) THEN
NB = 1
END IF
END IF
ILAENV = NB
RETURN
*
60 CONTINUE
*
* ISPEC = 2: minimum block size
*
NBMIN = 2
IF( C2.EQ.'GE' ) THEN
IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR. C3.EQ.
$ 'QLF' ) THEN
IF( SNAME ) THEN
NBMIN = 2
ELSE
NBMIN = 2
END IF
ELSE IF( C3.EQ.'HRD' ) THEN
IF( SNAME ) THEN
NBMIN = 2
ELSE
NBMIN = 2
END IF
ELSE IF( C3.EQ.'BRD' ) THEN
IF( SNAME ) THEN
NBMIN = 2
ELSE
NBMIN = 2
END IF
ELSE IF( C3.EQ.'TRI' ) THEN
IF( SNAME ) THEN
NBMIN = 2
ELSE
NBMIN = 2
END IF
END IF
ELSE IF( C2.EQ.'SY' ) THEN
IF( C3.EQ.'TRF' ) THEN
IF( SNAME ) THEN
NBMIN = 8
ELSE
NBMIN = 8
END IF
ELSE IF( SNAME .AND. C3.EQ.'TRD' ) THEN
NBMIN = 2
END IF
ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN
IF( C3.EQ.'TRD' ) THEN
NBMIN = 2
END IF
ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN
IF( C3( 1: 1 ).EQ.'G' ) THEN
IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
$ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
$ THEN
NBMIN = 2
END IF
ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN
IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
$ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
$ THEN
NBMIN = 2
END IF
END IF
ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN
IF( C3( 1: 1 ).EQ.'G' ) THEN
IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
$ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
$ THEN
NBMIN = 2
END IF
ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN
IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
$ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
$ THEN
NBMIN = 2
END IF
END IF
END IF
ILAENV = NBMIN
RETURN
*
70 CONTINUE
*
* ISPEC = 3: crossover point
*
NX = 0
IF( C2.EQ.'GE' ) THEN
IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR. C3.EQ.
$ 'QLF' ) THEN
IF( SNAME ) THEN
NX = 128
ELSE
NX = 128
END IF
ELSE IF( C3.EQ.'HRD' ) THEN
IF( SNAME ) THEN
NX = 128
ELSE
NX = 128
END IF
ELSE IF( C3.EQ.'BRD' ) THEN
IF( SNAME ) THEN
NX = 128
ELSE
NX = 128
END IF
END IF
ELSE IF( C2.EQ.'SY' ) THEN
IF( SNAME .AND. C3.EQ.'TRD' ) THEN
NX = 32
END IF
ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN
IF( C3.EQ.'TRD' ) THEN
NX = 32
END IF
ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN
IF( C3( 1: 1 ).EQ.'G' ) THEN
IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
$ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
$ THEN
NX = 128
END IF
END IF
ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN
IF( C3( 1: 1 ).EQ.'G' ) THEN
IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ.
$ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' )
$ THEN
NX = 128
END IF
END IF
END IF
ILAENV = NX
RETURN
*
80 CONTINUE
*
* ISPEC = 4: number of shifts (used by xHSEQR)
*
ILAENV = 6
RETURN
*
90 CONTINUE
*
* ISPEC = 5: minimum column dimension (not used)
*
ILAENV = 2
RETURN
*
100 CONTINUE
*
* ISPEC = 6: crossover point for SVD (used by xGELSS and xGESVD)
*
ILAENV = INT( REAL( MIN( N1, N2 ) )*1.6E0 )
RETURN
*
110 CONTINUE
*
* ISPEC = 7: number of processors (not used)
*
ILAENV = 1
RETURN
*
120 CONTINUE
*
* ISPEC = 8: crossover point for multishift (used by xHSEQR)
*
ILAENV = 50
RETURN
*
130 CONTINUE
*
* ISPEC = 9: maximum size of the subproblems at the bottom of the
* computation tree in the divide-and-conquer algorithm
* (used by xGELSD and xGESDD)
*
ILAENV = 25
RETURN
*
140 CONTINUE
*
* ISPEC = 10: ieee NaN arithmetic can be trusted not to trap
*
* ILAENV = 0
ILAENV = 1
IF( ILAENV.EQ.1 ) THEN
ILAENV = IEEECK( 1, 0.0, 1.0 )
END IF
RETURN
*
150 CONTINUE
*
* ISPEC = 11: infinity arithmetic can be trusted not to trap
*
* ILAENV = 0
ILAENV = 1
IF( ILAENV.EQ.1 ) THEN
ILAENV = IEEECK( 0, 0.0, 1.0 )
END IF
RETURN
*
160 CONTINUE
*
* 12 <= ISPEC <= 16: xHSEQR or one of its subroutines.
*
ILAENV = IPARMQ( ISPEC, NAME, OPTS, N1, N2, N3, N4 )
RETURN
*
* End of ILAENV
*
END

322
internal/testdata/dlasqtest/iparmq.f vendored Normal file
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@@ -0,0 +1,322 @@
*> \brief \b IPARMQ
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download IPARMQ + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/iparmq.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/iparmq.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/iparmq.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
*
* .. Scalar Arguments ..
* INTEGER IHI, ILO, ISPEC, LWORK, N
* CHARACTER NAME*( * ), OPTS*( * )
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> This program sets problem and machine dependent parameters
*> useful for xHSEQR and its subroutines. It is called whenever
*> ILAENV is called with 12 <= ISPEC <= 16
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] ISPEC
*> \verbatim
*> ISPEC is integer scalar
*> ISPEC specifies which tunable parameter IPARMQ should
*> return.
*>
*> ISPEC=12: (INMIN) Matrices of order nmin or less
*> are sent directly to xLAHQR, the implicit
*> double shift QR algorithm. NMIN must be
*> at least 11.
*>
*> ISPEC=13: (INWIN) Size of the deflation window.
*> This is best set greater than or equal to
*> the number of simultaneous shifts NS.
*> Larger matrices benefit from larger deflation
*> windows.
*>
*> ISPEC=14: (INIBL) Determines when to stop nibbling and
*> invest in an (expensive) multi-shift QR sweep.
*> If the aggressive early deflation subroutine
*> finds LD converged eigenvalues from an order
*> NW deflation window and LD.GT.(NW*NIBBLE)/100,
*> then the next QR sweep is skipped and early
*> deflation is applied immediately to the
*> remaining active diagonal block. Setting
*> IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a
*> multi-shift QR sweep whenever early deflation
*> finds a converged eigenvalue. Setting
*> IPARMQ(ISPEC=14) greater than or equal to 100
*> prevents TTQRE from skipping a multi-shift
*> QR sweep.
*>
*> ISPEC=15: (NSHFTS) The number of simultaneous shifts in
*> a multi-shift QR iteration.
*>
*> ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the
*> following meanings.
*> 0: During the multi-shift QR sweep,
*> xLAQR5 does not accumulate reflections and
*> does not use matrix-matrix multiply to
*> update the far-from-diagonal matrix
*> entries.
*> 1: During the multi-shift QR sweep,
*> xLAQR5 and/or xLAQRaccumulates reflections and uses
*> matrix-matrix multiply to update the
*> far-from-diagonal matrix entries.
*> 2: During the multi-shift QR sweep.
*> xLAQR5 accumulates reflections and takes
*> advantage of 2-by-2 block structure during
*> matrix-matrix multiplies.
*> (If xTRMM is slower than xGEMM, then
*> IPARMQ(ISPEC=16)=1 may be more efficient than
*> IPARMQ(ISPEC=16)=2 despite the greater level of
*> arithmetic work implied by the latter choice.)
*> \endverbatim
*>
*> \param[in] NAME
*> \verbatim
*> NAME is character string
*> Name of the calling subroutine
*> \endverbatim
*>
*> \param[in] OPTS
*> \verbatim
*> OPTS is character string
*> This is a concatenation of the string arguments to
*> TTQRE.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is integer scalar
*> N is the order of the Hessenberg matrix H.
*> \endverbatim
*>
*> \param[in] ILO
*> \verbatim
*> ILO is INTEGER
*> \endverbatim
*>
*> \param[in] IHI
*> \verbatim
*> IHI is INTEGER
*> It is assumed that H is already upper triangular
*> in rows and columns 1:ILO-1 and IHI+1:N.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is integer scalar
*> The amount of workspace available.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup auxOTHERauxiliary
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Little is known about how best to choose these parameters.
*> It is possible to use different values of the parameters
*> for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR.
*>
*> It is probably best to choose different parameters for
*> different matrices and different parameters at different
*> times during the iteration, but this has not been
*> implemented --- yet.
*>
*>
*> The best choices of most of the parameters depend
*> in an ill-understood way on the relative execution
*> rate of xLAQR3 and xLAQR5 and on the nature of each
*> particular eigenvalue problem. Experiment may be the
*> only practical way to determine which choices are most
*> effective.
*>
*> Following is a list of default values supplied by IPARMQ.
*> These defaults may be adjusted in order to attain better
*> performance in any particular computational environment.
*>
*> IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point.
*> Default: 75. (Must be at least 11.)
*>
*> IPARMQ(ISPEC=13) Recommended deflation window size.
*> This depends on ILO, IHI and NS, the
*> number of simultaneous shifts returned
*> by IPARMQ(ISPEC=15). The default for
*> (IHI-ILO+1).LE.500 is NS. The default
*> for (IHI-ILO+1).GT.500 is 3*NS/2.
*>
*> IPARMQ(ISPEC=14) Nibble crossover point. Default: 14.
*>
*> IPARMQ(ISPEC=15) Number of simultaneous shifts, NS.
*> a multi-shift QR iteration.
*>
*> If IHI-ILO+1 is ...
*>
*> greater than ...but less ... the
*> or equal to ... than default is
*>
*> 0 30 NS = 2+
*> 30 60 NS = 4+
*> 60 150 NS = 10
*> 150 590 NS = **
*> 590 3000 NS = 64
*> 3000 6000 NS = 128
*> 6000 infinity NS = 256
*>
*> (+) By default matrices of this order are
*> passed to the implicit double shift routine
*> xLAHQR. See IPARMQ(ISPEC=12) above. These
*> values of NS are used only in case of a rare
*> xLAHQR failure.
*>
*> (**) The asterisks (**) indicate an ad-hoc
*> function increasing from 10 to 64.
*>
*> IPARMQ(ISPEC=16) Select structured matrix multiply.
*> (See ISPEC=16 above for details.)
*> Default: 3.
*> \endverbatim
*>
* =====================================================================
INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
*
* -- LAPACK auxiliary routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER IHI, ILO, ISPEC, LWORK, N
CHARACTER NAME*( * ), OPTS*( * )
*
* ================================================================
* .. Parameters ..
INTEGER INMIN, INWIN, INIBL, ISHFTS, IACC22
PARAMETER ( INMIN = 12, INWIN = 13, INIBL = 14,
$ ISHFTS = 15, IACC22 = 16 )
INTEGER NMIN, K22MIN, KACMIN, NIBBLE, KNWSWP
PARAMETER ( NMIN = 75, K22MIN = 14, KACMIN = 14,
$ NIBBLE = 14, KNWSWP = 500 )
REAL TWO
PARAMETER ( TWO = 2.0 )
* ..
* .. Local Scalars ..
INTEGER NH, NS
* ..
* .. Intrinsic Functions ..
INTRINSIC LOG, MAX, MOD, NINT, REAL
* ..
* .. Executable Statements ..
IF( ( ISPEC.EQ.ISHFTS ) .OR. ( ISPEC.EQ.INWIN ) .OR.
$ ( ISPEC.EQ.IACC22 ) ) THEN
*
* ==== Set the number simultaneous shifts ====
*
NH = IHI - ILO + 1
NS = 2
IF( NH.GE.30 )
$ NS = 4
IF( NH.GE.60 )
$ NS = 10
IF( NH.GE.150 )
$ NS = MAX( 10, NH / NINT( LOG( REAL( NH ) ) / LOG( TWO ) ) )
IF( NH.GE.590 )
$ NS = 64
IF( NH.GE.3000 )
$ NS = 128
IF( NH.GE.6000 )
$ NS = 256
NS = MAX( 2, NS-MOD( NS, 2 ) )
END IF
*
IF( ISPEC.EQ.INMIN ) THEN
*
*
* ===== Matrices of order smaller than NMIN get sent
* . to xLAHQR, the classic double shift algorithm.
* . This must be at least 11. ====
*
IPARMQ = NMIN
*
ELSE IF( ISPEC.EQ.INIBL ) THEN
*
* ==== INIBL: skip a multi-shift qr iteration and
* . whenever aggressive early deflation finds
* . at least (NIBBLE*(window size)/100) deflations. ====
*
IPARMQ = NIBBLE
*
ELSE IF( ISPEC.EQ.ISHFTS ) THEN
*
* ==== NSHFTS: The number of simultaneous shifts =====
*
IPARMQ = NS
*
ELSE IF( ISPEC.EQ.INWIN ) THEN
*
* ==== NW: deflation window size. ====
*
IF( NH.LE.KNWSWP ) THEN
IPARMQ = NS
ELSE
IPARMQ = 3*NS / 2
END IF
*
ELSE IF( ISPEC.EQ.IACC22 ) THEN
*
* ==== IACC22: Whether to accumulate reflections
* . before updating the far-from-diagonal elements
* . and whether to use 2-by-2 block structure while
* . doing it. A small amount of work could be saved
* . by making this choice dependent also upon the
* . NH=IHI-ILO+1.
*
IPARMQ = 0
IF( NS.GE.KACMIN )
$ IPARMQ = 1
IF( NS.GE.K22MIN )
$ IPARMQ = 2
*
ELSE
* ===== invalid value of ispec =====
IPARMQ = -1
*
END IF
*
* ==== End of IPARMQ ====
*
END

125
internal/testdata/dlasqtest/lsame.f vendored Normal file
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@@ -0,0 +1,125 @@
*> \brief \b LSAME
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* LOGICAL FUNCTION LSAME( CA, CB )
*
* .. Scalar Arguments ..
* CHARACTER CA, CB
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> LSAME returns .TRUE. if CA is the same letter as CB regardless of
*> case.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] CA
*> \verbatim
*> \endverbatim
*>
*> \param[in] CB
*> \verbatim
*> CA and CB specify the single characters to be compared.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup auxOTHERauxiliary
*
* =====================================================================
LOGICAL FUNCTION LSAME( CA, CB )
*
* -- LAPACK auxiliary routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER CA, CB
* ..
*
* =====================================================================
*
* .. Intrinsic Functions ..
INTRINSIC ICHAR
* ..
* .. Local Scalars ..
INTEGER INTA, INTB, ZCODE
* ..
* .. Executable Statements ..
*
* Test if the characters are equal
*
LSAME = CA.EQ.CB
IF( LSAME )
$ RETURN
*
* Now test for equivalence if both characters are alphabetic.
*
ZCODE = ICHAR( 'Z' )
*
* Use 'Z' rather than 'A' so that ASCII can be detected on Prime
* machines, on which ICHAR returns a value with bit 8 set.
* ICHAR('A') on Prime machines returns 193 which is the same as
* ICHAR('A') on an EBCDIC machine.
*
INTA = ICHAR( CA )
INTB = ICHAR( CB )
*
IF( ZCODE.EQ.90 .OR. ZCODE.EQ.122 ) THEN
*
* ASCII is assumed - ZCODE is the ASCII code of either lower or
* upper case 'Z'.
*
IF( INTA.GE.97 .AND. INTA.LE.122 ) INTA = INTA - 32
IF( INTB.GE.97 .AND. INTB.LE.122 ) INTB = INTB - 32
*
ELSE IF( ZCODE.EQ.233 .OR. ZCODE.EQ.169 ) THEN
*
* EBCDIC is assumed - ZCODE is the EBCDIC code of either lower or
* upper case 'Z'.
*
IF( INTA.GE.129 .AND. INTA.LE.137 .OR.
$ INTA.GE.145 .AND. INTA.LE.153 .OR.
$ INTA.GE.162 .AND. INTA.LE.169 ) INTA = INTA + 64
IF( INTB.GE.129 .AND. INTB.LE.137 .OR.
$ INTB.GE.145 .AND. INTB.LE.153 .OR.
$ INTB.GE.162 .AND. INTB.LE.169 ) INTB = INTB + 64
*
ELSE IF( ZCODE.EQ.218 .OR. ZCODE.EQ.250 ) THEN
*
* ASCII is assumed, on Prime machines - ZCODE is the ASCII code
* plus 128 of either lower or upper case 'Z'.
*
IF( INTA.GE.225 .AND. INTA.LE.250 ) INTA = INTA - 32
IF( INTB.GE.225 .AND. INTB.LE.250 ) INTB = INTB - 32
END IF
LSAME = INTA.EQ.INTB
*
* RETURN
*
* End of LSAME
*
END

626
internal/testdata/dlasqtest/testdlasq1.f90 vendored Normal file
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@@ -0,0 +1,626 @@
program randomsys1
implicit none
integer, parameter :: nmax=1000
real(kind=8), dimension(nmax) :: b, x
real(kind=8), dimension(nmax,nmax) :: a
real(kind=8) :: err
integer :: i, info, lda, ldb, nrhs, n,iter
integer, dimension(nmax) :: ipiv
real(kind=8), dimension(100) :: d
real(kind=8), dimension(99) :: e
real(kind=8), dimension(400) :: work
d(1:100) = (/1.8334043365537367D+00, &
1.4451749896846686D+00, &
1.0018566447551758D-01, &
-7.2143260438744417D-01, &
-3.7864653015502087D-01, &
-9.0270111568850808D-01, &
1.2204305489831029D+00, &
-9.7628177811136485D-01, &
8.4199233511256721D-01, &
-2.7938817329922050D-01, &
3.6157779599908046D-01, &
-1.8563411313998144D+00, &
-5.7930081140992240D-01, &
7.4080550463379169D-01, &
1.7021409147402005D+00, &
-5.7992035328196923D-01, &
4.0877426434579855D-01, &
-7.1297236049446144D-01, &
-1.2214095798914903D+00, &
2.9037983248746674D-01, &
7.4685018821608473D-01, &
3.0213735481316539D-01, &
-1.5207207136907624D-01, &
-2.1332671668411556D+00, &
6.8744661834930676D-01, &
-2.0946670404018297D-01, &
-1.5221059713957628D+00, &
1.1117190383859539D+00, &
-6.1175948159744020D-01, &
-4.4149212620857964D-01, &
-5.5702632609947533D-01, &
1.4071858950692646D+00, &
-3.2329881667362437D-01, &
-3.1958092104323499D-01, &
9.0934520529412111D-01, &
9.7881421364746712D-01, &
-5.1202970940327841D-01, &
1.5040024724520102D+00, &
-7.1993831181468571D-01, &
-7.1819661000094503D-01, &
-1.3481185445933910D+00, &
-1.4984426192966893D+00, &
1.1356626654278745D+00, &
1.6427417967661164D+00, &
-1.4184643787388000D+00, &
2.9811560271518989D-01, &
7.8630022575860559D-01, &
-1.8262830018047089D+00, &
6.3058255632564841D-01, &
-2.0692752940382309D-02, &
-7.2726648905906033D-01, &
-1.0461446937034022D+00, &
1.2530345094987356D+00, &
-2.3583665341168443D+00, &
1.9177654334479410D-01, &
-1.3563410975095058D+00, &
-1.0669710425337906D+00, &
1.4840245472507219D+00, &
-6.9185935518981789D-01, &
1.6813910559942205D-01, &
-7.1255209442204559D-01, &
-1.0112797453604008D+00, &
2.8591746998403011D-01, &
-1.9403039239509563D+00, &
-8.1434141084858885D-02, &
1.3873918713367210D+00, &
-8.8212258376548647D-01, &
-1.2253510598547583D+00, &
-3.8677386127356073D-01, &
-1.0262656526479850D+00, &
2.9468734022014376D-01, &
2.3442965677966704D-01, &
1.2219251054024911D+00, &
2.6066505150099868D+00, &
-7.8543147636303856D-01, &
-9.8126277325503253D-01, &
1.1722358680271947D+00, &
-8.1477749181289072D-01, &
1.3437777060446568D-01, &
3.4626341297821356D-01, &
-4.5672026157532375D-01, &
3.0496975959999184D-01, &
3.4636683737604146D-01, &
1.5114807806635011D-01, &
-1.1376177393945328D+00, &
9.3419670621891793D-01, &
7.9186416310239138D-01, &
6.7230421440462595D-01, &
-2.3236847424852280D-01, &
-1.0927137499922757D+00, &
9.8562766620822340D-01, &
-1.1382935431007701D-01, &
-9.2072237463768225D-01, &
6.1142850054965170D-01, &
8.2752057022739134D-03, &
6.7197122515126417D-01, &
-1.1007816668204429D+00, &
-1.2196829073430047D+00, &
-6.1428585523321222D-01, &
6.4599803465517280D-01/)
e(1:99) = (/-9.6393084631802151D-01, &
2.5532567563781607D+00, &
8.2492664240014357D-01, &
8.2628261757058474D-01, &
7.3021658879350859D-01, &
3.4014431785419519D-02, &
3.2121571974900542D-01, &
2.5987166374572213D-02, &
-3.1150206355945814D-01, &
1.3429094629249927D+00, &
8.6246434952180806D-01, &
-8.3756967113851388D-01, &
9.5277237959592009D-01, &
1.1717152179539618D+00, &
2.5980977671460709D-01, &
-6.4468162556415265D-01, &
-1.3751364204170078D+00, &
2.9677172586579936D-01, &
-3.7071376979215720D-01, &
8.2912690407496381D-01, &
-8.6820437618589197D-01, &
5.2500961173269689D-01, &
1.0657701704030644D+00, &
-4.6621502244820201D-03, &
-1.9013997092621748D-01, &
1.5098985741543924D-01, &
1.0102557493909003D+00, &
8.8830298507891103D-01, &
2.0464938169302065D+00, &
4.7910192662606277D-01, &
1.4155288808120892D+00, &
-5.8169388172737679D-01, &
-9.8007278321065916D-01, &
2.4369633027015425D-01, &
1.6173163491335715D-01, &
6.6887624704464499D-01, &
-1.6500999383869115D+00, &
1.4380895281962367D+00, &
4.7508565250807777D-01, &
-3.1332991280327299D-01, &
3.1402552392574451D-01, &
5.6246373170551534D-01, &
2.5944662334710866D-01, &
4.8101648688789655D-01, &
1.7823376751423265D+00, &
3.0160656491545923D-01, &
-8.8915960863742050D-01, &
-4.4783548340444157D-01, &
8.9985836172311440D-01, &
-1.5626460660617920D+00, &
8.9972644535054036D-01, &
2.4456452268563592D-01, &
-3.1377944726557985D+00, &
1.6874136691232020D+00, &
2.4791290942030142D-01, &
1.7055713617986679D+00, &
1.7027580566127303D+00, &
-5.2969836953828042D-01, &
-8.6858804294195124D-01, &
7.6588136514601834D-01, &
8.6161822555855139D-01, &
6.5387844189250555D-01, &
7.0164941351276944D-01, &
4.1171318512873312D-01, &
7.6075070364872455D-01, &
8.5708035578209718D-02, &
-4.3558500874018535D-01, &
-6.2302104134015979D-01, &
8.4912051051824700D-01, &
-1.7120108380813925D-01, &
-9.7880552224113848D-01, &
1.1904436348486702D+00, &
7.0273864977367972D-01, &
-1.0213785672492079D+00, &
4.8392839864322634D-02, &
1.2611184618297511D-01, &
5.3330169134056482D-01, &
1.8070298106837654D+00, &
-2.8022831541922144D-01, &
8.0235047640662738D-01, &
-1.2615220404695868D+00, &
1.1878769364434660D+00, &
-2.1059219864297674D-01, &
3.2897539618854971D-01, &
-5.8928028913554642D-01, &
1.9164347352074701D-02, &
2.8035162764822374D-01, &
-9.6622429734784299D-02, &
3.4216241143907045D-01, &
-2.2358052317750254D+00, &
6.6284070879481805D-01, &
7.4316074303777269D-01, &
1.0280848437626724D+00, &
-2.0939898252763922D-01, &
-1.0268515265064981D+00, &
-1.2648527910628871D-01, &
4.8663846308033204D-01, &
1.2270171407392749D+00, &
-1.6189022502021406D+00/)
work(1:400) = (/6.0466028797961957D-01, &
9.4050908804501243D-01, &
6.6456005321849043D-01, &
4.3771418718698019D-01, &
4.2463749707126569D-01, &
6.8682307286710942D-01, &
6.5637019217476222D-02, &
1.5651925473279124D-01, &
9.6969518914484562D-02, &
3.0091186058528707D-01, &
5.1521262850206540D-01, &
8.1363996099009683D-01, &
2.1426387258237492D-01, &
3.8065718929968601D-01, &
3.1805817433032985D-01, &
4.6888984490242319D-01, &
2.8303415118044517D-01, &
2.9310185733681576D-01, &
6.7908467592021626D-01, &
2.1855305259276428D-01, &
2.0318687664732285D-01, &
3.6087141685690599D-01, &
5.7067327607102258D-01, &
8.6249143744788637D-01, &
2.9311424455385804D-01, &
2.9708256355629153D-01, &
7.5257303555161192D-01, &
2.0658266191369859D-01, &
8.6533501300156102D-01, &
6.9671916574663473D-01, &
5.2382030605000085D-01, &
2.8303083325889995D-02, &
1.5832827774512764D-01, &
6.0725343954551536D-01, &
9.7524161886057836D-01, &
7.9453623373871976D-02, &
5.9480859768306260D-01, &
5.9120651313875290D-02, &
6.9202458735311201D-01, &
3.0152268100655999D-01, &
1.7326623818270528D-01, &
5.4109985500873525D-01, &
5.4415557300088502D-01, &
2.7850762181610883D-01, &
4.2315220157182809D-01, &
5.3058571535070520D-01, &
2.5354050051506050D-01, &
2.8208099496492467D-01, &
7.8860491501934493D-01, &
3.6180548048031691D-01, &
8.8054312274161706D-01, &
2.9711226063977081D-01, &
8.9436172933045366D-01, &
9.7454618399116566D-02, &
9.7691686858626237D-01, &
7.4290998949843021D-02, &
2.2228941700678773D-01, &
6.8107831239257088D-01, &
2.4151508854715265D-01, &
3.1152244431052484D-01, &
9.3284642851843402D-01, &
7.4184895999182299D-01, &
8.0105504265266125D-01, &
7.3023147729480831D-01, &
1.8292491645390843D-01, &
4.2835708180680782D-01, &
8.9699195756187267D-01, &
6.8265348801324377D-01, &
9.7892935557668759D-01, &
9.2221225892172687D-01, &
9.0837275353887081D-02, &
4.9314199770488037D-01, &
9.2698680357441421D-01, &
9.5494544041678175D-01, &
3.4795396362822290D-01, &
6.9083883150567893D-01, &
7.1090719529999513D-01, &
5.6377959581526438D-01, &
6.4948946059294044D-01, &
5.5176504901277490D-01, &
7.5582350749159777D-01, &
4.0380328579570035D-01, &
1.3065111702897217D-01, &
9.8596472934024670D-01, &
8.9634174539621614D-01, &
3.2208397052088172D-01, &
7.2114776519267410D-01, &
6.4453978250932942D-01, &
8.5520507541911234D-02, &
6.6957529769977453D-01, &
6.2272831736370449D-01, &
3.6969284363982191D-01, &
2.3682254680548520D-01, &
5.3528189063440612D-01, &
1.8724610140105305D-01, &
2.3884070280531861D-01, &
6.2809817121836331D-01, &
1.2675292937260130D-01, &
2.8133029380535923D-01, &
4.1032284435628247D-01, &
4.3491247389145765D-01, &
6.2509502830053043D-01, &
5.5014692050772329D-01, &
6.2360882645293014D-01, &
7.2918072673429812D-01, &
8.3053391899480622D-01, &
5.1381551612136129D-04, &
7.3606860149543141D-01, &
3.9998376285699544D-01, &
4.9786811334270198D-01, &
6.0397810228292748D-01, &
4.0961827788499267D-01, &
2.9671281274886468D-02, &
1.9038945142366389D-03, &
2.8430411748625642D-03, &
9.1582131461295702D-01, &
5.8983418500491935D-01, &
5.5939244907101404D-01, &
8.1540517093336062D-01, &
8.7801175865240000D-01, &
4.5844247857565062D-01, &
6.0016559532333080D-01, &
2.6265150609689439D-02, &
8.4583278724804167D-01, &
2.4969320116349378D-01, &
6.4178429079958299D-01, &
2.4746660783662855D-01, &
1.7365584472313275D-01, &
5.9262375321244554D-01, &
8.1439455096702107D-01, &
6.9383813651720949D-01, &
3.0322547833006870D-02, &
5.3921010589094598D-01, &
9.7567481498731645D-01, &
7.5076305647959851D-01, &
2.9400631279501488D-01, &
7.5316127773675856D-01, &
1.5096404497960700D-01, &
3.5576726540923664D-01, &
8.3193085296981628D-01, &
2.3183004193767690D-01, &
6.2783460500002275D-01, &
4.9839430127597562D-01, &
8.9836089260366833D-02, &
2.5193959794895041D-02, &
3.9221618315402479D-01, &
5.8938308640079917D-01, &
9.2961163544903025D-01, &
5.7208680144308399D-01, &
5.8857634514348212D-01, &
4.1176268834501623D-01, &
5.5258038981424384D-01, &
4.9160739613162047D-01, &
9.5795391353751358D-01, &
7.9720854091080284D-01, &
1.0738111282075208D-01, &
7.8303497339600214D-01, &
3.9325099922888668D-01, &
1.3041384617379179D-01, &
1.9003276633920804D-01, &
7.3982578101583363D-01, &
6.5404140923127974D-01, &
9.8383788985732593D-02, &
5.2038028571222783D-01, &
9.9729663719935122D-02, &
1.5184340208190175D-01, &
7.6190262303755044D-02, &
3.1520808532012451D-01, &
1.5965092146489504D-01, &
1.3780406161952607D-01, &
3.2261068286779754D-01, &
5.3907451703947940D-01, &
5.7085162734549566D-01, &
5.1278175811108151D-01, &
6.8417513009745512D-01, &
6.5304020513536076D-01, &
5.2449975954986505D-01, &
6.5427013442414605D-01, &
7.1636837490167116D-01, &
6.3664421403817983D-01, &
1.2825909106361078D-02, &
3.0682195787138565D-02, &
9.8030874806304999D-02, &
3.6911170916434483D-01, &
8.2645412563474197D-01, &
3.4768170859156955D-01, &
3.4431501772636058D-01, &
2.5299982364784412D-01, &
2.1647114665497036D-01, &
5.5500213563479417D-01, &
4.0207084527183062D-01, &
5.0649706367641834D-01, &
1.6867966833433606D-01, &
3.3136826030698385D-01, &
8.2792809615055885D-01, &
7.0028787314581509D-01, &
5.7926259664335768D-02, &
9.9915949022033324D-01, &
4.1154036322047599D-01, &
1.1167463676480495D-01, &
7.8075408455849260D-01, &
9.2117624440742188D-02, &
5.3494624494407637D-02, &
7.1469581589162956D-01, &
2.5076227542918023D-01, &
8.4863292090315690D-01, &
9.7388187407067284D-01, &
2.1256094905031958D-01, &
2.1533783325605065D-02, &
9.4519476038882588D-01, &
9.2970155499924934D-02, &
6.4583337452397671D-01, &
3.1188554282705405D-01, &
4.4846436394045647D-01, &
4.8723924858036949D-01, &
8.2479676511350006D-02, &
6.7182910623463954D-01, &
4.0018828942364343D-01, &
9.0027514726431157D-01, &
9.4988320610125321D-01, &
3.1933126760711733D-01, &
4.9938549375241320D-01, &
4.0043231714181288D-01, &
1.9808670325451940D-02, &
6.4503886601944815D-01, &
4.2868843006993296D-01, &
3.3959675138730994D-01, &
8.8744750085050050D-01, &
2.3632747430436052D-01, &
7.6500821493327975D-01, &
3.5754647436084384D-02, &
7.2757725604152290D-01, &
6.2583662695812525D-01, &
5.1308750608785669D-01, &
7.2448356792351315D-02, &
7.2422905845916841D-01, &
8.7984484630570914D-01, &
9.7776347735771851D-01, &
8.4750026226468134D-01, &
8.3219793814993315D-01, &
2.4784452318699535D-01, &
9.1339906293647088D-01, &
7.5037210134653420D-02, &
8.3510380115435290D-01, &
6.2933169164530067D-01, &
7.5174057889673473D-01, &
6.3200343378879975D-01, &
9.6934213238731665D-02, &
1.4827369494876504D-02, &
5.8383474186253115D-01, &
6.8756195202154743D-02, &
9.9827381100849455D-01, &
6.4918841659842363D-01, &
9.8546557863324791D-01, &
8.3480576021921249D-01, &
3.3205608571906026D-01, &
6.6139318058334262D-01, &
9.5602062659660969D-01, &
3.1051027622482125D-01, &
1.8439069400202679D-01, &
9.6709434137177297D-01, &
8.3324181552815457D-01, &
3.0954845052732810D-01, &
8.0587176753764456D-01, &
4.1732584219038238D-01, &
7.1853044935277477D-01, &
4.0673677545039083D-01, &
8.9580326774414576D-01, &
9.5817636260259365D-01, &
1.8713221139656417D-02, &
7.9167230908208319D-01, &
4.2355315388584103D-01, &
1.5181277223073395D-02, &
4.3269824007906393D-01, &
9.0477623706573340D-01, &
8.5570441457488644D-01, &
4.2921642176334200D-02, &
6.5903053300775438D-01, &
3.4785904313005395D-01, &
5.0348679004869112D-01, &
8.3994742117055976D-01, &
2.3109568410543832D-02, &
1.2436351859954159D-01, &
2.6117561918821841D-01, &
8.3494750649349414D-01, &
3.1480479595597533D-01, &
7.6812064740880894D-03, &
8.9975012571752733D-01, &
3.7026753645051064D-01, &
1.0019940926941497D-01, &
6.4320402657020315D-01, &
7.6988908998308336D-01, &
7.9112533566198451D-01, &
2.6238190747072776D-01, &
3.4686388037925503D-01, &
2.1465371537694145D-01, &
8.2209289717657175D-01, &
3.5113429966521320D-01, &
5.9919425250588099D-01, &
5.7835125693111211D-01, &
4.1358098797631293D-01, &
1.1985050890286310D-01, &
9.1161370679159903D-01, &
5.3785580105748208D-02, &
2.2891758676059876D-01, &
3.2417396306138829D-01, &
3.5076512764716117D-01, &
3.4928874777426255D-01, &
3.0380212985436572D-01, &
9.6874615996581170D-01, &
6.7152655046083776D-01, &
2.0794312837315651D-01, &
9.6313940120247044D-01, &
3.0220237504213365D-01, &
8.0794108095480799D-01, &
1.3408416275024179D-01, &
9.4776028919455635D-01, &
6.4086482116825383D-01, &
9.5325875425035178D-01, &
8.0987422593395209D-01, &
1.8159084675756379D-01, &
9.4275737153737327D-01, &
8.3124103554376771D-01, &
4.9468043578205978D-01, &
8.5531034647693982D-01, &
7.1074391181909824D-01, &
2.7349475629159786D-01, &
4.0763287189198161D-01, &
9.0976128251911847D-01, &
9.4439713870030451D-01, &
4.9863245185560190D-01, &
2.8863831012730923D-01, &
9.7589525649963815D-01, &
4.5258447627808124D-01, &
4.4990698677957075D-02, &
3.1536198151820755D-01, &
9.5190614812037189D-01, &
7.5156308247423609D-01, &
5.3579099898961424D-01, &
6.6971458883510748D-01, &
8.6517499748328641D-01, &
4.5888445390388938D-01, &
5.7855090249582031D-01, &
4.8152982184966137D-01, &
5.5061576198318274D-01, &
9.5062324380815433D-01, &
5.0986542047295536D-01, &
7.4251472966182985D-01, &
4.9079401441435533D-01, &
6.6151414870689360D-02, &
2.6249066264989940D-01, &
9.2546794407799982D-01, &
3.7148665165822231D-01, &
4.0941940003107308D-01, &
4.1575196973399631D-01, &
9.7261599736539445D-02, &
9.0162762447969347D-01, &
4.4446597981328932D-03, &
2.7392454335102678D-01, &
1.0930666111680035D-01, &
8.5544841289295426D-01, &
2.5705535663902546D-01, &
9.8913209203202213D-01, &
9.2641142236812712D-01, &
1.7094603208839290D-01, &
3.0388712489325242D-01, &
5.3345144978115477D-01, &
1.7648961347647024D-01, &
8.1359077477652830D-01, &
7.0513712380125892D-01, &
2.5720755742139950D-01, &
2.5036892046498466D-01, &
3.3509436689927874D-01, &
7.5124063162526056D-01, &
4.8797826077860845D-03, &
8.4099320643626019D-01, &
2.2957358869665739D-01, &
1.3285547727582237D-02, &
9.4993740716879371D-01, &
8.9937146465701423D-01, &
9.6262420114388625D-01, &
4.3000361954927006D-02, &
7.1266261216467264D-01, &
5.1094098258212241D-02, &
4.0753210485857738D-01, &
4.7569737399615403D-01, &
3.4746838606940983D-01, &
4.0719938711096422D-02, &
5.9756620514440806D-01, &
2.6012467360309705D-01, &
8.3285585557738717D-01, &
9.6049750529821787D-01, &
9.3670756890653750D-01, &
2.2932023844733959D-01, &
7.2031310018914962D-01, &
7.5648232426876405D-01, &
4.5015392507594826D-01, &
3.3897738839543617D-01, &
4.7249205225111501D-01, &
9.8599436000817042D-01/)
n = 100
info = 0
open(unit = 4, STATUS='REPLACE', file = "gen4tests.txt")
open(unit = 3, STATUS='REPLACE', file = "gen3tests.txt")
open(unit = 5, STATUS='REPLACE', file = "gen5tests.txt")
call dlasq1(n, d, e, work, info)
close(5)
close(3)
close(4)
end

171
internal/testdata/dlasqtest/testdlasq2.f90 vendored Normal file
View File

@@ -0,0 +1,171 @@
! $CLASSHG/codes/lapack/random/randomsys1.f90
program randomsys1
implicit none
integer, parameter :: nmax=1000
real(kind=8), dimension(nmax) :: b, x
real(kind=8), dimension(nmax,nmax) :: a
real(kind=8) :: err
integer :: i, info, lda, ldb, nrhs, n,iter
integer, dimension(nmax) :: ipiv
real(kind=8), dimension(84) :: z
z(1:84) = (/2.3962280929192509D-01, &
6.4346010490580374D-01, &
5.4886677265274941D-01, &
1.8435046456575191D-01, &
4.2690013698472401D-01, &
6.2760930131666248D-01, &
8.7243363936287288D-02, &
5.3710399529030350D-01, &
8.4474604576675638D-01, &
4.0947669295022632D-01, &
2.0315141244999760D-01, &
8.2714283129979482D-01, &
9.6582843029739029D-01, &
3.7773539690481128D-01, &
6.4713340225873406D-01, &
6.7774351756798612D-01, &
4.4568905572928591D-01, &
1.7208265726837521D-01, &
3.5202074329011412D-01, &
3.2913965083413110D-01, &
7.4682622623737438D-01, &
2.7151044969605542D-01, &
5.6129178633962351D-01, &
1.3244294692867761D-01, &
7.9837660640147112D-01, &
2.0595995860196409D-01, &
2.6555102564257749D-02, &
1.9623902644848701D-01, &
7.8452468963715605D-03, &
8.2177375597112101D-01, &
9.4444982187044924D-01, &
4.6799576958310329D-01, &
1.1359180530395520D-01, &
1.6049482525711320D-01, &
8.4523811016138373D-01, &
8.5370708147160490D-01, &
3.0139325968162661D-01, &
2.5117154067021252D-01, &
2.0086476380364379D-01, &
2.6078975734443288D-01, &
2.5710509100784901D-01, &
6.2861740244633146D-01, &
4.7397018497236110D-01, &
8.6989475348440182D-01, &
6.4860795895959611D-01, &
8.8943219043019872D-01, &
7.9524758401855578D-01, &
8.8016617212154102D-01, &
2.1472721943810300D-01, &
9.5183566464760194D-01, &
7.1911522894148772D-01, &
1.1065249711733080D-01, &
9.5745872307341484D-01, &
6.4694742306793951D-01, &
5.8182607574435841D-01, &
1.2922028370755401D-02, &
2.7617229134380777D-01, &
8.0045359255855852D-01, &
3.2789738555900377D-01, &
5.7940374386642890D-01, &
2.3961554431041750D-02, &
6.6990484757537938D-01, &
1.8144929371280860D-01, &
2.8661849362222419D-01, &
6.5845572125062690D-01, &
5.8896512277754309D-01, &
6.3697665190607378D-02, &
1.3281935295985961D-01, &
7.4166314172628711D-01, &
5.0033182787066932D-01, &
3.1440772963953763D-02, &
9.9073931564031925D-01, &
3.4236965949145941D-03, &
6.9929220728508257D-01, &
7.5905196170645428D-01, &
2.5421825141163590D-01, &
3.3146571845550887D-01, &
5.7286596840196446D-01, &
9.9158547964144228D-01, &
4.8967497301052382D-01, &
5.6113697207961410D-01, &
6.0641422150435165D-01, &
8.5675901647669139D-02, &
2.5817319326781851D-01/)
n = 21
info = 0
open(unit = 2,STATUS='REPLACE', file = "gen2tests.txt")
open(unit = 4, STATUS='REPLACE', file = "gen4tests.txt")
open(unit = 3,STATUS='REPLACE', file = "gen3tests.txt")
open(unit = 5,STATUS='REPLACE', file = "gen5tests.txt")
write(2,*) "{"
write(2,'(9999(g0))',advance="no") "z: []float64{"
do i = 1, 4*n
write (2,'(99999(e24.16,a))',advance="no") z(i), ","
end do
write (2,*) "},"
write(2,*) "n: " ,n,","
call dlasq2(n, z, info)
write(2,'(9999(g0))', advance="no") "zOut: []float64{"
do i = 1, 4*n
write (2,'(99999(e24.16,a))', advance="no") z(i), ","
end do
write (2,*) "},"
write(2,*) "info:", info, ","
write(2,*) "},"
print *, "Done fixed dlasq2"
close(5)
close(3)
close(4)
close(2)
! For random tests
n = 21
open(unit = 2, STATUS='REPLACE', file = "gen2tests.txt")
open(unit = 4, STATUS='REPLACE', file = "gen4tests.txt")
open(unit = 3, STATUS='REPLACE', file = "gen3tests.txt")
open(unit = 5, STATUS='REPLACE', file = "gen5tests.txt")
do iter = 1, 2
call random_number(z(1:4*n))
write(2,*) "{"
write(2,'(9999(g0))', advance="no") "z: []float64{"
do i = 1, 4*n
write (2,'(99999(e24.16,a))', advance="no") z(i), ","
end do
write (2,*) "},"
write(2,*) "n: " ,n,","
call dlasq2(n, z, info)
write(2,'(9999(g0))', advance="no") "zOut: []float64{"
do i = 1, 4*n
write (2,'(99999(e24.16,a))', advance="no") z(i), ","
end do
write (2,*) "},"
write(2,*) "info:", info, ","
write(2,*) "},"
print *, "Done with dlasq2"
end do
close(5)
close(3)
close(4)
close(2)
end program randomsys1

132
internal/testdata/dlasqtest/testdlasq3.f90 vendored Normal file
View File

@@ -0,0 +1,132 @@
program testdlasq3
implicit none
! Dlasq3 tests
integer :: i0, n0, pp,ttype, nFail,iter,nDiv,n
real(kind=8), dimension(84) :: z
real(kind=8) :: dmin,desig,qmax,dmin1,dmin2,dn,dn1,dn2,g,tau,sigma
logical :: ieee
n = 84
ieee = .True.
z(1:84) = (/1.9143652461808209D+00, &
1.5643842977038900D+00, &
2.4933891621438989D-01, &
3.4998094847693051D-01, &
1.3159965131315450D+00, &
1.3638621124906269D+00, &
9.8984666119707590D-02, &
2.0147331685530781D-01, &
6.0239739795872871D-01, &
6.4655447927417942D-01, &
2.2100334106387809D-03, &
5.4827584804256833D-02, &
9.8618572336789667D-02, &
2.4281908107454921D-02, &
4.7563214844548191D-01, &
7.6546697639973529D-02, &
2.5887481436771148D-01, &
6.1277840695087704D-01, &
1.0786113766900041D-01, &
1.2172855586231640D-01, &
6.4428964922552456D-01, &
2.2938358048981550D-01, &
6.2032304866397048D-01, &
5.2276720640470942D-01, &
3.6956606786075852D-01, &
7.6452331847458654D-01, &
5.3788380542522651D-01, &
2.2536579805014259D-01, &
3.5625331812646233D-01, &
8.8204867223354833D-01, &
2.2221324964361449D-02, &
1.2088451318140349D-02, &
1.2750943030216850D+00, &
6.5487468521633574D-01, &
1.6473243548212180D-01, &
6.4244094276971109D-01, &
1.0075305765438660D+00, &
3.2695517365467008D-01, &
3.4538816017831181D-01, &
8.4530783837131718D-01, &
2.6793917191534039D-01, &
4.1167148387782809D-01, &
7.3286777366837230D-01, &
2.0165584821582411D-01, &
8.3608281383074101D-01, &
9.7375794521953263D-01, &
4.8136607095928219D-01, &
5.9519264227958080D-01, &
6.4953705136764595D-01, &
6.7618762481481709D-01, &
2.3254758802226480D-01, &
4.5471549751211121D-01, &
1.9936248028938069D-01, &
3.3218193673422552D-01, &
3.7823189169112570D-01, &
9.9728131577419957D-02, &
9.8304494035037460D-01, &
7.5610809968448423D-01, &
4.4297338640403672D-01, &
6.0516873235701607D-01, &
1.1732795506024030D+00, &
7.1957244803166864D-01, &
5.0355240691445868D-01, &
8.9668048897477137D-01, &
3.0589803950585209D-01, &
6.5888323539286620D-01, &
3.0146344334154529D-01, &
1.5056721102744461D-01, &
1.2894222375675779D+00, &
6.1246453109936005D-01, &
7.5833643057994404D-01, &
9.7842114980976291D-01, &
4.9778147794615712D-01, &
9.9938135774918690D-01, &
2.8414688478625982D-01, &
2.5673655077691432D-01, &
9.2575397942057647D-01, &
5.5092683856146663D-01, &
5.2313556054509897D-05, &
6.5897402564536967D-01, &
2.1178692213810329D-05, &
7.3492248268320243D-05, &
0.0000000000000000D+00, &
0.0000000000000000D+00/)
i0 = 1
n0 = 21
pp = 0
dmin = -0.0000000000000000D+00
sigma = 0.0000000000000000D+00
desig = 0.0000000000000000D+00
qmax = 2.1637041623952107D+00
nFail = 0
iter = 2
nDiv = 40
ttype = 0
dmin1 = 0.0000000000000000D+00
dmin2 = 0.0000000000000000D+00
dn = 0.0000000000000000D+00
dn1 = 0.0000000000000000D+00
dn2 = 0.0000000000000000D+00
g = 0.0000000000000000D+00
tau = 0.0000000000000000D+00
print *, "Starting Dlasq3"
open(unit = 4, file = "gen4tests.txt")
open(unit = 5, file = "gen5tests.txt")
call Dlasq3(i0, n0, z, pp, dmin, sigma, desig, qmax, nFail, iter, nDiv, ieee, ttype, dmin1, dmin2, dn, dn1, dn2, g, tau)
close(4)
close(5)
print *, "Done calling dlasq3"
print *, Z(1:n)
print *, I0, N0, PP
print *, DMIN, DESIG, SIGMA, QMAX
print *, NFAIL, ITER, NDIV, TTYPE
print *, DMIN1, DMIN2, DN, DN1, DN2, G, TAU
end

435
internal/testdata/dlasqtest/testdlasq4.f90 vendored Normal file
View File

@@ -0,0 +1,435 @@
program testdlasq4
implicit none
! Dlasq4 tests
integer :: i0, n0, pp, ttype, iter, nDiv, n, n0in
real(kind=8), dimension(401) :: z
real(kind=8) :: dmin, desig, qmax, dmin1, dmin2, dn, dn1, dn2, g, tau, sigma
logical :: ieee
z(1:401) = (/2.9266499599402414D+02, &
2.9276699640004830D+02, &
2.9210200041216615D+02, &
2.9171973344922628D+02, &
2.9254120660184350D+02, &
2.9246923723528141D+02, &
2.8739845025761718D+02, &
2.8713781898215319D+02, &
2.9216230331620721D+02, &
2.9216609319427272D+02, &
2.9037912623973870D+02, &
2.9019341222762625D+02, &
2.9184732870824223D+02, &
2.9211597271231784D+02, &
2.9133173969911888D+02, &
2.9116703928303986D+02, &
2.9158395177813247D+02, &
2.9142053084921997D+02, &
2.8936184155474774D+02, &
2.9014388604362898D+02, &
2.9216722380092682D+02, &
2.9216917065163557D+02, &
2.9033857172870131D+02, &
2.9017428768626024D+02, &
2.9187084534700494D+02, &
2.9185392666684271D+02, &
2.8851014988393416D+02, &
2.8849290783118727D+02, &
2.9182506564169046D+02, &
2.9184679532940385D+02, &
2.9022222656964715D+02, &
2.9051820223150668D+02, &
2.9219746119018231D+02, &
2.9219997046052623D+02, &
2.9076912988009974D+02, &
2.9110108536012547D+02, &
2.9226281758828725D+02, &
2.9246883105892533D+02, &
2.9221612201279271D+02, &
2.9059157967819368D+02, &
2.9112833071623868D+02, &
2.9210680427275844D+02, &
2.9199887004058536D+02, &
2.9151030826460186D+02, &
2.9154564759046622D+02, &
2.9212462005167004D+02, &
2.9212108612522559D+02, &
2.9225720737270348D+02, &
2.9226471402909704D+02, &
2.9186949422820902D+02, &
2.9179442772569342D+02, &
2.9025839700680774D+02, &
2.9028281327393216D+02, &
2.9168280284451140D+02, &
2.9168036127921908D+02, &
2.9115346030764749D+02, &
2.9115401102000044D+02, &
2.9212282665919003D+02, &
2.9212277159409672D+02, &
2.9212554020600300D+02, &
2.9212559651286460D+02, &
2.9050907549403615D+02, &
2.9050344542208029D+02, &
2.9211004769628386D+02, &
2.9211127836880860D+02, &
2.9159257985266015D+02, &
2.9158027318883302D+02, &
2.9042716308833894D+02, &
2.9043622253245718D+02, &
2.9134221002346220D+02, &
2.9134130414047053D+02, &
2.9193179671375327D+02, &
2.9193426987096007D+02, &
2.9145366956406895D+02, &
2.9145119646828226D+02, &
2.9144876630819033D+02, &
2.9145122608379586D+02, &
2.9058395601500280D+02, &
2.9055935887314877D+02, &
2.9123982459393329D+02, &
2.9125037059550806D+02, &
2.9111624624209884D+02, &
2.9110570030194424D+02, &
2.9250004994137356D+02, &
2.9254994096967755D+02, &
2.9166071282413282D+02, &
2.9116180260251298D+02, &
2.8862845048087325D+02, &
2.8925662460652461D+02, &
2.9012609983518610D+02, &
2.9010672249354360D+02, &
2.9142999275190090D+02, &
2.9150806548221971D+02, &
2.9078477842534176D+02, &
2.8840517363552317D+02, &
2.8946267131307206D+02, &
2.9189614533792309D+02, &
2.9232617409967031D+02, &
2.9223702224333306D+02, &
2.9149978725880743D+02, &
2.9168777367421643D+02, &
2.9213296087125275D+02, &
2.9211416223585388D+02, &
2.9151431726536367D+02, &
2.9159900781717892D+02, &
2.9215362494632291D+02, &
2.9214515589728342D+02, &
2.9229900293632022D+02, &
2.9231644811476662D+02, &
2.9119079594655176D+02, &
2.9016344223508082D+02, &
2.9040052826233938D+02, &
2.9146756071890462D+02, &
2.9216592215429023D+02, &
2.9212317137116514D+02, &
2.9220217331561315D+02, &
2.9227234439098311D+02, &
2.9210931773273273D+02, &
2.9139146663504778D+02, &
2.9047426145779627D+02, &
2.9113243832972501D+02, &
2.9163901100086372D+02, &
2.9155399887833846D+02, &
2.9145039523229758D+02, &
2.9151950918932886D+02, &
2.9116352441156198D+02, &
2.9094410515950784D+02, &
2.9056083843332891D+02, &
2.9097140423254604D+02, &
2.9185385310744653D+02, &
2.9181279658894493D+02, &
2.9031697123096876D+02, &
2.9033298229128292D+02, &
2.9212507489852788D+02, &
2.9212491479406674D+02, &
2.9123248207180859D+02, &
2.9123278004625678D+02, &
2.9210890357464513D+02, &
2.9210887378334229D+02, &
2.9240010366769212D+02, &
2.9240021314868147D+02, &
2.9212046105624000D+02, &
2.9212035158139264D+02, &
2.9215242607939217D+02, &
2.9215256473001551D+02, &
2.9086373488934720D+02, &
2.9084987044121846D+02, &
2.9162085042968522D+02, &
2.9163097873649599D+02, &
2.9113228736441005D+02, &
2.9112215911901944D+02, &
2.9210393504686402D+02, &
2.9211255232953414D+02, &
2.9191445519642213D+02, &
2.9182828243114074D+02, &
2.9127013482394887D+02, &
2.9129823908392501D+02, &
2.9220880435635905D+02, &
2.9220599393650343D+02, &
2.9144676491963560D+02, &
2.9145286023012017D+02, &
2.9148058174349006D+02, &
2.9147448649442555D+02, &
2.9186619188590822D+02, &
2.9187731897876392D+02, &
2.9151148084374620D+02, &
2.9150035381231066D+02, &
2.9224292392669071D+02, &
2.9224832614828313D+02, &
2.9140236136264468D+02, &
2.9134833920814032D+02, &
2.9241531971951883D+02, &
2.9247972954055604D+02, &
2.9164613863843044D+02, &
2.8920404894780614D+02, &
2.8913485112658549D+02, &
2.9142701775363003D+02, &
2.9213449277295280D+02, &
2.9191925854858397D+02, &
2.9217029610406047D+02, &
2.9224915292105180D+02, &
2.9220325626287905D+02, &
2.9212439945202976D+02, &
2.9057154227612733D+02, &
2.9093384291672965D+02, &
2.9183595231931184D+02, &
2.9179972231667176D+02, &
2.9133916987034183D+02, &
2.9135453536038978D+02, &
2.9047085843212886D+02, &
2.9031720414585078D+02, &
2.9113106705127024D+02, &
2.9119455617800747D+02, &
2.9230127009862616D+02, &
2.9229492119209442D+02, &
2.9098170102485551D+02, &
2.9110028345622749D+02, &
2.9215236246918653D+02, &
2.9215215113995436D+02, &
2.9124650182241129D+02, &
2.9124684419934567D+02, &
2.9216244260160767D+02, &
2.9216240837005626D+02, &
2.9314769094184447D+02, &
2.9314772207133655D+02, &
2.9212215646682506D+02, &
2.9212184517804621D+02, &
2.9224739389310008D+02, &
2.9224802593241526D+02, &
2.8978611958992855D+02, &
2.8915408641678846D+02, &
2.9118533307571403D+02, &
2.9194553410039072D+02, &
2.9244688594134544D+02, &
2.9237086584501975D+02, &
2.9189894464487475D+02, &
2.9210832103555418D+02, &
2.9227685116407457D+02, &
2.9225842459914986D+02, &
2.9224821267514392D+02, &
2.9226591109467802D+02, &
2.9158625025645608D+02, &
2.9140926612253548D+02, &
2.9125298964526195D+02, &
2.9136239316241648D+02, &
2.9182040805585694D+02, &
2.9171100460012258D+02, &
2.9126693393315793D+02, &
2.9130800749967943D+02, &
2.9084722625682167D+02, &
2.9043649120580767D+02, &
2.9153791610078673D+02, &
2.9210440912405335D+02, &
2.9188686486416555D+02, &
2.9138068978583891D+02, &
2.9158124399039616D+02, &
2.9213540811751852D+02, &
2.9211624446790427D+02, &
2.9138960755567365D+02, &
2.9060415959100914D+02, &
2.9118025885063923D+02, &
2.9132902926505932D+02, &
2.9120918643494110D+02, &
2.9222955158764825D+02, &
2.9236106160611405D+02, &
2.9219941546106151D+02, &
2.9167905448737707D+02, &
2.8956733560159137D+02, &
2.9016660738228080D+02, &
2.9069372888915495D+02, &
2.9058385568123452D+02, &
2.9219861470697771D+02, &
2.9223599112669444D+02, &
2.9150234673408067D+02, &
2.9112858259833354D+02, &
2.9011809831967531D+02, &
2.9046138673473865D+02, &
2.9176526297220903D+02, &
2.9173093419212285D+02, &
2.9150067445343569D+02, &
2.9152418894132262D+02, &
2.9197021328944544D+02, &
2.9194669886297868D+02, &
2.9168012546172463D+02, &
2.9169701864791432D+02, &
2.9061916960844030D+02, &
2.9045023836074438D+02, &
2.9212529304266053D+02, &
2.9217230349727680D+02, &
2.9156357220873417D+02, &
2.9093467723991887D+02, &
2.9015918793416472D+02, &
2.9095983823965622D+02, &
2.9124303667219704D+02, &
2.9116297170306802D+02, &
2.9162557939634507D+02, &
2.9193291492830070D+02, &
2.9138731414547760D+02, &
2.9079978674942083D+02, &
2.9159254111122891D+02, &
2.9228695093326087D+02, &
2.9225423965335352D+02, &
2.9126542837357596D+02, &
2.9173807466948557D+02, &
2.9270696227984581D+02, &
2.9274075480094893D+02, &
2.9210759999419366D+02, &
2.9091701924155882D+02, &
2.9163130710260498D+02, &
2.9157158980248664D+02, &
2.9031984685457667D+02, &
2.8939239820067894D+02, &
2.9070124438246870D+02, &
2.9196350995833507D+02, &
2.9189730956351508D+02, &
2.9047434516138509D+02, &
2.9050934070611282D+02, &
2.9179387236503283D+02, &
2.9179037287198020D+02, &
2.9197909575321057D+02, &
2.9198343084479546D+02, &
2.9146450345905629D+02, &
2.9146016842889151D+02, &
2.9233889755268928D+02, &
2.9234209014701219D+02, &
2.9032302536354865D+02, &
2.8837665454569191D+02, &
2.8923259893670223D+02, &
2.9119948081590582D+02, &
2.9158422265927129D+02, &
2.9138706789415261D+02, &
2.9131767302238063D+02, &
2.9147948119882238D+02, &
2.9186937598758146D+02, &
2.9170756787255982D+02, &
2.9181460198203825D+02, &
2.9210008868832023D+02, &
2.9132088639794199D+02, &
2.9113460155819826D+02, &
2.9159448593680958D+02, &
2.9214172380575934D+02, &
2.9182660907964311D+02, &
2.8938570202792107D+02, &
2.8829979954353007D+02, &
2.9064250900128923D+02, &
2.9110347860364448D+02, &
2.9039527564479215D+02, &
2.9152783923893156D+02, &
2.9213818222324863D+02, &
2.9211881276563861D+02, &
2.9133414472425187D+02, &
2.9125375097531855D+02, &
2.9190226937530139D+02, &
2.9164903795105636D+02, &
2.8851961249369930D+02, &
2.8835729910731652D+02, &
2.9144629542849515D+02, &
2.9171485796658368D+02, &
2.9126891989861593D+02, &
2.9051052150188838D+02, &
2.9113570969073521D+02, &
2.9141652614094619D+02, &
2.9133186866181995D+02, &
2.8912484642922516D+02, &
2.8915669391948876D+02, &
2.9117142770169869D+02, &
2.9117110928821620D+02, &
2.9183490795481288D+02, &
2.9183646161652371D+02, &
2.9254379194824975D+02, &
2.9254363658822064D+02, &
2.9192127768678108D+02, &
2.9192154096878102D+02, &
2.9151073810022524D+02, &
2.9151047487964541D+02, &
2.9013993357169915D+02, &
2.9014000572685774D+02, &
2.9145714571416084D+02, &
2.9145713856006512D+02, &
2.9196091751473017D+02, &
2.9196093255283131D+02, &
2.9195731369267685D+02, &
2.9195729871599588D+02, &
2.9149460806187619D+02, &
2.9149461579988633D+02, &
2.9034687539457741D+02, &
2.9034679862867739D+02, &
2.9010765498373922D+02, &
2.9010767881379803D+02, &
2.8967492890608241D+02, &
2.8967469674750663D+02, &
2.9215189060671338D+02, &
2.9215194287124120D+02, &
2.8956132995364590D+02, &
2.8950907156783751D+02, &
2.9210783379750950D+02, &
2.9211890340058585D+02, &
2.9139896954309916D+02, &
2.9128827357375536D+02, &
2.9190012628763964D+02, &
2.9212457714005234D+02, &
2.9221336158434212D+02, &
2.9217879707919576D+02, &
2.9127472708852724D+02, &
2.9132783649002283D+02, &
2.9227509889951233D+02, &
2.9226978796550475D+02, &
2.9142078378447616D+02, &
2.9142906715955786D+02, &
2.9017517054475991D+02, &
2.8992337408144391D+02, &
2.8477362931531121D+02, &
2.8514676291150971D+02, &
2.8393423954726200D+02, &
2.8313625395453965D+02, &
2.8449999402409759D+02, &
2.8534282615303522D+02, &
2.8523140662657408D+02, &
2.8739845025761718D+02, &
2.8713781898215319D+02, &
0.0000000000000000D+00/)
i0 = 1
n0 = 100
pp = 1
n0in = 100
dmin = 7.9798559272231942D+282
dmin1 = 7.9798559272231942D+282
dmin2 = 2.3215857579138407D+285
dn = 2.3140662657409930D+284
dn1 = 7.9798559272231942D+282
dn2 = 8.2833136615500372D+288
g = 2.5000000000000000D-01
tau = 6.1420124051338430D+283
ttype = -4
ieee = .True.
print *, "Starting Dlasq4"
call Dlasq4(i0, n0, z, pp, n0in, dmin, dmin1, dmin2, dn, dn1, dn2, tau, ttype, g)
print *, "Done calling dlasq4"
print *, "tau = ", tau
print *, tau, ttype, g
end

99
internal/testdata/dlasqtest/xerbla.f vendored Normal file
View File

@@ -0,0 +1,99 @@
*> \brief \b XERBLA
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download XERBLA + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/xerbla.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/xerbla.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/xerbla.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE XERBLA( SRNAME, INFO )
*
* .. Scalar Arguments ..
* CHARACTER*(*) SRNAME
* INTEGER INFO
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> XERBLA is an error handler for the LAPACK routines.
*> It is called by an LAPACK routine if an input parameter has an
*> invalid value. A message is printed and execution stops.
*>
*> Installers may consider modifying the STOP statement in order to
*> call system-specific exception-handling facilities.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SRNAME
*> \verbatim
*> SRNAME is CHARACTER*(*)
*> The name of the routine which called XERBLA.
*> \endverbatim
*>
*> \param[in] INFO
*> \verbatim
*> INFO is INTEGER
*> The position of the invalid parameter in the parameter list
*> of the calling routine.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup auxOTHERauxiliary
*
* =====================================================================
SUBROUTINE XERBLA( SRNAME, INFO )
*
* -- LAPACK auxiliary routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER*(*) SRNAME
INTEGER INFO
* ..
*
* =====================================================================
*
* .. Intrinsic Functions ..
INTRINSIC LEN_TRIM
* ..
* .. Executable Statements ..
*
WRITE( *, FMT = 9999 )SRNAME( 1:LEN_TRIM( SRNAME ) ), INFO
*
STOP
*
9999 FORMAT( ' ** On entry to ', A, ' parameter number ', I2, ' had ',
$ 'an illegal value' )
*
* End of XERBLA
*
END

7
lapack.go
View File

@@ -91,3 +91,10 @@ const (
Top Pivot = 'T'
Bottom Pivot = 'B'
)
type DecompUpdate byte
const (
ApplyP DecompUpdate = 'P'
ApplyQ DecompUpdate = 'Q'
)

54
native/dgebd2.go
View File

@@ -4,6 +4,8 @@
package native
import "github.com/gonum/blas"
// Dgebd2 reduces an m×n matrix A to upper or lower bidiagonal form by an orthogonal
// transformation.
// Q^T * A * P = B
@@ -13,14 +15,58 @@ package native
func (impl Implementation) Dgebd2(m, n int, a []float64, lda int, d, e, tauQ, tauP, work []float64) {
checkMatrix(m, n, a, lda)
if len(d) < min(m, n) {
panic("lapack: insufficient d")
panic(badD)
}
if len(e) < min(m, n)-1 {
panic("lapack: insufficient e")
panic(badE)
}
if m > n {
if len(tauQ) < min(m, n) {
panic(badTauQ)
}
if len(tauP) < min(m, n) {
panic(badTauP)
}
if len(work) < max(m, n) {
panic(badWork)
}
if m >= n {
for i := 0; i < n; i++ {
impl.Dlarfg(m-i, a[i*lda+i], a[min(i+1, m-1)*lda+i:], 1)
a[i*lda+i], tauQ[i] = impl.Dlarfg(m-i, a[i*lda+i], a[min(i+1, m-1)*lda+i:], lda)
d[i] = a[i*lda+i]
a[i*lda+i] = 1
// Apply H[i] to A[i:m, i+1:n] from the left.
if i < n-1 {
impl.Dlarf(blas.Left, m-i, n-i-1, a[i*lda+i:], lda, tauQ[i], a[i*lda+i+1:], lda, work)
}
a[i*lda+i] = d[i]
if i < n-1 {
a[i*lda+i+1], tauP[i] = impl.Dlarfg(n-i-1, a[i*lda+i+1], a[i*lda+min(i+2, n-1):], 1)
e[i] = a[i*lda+i+1]
a[i*lda+i+1] = 1
impl.Dlarf(blas.Right, m-i-1, n-i-1, a[i*lda+i+1:], 1, tauP[i], a[(i+1)*lda+i+1:], lda, work)
a[i*lda+i+1] = e[i]
} else {
tauP[i] = 0
}
}
return
}
for i := 0; i < m; i++ {
a[i*lda+i], tauP[i] = impl.Dlarfg(n-i, a[i*lda+i], a[i*lda+min(i+1, n-1):], 1)
d[i] = a[i*lda+i]
a[i*lda+i] = 1
if i < m-1 {
impl.Dlarf(blas.Right, m-i-1, n-i, a[i*lda+i:], 1, tauP[i], a[(i+1)*lda+i:], lda, work)
}
a[i*lda+i] = d[i]
if i < m-1 {
a[(i+1)*lda+i], tauQ[i] = impl.Dlarfg(m-i-1, a[(i+1)*lda+i], a[min(i+2, m-1)*lda+i:], lda)
e[i] = a[(i+1)*lda+i]
a[(i+1)*lda+i] = 1
impl.Dlarf(blas.Left, m-i-1, n-i-1, a[(i+1)*lda+i:], lda, tauQ[i], a[(i+1)*lda+i+1:], lda, work)
a[(i+1)*lda+i] = e[i]
} else {
tauQ[i] = 0
}
}
}

140
native/dgebrd.go Normal file
View File

@@ -0,0 +1,140 @@
// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package native
import (
"github.com/gonum/blas"
"github.com/gonum/blas/blas64"
)
// Dgebrd reduces a general m×n matrix A to upper or lower bidiagonal form B by
// an orthogonal transformation:
// Q^T * A * P = B.
// The diagonal elements of B are stored in d and the off diagonal elements stored
// in e. These are additionally stored along the diagonal of A and the off-diagonal
// of A. If m >= n B is an upper-bidiagonal matrix, and if m < n B is a
// lower-bidiagonal matrix.
//
// The remaining elements of A store the data needed to construct Q and P.
// The matrices Q and P are products of elementary reflectors
// Q = H_1 * H_2 * ... * H_nb
// P = G_1 * G_2 * ... * G_nb
// where
// H_i = I - tauQ[i] * v_i * v_i^T
// G_i = I - tauP[i] * u_i * u_i^T
//
// As an example, on exit the entries of A when m = 6, and n = 5
// ( d e u1 u1 u1 )
// ( v1 d e u2 u2 )
// ( v1 v2 d e u3 )
// ( v1 v2 v3 d e )
// ( v1 v2 v3 v4 d )
// ( v1 v2 v3 v4 v5 )
// and when m = 5, n = 6
// ( d u1 u1 u1 u1 u1 )
// ( e d u2 u2 u2 u2 )
// ( v1 e d u3 u3 u3 )
// ( v1 v2 e d u4 u4 )
// ( v1 v2 v3 e d u5 )
//
// d, tauQ, and tauP must all have length at least min(m,n), and e must have
// length min(m,n) - 1.
//
// Work is temporary storage, and lwork specifies the usable memory length.
// At minimum, lwork >= max(m,n) and this function will panic otherwise.
// Dgebrd is blocked decomposition, but the block size is limited
// by the temporary space available. If lwork == -1, instead of performing Dgebrd,
// the optimal work length will be stored into work[0].
func (impl Implementation) Dgebrd(m, n int, a []float64, lda int, d, e, tauQ, tauP, work []float64, lwork int) {
checkMatrix(m, n, a, lda)
minmn := min(m, n)
if len(d) < minmn {
panic(badD)
}
if len(e) < minmn-1 {
panic(badE)
}
if len(tauQ) < minmn {
panic(badTauQ)
}
if len(tauP) < minmn {
panic(badTauP)
}
// Calculate optimal work.
nb := impl.Ilaenv(1, "DGEBRD", " ", m, n, -1, -1)
if lwork == -1 {
lworkOpt := (m + n) * nb
work[0] = float64(lworkOpt)
return
}
ws := max(m, n)
if lwork < ws {
panic(badWork)
}
if len(work) < lwork {
panic(badWork)
}
var nx int
if nb > 1 && nb < minmn {
nx = max(nb, impl.Ilaenv(3, "DGEBRD", " ", m, n, -1, -1))
if nx < minmn {
ws = (m + n) * nb
if lwork < ws {
nbmin := impl.Ilaenv(2, "DGEBRD", " ", m, n, -1, -1)
if lwork >= (m+n)*nbmin {
nb = lwork / (m + n)
} else {
nb = 1
nx = minmn
}
}
}
} else {
nx = minmn
}
bi := blas64.Implementation()
ldworkx := nb
ldworky := nb
var i int
// Netlib lapack has minmn - nx, but this makes the last nx rows (which by
// default is large) be unblocked. As written here, the blocking is more
// consistent.
for i = 0; i < minmn-nb; i += nb {
// Reduce rows and columns i:i+nb to bidiagonal form and return
// the matrices X and Y which are needed to update the unreduced
// part of the matrix.
// X is stored in the first m rows of work, y in the next rows.
x := work[:m*ldworkx]
y := work[m*ldworkx:]
impl.Dlabrd(m-i, n-i, nb, a[i*lda+i:], lda,
d[i:], e[i:], tauQ[i:], tauP[i:],
x, ldworkx, y, ldworky)
// Update the trailing submatrix A[i+nb:m,i+nb:n], using an update
// of the form A := A - V*Y**T - X*U**T
bi.Dgemm(blas.NoTrans, blas.Trans, m-i-nb, n-i-nb, nb,
-1, a[(i+nb)*lda+i:], lda, y[nb*ldworky:], ldworky,
1, a[(i+nb)*lda+i+nb:], lda)
bi.Dgemm(blas.NoTrans, blas.NoTrans, m-i-nb, n-i-nb, nb,
-1, x[nb*ldworkx:], ldworkx, a[i*lda+i+nb:], lda,
1, a[(i+nb)*lda+i+nb:], lda)
// Copy diagonal and off-diagonal elements of B back into A.
if m >= n {
for j := i; j < i+nb; j++ {
a[j*lda+j] = d[j]
a[j*lda+j+1] = e[j]
}
} else {
for j := i; j < i+nb; j++ {
a[j*lda+j] = d[j]
a[(j+1)*lda+j] = e[j]
}
}
}
// Use unblocked code to reduce the remainder of the matrix.
impl.Dgebd2(m-i, n-i, a[i*lda+i:], lda, d[i:], e[i:], tauQ[i:], tauP[i:], work)
}

2
native/dgetrf.go
View File

@@ -29,7 +29,7 @@ func (impl Implementation) Dgetrf(m, n int, a []float64, lda int, ipiv []int) (o
panic(badIpiv)
}
if m == 0 || n == 0 {
return
return false
}
bi := blas64.Implementation()
nb := impl.Ilaenv(1, "DGETRF", " ", m, n, -1, -1)

148
native/dlabrd.go Normal file
View File

@@ -0,0 +1,148 @@
// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package native
import (
"github.com/gonum/blas"
"github.com/gonum/blas/blas64"
)
// Dlabrd reduces the first NB rows and columns of a real general m×n matrix
// A to upper or lower bidiagonal form by an orthogonal transformation
// Q**T * A * P
// If m >= n, A is reduced to upper bidiagonal form and upon exit the elements
// on and below the diagonal in the first nb columns represent the elementary
// reflectors, and the elements above the diagonal in the first nb rows represent
// the matrix P. If m < n, A is reduced to lower bidiagonal form and the elements
// P is instead stored above the diagonal.
//
// The reduction to bidiagonal form is stored in d and e, where d are the diagonal
// elements, and e are the off-diagonal elements.
//
// The matrices Q and P are products of elementary reflectors
// Q = H_1 * H_2 * ... * H_nb
// P = G_1 * G_2 * ... * G_nb
// where
// H_i = I - tauQ[i] * v_i * v_i^T
// G_i = I - tauP[i] * u_i * u_i^T
//
// As an example, on exit the entries of A when m = 6, n = 5, and nb = 2
// ( 1 1 u1 u1 u1 )
// ( v1 1 1 u2 u2 )
// ( v1 v2 a a a )
// ( v1 v2 a a a )
// ( v1 v2 a a a )
// ( v1 v2 a a a )
// and when m = 5, n = 6, and nb = 2
// ( 1 u1 u1 u1 u1 u1 )
// ( 1 1 u2 u2 u2 u2 )
// ( v1 1 a a a a )
// ( v1 v2 a a a a )
// ( v1 v2 a a a a )
//
// Dlabrd also returns the matrices X and Y which are used with U and V to
// apply the transformatino to the unreduced part of the matrix
// A := A - V*Y^T - X*U^T
// and returns the matrices X and Y which are needed to apply the
// transformation to the unreduced part of A.
//
// X is an m×nb matrix, Y is an n×nb matrix. d, e, taup, and tauq must all have
// length at least nb. Dlabrd will panic if these size constraints are violated.
func (impl Implementation) Dlabrd(m, n, nb int, a []float64, lda int, d, e, tauQ, tauP, x []float64, ldx int, y []float64, ldy int) {
checkMatrix(m, n, a, lda)
checkMatrix(m, nb, x, ldx)
checkMatrix(n, nb, y, ldy)
if len(d) < nb {
panic(badD)
}
if len(e) < nb {
panic(badE)
}
if len(tauQ) < nb {
panic(badTauQ)
}
if len(tauP) < nb {
panic(badTauP)
}
if m <= 0 || n <= 0 {
return
}
bi := blas64.Implementation()
if m >= n {
// Reduce to upper bidiagonal form.
for i := 0; i < nb; i++ {
bi.Dgemv(blas.NoTrans, m-i, i, -1, a[i*lda:], lda, y[i*ldy:], 1, 1, a[i*lda+i:], lda)
bi.Dgemv(blas.NoTrans, m-i, i, -1, x[i*ldx:], ldx, a[i:], lda, 1, a[i*lda+i:], lda)
a[i*lda+i], tauQ[i] = impl.Dlarfg(m-i, a[i*lda+i], a[min(i+1, m-1)*lda+i:], lda)
d[i] = a[i*lda+i]
if i < n-1 {
// Compute Y[i+1:n, i].
a[i*lda+i] = 1
bi.Dgemv(blas.Trans, m-i, n-i-1, 1, a[i*lda+i+1:], lda, a[i*lda+i:], lda, 0, y[(i+1)*ldy+i:], ldy)
bi.Dgemv(blas.Trans, m-i, i, 1, a[i*lda:], lda, a[i*lda+i:], lda, 0, y[i:], ldy)
bi.Dgemv(blas.NoTrans, n-i-1, i, -1, y[(i+1)*ldy:], ldy, y[i:], ldy, 1, y[(i+1)*ldy+i:], ldy)
bi.Dgemv(blas.Trans, m-i, i, 1, x[i*ldx:], ldx, a[i*lda+i:], lda, 0, y[i:], ldy)
bi.Dgemv(blas.Trans, i, n-i-1, -1, a[i+1:], lda, y[i:], ldy, 1, y[(i+1)*ldy+i:], ldy)
bi.Dscal(n-i-1, tauQ[i], y[(i+1)*ldy+i:], ldy)
// Update A[i, i+1:n].
bi.Dgemv(blas.NoTrans, n-i-1, i+1, -1, y[(i+1)*ldy:], ldy, a[i*lda:], 1, 1, a[i*lda+i+1:], 1)
bi.Dgemv(blas.Trans, i, n-i-1, -1, a[i+1:], lda, x[i*ldx:], 1, 1, a[i*lda+i+1:], 1)
// Generate reflection P[i] to annihilate A[i, i+2:n].
a[i*lda+i+1], tauP[i] = impl.Dlarfg(n-i-1, a[i*lda+i+1], a[i*lda+min(i+2, n-1):], 1)
e[i] = a[i*lda+i+1]
a[i*lda+i+1] = 1
// Compute X[i+1:m, i].
bi.Dgemv(blas.NoTrans, m-i-1, n-i-1, 1, a[(i+1)*lda+i+1:], lda, a[i*lda+i+1:], 1, 0, x[(i+1)*ldx+i:], ldx)
bi.Dgemv(blas.Trans, n-i-1, i+1, 1, y[(i+1)*ldy:], ldy, a[i*lda+i+1:], 1, 0, x[i:], ldx)
bi.Dgemv(blas.NoTrans, m-i-1, i+1, -1, a[(i+1)*lda:], lda, x[i:], ldx, 1, x[(i+1)*ldx+i:], ldx)
bi.Dgemv(blas.NoTrans, i, n-i-1, 1, a[i+1:], lda, a[i*lda+i+1:], 1, 0, x[i:], ldx)
bi.Dgemv(blas.NoTrans, m-i-1, i, -1, x[(i+1)*ldx:], ldx, x[i:], ldx, 1, x[(i+1)*ldx+i:], ldx)
bi.Dscal(m-i-1, tauP[i], x[(i+1)*ldx+i:], ldx)
}
}
return
}
// Reduce to lower bidiagonal form.
for i := 0; i < nb; i++ {
// Update A[i,i:n]
bi.Dgemv(blas.NoTrans, n-i, i, -1, y[i*ldy:], ldy, a[i*lda:], 1, 1, a[i*lda+i:], 1)
bi.Dgemv(blas.Trans, i, n-i, -1, a[i:], lda, x[i*ldx:], 1, 1, a[i*lda+i:], 1)
// Generate reflection P[i] to annihilate A[i, i+1:n]
a[i*lda+i], tauP[i] = impl.Dlarfg(n-i, a[i*lda+i], a[i*lda+min(i+1, n-1):], 1)
d[i] = a[i*lda+i]
if i < m-1 {
a[i*lda+i] = 1
// Compute X[i+1:m, i].
bi.Dgemv(blas.NoTrans, m-i-1, n-i, 1, a[(i+1)*lda+i:], lda, a[i*lda+i:], 1, 0, x[(i+1)*ldx+i:], ldx)
bi.Dgemv(blas.Trans, n-i, i, 1, y[i*ldy:], ldy, a[i*lda+i:], 1, 0, x[i:], ldx)
bi.Dgemv(blas.NoTrans, m-i-1, i, -1, a[(i+1)*lda:], lda, x[i:], ldx, 1, x[(i+1)*ldx+i:], ldx)
bi.Dgemv(blas.NoTrans, i, n-i, 1, a[i:], lda, a[i*lda+i:], 1, 0, x[i:], ldx)
bi.Dgemv(blas.NoTrans, m-i-1, i, -1, x[(i+1)*ldx:], ldx, x[i:], ldx, 1, x[(i+1)*ldx+i:], ldx)
bi.Dscal(m-i-1, tauP[i], x[(i+1)*ldx+i:], ldx)
// Update A[i+1:m, i].
bi.Dgemv(blas.NoTrans, m-i-1, i, -1, a[(i+1)*lda:], lda, y[i*ldy:], 1, 1, a[(i+1)*lda+i:], lda)
bi.Dgemv(blas.NoTrans, m-i-1, i+1, -1, x[(i+1)*ldx:], ldx, a[i:], lda, 1, a[(i+1)*lda+i:], lda)
// Generate reflection Q[i] to annihilate A[i+2:m, i].
a[(i+1)*lda+i], tauQ[i] = impl.Dlarfg(m-i-1, a[(i+1)*lda+i], a[min(i+2, m-1)*lda+i:], lda)
e[i] = a[(i+1)*lda+i]
a[(i+1)*lda+i] = 1
// Compute Y[i+1:n, i].
bi.Dgemv(blas.Trans, m-i-1, n-i-1, 1, a[(i+1)*lda+i+1:], lda, a[(i+1)*lda+i:], lda, 0, y[(i+1)*ldy+i:], ldy)
bi.Dgemv(blas.Trans, m-i-1, i, 1, a[(i+1)*lda:], lda, a[(i+1)*lda+i:], lda, 0, y[i:], ldy)
bi.Dgemv(blas.NoTrans, n-i-1, i, -1, y[(i+1)*ldy:], ldy, y[i:], ldy, 1, y[(i+1)*ldy+i:], ldy)
bi.Dgemv(blas.Trans, m-i-1, i+1, 1, x[(i+1)*ldx:], ldx, a[(i+1)*lda+i:], lda, 0, y[i:], ldy)
bi.Dgemv(blas.Trans, i+1, n-i-1, -1, a[i+1:], lda, y[i:], ldy, 1, y[(i+1)*ldy+i:], ldy)
bi.Dscal(n-i-1, tauQ[i], y[(i+1)*ldy+i:], ldy)
}
}
}

5
native/dlacpy.go
View File

@@ -21,20 +21,19 @@ func (impl Implementation) Dlacpy(uplo blas.Uplo, m, n int, a []float64, lda int
b[i*ldb+j] = a[i*lda+j]
}
}
return
case blas.Lower:
for i := 0; i < m; i++ {
for j := 0; j < min(i, n); j++ {
b[i*ldb+j] = a[i*lda+j]
}
}
return
case blas.All:
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
b[i*ldb+j] = a[i*lda+j]
}
}
return
}
}

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// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package native
import (
"math"
"github.com/gonum/blas/blas64"
"github.com/gonum/lapack"
)
// Dlasq1 computes the singular values of an n×n bidiagonal matrix with diagonal
// d and off-diagonal e. On exit, d contains the singular values in decreasing
// order, and e is overwritten. d must have length at least n, e must have
// length at least n-1, and the input work must have length at least 4*n. Dlasq1
// will panic if these conditions are not met.
func (impl Implementation) Dlasq1(n int, d, e, work []float64) (info int) {
// TODO(btracey): replace info with an error.
if n < 0 {
panic(nLT0)
}
if len(work) < 4*n {
panic(badWork)
}
if len(d) < n {
panic("lapack: length of d less than n")
}
if len(e) < n-1 {
panic("lapack: length of e less than n-1")
}
if n == 0 {
return info
}
if n == 1 {
d[0] = math.Abs(d[0])
return info
}
if n == 2 {
d[1], d[0] = impl.Dlas2(d[0], e[0], d[1])
return info
}
// Estimate the largest singular value.
var sigmx float64
for i := 0; i < n-1; i++ {
d[i] = math.Abs(d[i])
sigmx = math.Max(sigmx, math.Abs(e[i]))
}
d[n-1] = math.Abs(d[n-1])
// Early return if sigmx is zero (matrix is already diagonal).
if sigmx == 0 {
impl.Dlasrt(lapack.SortDecreasing, n, d)
return info
}
for i := 0; i < n; i++ {
sigmx = math.Max(sigmx, d[i])
}
// Copy D and E into WORK (in the Z format) and scale (squaring the
// input data makes scaling by a power of the radix pointless).
eps := dlamchP
safmin := dlamchS
scale := math.Sqrt(eps / safmin)
bi := blas64.Implementation()
bi.Dcopy(n, d, 1, work, 2)
bi.Dcopy(n-1, e, 1, work[1:], 2)
impl.Dlascl(lapack.General, 0, 0, sigmx, scale, 2*n-1, 1, work, 1)
// Compute the q's and e's.
for i := 0; i < 2*n-1; i++ {
work[i] *= work[i]
}
work[2*n-1] = 0
info = impl.Dlasq2(n, work)
if info == 0 {
for i := 0; i < n; i++ {
d[i] = math.Sqrt(work[i])
}
impl.Dlascl(lapack.General, 0, 0, scale, sigmx, n, 1, d, 1)
} else if info == 2 {
// Maximum number of iterations exceeded. Move data from work
// into D and E so the calling subroutine can try to finish.
for i := 0; i < n; i++ {
d[i] = math.Sqrt(work[2*i])
e[i] = math.Sqrt(work[2*i+1])
}
impl.Dlascl(lapack.General, 0, 0, scale, sigmx, n, 1, d, 1)
impl.Dlascl(lapack.General, 0, 0, scale, sigmx, n, 1, e, 1)
}
return info
}

367
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// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package native
import (
"math"
"github.com/gonum/lapack"
)
// Dlasq2 computes all the eigenvalues of the symmetric positive
// definite tridiagonal matrix associated with the qd array Z. Eigevalues
// are computed to high relative accuracy avoiding denormalization, underflow
// and overflow.
//
// To see the relation of Z to the tridiagonal matrix, let L be a
// unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and
// let U be an upper bidiagonal matrix with 1's above and diagonal
// Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the
// symmetric tridiagonal to which it is similar.
//
// info returns a status error. The return codes mean as follows:
// 0: The algorithm completed successfully.
// 1: A split was marked by a positive value in e.
// 2: Current block of Z not diagonalized after 100*n iterations (in inner
// while loop). On exit Z holds a qd array with the same eigenvalues as
// the given Z.
// 3: Termination criterion of outer while loop not met (program created more
// than N unreduced blocks).
//
// z must have length at least 4*n, and must not contain any negative elements.
// Dlasq2 will panic otherwise.
func (impl Implementation) Dlasq2(n int, z []float64) (info int) {
// TODO(btracey): make info an error.
if len(z) < 4*n {
panic(badZ)
}
const cbias = 1.5
eps := dlamchP
safmin := dlamchS
tol := eps * 100
tol2 := tol * tol
if n < 0 {
panic(nLT0)
}
if n == 0 {
return info
}
if n == 1 {
if z[0] < 0 {
panic(negZ)
}
return info
}
if n == 2 {
if z[1] < 0 || z[2] < 0 {
panic("lapack: bad z value")
} else if z[2] > z[0] {
z[0], z[2] = z[2], z[0]
}
z[4] = z[0] + z[1] + z[2]
if z[1] > z[2]*tol2 {
t := 0.5 * (z[0] - z[2] + z[1])
s := z[2] * (z[1] / t)
if s <= t {
s = z[2] * (z[1] / (t * (1 + math.Sqrt(1+s/t))))
} else {
s = z[2] * (z[1] / (t + math.Sqrt(t)*math.Sqrt(t+s)))
}
t = z[0] + s + z[1]
z[2] *= z[0] / t
z[0] = t
}
z[1] = z[2]
z[5] = z[1] + z[0]
return info
}
// Check for negative data and compute sums of q's and e's.
z[2*n-1] = 0
emin := z[1]
var d, e, qmax, zmax float64
var i1, n1 int
for k := 0; k < 2*(n-1); k += 2 {
if z[k] < 0 || z[k+1] < 0 {
panic("lapack: bad z value")
}
d += z[k]
e += z[k+1]
qmax = math.Max(qmax, z[k])
emin = math.Min(emin, z[k+1])
zmax = math.Max(math.Max(qmax, zmax), z[k+1])
}
if z[2*(n-1)] < 0 {
panic("lapack: bad z value")
}
d += z[2*(n-1)]
qmax = math.Max(qmax, z[2*(n-1)])
zmax = math.Max(qmax, zmax)
// Check for diagonality.
if e == 0 {
for k := 1; k < n; k++ {
z[k] = z[2*k]
}
impl.Dlasrt(lapack.SortDecreasing, n, z)
z[2*(n-1)] = d
return info
}
trace := d + e
// Check for zero data.
if trace == 0 {
z[2*(n-1)] = 0
return info
}
// Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...).
for k := 2 * n; k >= 2; k -= 2 {
z[2*k-1] = 0
z[2*k-2] = z[k-1]
z[2*k-3] = 0
z[2*k-4] = z[k-2]
}
i0 := 0
n0 := n - 1
// Reverse the qd-array, if warranted.
// z[4*i0-3] --> z[4*(i0+1)-3-1] --> z[4*i0]
if cbias*z[4*i0] < z[4*n0] {
ipn4Out := 4 * (i0 + n0 + 2)
for i4loop := 4 * (i0 + 1); i4loop <= 2*(i0+n0+1); i4loop += 4 {
i4 := i4loop - 1
ipn4 := ipn4Out - 1
z[i4-3], z[ipn4-i4-4] = z[ipn4-i4-4], z[i4-3]
z[i4-1], z[ipn4-i4-6] = z[ipn4-i4-6], z[i4-1]
}
}
// Initial split checking via dqd and Li's test.
pp := 0
for k := 0; k < 2; k++ {
d = z[4*n0+pp]
for i4loop := 4*n0 + pp; i4loop >= 4*(i0+1)+pp; i4loop -= 4 {
i4 := i4loop - 1
if z[i4-1] <= tol2*d {
z[i4-1] = math.Copysign(0, -1)
d = z[i4-3]
} else {
d = z[i4-3] * (d / (d + z[i4-1]))
}
}
// dqd maps Z to ZZ plus Li's test.
emin = z[4*(i0+1)+pp]
d = z[4*i0+pp]
for i4loop := 4*(i0+1) + pp; i4loop <= 4*n0+pp; i4loop += 4 {
i4 := i4loop - 1
z[i4-2*pp-2] = d + z[i4-1]
if z[i4-1] <= tol2*d {
z[i4-1] = math.Copysign(0, -1)
z[i4-2*pp-2] = d
z[i4-2*pp] = 0
d = z[i4+1]
} else if safmin*z[i4+1] < z[i4-2*pp-2] && safmin*z[i4-2*pp-2] < z[i4+1] {
tmp := z[i4+1] / z[i4-2*pp-2]
z[i4-2*pp] = z[i4-1] * tmp
d *= tmp
} else {
z[i4-2*pp] = z[i4+1] * (z[i4-1] / z[i4-2*pp-2])
d = z[i4+1] * (d / z[i4-2*pp-2])
}
emin = math.Min(emin, z[i4-2*pp])
}
z[4*(n0+1)-pp-3] = d
// Now find qmax.
qmax = z[4*(i0+1)-pp-3]
for i4loop := 4*(i0+1) - pp + 2; i4loop <= 4*(n0+1)+pp-2; i4loop += 4 {
i4 := i4loop - 1
qmax = math.Max(qmax, z[i4])
}
// Prepare for the next iteration on K.
pp = 1 - pp
}
// Initialise variables to pass to DLASQ3.
var ttype int
var dmin1, dmin2, dn, dn1, dn2, g, tau float64
var tempq float64
iter := 2
var nFail int
nDiv := 2 * (n0 - i0)
var i4 int
Whila:
for iwhila := 1; iwhila <= n+1; iwhila++ {
if n0 < 0 {
goto OneSeventy
}
// While array unfinished do
// e[n0] holds the value of sigma when submatrix in i0:n0
// splits from the rest of the array, but is negated.
var desig float64
var sigma float64
if n0 != n-1 {
sigma = -z[4*(n0+1)-2]
}
if sigma < 0 {
info = 1
return info
}
// Find last unreduced submatrix's top index i0, find qmax and
// emin. Find Gershgorin-type bound if Q's much greater than E's.
var emax float64
if n0 > i0 {
emin = math.Abs(z[4*(n0+1)-6])
} else {
emin = 0
}
qmin := z[4*(n0+1)-4]
qmax = qmin
zSmall := false
for i4loop := 4 * (n0 + 1); i4loop >= 8; i4loop -= 4 {
i4 = i4loop - 1
if z[i4-5] <= 0 {
zSmall = true
break
}
if qmin >= 4*emax {
qmin = math.Min(qmin, z[i4-3])
emax = math.Max(emax, z[i4-5])
}
qmax = math.Max(qmax, z[i4-7]+z[i4-5])
emin = math.Min(emin, z[i4-5])
}
if !zSmall {
i4 = 3
}
i0 = (i4+1)/4 - 1
pp = 0
if n0-i0 > 1 {
dee := z[4*i0]
deemin := dee
kmin := i0
for i4loop := 4*(i0+1) + 1; i4loop <= 4*(n0+1)-3; i4loop += 4 {
i4 := i4loop - 1
dee = z[i4] * (dee / (dee + z[i4-2]))
if dee <= deemin {
deemin = dee
kmin = (i4+4)/4 - 1
}
}
if (kmin-i0)*2 < n0-kmin && deemin <= 0.5*z[4*n0] {
ipn4Out := 4 * (i0 + n0 + 2)
pp = 2
for i4loop := 4 * (i0 + 1); i4loop <= 2*(i0+n0+1); i4loop += 4 {
i4 := i4loop - 1
ipn4 := ipn4Out - 1
z[i4-3], z[ipn4-i4-4] = z[ipn4-i4-4], z[i4-3]
z[i4-2], z[ipn4-i4-3] = z[ipn4-i4-3], z[i4-2]
z[i4-1], z[ipn4-i4-6] = z[ipn4-i4-6], z[i4-1]
z[i4], z[ipn4-i4-5] = z[ipn4-i4-5], z[i4]
}
}
}
// Put -(initial shift) into DMIN.
dmin := -math.Max(0, qmin-2*math.Sqrt(qmin)*math.Sqrt(emax))
// Now i0:n0 is unreduced.
// PP = 0 for ping, PP = 1 for pong.
// PP = 2 indicates that flipping was applied to the Z array and
// and that the tests for deflation upon entry in Dlasq3
// should not be performed.
nbig := 100 * (n0 - i0 + 1)
for iwhilb := 0; iwhilb < nbig; iwhilb++ {
if i0 > n0 {
continue Whila
}
// While submatrix unfinished take a good dqds step.
i0, n0, pp, dmin, sigma, desig, qmax, nFail, iter, nDiv, ttype, dmin1, dmin2, dn, dn1, dn2, g, tau =
impl.Dlasq3(i0, n0, z, pp, dmin, sigma, desig, qmax, nFail, iter, nDiv, ttype, dmin1, dmin2, dn, dn1, dn2, g, tau)
pp = 1 - pp
// When emin is very small check for splits.
if pp == 0 && n0-i0 >= 3 {
if z[4*(n0+1)-1] <= tol2*qmax || z[4*(n0+1)-2] <= tol2*sigma {
splt := i0 - 1
qmax = z[4*i0]
emin = z[4*(i0+1)-2]
oldemn := z[4*(i0+1)-1]
for i4loop := 4 * (i0 + 1); i4loop <= 4*(n0-2); i4loop += 4 {
i4 := i4loop - 1
if z[i4] <= tol2*z[i4-3] || z[i4-1] <= tol2*sigma {
z[i4-1] = -sigma
splt = i4 / 4
qmax = 0
emin = z[i4+3]
oldemn = z[i4+4]
} else {
qmax = math.Max(qmax, z[i4+1])
emin = math.Min(emin, z[i4-1])
oldemn = math.Min(oldemn, z[i4])
}
}
z[4*(n0+1)-2] = emin
z[4*(n0+1)-1] = oldemn
i0 = splt + 1
}
}
}
// Maximum number of iterations exceeded, restore the shift
// sigma and place the new d's and e's in a qd array.
// This might need to be done for several blocks.
info = 2
i1 = i0
n1 = n0
OneFourtyFive:
tempq = z[4*i0]
z[4*i0] += sigma
for k := i0 + 1; k <= n0; k++ {
tempe := z[4*(k+1)-6]
z[4*(k+1)-6] *= tempq / z[4*(k+1)-8]
tempq = z[4*k]
z[4*k] += sigma + tempe - z[4*(k+1)-6]
}
// Prepare to do this on the previous block if there is one.
if i1 > 0 {
n1 = i1 - 1
for i1 >= 1 && z[4*(i1+1)-6] >= 0 {
i1 -= 1
}
sigma = -z[4*(n1+1)-2]
goto OneFourtyFive
}
for k := 0; k < n; k++ {
z[2*k] = z[4*k]
// Only the block 1..N0 is unfinished. The rest of the e's
// must be essentially zero, although sometimes other data
// has been stored in them.
if k < n0 {
z[2*(k+1)-1] = z[4*(k+1)-1]
} else {
z[2*(k+1)] = 0
}
}
return info
}
info = 3
return
OneSeventy:
// Move q's to the front.
for k := 1; k < n; k++ {
z[k] = z[4*k]
}
// Sort and compute sum of eigenvalues.
impl.Dlasrt(lapack.SortDecreasing, n, z)
e = 0
for k := n - 1; k >= 0; k-- {
e += z[k]
}
// Store trace, sum(eigenvalues) and information on performance.
z[2*n] = trace
z[2*n+1] = e
z[2*n+2] = float64(iter)
z[2*n+3] = float64(nDiv) / float64(n*n)
z[2*n+4] = 100 * float64(nFail) / float64(iter)
return info
}

154
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// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package native
import "math"
// Dlasq3 checks for deflation, computes a shift (tau) and calls dqds.
// In case of failure it changes shifts, and tries again until output
// is positive.
func (impl Implementation) Dlasq3(i0, n0 int, z []float64, pp int, dmin, sigma, desig, qmax float64, nFail, iter, nDiv int, ttype int, dmin1, dmin2, dn, dn1, dn2, g, tau float64) (
i0Out, n0Out, ppOut int, dminOut, sigmaOut, desigOut, qmaxOut float64, nFailOut, iterOut, nDivOut, ttypeOut int, dmin1Out, dmin2Out, dnOut, dn1Out, dn2Out, gOut, tauOut float64) {
const cbias = 1.5
n0in := n0
eps := dlamchP
tol := eps * 100
tol2 := tol * tol
var nn int
var t float64
for {
if n0 < i0 {
return i0, n0, pp, dmin, sigma, desig, qmax, nFail, iter, nDiv, ttype, dmin1, dmin2, dn, dn1, dn2, g, tau
}
if n0 == i0 {
goto Twenty
}
nn = 4*(n0+1) + pp - 1
if n0 == i0+1 {
goto Fourty
}
// Check whether e[n0-1] is negligible, 1 eigenvalue.
if z[nn-5] > tol2*(sigma+z[nn-3]) && z[nn-2*pp-4] > tol2*z[nn-7] {
goto Thirty
}
Twenty:
z[4*(n0+1)-4] = z[4*(n0+1)+pp-4] + sigma
n0--
continue
// Check whether e[n0-2] is negligible, 2 eigenvalues.
Thirty:
if z[nn-9] > tol2*sigma && z[nn-2*pp-8] > tol2*z[nn-11] {
break
}
Fourty:
if z[nn-3] > z[nn-7] {
z[nn-3], z[nn-7] = z[nn-7], z[nn-3]
}
t = 0.5 * (z[nn-7] - z[nn-3] + z[nn-5])
if z[nn-5] > z[nn-3]*tol2 && t != 0 {
s := z[nn-3] * (z[nn-5] / t)
if s <= t {
s = z[nn-3] * (z[nn-5] / (t * (1 + math.Sqrt(1+s/t))))
} else {
s = z[nn-3] * (z[nn-5] / (t + math.Sqrt(t)*math.Sqrt(t+s)))
}
t = z[nn-7] + (s + z[nn-5])
z[nn-3] *= z[nn-7] / t
z[nn-7] = t
}
z[4*(n0+1)-8] = z[nn-7] + sigma
z[4*(n0+1)-4] = z[nn-3] + sigma
n0 -= 2
}
if pp == 2 {
pp = 0
}
// Reverse the qd-array, if warranted.
if dmin <= 0 || n0 < n0in {
if cbias*z[4*(i0+1)+pp-4] < z[4*(n0+1)+pp-4] {
ipn4Out := 4 * (i0 + n0 + 2)
for j4loop := 4 * (i0 + 1); j4loop <= 2*((i0+1)+(n0+1)-1); j4loop += 4 {
ipn4 := ipn4Out - 1
j4 := j4loop - 1
z[j4-3], z[ipn4-j4-4] = z[ipn4-j4-4], z[j4-3]
z[j4-2], z[ipn4-j4-3] = z[ipn4-j4-3], z[j4-2]
z[j4-1], z[ipn4-j4-6] = z[ipn4-j4-6], z[j4-1]
z[j4], z[ipn4-j4-5] = z[ipn4-j4-5], z[j4]
}
if n0-i0 <= 4 {
z[4*(n0+1)+pp-2] = z[4*(i0+1)+pp-2]
z[4*(n0+1)-pp-1] = z[4*(i0+1)-pp-1]
}
dmin2 = math.Min(dmin2, z[4*(i0+1)-pp-2])
z[4*(n0+1)+pp-2] = math.Min(math.Min(z[4*(n0+1)+pp-2], z[4*(i0+1)+pp-2]), z[4*(i0+1)+pp+2])
z[4*(n0+1)-pp-1] = math.Min(math.Min(z[4*(n0+1)-pp-1], z[4*(i0+1)-pp-1]), z[4*(i0+1)-pp+3])
qmax = math.Max(math.Max(qmax, z[4*(i0+1)+pp-4]), z[4*(i0+1)+pp])
dmin = math.Copysign(0, -1) // Fortran code has -zero, but -0 in go is 0
}
}
// Choose a shift.
tau, ttype, g = impl.Dlasq4(i0, n0, z, pp, n0in, dmin, dmin1, dmin2, dn, dn1, dn2, tau, ttype, g)
// Call dqds until dmin > 0.
Seventy:
i0, n0, pp, tau, sigma, dmin, dmin1, dmin2, dn, dn1, dn2 = impl.Dlasq5(i0, n0, z, pp, tau, sigma, dmin, dmin1, dmin2, dn, dn1, dn2)
nDiv += n0 - i0 + 2
iter++
if dmin >= 0 && dmin1 >= 0 {
// Success.
goto Ninety
} else if dmin < 0 && dmin1 > 0 && z[4*n0-pp-1] < tol*(sigma+dn1) && math.Abs(dn) < tol*sigma {
// Convergence hidden by negative dn.
z[4*n0-pp+1] = 0
dmin = 0
goto Ninety
} else if dmin < 0 {
// Tau too big. Select new Tau and try again.
nFail++
if ttype < -22 {
// Failed twice. Play it safe.
tau = 0
} else if dmin1 > 0 {
// Late failure. Gives excellent shift.
tau = (tau + dmin) * (1 - 2*eps)
ttype -= 11
} else {
// Early failure. Divide by 4.
tau = tau / 4
ttype -= 12
}
goto Seventy
} else if math.IsNaN(dmin) {
if tau == 0 {
goto Eighty
} else {
tau = 0
goto Seventy
}
} else {
// Possible underflow. Play it safe.
goto Eighty
}
Eighty:
// Risk of underflow
dmin, dmin1, dmin2, dn, dn1, dn2 = impl.Dlasq6(i0, n0, z, pp, dmin, dmin1, dmin2, dn, dn1, dn2)
nDiv += n0 - i0 + 2
iter++
tau = 0
Ninety:
if tau < sigma {
desig += tau
t = sigma + desig
desig -= t - sigma
} else {
t = sigma + tau
desig += sigma - (t - tau)
}
sigma = t
return i0, n0, pp, dmin, sigma, desig, qmax, nFail, iter, nDiv, ttype, dmin1, dmin2, dn, dn1, dn2, g, tau
}

237
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// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package native
import "math"
// Dlasq4 computes an approximation to the smallest eigenvalue using values of d
// from the previous transform.
// i0, n0, and n0in are zero-indexed.
func (impl Implementation) Dlasq4(i0, n0 int, z []float64, pp int, n0in int, dmin, dmin1, dmin2, dn, dn1, dn2, tau float64, ttype int, g float64) (tauOut float64, ttypeOut int, gOut float64) {
const (
cnst1 = 0.563
cnst2 = 1.01
cnst3 = 1.05
cnstthird = 0.333 // TODO(btracey): Fix?
)
// A negative dmin forces the shift to take that absolute value
// ttype records the type of shift.
if dmin <= 0 {
tau = -dmin
ttype = -1
return tau, ttype, g
}
nn := 4*(n0+1) + pp - 1 // -1 for zero indexing
s := math.NaN() // Poison s so that failure to take a path below is obvious
if n0in == n0 {
// No eigenvalues deflated.
if dmin == dn || dmin == dn1 {
b1 := math.Sqrt(z[nn-3]) * math.Sqrt(z[nn-5])
b2 := math.Sqrt(z[nn-7]) * math.Sqrt(z[nn-9])
a2 := z[nn-7] + z[nn-5]
if dmin == dn && dmin1 == dn1 {
gap2 := dmin2 - a2 - dmin2/4
var gap1 float64
if gap2 > 0 && gap2 > b2 {
gap1 = a2 - dn - (b2/gap2)*b2
} else {
gap1 = a2 - dn - (b1 + b2)
}
if gap1 > 0 && gap1 > b1 {
s = math.Max(dn-(b1/gap1)*b1, 0.5*dmin)
ttype = -2
} else {
s = 0
if dn > b1 {
s = dn - b1
}
if a2 > b1+b2 {
s = math.Min(s, a2-(b1+b2))
}
s = math.Max(s, cnstthird*dmin)
ttype = -3
}
} else {
ttype = -4
s = dmin / 4
var gam float64
var np int
if dmin == dn {
gam = dn
a2 = 0
if z[nn-5] > z[nn-7] {
return tau, ttype, g
}
b2 = z[nn-5] / z[nn-7]
np = nn - 9
} else {
np = nn - 2*pp
b2 = z[np-2]
gam = dn1
if z[np-4] > z[np-2] {
return tau, ttype, g
}
a2 = z[np-4] / z[np-2]
if z[nn-9] > z[nn-11] {
return tau, ttype, g
}
b2 = z[nn-9] / z[nn-11]
np = nn - 13
}
// Approximate contribution to norm squared from i < nn-1.
a2 += b2
for i4loop := np + 1; i4loop >= 4*(i0+1)-1+pp; i4loop -= 4 {
i4 := i4loop - 1
if b2 == 0 {
break
}
b1 = b2
if z[i4] > z[i4-2] {
return tau, ttype, g
}
b2 *= z[i4] / z[i4-2]
a2 += b2
if 100*math.Max(b2, b1) < a2 || cnst1 < a2 {
break
}
}
a2 *= cnst3
// Rayleigh quotient residual bound.
if a2 < cnst1 {
s = gam * (1 - math.Sqrt(a2)) / (1 + a2)
}
}
} else if dmin == dn2 {
ttype = -5
s = dmin / 4
// Compute contribution to norm squared from i > nn-2.
np := nn - 2*pp
b1 := z[np-2]
b2 := z[np-6]
gam := dn2
if z[np-8] > b2 || z[np-4] > b1 {
return tau, ttype, g
}
a2 := (z[np-8] / b2) * (1 + z[np-4]/b1)
// Approximate contribution to norm squared from i < nn-2.
if n0-i0 > 2 {
b2 = z[nn-13] / z[nn-15]
a2 += b2
for i4loop := (nn + 1) - 17; i4loop >= 4*(i0+1)-1+pp; i4loop -= 4 {
i4 := i4loop - 1
if b2 == 0 {
break
}
b1 = b2
if z[i4] > z[i4-2] {
return tau, ttype, g
}
b2 *= z[i4] / z[i4-2]
a2 += b2
if 100*math.Max(b2, b1) < a2 || cnst1 < a2 {
break
}
}
a2 *= cnst3
}
if a2 < cnst1 {
s = gam * (1 - math.Sqrt(a2)) / (1 + a2)
}
} else {
// Case 6, no information to guide us.
if ttype == -6 {
g += cnstthird * (1 - g)
} else if ttype == -18 {
g = cnstthird / 4
} else {
g = 1.0 / 4
}
s = g * dmin
ttype = -6
}
} else if n0in == (n0 + 1) {
// One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN.
if dmin1 == dn1 && dmin2 == dn2 {
ttype = -7
s = cnstthird * dmin1
if z[nn-5] > z[nn-7] {
return tau, ttype, g
}
b1 := z[nn-5] / z[nn-7]
b2 := b1
if b2 != 0 {
for i4loop := 4*(n0+1) - 9 + pp; i4loop >= 4*(i0+1)-1+pp; i4loop -= 4 {
i4 := i4loop - 1
a2 := b1
if z[i4] > z[i4-2] {
return tau, ttype, g
}
b1 *= z[i4] / z[i4-2]
b2 += b1
if 100*math.Max(b1, a2) < b2 {
break
}
}
}
b2 = math.Sqrt(cnst3 * b2)
a2 := dmin1 / (1 + b2*b2)
gap2 := 0.5*dmin2 - a2
if gap2 > 0 && gap2 > b2*a2 {
s = math.Max(s, a2*(1-cnst2*a2*(b2/gap2)*b2))
} else {
s = math.Max(s, a2*(1-cnst2*b2))
ttype = -8
}
} else {
s = dmin1 / 4
if dmin1 == dn1 {
s = 0.5 * dmin1
}
ttype = -9
}
} else if n0in == (n0 + 2) {
// Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN.
if dmin2 == dn2 && 2*z[nn-5] < z[nn-7] {
ttype = -10
s = cnstthird * dmin2
if z[nn-5] > z[nn-7] {
return tau, ttype, g
}
b1 := z[nn-5] / z[nn-7]
b2 := b1
if b2 != 0 {
for i4loop := 4*(n0+1) - 9 + pp; i4loop >= 4*(i0+1)-1+pp; i4loop -= 4 {
i4 := i4loop - 1
if z[i4] > z[i4-2] {
return tau, ttype, g
}
b1 *= z[i4] / z[i4-2]
b2 += b1
if 100*b1 < b2 {
break
}
}
}
b2 = math.Sqrt(cnst3 * b2)
a2 := dmin2 / (1 + b2*b2)
gap2 := z[nn-7] + z[nn-9] - math.Sqrt(z[nn-11])*math.Sqrt(z[nn-9]) - a2
if gap2 > 0 && gap2 > b2*a2 {
s = math.Max(s, a2*(1-cnst2*a2*(b2/gap2)*b2))
} else {
s = math.Max(s, a2*(1-cnst2*b2))
}
} else {
s = dmin2 / 4
ttype = -11
}
} else if n0in > n0+2 {
// Case 12, more than two eigenvalues deflated. No information.
s = 0
ttype = -12
}
tau = s
return tau, ttype, g
}

129
native/dlasq5.go Normal file
View File

@@ -0,0 +1,129 @@
// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package native
import "math"
// Dlasq5 computes one dqds transform in ping-pong form.
// i0 and n0 are zero-indexed.
func (impl Implementation) Dlasq5(i0, n0 int, z []float64, pp int, tau, sigma, dmin, dmin1, dmin2, dn, dnm1, dnm2 float64) (i0Out, n0Out, ppOut int, tauOut, sigmaOut, dminOut, dmin1Out, dmin2Out, dnOut, dnm1Out, dnm2Out float64) {
// TODO(btracey): It seems like outputs listed in the reference implementation
// are actually true outputs, unlike other functions where the value is
// preserved through the call. When a more full test suite exists, make them
// true outputs if it turns out the value does not need to be preserved through
// the call.
// The lapack function has inputs for ieee and eps, but Go requires ieee so
// these are unnecessary.
if n0-i0-1 <= 0 {
return i0, n0, pp, tau, sigma, dmin, dmin1, dmin2, dn, dnm1, dnm2
}
eps := dlamchP
dthresh := eps * (sigma + tau)
if tau < dthresh*0.5 {
tau = 0
}
var j4 int
var emin float64
if tau != 0 {
j4 = 4*i0 + pp
emin = z[j4+4]
d := z[j4] - tau
dmin = d
dmin1 = -z[j4]
if pp == 0 {
for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 {
j4 := j4loop - 1
z[j4-2] = d + z[j4-1]
tmp := z[j4+1] / z[j4-2]
d = d*tmp - tau
dmin = math.Min(dmin, d)
z[j4] = z[j4-1] * tmp
emin = math.Min(z[j4], emin)
}
} else {
for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 {
j4 := j4loop - 1
z[j4-3] = d + z[j4]
tmp := z[j4+2] / z[j4-3]
d = d*tmp - tau
dmin = math.Min(dmin, d)
z[j4-1] = z[j4] * tmp
emin = math.Min(z[j4-1], emin)
}
}
// Unroll the last two steps.
dnm2 = d
dmin2 = dmin
j4 = 4*((n0+1)-2) - pp - 1
j4p2 := j4 + 2*pp - 1
z[j4-2] = dnm2 + z[j4p2]
z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2])
dnm1 = z[j4p2+2]*(dnm2/z[j4-2]) - tau
dmin = math.Min(dmin, dnm1)
dmin1 = dmin
j4 += 4
j4p2 = j4 + 2*pp - 1
z[j4-2] = dnm1 + z[j4p2]
z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2])
dn = z[j4p2+2]*(dnm1/z[j4-2]) - tau
dmin = math.Min(dmin, dn)
} else {
// This is the version that sets d's to zero if they are small enough
j4 = 4*(i0+1) + pp - 4
emin = z[j4+4]
d := z[j4] - tau
dmin = d
dmin1 = -z[j4]
if pp == 0 {
for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 {
j4 := j4loop - 1
z[j4-2] = d + z[j4-1]
tmp := z[j4+1] / z[j4-2]
d = d*tmp - tau
if d < dthresh {
d = 0
}
dmin = math.Min(dmin, d)
z[j4] = z[j4-1] * tmp
emin = math.Min(z[j4], emin)
}
} else {
for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 {
j4 := j4loop - 1
z[j4-3] = d + z[j4]
tmp := z[j4+2] / z[j4-3]
d = d*tmp - tau
if d < dthresh {
d = 0
}
dmin = math.Min(dmin, d)
z[j4-1] = z[j4] * tmp
emin = math.Min(z[j4-1], emin)
}
}
// Unroll the last two steps.
dnm2 = d
dmin2 = dmin
j4 = 4*((n0+1)-2) - pp - 1
j4p2 := j4 + 2*pp - 1
z[j4-2] = dnm2 + z[j4p2]
z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2])
dnm1 = z[j4p2+2]*(dnm2/z[j4-2]) - tau
dmin = math.Min(dmin, dnm1)
dmin1 = dmin
j4 += 4
j4p2 = j4 + 2*pp - 1
z[j4-2] = dnm1 + z[j4p2]
z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2])
dn = z[j4p2+2]*(dnm1/z[j4-2]) - tau
dmin = math.Min(dmin, dn)
}
z[j4+2] = dn
z[4*(n0+1)-pp-1] = emin
return i0, n0, pp, tau, sigma, dmin, dmin1, dmin2, dn, dnm1, dnm2
}

112
native/dlasq6.go Normal file
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@@ -0,0 +1,112 @@
// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package native
import "math"
// Dlasq6 computes one dqd transform in ping-pong form with protection against
// overflow and underflow. z has length at least 4*(n0+1) and holds the qd array.
// i0 is the zero-based first index.
// n0 is the zero-based last index.
func (impl Implementation) Dlasq6(i0, n0 int, z []float64, pp int, dmin, dmin1, dmin2, dn, dnm1, dnm2 float64) (dminOut, dmin1Out, dmin2Out, dnOut, dnm1Out, dnm2Out float64) {
// TODO(btracey): It seems like outputs listed in the reference implementation
// are actually true outputs, unlike other functions where the value is
// preserved through the call. When a more full test suite exists, make them
// true outputs if it turns out the value does not need to be preserved through
// the call.
if len(z) < 4*(n0+1) {
panic(badZ)
}
if n0-i0-1 <= 0 {
return dmin, dmin1, dmin2, dn, dnm1, dnm2
}
safmin := dlamchS
j4 := 4*(i0+1) + pp - 4 // -4 rather than -3 for zero indexing
emin := z[j4+4]
d := z[j4]
dmin = d
if pp == 0 {
for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 {
j4 := j4loop - 1 // Translate back to zero-indexed
z[j4-2] = d + z[j4-1]
if z[j4-2] == 0 {
z[j4] = 0
d = z[j4+1]
dmin = d
emin = 0
} else if safmin*z[j4+1] < z[j4-2] && safmin*z[j4-2] < z[j4+1] {
tmp := z[j4+1] / z[j4-2]
z[j4] = z[j4-1] * tmp
d *= tmp
} else {
z[j4] = z[j4+1] * (z[j4-1] / z[j4-2])
d = z[j4+1] * (d / z[j4-2])
}
dmin = math.Min(dmin, d)
emin = math.Min(emin, z[j4])
}
} else {
for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 {
j4 := j4loop - 1
z[j4-3] = d + z[j4]
if z[j4-3] == 0 {
z[j4-1] = 0
d = z[j4+2]
dmin = d
emin = 0
} else if safmin*z[j4+2] < z[j4-3] && safmin*z[j4-3] < z[j4+2] {
tmp := z[j4+2] / z[j4-3]
z[j4-1] = z[j4] * tmp
d *= tmp
} else {
z[j4-1] = z[j4+2] * (z[j4] / z[j4-3])
d = z[j4+2] * (d / z[j4-3])
}
dmin = math.Min(dmin, d)
emin = math.Min(emin, z[j4-1])
}
}
// Unroll last two steps
dnm2 = d
dmin2 = dmin
j4 = 4*(n0-2) - pp - 1
j4p2 := j4 + 2*pp - 1
z[j4-2] = dnm2 + z[j4p2]
if z[j4-2] == 0 {
z[j4] = 0
dnm1 = z[j4p2+2]
dmin = dnm1
emin = 0
} else if safmin*z[j4p2+2] < z[j4-2] && safmin*z[j4-2] < z[j4p2+2] {
tmp := z[j4p2+2] / z[j4-2]
z[j4] = z[j4p2] * tmp
dnm1 = dnm2 * tmp
} else {
z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2])
dnm1 = z[j4p2] * (dnm2 / z[j4-2])
}
dmin = math.Min(dmin, dnm1)
dmin1 = dmin
j4 += 4
j4p2 = j4 + 2*pp - 1
z[j4-2] = dnm1 + z[j4p2]
if z[j4-2] == 0 {
z[j4] = 0
dn = z[j4p2+2]
dmin = dn
emin = 0
} else if safmin*z[j4p2+2] < z[j4-2] && safmin*z[j4-2] < z[j4p2+2] {
tmp := z[j4p2+2] / z[j4-2]
z[j4] = z[j4p2] * tmp
dn = dnm1 * tmp
} else {
z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2])
dn = z[j4p2] * (dnm2 / z[j4-2])
}
dmin = math.Min(dmin, dn)
z[j4+2] = dn
z[4*(n0+1)-pp-1] = emin
return dmin, dmin1, dmin2, dn, dnm1, dnm2
}

4
native/dlasrt.go
View File

@@ -20,8 +20,8 @@ func (impl Implementation) Dlasrt(s lapack.Sort, n int, d []float64) {
default:
panic("lapack: bad sort")
case lapack.SortIncreasing:
sort.Sort(sort.Reverse(sort.Float64Slice(d)))
case lapack.SortDecreasing:
sort.Float64s(d)
case lapack.SortDecreasing:
sort.Sort(sort.Reverse(sort.Float64Slice(d)))
}
}

1
native/dlaswp.go
View File

@@ -19,5 +19,4 @@ func (impl Implementation) Dlaswp(n int, a []float64, lda, k1, k2 int, ipiv []in
for k := k2; k >= k1; k-- {
bi.Dswap(n, a[k*lda:], 1, a[ipiv[k]*lda:], 1)
}
return
}

2
native/dlatrs.go
View File

@@ -43,7 +43,7 @@ func (impl Implementation) Dlatrs(uplo blas.Uplo, trans blas.Transpose, diag bla
checkVector(n, cnorm, 1)
if n == 0 {
return
return 0
}
scale = 1
bi := blas64.Implementation()

7
native/dorml2.go
View File

@@ -54,7 +54,7 @@ func (impl Implementation) Dorml2(side blas.Side, trans blas.Transpose, m, n, k
impl.Dlarf(side, m-i, n, a[i*lda+i:], 1, tau[i], c[i*ldc:], ldc, work)
a[i*lda+i] = aii
}
return
case left && !notran:
for i := k - 1; i >= 0; i-- {
aii := a[i*lda+i]
@@ -62,7 +62,7 @@ func (impl Implementation) Dorml2(side blas.Side, trans blas.Transpose, m, n, k
impl.Dlarf(side, m-i, n, a[i*lda+i:], 1, tau[i], c[i*ldc:], ldc, work)
a[i*lda+i] = aii
}
return
case !left && notran:
for i := k - 1; i >= 0; i-- {
aii := a[i*lda+i]
@@ -70,7 +70,7 @@ func (impl Implementation) Dorml2(side blas.Side, trans blas.Transpose, m, n, k
impl.Dlarf(side, m, n-i, a[i*lda+i:], 1, tau[i], c[i:], ldc, work)
a[i*lda+i] = aii
}
return
case !left && !notran:
for i := 0; i < k; i++ {
aii := a[i*lda+i]
@@ -78,6 +78,5 @@ func (impl Implementation) Dorml2(side blas.Side, trans blas.Transpose, m, n, k
impl.Dlarf(side, m, n-i, a[i*lda+i:], 1, tau[i], c[i:], ldc, work)
a[i*lda+i] = aii
}
return
}
}

7
native/dormlq.go
View File

@@ -108,7 +108,7 @@ func (impl Implementation) Dormlq(side blas.Side, trans blas.Transpose, m, n, k
c[i*ldc:], ldc,
work, ldwork)
}
return
case left && !notran:
for i := ((k - 1) / nb) * nb; i >= 0; i -= nb {
ib := min(nb, k-i)
@@ -122,7 +122,7 @@ func (impl Implementation) Dormlq(side blas.Side, trans blas.Transpose, m, n, k
c[i*ldc:], ldc,
work, ldwork)
}
return
case !left && notran:
for i := ((k - 1) / nb) * nb; i >= 0; i -= nb {
ib := min(nb, k-i)
@@ -136,7 +136,7 @@ func (impl Implementation) Dormlq(side blas.Side, trans blas.Transpose, m, n, k
c[i:], ldc,
work, ldwork)
}
return
case !left && !notran:
for i := 0; i < k; i += nb {
ib := min(nb, k-i)
@@ -150,6 +150,5 @@ func (impl Implementation) Dormlq(side blas.Side, trans blas.Transpose, m, n, k
c[i:], ldc,
work, ldwork)
}
return
}
}

7
native/dormqr.go
View File

@@ -96,7 +96,7 @@ func (impl Implementation) Dormqr(side blas.Side, trans blas.Transpose, m, n, k
c[i*ldc:], ldc,
work, ldwork)
}
return
case left && !notran:
for i := 0; i < k; i += nb {
ib := min(nb, k-i)
@@ -110,7 +110,7 @@ func (impl Implementation) Dormqr(side blas.Side, trans blas.Transpose, m, n, k
c[i*ldc:], ldc,
work, ldwork)
}
return
case !left && notran:
for i := 0; i < k; i += nb {
ib := min(nb, k-i)
@@ -124,7 +124,7 @@ func (impl Implementation) Dormqr(side blas.Side, trans blas.Transpose, m, n, k
c[i:], ldc,
work, ldwork)
}
return
case !left && !notran:
for i := ((k - 1) / nb) * nb; i >= 0; i -= nb {
ib := min(nb, k-i)
@@ -138,6 +138,5 @@ func (impl Implementation) Dormqr(side blas.Side, trans blas.Transpose, m, n, k
c[i:], ldc,
work, ldwork)
}
return
}
}

2
native/dtrtri.go
View File

@@ -20,7 +20,7 @@ func (impl Implementation) Dtrtri(uplo blas.Uplo, diag blas.Diag, n int, a []flo
panic(badDiag)
}
if n == 0 {
return
return false
}
nonUnit := diag == blas.NonUnit
if nonUnit {

11
native/general.go
View File

@@ -20,8 +20,10 @@ var _ lapack.Float64 = Implementation{}
// This list is duplicated in lapack/cgo. Keep in sync.
const (
absIncNotOne = "lapack: increment not one or negative one"
badD = "lapack: d has insufficient length"
badDiag = "lapack: bad diag"
badDirect = "lapack: bad direct"
badE = "lapack: e has insufficient length"
badIpiv = "lapack: insufficient permutation length"
badLdA = "lapack: index of a out of range"
badNorm = "lapack: bad norm"
@@ -30,15 +32,19 @@ const (
badSlice = "lapack: bad input slice length"
badStore = "lapack: bad store"
badTau = "lapack: tau has insufficient length"
badTauQ = "lapack: tauQ has insufficient length"
badTauP = "lapack: tauP has insufficient length"
badTrans = "lapack: bad trans"
badUplo = "lapack: illegal triangle"
badWork = "lapack: insufficient working memory"
badWorkStride = "lapack: insufficient working array stride"
badZ = "lapack: insufficient z length"
kGTM = "lapack: k > m"
kGTN = "lapack: k > n"
kLT0 = "lapack: k < 0"
mLTN = "lapack: m < n"
negDimension = "lapack: negative matrix dimension"
negZ = "lapack: negative z value"
nLT0 = "lapack: n < 0"
nLTM = "lapack: n < m"
shortWork = "lapack: working array shorter than declared"
@@ -92,8 +98,9 @@ var (
// dlamchS is the "safe min", that is, the lowest number such that 1/sfmin does
// not overflow. The Netlib code for calculating this number is not correct --
// it overflows. Found by trial and error, it is equal to (1/math.MaxFloat64) * (1+ 6*eps)
dlamchS = math.Float64frombits(0x4000000000001)
// it overflows.
// Found from printing out from FORTRAN
dlamchS = 2.2250738585072014E-308
smlnum = dlamchS / dlamchP
bignum = 1 / smlnum

32
native/lapack_test.go
View File

@@ -12,6 +12,14 @@ import (
var impl = Implementation{}
func TestDgebd2(t *testing.T) {
testlapack.Dgebd2Test(t, impl)
}
func TestDgebrd(t *testing.T) {
testlapack.DgebrdTest(t, impl)
}
func TestDgecon(t *testing.T) {
testlapack.DgeconTest(t, impl)
}
@@ -52,6 +60,10 @@ func TestDgetrs(t *testing.T) {
testlapack.DgetrsTest(t, impl)
}
func TestDlabrd(t *testing.T) {
testlapack.DlabrdTest(t, impl)
}
func TestDlacpy(t *testing.T) {
testlapack.DlacpyTest(t, impl)
}
@@ -96,6 +108,26 @@ func TestDlartg(t *testing.T) {
testlapack.DlartgTest(t, impl)
}
func TestDlasq1(t *testing.T) {
testlapack.Dlasq1Test(t, impl)
}
func TestDlasq2(t *testing.T) {
testlapack.Dlasq2Test(t, impl)
}
func TestDlasq3(t *testing.T) {
testlapack.Dlasq3Test(t, impl)
}
func TestDlasq4(t *testing.T) {
testlapack.Dlasq4Test(t, impl)
}
func TestDlasq5(t *testing.T) {
testlapack.Dlasq5Test(t, impl)
}
func TestDlasr(t *testing.T) {
testlapack.DlasrTest(t, impl)
}

53
testlapack/dgebd2.go Normal file
View File

@@ -0,0 +1,53 @@
// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package testlapack
import (
"math/rand"
"testing"
)
type Dgebd2er interface {
Dgebd2(m, n int, a []float64, lda int, d, e, tauq, taup, work []float64)
}
func Dgebd2Test(t *testing.T, impl Dgebd2er) {
for _, test := range []struct {
m, n, lda int
}{
{3, 4, 0},
{4, 3, 0},
{3, 4, 10},
{4, 3, 10},
} {
m := test.m
n := test.n
lda := test.lda
if lda == 0 {
lda = n
}
nb := min(m, n) // 'nb' name parallel with Dlabrd code.
a := make([]float64, m*lda)
for i := range a {
a[i] = rand.NormFloat64()
}
d := nanSlice(nb)
e := nanSlice(nb - 1)
tauP := nanSlice(nb)
tauQ := nanSlice(nb)
work := nanSlice(max(m, n))
aCopy := make([]float64, len(a))
copy(aCopy, a)
impl.Dgebd2(m, n, a, lda, d, e, tauQ, tauP, work)
if m >= n && nb == n {
tauP[n-1] = 0
}
if m < n && nb == m {
tauQ[m-1] = 0
}
checkBidiagonal(t, m, n, nb, a, lda, d, e, tauP, tauQ, aCopy)
}
}

134
testlapack/dgebrd.go Normal file
View File

@@ -0,0 +1,134 @@
// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package testlapack
import (
"math"
"math/rand"
"testing"
"github.com/gonum/floats"
)
type Dgebrder interface {
Dgebrd(m, n int, a []float64, lda int, d, e, tauQ, tauP, work []float64, lwork int)
Dgebd2er
}
func DgebrdTest(t *testing.T, impl Dgebrder) {
for _, test := range []struct {
m, n, lda int
}{
{100, 100, 0},
{100, 150, 0},
{150, 100, 0},
{100, 100, 200},
{100, 150, 200},
{150, 100, 200},
{300, 300, 0},
{300, 400, 0},
{400, 300, 0},
{300, 300, 500},
{300, 400, 500},
{300, 400, 500},
} {
m := test.m
n := test.n
lda := test.lda
if lda == 0 {
lda = n
}
minmn := min(m, n)
a := make([]float64, m*lda)
for i := range a {
a[i] = rand.NormFloat64()
}
d := make([]float64, minmn)
e := make([]float64, minmn)
tauP := make([]float64, minmn)
tauQ := make([]float64, minmn)
work := make([]float64, max(m, n))
for i := range work {
work[i] = math.NaN()
}
// Store a.
aCopy := make([]float64, len(a))
copy(aCopy, a)
// Compute the true answer with the unblocked algorithm.
impl.Dgebd2(m, n, a, lda, d, e, tauQ, tauP, work)
aAns := make([]float64, len(a))
copy(aAns, a)
dAns := make([]float64, len(d))
copy(dAns, d)
eAns := make([]float64, len(e))
copy(eAns, e)
tauQAns := make([]float64, len(tauQ))
copy(tauQAns, tauQ)
tauPAns := make([]float64, len(tauP))
copy(tauPAns, tauP)
// Test with optimal work.
lwork := -1
copy(a, aCopy)
impl.Dgebrd(m, n, a, lda, d, e, tauQ, tauP, work, lwork)
work = make([]float64, int(work[0]))
lwork = len(work)
impl.Dgebrd(m, n, a, lda, d, e, tauQ, tauP, work, lwork)
// Test answers
if !floats.EqualApprox(a, aAns, 1e-10) {
t.Errorf("a mismatch")
}
if !floats.EqualApprox(d, dAns, 1e-10) {
t.Errorf("d mismatch")
}
if !floats.EqualApprox(e, eAns, 1e-10) {
t.Errorf("e mismatch")
}
if !floats.EqualApprox(tauQ, tauQAns, 1e-10) {
t.Errorf("tauQ mismatch")
}
if !floats.EqualApprox(tauP, tauPAns, 1e-10) {
t.Errorf("tauP mismatch")
}
// Test with shorter than optimal work.
lwork--
copy(a, aCopy)
for i := range d {
d[i] = 0
}
for i := range e {
e[i] = 0
}
for i := range tauP {
tauP[i] = 0
}
for i := range tauQ {
tauQ[i] = 0
}
impl.Dgebrd(m, n, a, lda, d, e, tauQ, tauP, work, lwork)
// Test answers
if !floats.EqualApprox(a, aAns, 1e-10) {
t.Errorf("a mismatch")
}
if !floats.EqualApprox(d, dAns, 1e-10) {
t.Errorf("d mismatch")
}
if !floats.EqualApprox(e, eAns, 1e-10) {
t.Errorf("e mismatch")
}
if !floats.EqualApprox(tauQ, tauQAns, 1e-10) {
t.Errorf("tauQ mismatch")
}
if !floats.EqualApprox(tauP, tauPAns, 1e-10) {
t.Errorf("tauP mismatch")
}
}
}

26
testlapack/dgetrs.go
View File

@@ -15,38 +15,30 @@ type Dgetrser interface {
}
func DgetrsTest(t *testing.T, impl Dgetrser) {
// TODO(btracey): Put more thought into creating more regularized matrices
// and what correct tolerances should be. Consider also seeding the random
// number in this test to make it more robust to code changes in other
// parts of the suite.
for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
for _, test := range []struct {
n, nrhs, lda, ldb int
tol float64
}{
{3, 3, 0, 0, 1e-12},
{3, 3, 0, 0, 1e-12},
{3, 5, 0, 0, 1e-12},
{3, 5, 0, 0, 1e-12},
{5, 3, 0, 0, 1e-12},
{5, 3, 0, 0, 1e-12},
{3, 3, 8, 10, 1e-12},
{3, 3, 8, 10, 1e-12},
{3, 5, 8, 10, 1e-12},
{3, 5, 8, 10, 1e-12},
{5, 3, 8, 10, 1e-12},
{5, 3, 8, 10, 1e-12},
{300, 300, 0, 0, 1e-10},
{300, 300, 0, 0, 1e-10},
{300, 500, 0, 0, 1e-10},
{300, 500, 0, 0, 1e-10},
{500, 300, 0, 0, 1e-10},
{500, 300, 0, 0, 1e-10},
{300, 300, 0, 0, 1e-8},
{300, 500, 0, 0, 1e-8},
{500, 300, 0, 0, 1e-8},
{300, 300, 700, 600, 1e-10},
{300, 300, 700, 600, 1e-10},
{300, 500, 700, 600, 1e-10},
{300, 500, 700, 600, 1e-10},
{300, 300, 700, 600, 1e-8},
{300, 500, 700, 600, 1e-8},
{500, 300, 700, 600, 1e-8},
{500, 300, 700, 600, 1e-10},
} {
n := test.n
nrhs := test.nrhs

106
testlapack/dlabrd.go Normal file
View File

@@ -0,0 +1,106 @@
// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package testlapack
import (
"math"
"math/rand"
"testing"
)
type Dlabrder interface {
Dlabrd(m, n, nb int, a []float64, lda int, d, e, tauq, taup, x []float64, ldx int, y []float64, ldy int)
}
func DlabrdTest(t *testing.T, impl Dlabrder) {
for _, test := range []struct {
m, n, nb, lda, ldx, ldy int
}{
{4, 5, 2, 0, 0, 0},
{4, 5, 4, 0, 0, 0},
{5, 5, 2, 0, 0, 0},
{5, 5, 5, 0, 0, 0},
{5, 4, 4, 0, 0, 0},
{5, 4, 4, 0, 0, 0},
{4, 5, 2, 10, 11, 12},
{4, 5, 4, 10, 11, 12},
{5, 5, 2, 10, 11, 12},
{5, 5, 5, 10, 11, 12},
{5, 4, 2, 10, 11, 12},
{5, 4, 4, 10, 11, 12},
{4, 5, 2, 11, 12, 10},
{4, 5, 4, 11, 12, 10},
{5, 5, 2, 11, 12, 10},
{5, 5, 5, 11, 12, 10},
{5, 4, 2, 11, 12, 10},
{5, 4, 4, 11, 12, 10},
{4, 5, 2, 12, 11, 10},
{4, 5, 4, 12, 11, 10},
{5, 5, 2, 12, 11, 10},
{5, 5, 5, 12, 11, 10},
{5, 4, 2, 12, 11, 10},
{5, 4, 4, 12, 11, 10},
} {
m := test.m
n := test.n
nb := test.nb
lda := test.lda
if lda == 0 {
lda = n
}
ldy := test.ldy
if ldy == 0 {
ldy = nb
}
ldx := test.ldx
if ldx == 0 {
ldx = nb
}
a := make([]float64, m*lda)
for i := range a {
a[i] = rand.NormFloat64()
}
d := make([]float64, nb)
for i := range d {
d[i] = math.NaN()
}
e := make([]float64, nb)
for i := range e {
e[i] = math.NaN()
}
tauP := make([]float64, nb)
for i := range tauP {
tauP[i] = math.NaN()
}
tauQ := make([]float64, nb)
for i := range tauP {
tauQ[i] = math.NaN()
}
x := make([]float64, m*ldx)
for i := range x {
x[i] = rand.NormFloat64()
}
y := make([]float64, n*ldy)
for i := range y {
y[i] = rand.NormFloat64()
}
aCopy := make([]float64, len(a))
copy(aCopy, a)
// Compute the reduction.
impl.Dlabrd(m, n, nb, a, lda, d, e, tauQ, tauP, x, ldx, y, ldy)
if m >= n && nb == n {
tauP[n-1] = 0
}
if m < n && nb == m {
tauQ[m-1] = 0
}
checkBidiagonal(t, m, n, nb, a, lda, d, e, tauP, tauQ, aCopy)
}
}

95
testlapack/dlasq1.go Normal file
View File

@@ -0,0 +1,95 @@
// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package testlapack
import (
"fmt"
"math"
"math/rand"
"testing"
"github.com/gonum/blas"
"github.com/gonum/blas/blas64"
)
func printDlasq1FortranInput(d, e, work []float64, n int) {
printFortranArray(d, "d")
printFortranArray(e, "e")
printFortranArray(work, "work")
fmt.Println("n = ", n)
fmt.Println("info = 0")
}
type Dlasq1er interface {
Dlasq1(n int, d, e, work []float64) int
Dgetrfer
}
func Dlasq1Test(t *testing.T, impl Dlasq1er) {
bi := blas64.Implementation()
// TODO(btracey): Increase the size of this test when we have a more numerically
// stable way to test the singular values.
for _, n := range []int{1, 2, 5, 8} {
work := make([]float64, 4*n)
d := make([]float64, n)
e := make([]float64, n-1)
for cas := 0; cas < 1; cas++ {
for i := range work {
work[i] = rand.Float64()
}
for i := range d {
d[i] = rand.NormFloat64() + 10
}
for i := range e {
e[i] = rand.NormFloat64()
}
ldm := n
m := make([]float64, n*ldm)
// Set up the matrix
for i := 0; i < n; i++ {
m[i*ldm+i] = d[i]
if i != n-1 {
m[(i+1)*ldm+i] = e[i]
}
}
ldmm := n
mm := make([]float64, n*ldmm)
bi.Dgemm(blas.Trans, blas.NoTrans, n, n, n, 1, m, ldm, m, ldm, 0, mm, ldmm)
impl.Dlasq1(n, d, e, work)
// Check that they are singular values. The
// singular values are the square roots of the
// eigenvalues of X^T * X
mmCopy := make([]float64, len(mm))
copy(mmCopy, mm)
ipiv := make([]int, n)
for elem, sv := range d[0:n] {
copy(mm, mmCopy)
lambda := sv * sv
for i := 0; i < n; i++ {
mm[i*ldm+i] -= lambda
}
// Compute LU.
ok := impl.Dgetrf(n, n, mm, ldmm, ipiv)
if !ok {
// Definitely singular.
continue
}
// Compute determinant
var logdet float64
for i := 0; i < n; i++ {
v := mm[i*ldm+i]
logdet += math.Log(math.Abs(v))
}
if math.Exp(logdet) > 2 {
t.Errorf("Incorrect singular value. n = %d, cas = %d, elem = %d, det = %v", n, cas, elem, math.Exp(logdet))
}
}
}
}
}

720
testlapack/dlasq2.go Normal file
View File

@@ -0,0 +1,720 @@
// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package testlapack
import (
"fmt"
"math"
"math/rand"
"testing"
"github.com/gonum/floats"
)
func printDlasq2FortranInput(z []float64, n int) {
printFortranArray(z, "z")
fmt.Println("n = ", n)
fmt.Println("info = 0")
}
type Dlasq2er interface {
Dgetrfer
Dlasq2(n int, z []float64) (info int)
}
func Dlasq2Test(t *testing.T, impl Dlasq2er) {
dTol := 1e-6
// Answers from calling the netlib Dlasq2 function directly.
for c, test := range []struct {
n int
z []float64
info int
zOut []float64
}{
{
z: []float64{0.9975595900926172E+00, 0.5668247076112733E+00, 0.9659153754961249E+00, 0.7479276854714322E+00, 0.3673908973747557E+00, 0.4806368987547315E+00, 0.7375426363398452E-01, 0.5355229277727247E-02, 0.3470812885180155E+00, 0.3422438160728350E+00, 0.2179517263384726E+00, 0.1331604100136593E+00, 0.9005245144218924E+00, 0.3867660104574036E+00, 0.4454822893878481E+00, 0.6619321808958428E+00, 0.1610830043055933E-01, 0.6508548361039168E+00, 0.6464088254838254E+00, 0.3229872909405558E+00, 0.8556924028853313E+00, 0.4012869193638139E+00, 0.2068743292187569E+00, 0.9685394642165999E+00, 0.5983995343181346E+00, 0.6729807327762632E+00, 0.4568823106729620E+00, 0.3300151235733747E+00, 0.1003829265021773E+00, 0.7554533047597268E+00, 0.6056932669802318E+00, 0.7190479134084530E+00, 0.8973346038865299E+00, 0.6582291204811077E+00, 0.1507168371301046E+00, 0.6123149049967000E+00, 0.9786602381321465E+00, 0.9991422694268032E+00, 0.2567979861831603E+00, 0.5508654031552206E+00, 0.6590475178936379E+00, 0.5540051353968156E+00, 0.9777600986094505E+00, 0.9019233044604550E+00, 0.6579246844202109E+00, 0.7288585083995637E+00, 0.4024552650632751E+00, 0.9286276631540373E+00, 0.1478351900438915E+00, 0.6745292990637881E+00, 0.7696143092758962E+00, 0.3393225521457851E+00, 0.1158188549489931E+00, 0.6143691843615144E+00, 0.8206171394658319E+00, 0.9470946559240657E+00, 0.7311286518535550E+00, 0.4976039064630389E+00, 0.3748017407872005E+00, 0.4215058560045335E+00, 0.5529030382557849E+00, 0.9979192791781042E+00, 0.9903947480415133E+00, 0.7463096553073095E+00, 0.9537590617479789E+00, 0.9327469033343772E-01, 0.7340236871158429E+00, 0.7517616159256260E+00, 0.9468485056759987E+00, 0.7061763632511533E+00, 0.8138096664824992E+00, 0.5585945195965548E+00, 0.6170557687507783E-01, 0.4803807801853603E+00, 0.5976897721963292E+00, 0.1375319188363359E+00, 0.5873952004066820E+00, 0.5199682629163997E+00, 0.8858783448129579E+00, 0.3038101719904888E+00, 0.6696573039722583E+00, 0.6649400915297697E+00, 0.5036768993979404E+00, 0.2615751204119269E+00},
n: 21,
zOut: []float64{0.2550031738262204E+01, 0.2480977513501848E+01, 0.2366602269912148E+01, 0.2169993432366266E+01, 0.1810817848712033E+01, 0.1681677309759878E+01, 0.1303743375476047E+01, 0.1202161769544433E+01, 0.1183377192742860E+01, 0.1094206688544886E+01, 0.9154376259418607E+00, 0.8241395430971566E+00, 0.7318275341991307E+00, 0.5186198053161721E+00, 0.4143051093784424E+00, 0.2112065329503869E+00, 0.1093987140067686E+00, 0.9751785856405315E-01, 0.2818174710670554E-01, 0.1697846193036144E-01, 0.2117542506861687E-04, 0.5241368559131172E-22, 0.4369342452764876E-18, 0.4084491703488284E-18, 0.1303743375476047E+01, 0.0000000000000000E+00, 0.2325140442247288E-18, 0.2353545363971710E-18, 0.1202161769544433E+01, 0.0000000000000000E+00, 0.2163565864913247E-18, 0.2222159192042978E-18, 0.1183377192742860E+01, 0.2033579915108999E-22, 0.2652482201353177E-18, 0.2438256017573345E-18, 0.1094206688544886E+01, 0.3167883469916549E-16, 0.9806070694382835E-18, 0.1224486171222500E-17, 0.9154376259418607E+00, 0.2764930279233778E-14, 0.2171122324673871E+02, 0.2171122324673871E+02, 0.1020000000000000E+03, 0.3081632653061225E+01, 0.2941176470588236E+01, 0.2548071704976161E-16, 0.7318275341991307E+00, 0.4959852501050381E-23, 0.8676862906242004E-16, 0.1414000300319855E-15, 0.5186198053161721E+00, 0.1503295986001297E-14, 0.3452895805257589E-14, 0.7981257539768321E-14, 0.4143051093784424E+00, 0.1303656847202082E-15, 0.9855809897129084E-12, 0.2614986238618434E-11, 0.2112065329503869E+00, 0.8411884198867843E-17, 0.2293573303077261E-09, 0.9833566024906726E-10, 0.1093987140067686E+00, 0.2696165428113804E-17, 0.5825676764620370E-08, 0.2638661645752538E-08, 0.9751785856405315E-01, 0.6617412588681544E-21, 0.2809066689524106E-07, 0.6165545233233256E-07, 0.2818174710670554E-01, 0.1396210563637443E-18, 0.2854399814229969E-05, 0.1344352644992036E-05, 0.1697846193036144E-01, 0.6162975822039155E-31, 0.3724766654883956E-05, 0.4695180568393632E-05, 0.2117542506861687E-04, 0.0000000000000000E+00, 0.9895328911616120E-03, 0.1620493249248586E-02},
info: 0,
},
{
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z: []float64{0.3441168249350421E+00, 0.7064572711980356E+00, 0.6589781374655990E+00, 0.8687841598825752E+00, 0.7811747459515918E+00, 0.7470750719206745E+00, 0.7591454338662803E+00, 0.7956934079357347E-01, 0.3416983743372617E+00, 0.3365394610260509E+00, 0.8635365040683821E+00, 0.4793906833418223E+00, 0.9394584418725971E+00, 0.7354375226759881E+00, 0.3959912256877245E+00, 0.4088558388864650E+00, 0.6899389113237457E+00, 0.6329180251180861E+00, 0.6760812245614891E+00, 0.1743991444245150E+00, 0.3881927716152306E+00, 0.2103848624556167E+00, 0.5309784956583943E+00, 0.5758384660199964E+00, 0.6542468116269122E+00, 0.2141275453071043E+00, 0.4917208240158387E+00, 0.6996271491850585E+00, 0.7074081025976766E+00, 0.1896811377589238E+00, 0.4872676647104760E+00, 0.8987347035581787E+00, 0.1651654313203957E+00, 0.7969431328829826E+00, 0.8979672856778195E+00, 0.2621352236509209E+00, 0.2994430908669790E+00, 0.8412000921937168E+00, 0.6910228781616401E-01, 0.9849719192333963E+00, 0.2835195798153757E+00, 0.6126955834278749E+00, 0.9957514180764350E+00, 0.4133859474205875E+00, 0.2126790023013077E+00, 0.9230696247878700E-01, 0.5165813646587417E+00, 0.9232126059423650E+00, 0.6160486127374017E+00, 0.5529065454633691E+00, 0.6862175458708878E+00, 0.2677675454795836E-01, 0.6729513992144193E+00, 0.8612993184178528E+00, 0.5455358966165057E+00, 0.2518716982253303E+00, 0.5312849864208884E+00, 0.7551228210749875E+00, 0.1095520838657484E+00, 0.8767983608629261E+00, 0.9578119141004069E+00, 0.6878921114137557E+00, 0.2890574974795965E+00, 0.9851780344062913E+00, 0.9392886821673129E+00, 0.4125982690623264E+00, 0.6817912182549608E+00, 0.7805388095263401E+00, 0.1567802887930034E+00, 0.1901362770322003E+00, 0.5155717108920093E+00, 0.5470641908290981E+00, 0.9496522047623522E+00, 0.4367251554723609E+00, 0.7016249991347693E+00, 0.6652534390290816E+00, 0.3892590437090979E+00, 0.1464591367640408E+00, 0.9179795596761495E+00, 0.1527313083317114E+00, 0.8661173016992874E+00, 0.8044520995141484E+00, 0.4399581275677011E+00, 0.6590078920726725E+00},
n: 21,
zOut: []float64{0.2654671686308588E+01, 0.2409077903364995E+01, 0.2090082174851482E+01, 0.1940605709090538E+01, 0.1909776782011245E+01, 0.1629990303184568E+01, 0.1566043989638403E+01, 0.1473218419964192E+01, 0.1321200673977518E+01, 0.1275771383585936E+01, 0.9826159405158056E+00, 0.8184731809209335E+00, 0.6715230178331039E+00, 0.5669018352800101E+00, 0.3641671875118937E+00, 0.2699135892930649E+00, 0.1446269090001342E+00, 0.8937359624216266E-01, 0.5860931848549461E-01, 0.3094108728329079E-01, 0.6182329613034853E-03, 0.9233403587623171E-22, 0.2552413399194827E-12, 0.1309204970235786E-12, 0.1566043989638403E+01, 0.2003762315848454E-18, 0.9222125989396634E-12, 0.1831545934750265E-11, 0.1473218419964192E+01, 0.1899959664962892E-11, 0.5682525570474145E-10, 0.1113952503246639E-09, 0.1321200673977518E+01, 0.5311918312726658E-16, 0.2115322762070563E-08, 0.1208354514490733E-08, 0.1275771383585936E+01, 0.1424261829852281E-16, 0.6059411460508015E-08, 0.1032477558436010E-07, 0.9826159405158056E+00, 0.5397353496908506E-22, 0.2226820292130466E+02, 0.2226820292130466E+02, 0.9500000000000000E+02, 0.2927437641723356E+01, 0.1052631578947368E+01, 0.2555943178691847E-06, 0.6715230178331039E+00, 0.1218922493912602E-18, 0.4789189736721279E-06, 0.5466231772857101E-06, 0.5669018352800101E+00, 0.1893266172530428E-27, 0.9952011217509916E-06, 0.1128113648538554E-05, 0.3641671875118937E+00, 0.1993230626440035E-24, 0.2427606592544749E-05, 0.2156829827516489E-05, 0.2699135892930649E+00, 0.2761013168273541E-29, 0.3900010091178873E-05, 0.3393761026267541E-05, 0.1446269090001342E+00, 0.2150416673893778E-15, 0.8242388755752233E-05, 0.1105863902029246E-04, 0.8937359624216266E-01, 0.2934562567422164E-27, 0.3455780897358792E-04, 0.2250328346305790E-04, 0.5860931848549461E-01, 0.8147325136863849E-21, 0.2346512312055719E-04, 0.8962661529405173E-05, 0.3094108728329079E-01, 0.2460979885389816E-17, 0.5238375287742530E-03, 0.1080192509223090E-02, 0.6182329613034853E-03, 0.8383483586160605E-23, 0.7400552677463828E-02, 0.1581674273722876E-01},
info: 0,
},
{
z: []float64{0.7940281584071446E+00, 0.8540600349699839E+00, 0.8158431165852809E-01, 0.5431841788581357E+00, 0.3696613346727944E+00, 0.2343742079469738E+00, 0.4891909888056500E-01, 0.6769876984160987E+00, 0.4777767465052760E+00, 0.1867381312399053E+00, 0.2018744873845245E+00, 0.5511201479607295E+00, 0.6938788283912793E+00, 0.8167542438070282E+00, 0.7904606414789531E+00, 0.9443564310071292E+00, 0.7287247677237652E-01, 0.8645122013586991E+00, 0.1884651475116826E+00, 0.3844755283611681E+00, 0.9959264361467982E+00, 0.6424370932833342E+00, 0.1972122925077952E+00, 0.2842024247377670E+00, 0.9819646913482807E+00, 0.9118347224008859E+00, 0.8184691845197246E+00, 0.7051587281589254E+00, 0.7604703230109544E+00, 0.6312964755149379E+00, 0.5240863862347888E+00, 0.3442050916384676E-01, 0.2415614308212055E+00, 0.2814868323669945E+00, 0.6529284673126197E+00, 0.3727305084153835E+00, 0.5033733868757848E+00, 0.2317122058804952E+00, 0.7555584130128312E+00, 0.5854566742645219E+00, 0.5481204696337160E+00, 0.8479425268049923E+00, 0.2310874615764000E+00, 0.1250993726775007E-01, 0.6243285982203539E-01, 0.8533587246073391E+00, 0.9203815588639257E+00, 0.9256849509751471E+00, 0.6691405057262187E+00, 0.8847091531299658E+00, 0.6783572983386376E+00, 0.4701257141291857E+00, 0.8976078424378102E+00, 0.8575018884445876E+00, 0.4119363561363949E+00, 0.2824477027676924E+00, 0.2787507690368071E+00, 0.7994878185780909E+00, 0.6141832897278305E+00, 0.6772728066124333E+00, 0.1568652581579784E+00, 0.8025492691231176E+00, 0.2609459151100056E+00, 0.4956700691019098E+00, 0.1008839464621498E+00, 0.6129709499983976E+00, 0.4551038858718992E-02, 0.8382785474023564E+00, 0.9327452694814308E+00, 0.9710431593941808E+00, 0.3785578217695214E+00, 0.9620839159000718E+00, 0.3183561960196257E-01, 0.9167635157854341E+00, 0.8989971039988554E+00, 0.2723769512210017E-01, 0.4176537489735596E+00, 0.9619881273217982E+00, 0.8761769579995293E+00, 0.6385245520487358E+00, 0.6821739872929905E+00, 0.3927943300877799E+00, 0.3299501391296433E-01, 0.6026481165267817E+00},
n: 21,
zOut: []float64{0.2841529467847260E+01, 0.2556740368064117E+01, 0.2029069210305357E+01, 0.1816492749229813E+01, 0.1807397947918166E+01, 0.1724050761249482E+01, 0.1394683696862690E+01, 0.1363282300837870E+01, 0.1235317529564993E+01, 0.1007821728138393E+01, 0.9728972767837659E+00, 0.8110838192609224E+00, 0.6190683239156912E+00, 0.3314348466978195E+00, 0.2969816495631171E+00, 0.2506421226611442E+00, 0.1551624233480766E+00, 0.1141049603637759E+00, 0.6806098279643324E-01, 0.4065442795375918E-01, 0.1509783792061944E-04, 0.2745446733802996E-19, 0.2334033424405603E-14, 0.7232047343832039E-15, 0.1394683696862690E+01, 0.7652022750203868E-17, 0.1502464319787860E-09, 0.5990324067027169E-10, 0.1363282300837870E+01, 0.5511008105786353E-19, 0.1215529748555577E-07, 0.3576186028975079E-08, 0.1235317529564993E+01, 0.6271335389136957E-17, 0.2589527811059762E-05, 0.3563684464760320E-05, 0.1007821728138393E+01, 0.6928731028484552E-15, 0.2286607739649456E-04, 0.2916328836696281E-04, 0.9728972767837659E+00, 0.4013724285764508E-25, 0.2143649169120057E+02, 0.2143649169120056E+02, 0.1080000000000000E+03, 0.3174603174603174E+01, 0.5555555555555555E+01, 0.5006788488237952E-04, 0.6190683239156912E+00, 0.1272779738919789E-24, 0.5392273695714327E-05, 0.6586751690782050E-05, 0.3314348466978195E+00, 0.9952016744778614E-24, 0.4588114650322476E-05, 0.4104030919118472E-05, 0.2969816495631171E+00, 0.1254277227268884E-20, 0.1579210272170037E-05, 0.2523508055026877E-05, 0.2506421226611442E+00, 0.1514835081255253E-22, 0.9117975197333799E-05, 0.1415311657319248E-04, 0.1551624233480766E+00, 0.3272195034856757E-26, 0.3128414626489953E-04, 0.4770966856082524E-04, 0.1141049603637759E+00, 0.7575261888623807E-20, 0.6277758538102519E-05, 0.4644422903178713E-05, 0.6806098279643324E-01, 0.3715389965619895E-21, 0.5956965112658162E-05, 0.4447744978930882E-05, 0.4065442795375918E-01, 0.1972152263052530E-30, 0.2965586553650948E-04, 0.1900611263569203E-04, 0.1509783792061944E-04, 0.1009741958682895E-26, 0.1608958133772104E-02, 0.9583670521235791E-03},
info: 0,
},
} {
z := make([]float64, len(test.z))
copy(z, test.z)
info := impl.Dlasq2(test.n, z)
if !floats.EqualApprox(test.zOut, z, dTol) {
diff := make([]float64, len(z))
floats.SubTo(diff, z, test.zOut)
for i := range diff {
diff[i] = math.Abs(diff[i])
}
t.Errorf("Case %v, Z Mismatch", c)
}
if test.info != info {
t.Errorf("Info mismatch. Want %v, got %v", test.info, info)
}
}
// Perform a bunch of random tests to check for access out of bounds or
// infinite loops.
// TODO(btracey): Implement direct tests.
// bi := blas64.Implementation()
for _, n := range []int{5, 8, 20, 25} {
for k := 0; k < 10; k++ {
z := make([]float64, 4*n)
for i := range z {
z[i] = rand.Float64()
}
zCopy := make([]float64, len(z))
copy(zCopy, z)
// Compute the eigenvalues
impl.Dlasq2(n, z)
// Below is the code to test the eigenvalues. Eventually implement
// real tests.
// The code below is missing the transformation from L and U into
// the symmetric tridiagonal matrix.
// See discussion http://icl.cs.utk.edu/lapack-forum/viewtopic.php?f=5&t=4839
// for format.
/*
ldl := n
ldu := n
u := make([]float64, n*n)
for i := 0; i < n; i++ {
u[i*ldu+i] = zCopy[2*i]
if i != n-1 {
u[i*ldu+i+1] = 1
}
}
l := make([]float64, n*n)
for i := 0; i < n; i++ {
l[i*ldl+i] = 1
if i != n-1 {
l[(i+1)*ldl+i] = zCopy[2*i+1]
}
}
ldTriDi := n
triDi := make([]float64, n*n)
bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, l, ldl, u, ldu, 0, triDi, ldTriDi)
tridi2 := make([]float64, n*n)
bi.Dgemm(blas.Trans, blas.NoTrans, n, n, n, 1, triDi, n, triDi, n, 0, tridi2, n)
// Eigenvalues have the property that det(A - lambda I ) = 0
triDiCopy := make([]float64, len(triDi))
copy(triDiCopy, triDi)
for _, lambda := range z[1:n] {
copy(triDi, triDiCopy)
for i := 0; i < n; i++ {
triDi[i*n+i] -= lambda
}
// Compute LU
//ipiv := make([]int, n)
//impl.Dgetrf(n, n, triDi, n, ipiv)
ok := impl.Dpotrf(blas.Upper, n, triDi, n)
fmt.Println(ok)
var det float64
for i := 0; i < n; i++ {
det += math.Log(math.Abs(triDi[i*n+i]))
}
fmt.Println("det = ", math.Exp(det))
}
*/
}
}
}

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3121
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33
testlapack/fortran.go Normal file
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@@ -0,0 +1,33 @@
// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package testlapack
import (
"fmt"
"strings"
)
// This file implements types for helping to convert to Fortran testing capabilities.
// fortran64 is a float64 type that prints as a double precision constant in
// Fortran format.
type fortran64 float64
func (f fortran64) String() string {
// Replace exponent with D
s := fmt.Sprintf("%0.16E", f)
s = strings.Replace(s, "E", "D", 1)
return s
}
// printFortranArray prints a Go slice as an array that can be copied into a
// fortran script.
func printFortranArray(z []float64, name string) {
fmt.Printf("%s(1:%d) = (/%v, &\n", name, len(z), fortran64(z[0]))
for i := 1; i < len(z)-1; i++ {
fmt.Printf("%v, &\n", fortran64(z[i]))
}
fmt.Printf("%s/)\n", fortran64(z[len(z)-1]))
}

227
testlapack/general.go
View File

@@ -6,6 +6,8 @@ package testlapack
import (
"fmt"
"math"
"testing"
"github.com/gonum/blas"
"github.com/gonum/blas/blas64"
@@ -26,6 +28,15 @@ func min(a, b int) int {
return b
}
// nanSlice allocates a new slice of length n filled with NaN.
func nanSlice(n int) []float64 {
s := make([]float64, n)
for i := range s {
s[i] = math.NaN()
}
return s
}
// extractVMat collects the single reflectors from a into a matrix.
func extractVMat(m, n int, a []float64, lda int, direct lapack.Direct, store lapack.StoreV) blas64.General {
k := min(m, n)
@@ -299,6 +310,222 @@ func constructQK(kind string, m, n, k int, a []float64, lda int, tau []float64)
return q
}
// checkBidiagonal checks the bidiagonal decomposition from dlabrd and dgebd2.
// The input to this function is the answer returned from the routines, stored
// in a, d, e, tauP, and tauQ. The data of original A matrix (before
// decomposition) is input in aCopy.
//
// checkBidiagonal constructs the V and U matrices, and from them constructs Q
// and P. Using these constructions, it checks that Q^T * A * P and checks that
// the result is bidiagonal.
func checkBidiagonal(t *testing.T, m, n, nb int, a []float64, lda int, d, e, tauP, tauQ, aCopy []float64) {
// Check the answer.
// Construct V.and U
ldv := nb
v := blas64.General{
Rows: m,
Cols: nb,
Stride: ldv,
Data: make([]float64, m*ldv),
}
if m >= n {
for i := 0; i < m; i++ {
for j := 0; j <= min(nb-1, i); j++ {
if i == j {
v.Data[i*ldv+j] = 1
continue
}
v.Data[i*ldv+j] = a[i*lda+j]
}
}
} else {
for i := 1; i < m; i++ {
for j := 0; j <= min(nb-1, i-1); j++ {
if i-1 == j {
v.Data[i*ldv+j] = 1
continue
}
v.Data[i*ldv+j] = a[i*lda+j]
}
}
}
ldu := n
u := blas64.General{
Rows: nb,
Cols: n,
Stride: ldu,
Data: make([]float64, nb*ldu),
}
if m < n {
for i := 0; i < nb; i++ {
for j := i; j < n; j++ {
if i == j {
u.Data[i*ldu+j] = 1
continue
}
u.Data[i*ldu+j] = a[i*lda+j]
}
}
} else {
for i := 0; i < nb; i++ {
for j := i + 1; j < n; j++ {
if j-1 == i {
u.Data[i*ldu+j] = 1
continue
}
u.Data[i*ldu+j] = a[i*lda+j]
}
}
}
// Check the reconstruction Q^T * A * P
qMat := blas64.General{
Rows: m,
Cols: m,
Stride: m,
Data: make([]float64, m*m),
}
hMat := blas64.General{
Rows: m,
Cols: m,
Stride: m,
Data: make([]float64, m*m),
}
pMat := blas64.General{
Rows: n,
Cols: n,
Stride: n,
Data: make([]float64, n*n),
}
gMat := blas64.General{
Rows: n,
Cols: n,
Stride: n,
Data: make([]float64, n*n),
}
// set Q and P to I
for i := 0; i < m; i++ {
qMat.Data[i*qMat.Stride+i] = 1
}
for i := 0; i < n; i++ {
pMat.Data[i*pMat.Stride+i] = 1
}
for i := 0; i < nb; i++ {
qCopy := blas64.General{Rows: qMat.Rows, Cols: qMat.Cols, Stride: qMat.Stride, Data: make([]float64, len(qMat.Data))}
copy(qCopy.Data, qMat.Data)
pCopy := blas64.General{Rows: pMat.Rows, Cols: pMat.Cols, Stride: pMat.Stride, Data: make([]float64, len(pMat.Data))}
copy(pCopy.Data, pMat.Data)
// Set g and h to I
for i := 0; i < m; i++ {
for j := 0; j < m; j++ {
if i == j {
hMat.Data[i*m+j] = 1
} else {
hMat.Data[i*m+j] = 0
}
}
}
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
if i == j {
gMat.Data[i*n+j] = 1
} else {
gMat.Data[i*n+j] = 0
}
}
}
// H -= tauQ[i] * v[i] * v[i]^t
vi := blas64.Vector{
Inc: v.Stride,
Data: v.Data[i:],
}
blas64.Ger(-tauQ[i], vi, vi, hMat)
// G -= tauP[i] * u[i] * u[i]^T
ui := blas64.Vector{
Inc: 1,
Data: u.Data[i*u.Stride:],
}
blas64.Ger(-tauP[i], ui, ui, gMat)
// Q = Q * G[1]
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, qCopy, hMat, 0, qMat)
// P = P * G[i]
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, pCopy, gMat, 0, pMat)
}
// Compute Q^T * A * P
aMat := blas64.General{
Rows: m,
Cols: n,
Stride: lda,
Data: make([]float64, len(aCopy)),
}
copy(aMat.Data, aCopy)
tmp1 := blas64.General{
Rows: m,
Cols: n,
Stride: n,
Data: make([]float64, m*n),
}
blas64.Gemm(blas.Trans, blas.NoTrans, 1, qMat, aMat, 0, tmp1)
tmp2 := blas64.General{
Rows: m,
Cols: n,
Stride: n,
Data: make([]float64, m*n),
}
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmp1, pMat, 0, tmp2)
// Check that the first nb rows and cols of tm2 are upper bidiagonal
// if m >= n, and lower bidiagonal otherwise.
correctDiag := true
matchD := true
matchE := true
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
if i >= nb && j >= nb {
continue
}
v := tmp2.Data[i*tmp2.Stride+j]
if i == j {
if math.Abs(d[i]-v) > 1e-12 {
matchD = false
}
continue
}
if m >= n && i == j-1 {
if math.Abs(e[j-1]-v) > 1e-12 {
matchE = false
}
continue
}
if m < n && i-1 == j {
if math.Abs(e[i-1]-v) > 1e-12 {
matchE = false
}
continue
}
if math.Abs(v) > 1e-12 {
correctDiag = false
}
}
}
if !correctDiag {
t.Errorf("Updated A not bi-diagonal")
}
if !matchD {
fmt.Println("d = ", d)
t.Errorf("D Mismatch")
}
if !matchE {
t.Errorf("E mismatch")
}
}
// printRowise prints the matrix with one row per line. This is useful for debugging.
// If beyond is true, it prints beyond the final column to lda. If false, only
// the columns are printed.