diff --git a/internal/testdata/dlaqr5test/dgemm.f b/internal/testdata/dlaqr5test/dgemm.f deleted file mode 100644 index 4bae243a..00000000 --- a/internal/testdata/dlaqr5test/dgemm.f +++ /dev/null @@ -1,384 +0,0 @@ -*> \brief \b DGEMM -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION ALPHA,BETA -* INTEGER K,LDA,LDB,LDC,M,N -* CHARACTER TRANSA,TRANSB -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGEMM performs one of the matrix-matrix operations -*> -*> C := alpha*op( A )*op( B ) + beta*C, -*> -*> where op( X ) is one of -*> -*> op( X ) = X or op( X ) = X**T, -*> -*> alpha and beta are scalars, and A, B and C are matrices, with op( A ) -*> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] TRANSA -*> \verbatim -*> TRANSA is CHARACTER*1 -*> On entry, TRANSA specifies the form of op( A ) to be used in -*> the matrix multiplication as follows: -*> -*> TRANSA = 'N' or 'n', op( A ) = A. -*> -*> TRANSA = 'T' or 't', op( A ) = A**T. -*> -*> TRANSA = 'C' or 'c', op( A ) = A**T. -*> \endverbatim -*> -*> \param[in] TRANSB -*> \verbatim -*> TRANSB is CHARACTER*1 -*> On entry, TRANSB specifies the form of op( B ) to be used in -*> the matrix multiplication as follows: -*> -*> TRANSB = 'N' or 'n', op( B ) = B. -*> -*> TRANSB = 'T' or 't', op( B ) = B**T. -*> -*> TRANSB = 'C' or 'c', op( B ) = B**T. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> On entry, M specifies the number of rows of the matrix -*> op( A ) and of the matrix C. M must be at least zero. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the number of columns of the matrix -*> op( B ) and the number of columns of the matrix C. N must be -*> at least zero. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> On entry, K specifies the number of columns of the matrix -*> op( A ) and the number of rows of the matrix op( B ). K must -*> be at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION. -*> On entry, ALPHA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is -*> k when TRANSA = 'N' or 'n', and is m otherwise. -*> Before entry with TRANSA = 'N' or 'n', the leading m by k -*> part of the array A must contain the matrix A, otherwise -*> the leading k by m part of the array A must contain the -*> matrix A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. When TRANSA = 'N' or 'n' then -*> LDA must be at least max( 1, m ), otherwise LDA must be at -*> least max( 1, k ). -*> \endverbatim -*> -*> \param[in] B -*> \verbatim -*> B is DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is -*> n when TRANSB = 'N' or 'n', and is k otherwise. -*> Before entry with TRANSB = 'N' or 'n', the leading k by n -*> part of the array B must contain the matrix B, otherwise -*> the leading n by k part of the array B must contain the -*> matrix B. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> On entry, LDB specifies the first dimension of B as declared -*> in the calling (sub) program. When TRANSB = 'N' or 'n' then -*> LDB must be at least max( 1, k ), otherwise LDB must be at -*> least max( 1, n ). -*> \endverbatim -*> -*> \param[in] BETA -*> \verbatim -*> BETA is DOUBLE PRECISION. -*> On entry, BETA specifies the scalar beta. When BETA is -*> supplied as zero then C need not be set on input. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array of DIMENSION ( LDC, n ). -*> Before entry, the leading m by n part of the array C must -*> contain the matrix C, except when beta is zero, in which -*> case C need not be set on entry. -*> On exit, the array C is overwritten by the m by n matrix -*> ( alpha*op( A )*op( B ) + beta*C ). -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> On entry, LDC specifies the first dimension of C as declared -*> in the calling (sub) program. LDC must be at least -*> max( 1, m ). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \date November 2015 -* -*> \ingroup double_blas_level3 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 3 Blas routine. -*> -*> -- Written on 8-February-1989. -*> Jack Dongarra, Argonne National Laboratory. -*> Iain Duff, AERE Harwell. -*> Jeremy Du Croz, Numerical Algorithms Group Ltd. -*> Sven Hammarling, Numerical Algorithms Group Ltd. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* -* -- Reference BLAS level3 routine (version 3.6.0) -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2015 -* -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER K,LDA,LDB,LDC,M,N - CHARACTER TRANSA,TRANSB -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) -* .. -* -* ===================================================================== -* -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Local Scalars .. - DOUBLE PRECISION TEMP - INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB - LOGICAL NOTA,NOTB -* .. -* .. Parameters .. - DOUBLE PRECISION ONE,ZERO - PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) -* .. -* -* Set NOTA and NOTB as true if A and B respectively are not -* transposed and set NROWA, NCOLA and NROWB as the number of rows -* and columns of A and the number of rows of B respectively. -* - NOTA = LSAME(TRANSA,'N') - NOTB = LSAME(TRANSB,'N') - IF (NOTA) THEN - NROWA = M - NCOLA = K - ELSE - NROWA = K - NCOLA = M - END IF - IF (NOTB) THEN - NROWB = K - ELSE - NROWB = N - END IF -* -* Test the input parameters. -* - INFO = 0 - IF ((.NOT.NOTA) .AND. (.NOT.LSAME(TRANSA,'C')) .AND. - + (.NOT.LSAME(TRANSA,'T'))) THEN - INFO = 1 - ELSE IF ((.NOT.NOTB) .AND. (.NOT.LSAME(TRANSB,'C')) .AND. - + (.NOT.LSAME(TRANSB,'T'))) THEN - INFO = 2 - ELSE IF (M.LT.0) THEN - INFO = 3 - ELSE IF (N.LT.0) THEN - INFO = 4 - ELSE IF (K.LT.0) THEN - INFO = 5 - ELSE IF (LDA.LT.MAX(1,NROWA)) THEN - INFO = 8 - ELSE IF (LDB.LT.MAX(1,NROWB)) THEN - INFO = 10 - ELSE IF (LDC.LT.MAX(1,M)) THEN - INFO = 13 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('DGEMM ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF ((M.EQ.0) .OR. (N.EQ.0) .OR. - + (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN -* -* And if alpha.eq.zero. -* - IF (ALPHA.EQ.ZERO) THEN - IF (BETA.EQ.ZERO) THEN - DO 20 J = 1,N - DO 10 I = 1,M - C(I,J) = ZERO - 10 CONTINUE - 20 CONTINUE - ELSE - DO 40 J = 1,N - DO 30 I = 1,M - C(I,J) = BETA*C(I,J) - 30 CONTINUE - 40 CONTINUE - END IF - RETURN - END IF -* -* Start the operations. -* - IF (NOTB) THEN - IF (NOTA) THEN -* -* Form C := alpha*A*B + beta*C. -* - DO 90 J = 1,N - IF (BETA.EQ.ZERO) THEN - DO 50 I = 1,M - C(I,J) = ZERO - 50 CONTINUE - ELSE IF (BETA.NE.ONE) THEN - DO 60 I = 1,M - C(I,J) = BETA*C(I,J) - 60 CONTINUE - END IF - DO 80 L = 1,K - TEMP = ALPHA*B(L,J) - DO 70 I = 1,M - C(I,J) = C(I,J) + TEMP*A(I,L) - 70 CONTINUE - 80 CONTINUE - 90 CONTINUE - ELSE -* -* Form C := alpha*A**T*B + beta*C -* - DO 120 J = 1,N - DO 110 I = 1,M - TEMP = ZERO - DO 100 L = 1,K - TEMP = TEMP + A(L,I)*B(L,J) - 100 CONTINUE - IF (BETA.EQ.ZERO) THEN - C(I,J) = ALPHA*TEMP - ELSE - C(I,J) = ALPHA*TEMP + BETA*C(I,J) - END IF - 110 CONTINUE - 120 CONTINUE - END IF - ELSE - IF (NOTA) THEN -* -* Form C := alpha*A*B**T + beta*C -* - DO 170 J = 1,N - IF (BETA.EQ.ZERO) THEN - DO 130 I = 1,M - C(I,J) = ZERO - 130 CONTINUE - ELSE IF (BETA.NE.ONE) THEN - DO 140 I = 1,M - C(I,J) = BETA*C(I,J) - 140 CONTINUE - END IF - DO 160 L = 1,K - TEMP = ALPHA*B(J,L) - DO 150 I = 1,M - C(I,J) = C(I,J) + TEMP*A(I,L) - 150 CONTINUE - 160 CONTINUE - 170 CONTINUE - ELSE -* -* Form C := alpha*A**T*B**T + beta*C -* - DO 200 J = 1,N - DO 190 I = 1,M - TEMP = ZERO - DO 180 L = 1,K - TEMP = TEMP + A(L,I)*B(J,L) - 180 CONTINUE - IF (BETA.EQ.ZERO) THEN - C(I,J) = ALPHA*TEMP - ELSE - C(I,J) = ALPHA*TEMP + BETA*C(I,J) - END IF - 190 CONTINUE - 200 CONTINUE - END IF - END IF -* - RETURN -* -* End of DGEMM . -* - END diff --git a/internal/testdata/dlaqr5test/dlacpy.f b/internal/testdata/dlaqr5test/dlacpy.f deleted file mode 100644 index a9a23c94..00000000 --- a/internal/testdata/dlaqr5test/dlacpy.f +++ /dev/null @@ -1,156 +0,0 @@ -*> \brief \b DLACPY copies all or part of one two-dimensional array to another. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLACPY + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLACPY( UPLO, M, N, A, LDA, B, LDB ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER LDA, LDB, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLACPY copies all or part of a two-dimensional matrix A to another -*> matrix B. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> Specifies the part of the matrix A to be copied to B. -*> = 'U': Upper triangular part -*> = 'L': Lower triangular part -*> Otherwise: All of the matrix A -*> \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] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> The m by n matrix A. If UPLO = 'U', only the upper triangle -*> or trapezoid is accessed; if UPLO = 'L', only the lower -*> triangle or trapezoid is accessed. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[out] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension (LDB,N) -*> On exit, B = A in the locations specified by UPLO. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of the array B. LDB >= max(1,M). -*> \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 DLACPY( UPLO, M, N, A, LDA, B, LDB ) -* -* -- 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 UPLO - INTEGER LDA, LDB, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), B( LDB, * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I, J -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. Intrinsic Functions .. - INTRINSIC MIN -* .. -* .. Executable Statements .. -* - IF( LSAME( UPLO, 'U' ) ) THEN - DO 20 J = 1, N - DO 10 I = 1, MIN( J, M ) - B( I, J ) = A( I, J ) - 10 CONTINUE - 20 CONTINUE - ELSE IF( LSAME( UPLO, 'L' ) ) THEN - DO 40 J = 1, N - DO 30 I = J, M - B( I, J ) = A( I, J ) - 30 CONTINUE - 40 CONTINUE - ELSE - DO 60 J = 1, N - DO 50 I = 1, M - B( I, J ) = A( I, J ) - 50 CONTINUE - 60 CONTINUE - END IF - RETURN -* -* End of DLACPY -* - END diff --git a/internal/testdata/dlaqr5test/dlamch.f b/internal/testdata/dlaqr5test/dlamch.f deleted file mode 100644 index 22a16218..00000000 --- a/internal/testdata/dlaqr5test/dlamch.f +++ /dev/null @@ -1,189 +0,0 @@ -*> \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 2015 -* -*> \ingroup auxOTHERauxiliary -* -* ===================================================================== - DOUBLE PRECISION FUNCTION DLAMCH( CMACH ) -* -* -- LAPACK auxiliary routine (version 3.6.0) -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2015 -* -* .. Scalar Arguments .. - CHARACTER CMACH -* .. -* -* ===================================================================== -* -* .. 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 2015 -*> \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 3.6.0) -- -* 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 -* -************************************************************************ diff --git a/internal/testdata/dlaqr5test/dlapy2.f b/internal/testdata/dlaqr5test/dlapy2.f deleted file mode 100644 index d43b0d5d..00000000 --- a/internal/testdata/dlaqr5test/dlapy2.f +++ /dev/null @@ -1,104 +0,0 @@ -*> \brief \b DLAPY2 returns sqrt(x2+y2). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAPY2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* DOUBLE PRECISION FUNCTION DLAPY2( X, Y ) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION X, Y -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary -*> overflow. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] X -*> \verbatim -*> X is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in] Y -*> \verbatim -*> Y is DOUBLE PRECISION -*> X and Y specify the values x and y. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \date September 2012 -* -*> \ingroup auxOTHERauxiliary -* -* ===================================================================== - DOUBLE PRECISION FUNCTION DLAPY2( X, Y ) -* -* -- 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 X, Y -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D0 ) - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D0 ) -* .. -* .. Local Scalars .. - DOUBLE PRECISION W, XABS, YABS, Z -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN, SQRT -* .. -* .. Executable Statements .. -* - XABS = ABS( X ) - YABS = ABS( Y ) - W = MAX( XABS, YABS ) - Z = MIN( XABS, YABS ) - IF( Z.EQ.ZERO ) THEN - DLAPY2 = W - ELSE - DLAPY2 = W*SQRT( ONE+( Z / W )**2 ) - END IF - RETURN -* -* End of DLAPY2 -* - END diff --git a/internal/testdata/dlaqr5test/dlaqr5data.zip b/internal/testdata/dlaqr5test/dlaqr5data.zip deleted file mode 100644 index 215bfb61..00000000 Binary files a/internal/testdata/dlaqr5test/dlaqr5data.zip and /dev/null differ diff --git a/internal/testdata/dlaqr5test/dlarfg.f b/internal/testdata/dlaqr5test/dlarfg.f deleted file mode 100644 index ce91d33c..00000000 --- a/internal/testdata/dlaqr5test/dlarfg.f +++ /dev/null @@ -1,196 +0,0 @@ -*> \brief \b DLARFG generates an elementary reflector (Householder matrix). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLARFG + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU ) -* -* .. Scalar Arguments .. -* INTEGER INCX, N -* DOUBLE PRECISION ALPHA, TAU -* .. -* .. Array Arguments .. -* DOUBLE PRECISION X( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLARFG generates a real elementary reflector H of order n, such -*> that -*> -*> H * ( alpha ) = ( beta ), H**T * H = I. -*> ( x ) ( 0 ) -*> -*> where alpha and beta are scalars, and x is an (n-1)-element real -*> vector. H is represented in the form -*> -*> H = I - tau * ( 1 ) * ( 1 v**T ) , -*> ( v ) -*> -*> where tau is a real scalar and v is a real (n-1)-element -*> vector. -*> -*> If the elements of x are all zero, then tau = 0 and H is taken to be -*> the unit matrix. -*> -*> Otherwise 1 <= tau <= 2. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the elementary reflector. -*> \endverbatim -*> -*> \param[in,out] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION -*> On entry, the value alpha. -*> On exit, it is overwritten with the value beta. -*> \endverbatim -*> -*> \param[in,out] X -*> \verbatim -*> X is DOUBLE PRECISION array, dimension -*> (1+(N-2)*abs(INCX)) -*> On entry, the vector x. -*> On exit, it is overwritten with the vector v. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> The increment between elements of X. INCX > 0. -*> \endverbatim -*> -*> \param[out] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION -*> The value tau. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \date September 2012 -* -*> \ingroup doubleOTHERauxiliary -* -* ===================================================================== - SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU ) -* -* -- 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 .. - INTEGER INCX, N - DOUBLE PRECISION ALPHA, TAU -* .. -* .. Array Arguments .. - DOUBLE PRECISION X( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER J, KNT - DOUBLE PRECISION BETA, RSAFMN, SAFMIN, XNORM -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH, DLAPY2, DNRM2 - EXTERNAL DLAMCH, DLAPY2, DNRM2 -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, SIGN -* .. -* .. External Subroutines .. - EXTERNAL DSCAL -* .. -* .. Executable Statements .. -* - IF( N.LE.1 ) THEN - TAU = ZERO - RETURN - END IF -* - XNORM = DNRM2( N-1, X, INCX ) -* - IF( XNORM.EQ.ZERO ) THEN -* -* H = I -* - TAU = ZERO - ELSE -* -* general case -* - BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA ) - SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' ) - KNT = 0 - IF( ABS( BETA ).LT.SAFMIN ) THEN -* -* XNORM, BETA may be inaccurate; scale X and recompute them -* - RSAFMN = ONE / SAFMIN - 10 CONTINUE - KNT = KNT + 1 - CALL DSCAL( N-1, RSAFMN, X, INCX ) - BETA = BETA*RSAFMN - ALPHA = ALPHA*RSAFMN - IF( ABS( BETA ).LT.SAFMIN ) - $ GO TO 10 -* -* New BETA is at most 1, at least SAFMIN -* - XNORM = DNRM2( N-1, X, INCX ) - BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA ) - END IF - TAU = ( BETA-ALPHA ) / BETA - CALL DSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX ) -* -* If ALPHA is subnormal, it may lose relative accuracy -* - DO 20 J = 1, KNT - BETA = BETA*SAFMIN - 20 CONTINUE - ALPHA = BETA - END IF -* - RETURN -* -* End of DLARFG -* - END diff --git a/internal/testdata/dlaqr5test/dnrm2.f b/internal/testdata/dlaqr5test/dnrm2.f deleted file mode 100644 index 5ea257a2..00000000 --- a/internal/testdata/dlaqr5test/dnrm2.f +++ /dev/null @@ -1,112 +0,0 @@ -*> \brief \b DNRM2 -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX) -* -* .. Scalar Arguments .. -* INTEGER INCX,N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION X(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DNRM2 returns the euclidean norm of a vector via the function -*> name, so that -*> -*> DNRM2 := sqrt( x'*x ) -*> \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 -*> -*> -- This version written on 25-October-1982. -*> Modified on 14-October-1993 to inline the call to DLASSQ. -*> Sven Hammarling, Nag Ltd. -*> \endverbatim -*> -* ===================================================================== - DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX) -* -* -- 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,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION X(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE,ZERO - PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) -* .. -* .. Local Scalars .. - DOUBLE PRECISION ABSXI,NORM,SCALE,SSQ - INTEGER IX -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS,SQRT -* .. - IF (N.LT.1 .OR. INCX.LT.1) THEN - NORM = ZERO - ELSE IF (N.EQ.1) THEN - NORM = ABS(X(1)) - ELSE - SCALE = ZERO - SSQ = ONE -* The following loop is equivalent to this call to the LAPACK -* auxiliary routine: -* CALL DLASSQ( N, X, INCX, SCALE, SSQ ) -* - DO 10 IX = 1,1 + (N-1)*INCX,INCX - IF (X(IX).NE.ZERO) THEN - ABSXI = ABS(X(IX)) - IF (SCALE.LT.ABSXI) THEN - SSQ = ONE + SSQ* (SCALE/ABSXI)**2 - SCALE = ABSXI - ELSE - SSQ = SSQ + (ABSXI/SCALE)**2 - END IF - END IF - 10 CONTINUE - NORM = SCALE*SQRT(SSQ) - END IF -* - DNRM2 = NORM - RETURN -* -* End of DNRM2. -* - END diff --git a/internal/testdata/dlaqr5test/dscal.f b/internal/testdata/dlaqr5test/dscal.f deleted file mode 100644 index 3337de8e..00000000 --- a/internal/testdata/dlaqr5test/dscal.f +++ /dev/null @@ -1,110 +0,0 @@ -*> \brief \b DSCAL -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DSCAL(N,DA,DX,INCX) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION DA -* INTEGER INCX,N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION DX(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSCAL scales a vector by a constant. -*> uses unrolled loops for increment 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 3/93 to return if incx .le. 0. -*> modified 12/3/93, array(1) declarations changed to array(*) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DSCAL(N,DA,DX,INCX) -* -* -- 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 .. - DOUBLE PRECISION DA - INTEGER INCX,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I,M,MP1,NINCX -* .. -* .. Intrinsic Functions .. - INTRINSIC MOD -* .. - IF (N.LE.0 .OR. INCX.LE.0) RETURN - IF (INCX.EQ.1) THEN -* -* code for increment equal to 1 -* -* -* clean-up loop -* - M = MOD(N,5) - IF (M.NE.0) THEN - DO I = 1,M - DX(I) = DA*DX(I) - END DO - IF (N.LT.5) RETURN - END IF - MP1 = M + 1 - DO I = MP1,N,5 - DX(I) = DA*DX(I) - DX(I+1) = DA*DX(I+1) - DX(I+2) = DA*DX(I+2) - DX(I+3) = DA*DX(I+3) - DX(I+4) = DA*DX(I+4) - END DO - ELSE -* -* code for increment not equal to 1 -* - NINCX = N*INCX - DO I = 1,NINCX,INCX - DX(I) = DA*DX(I) - END DO - END IF - RETURN - END diff --git a/internal/testdata/dlaqr5test/dtrmm.f b/internal/testdata/dlaqr5test/dtrmm.f deleted file mode 100644 index cbd5ce70..00000000 --- a/internal/testdata/dlaqr5test/dtrmm.f +++ /dev/null @@ -1,415 +0,0 @@ -*> \brief \b DTRMM -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION ALPHA -* INTEGER LDA,LDB,M,N -* CHARACTER DIAG,SIDE,TRANSA,UPLO -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A(LDA,*),B(LDB,*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DTRMM performs one of the matrix-matrix operations -*> -*> B := alpha*op( A )*B, or B := alpha*B*op( A ), -*> -*> where alpha is a scalar, B is an m by n matrix, A is a unit, or -*> non-unit, upper or lower triangular matrix and op( A ) is one of -*> -*> op( A ) = A or op( A ) = A**T. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> On entry, SIDE specifies whether op( A ) multiplies B from -*> the left or right as follows: -*> -*> SIDE = 'L' or 'l' B := alpha*op( A )*B. -*> -*> SIDE = 'R' or 'r' B := alpha*B*op( A ). -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the matrix A is an upper or -*> lower triangular matrix as follows: -*> -*> UPLO = 'U' or 'u' A is an upper triangular matrix. -*> -*> UPLO = 'L' or 'l' A is a lower triangular matrix. -*> \endverbatim -*> -*> \param[in] TRANSA -*> \verbatim -*> TRANSA is CHARACTER*1 -*> On entry, TRANSA specifies the form of op( A ) to be used in -*> the matrix multiplication as follows: -*> -*> TRANSA = 'N' or 'n' op( A ) = A. -*> -*> TRANSA = 'T' or 't' op( A ) = A**T. -*> -*> TRANSA = 'C' or 'c' op( A ) = A**T. -*> \endverbatim -*> -*> \param[in] DIAG -*> \verbatim -*> DIAG is CHARACTER*1 -*> On entry, DIAG specifies whether or not A is unit triangular -*> as follows: -*> -*> DIAG = 'U' or 'u' A is assumed to be unit triangular. -*> -*> DIAG = 'N' or 'n' A is not assumed to be unit -*> triangular. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> On entry, M specifies the number of rows of B. M must be at -*> least zero. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the number of columns of B. N must be -*> at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION. -*> On entry, ALPHA specifies the scalar alpha. When alpha is -*> zero then A is not referenced and B need not be set before -*> entry. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m -*> when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. -*> Before entry with UPLO = 'U' or 'u', the leading k by k -*> upper triangular part of the array A must contain the upper -*> triangular matrix and the strictly lower triangular part of -*> A is not referenced. -*> Before entry with UPLO = 'L' or 'l', the leading k by k -*> lower triangular part of the array A must contain the lower -*> triangular matrix and the strictly upper triangular part of -*> A is not referenced. -*> Note that when DIAG = 'U' or 'u', the diagonal elements of -*> A are not referenced either, but are assumed to be unity. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. When SIDE = 'L' or 'l' then -*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' -*> then LDA must be at least max( 1, n ). -*> \endverbatim -*> -*> \param[in,out] B -*> \verbatim -*> B is DOUBLE PRECISION array of DIMENSION ( LDB, n ). -*> Before entry, the leading m by n part of the array B must -*> contain the matrix B, and on exit is overwritten by the -*> transformed matrix. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> On entry, LDB specifies the first dimension of B as declared -*> in the calling (sub) program. LDB must be at least -*> max( 1, m ). -*> \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_level3 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 3 Blas routine. -*> -*> -- Written on 8-February-1989. -*> Jack Dongarra, Argonne National Laboratory. -*> Iain Duff, AERE Harwell. -*> Jeremy Du Croz, Numerical Algorithms Group Ltd. -*> Sven Hammarling, Numerical Algorithms Group Ltd. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) -* -* -- Reference BLAS level3 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 .. - DOUBLE PRECISION ALPHA - INTEGER LDA,LDB,M,N - CHARACTER DIAG,SIDE,TRANSA,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),B(LDB,*) -* .. -* -* ===================================================================== -* -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Local Scalars .. - DOUBLE PRECISION TEMP - INTEGER I,INFO,J,K,NROWA - LOGICAL LSIDE,NOUNIT,UPPER -* .. -* .. Parameters .. - DOUBLE PRECISION ONE,ZERO - PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) -* .. -* -* Test the input parameters. -* - LSIDE = LSAME(SIDE,'L') - IF (LSIDE) THEN - NROWA = M - ELSE - NROWA = N - END IF - NOUNIT = LSAME(DIAG,'N') - UPPER = LSAME(UPLO,'U') -* - INFO = 0 - IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN - INFO = 1 - ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN - INFO = 2 - ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND. - + (.NOT.LSAME(TRANSA,'T')) .AND. - + (.NOT.LSAME(TRANSA,'C'))) THEN - INFO = 3 - ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN - INFO = 4 - ELSE IF (M.LT.0) THEN - INFO = 5 - ELSE IF (N.LT.0) THEN - INFO = 6 - ELSE IF (LDA.LT.MAX(1,NROWA)) THEN - INFO = 9 - ELSE IF (LDB.LT.MAX(1,M)) THEN - INFO = 11 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('DTRMM ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF (M.EQ.0 .OR. N.EQ.0) RETURN -* -* And when alpha.eq.zero. -* - IF (ALPHA.EQ.ZERO) THEN - DO 20 J = 1,N - DO 10 I = 1,M - B(I,J) = ZERO - 10 CONTINUE - 20 CONTINUE - RETURN - END IF -* -* Start the operations. -* - IF (LSIDE) THEN - IF (LSAME(TRANSA,'N')) THEN -* -* Form B := alpha*A*B. -* - IF (UPPER) THEN - DO 50 J = 1,N - DO 40 K = 1,M - IF (B(K,J).NE.ZERO) THEN - TEMP = ALPHA*B(K,J) - DO 30 I = 1,K - 1 - B(I,J) = B(I,J) + TEMP*A(I,K) - 30 CONTINUE - IF (NOUNIT) TEMP = TEMP*A(K,K) - B(K,J) = TEMP - END IF - 40 CONTINUE - 50 CONTINUE - ELSE - DO 80 J = 1,N - DO 70 K = M,1,-1 - IF (B(K,J).NE.ZERO) THEN - TEMP = ALPHA*B(K,J) - B(K,J) = TEMP - IF (NOUNIT) B(K,J) = B(K,J)*A(K,K) - DO 60 I = K + 1,M - B(I,J) = B(I,J) + TEMP*A(I,K) - 60 CONTINUE - END IF - 70 CONTINUE - 80 CONTINUE - END IF - ELSE -* -* Form B := alpha*A**T*B. -* - IF (UPPER) THEN - DO 110 J = 1,N - DO 100 I = M,1,-1 - TEMP = B(I,J) - IF (NOUNIT) TEMP = TEMP*A(I,I) - DO 90 K = 1,I - 1 - TEMP = TEMP + A(K,I)*B(K,J) - 90 CONTINUE - B(I,J) = ALPHA*TEMP - 100 CONTINUE - 110 CONTINUE - ELSE - DO 140 J = 1,N - DO 130 I = 1,M - TEMP = B(I,J) - IF (NOUNIT) TEMP = TEMP*A(I,I) - DO 120 K = I + 1,M - TEMP = TEMP + A(K,I)*B(K,J) - 120 CONTINUE - B(I,J) = ALPHA*TEMP - 130 CONTINUE - 140 CONTINUE - END IF - END IF - ELSE - IF (LSAME(TRANSA,'N')) THEN -* -* Form B := alpha*B*A. -* - IF (UPPER) THEN - DO 180 J = N,1,-1 - TEMP = ALPHA - IF (NOUNIT) TEMP = TEMP*A(J,J) - DO 150 I = 1,M - B(I,J) = TEMP*B(I,J) - 150 CONTINUE - DO 170 K = 1,J - 1 - IF (A(K,J).NE.ZERO) THEN - TEMP = ALPHA*A(K,J) - DO 160 I = 1,M - B(I,J) = B(I,J) + TEMP*B(I,K) - 160 CONTINUE - END IF - 170 CONTINUE - 180 CONTINUE - ELSE - DO 220 J = 1,N - TEMP = ALPHA - IF (NOUNIT) TEMP = TEMP*A(J,J) - DO 190 I = 1,M - B(I,J) = TEMP*B(I,J) - 190 CONTINUE - DO 210 K = J + 1,N - IF (A(K,J).NE.ZERO) THEN - TEMP = ALPHA*A(K,J) - DO 200 I = 1,M - B(I,J) = B(I,J) + TEMP*B(I,K) - 200 CONTINUE - END IF - 210 CONTINUE - 220 CONTINUE - END IF - ELSE -* -* Form B := alpha*B*A**T. -* - IF (UPPER) THEN - DO 260 K = 1,N - DO 240 J = 1,K - 1 - IF (A(J,K).NE.ZERO) THEN - TEMP = ALPHA*A(J,K) - DO 230 I = 1,M - B(I,J) = B(I,J) + TEMP*B(I,K) - 230 CONTINUE - END IF - 240 CONTINUE - TEMP = ALPHA - IF (NOUNIT) TEMP = TEMP*A(K,K) - IF (TEMP.NE.ONE) THEN - DO 250 I = 1,M - B(I,K) = TEMP*B(I,K) - 250 CONTINUE - END IF - 260 CONTINUE - ELSE - DO 300 K = N,1,-1 - DO 280 J = K + 1,N - IF (A(J,K).NE.ZERO) THEN - TEMP = ALPHA*A(J,K) - DO 270 I = 1,M - B(I,J) = B(I,J) + TEMP*B(I,K) - 270 CONTINUE - END IF - 280 CONTINUE - TEMP = ALPHA - IF (NOUNIT) TEMP = TEMP*A(K,K) - IF (TEMP.NE.ONE) THEN - DO 290 I = 1,M - B(I,K) = TEMP*B(I,K) - 290 CONTINUE - END IF - 300 CONTINUE - END IF - END IF - END IF -* - RETURN -* -* End of DTRMM . -* - END diff --git a/internal/testdata/dlaqr5test/lsame.f b/internal/testdata/dlaqr5test/lsame.f deleted file mode 100644 index 315304c3..00000000 --- a/internal/testdata/dlaqr5test/lsame.f +++ /dev/null @@ -1,125 +0,0 @@ -*> \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 diff --git a/internal/testdata/dlaqr5test/main.go b/internal/testdata/dlaqr5test/main.go index a34dbbe2..1ef02faf 100644 --- a/internal/testdata/dlaqr5test/main.go +++ b/internal/testdata/dlaqr5test/main.go @@ -2,81 +2,49 @@ // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. -// This program generates test data for Dlaqr5. Test cases are stored as text -// files inside dlaqr5data.zip archive which is then read by testlapack/dlaqr5.go. +// This program generates test data for Dlaqr5. Test cases are stored in +// gzip-compressed JSON file testlapack/testdata/dlaqr5data.json.gz which is +// read during testing by testlapack/dlaqr5.go. // // This program uses cgo to call Fortran version of DLAQR5. Therefore, matrices -// generated by hessrand and eye are in column-major format but are written into -// test case files in row-major format. See writeCase and writeCaseWant for -// details. +// passed to the Fortran routine are in column-major format but are written into +// the output file in row-major format. package main -// void dlaqr5_(int* wantt, int* wantz, int* kacc22, int* n, int* ktop, int* kbot, int* nshfts, -// double* sr, double* si, double* h, int* ldh, int* iloz, int* ihiz, -// double* z, int* ldz, double* v, int* ldv, double* u, int* ldu, -// int* nv, double* wv, int* ldwv, int* nh, double* wh, int* ldwh); -import "C" - import ( - "archive/zip" - "fmt" - "io" + "compress/gzip" + "encoding/json" "log" "math/rand" "os" + "path/filepath" + + "github.com/gonum/lapack/internal/testdata/netlib" ) -func fortranDlaqr5(wantt, wantz bool, kacc22 int, n, ktop, kbot int, nshfts int, sr, si []float64, h []float64, - ldh int, iloz, ihiz int, z []float64, ldz int, v []float64, ldv int, - u []float64, ldu int, nh int, wh []float64, ldwh int, nv int, wv []float64, ldwv int) { - func() { - wt := C.int(0) - if wantt { - wt = 1 - } - wz := C.int(0) - if wantz { - wz = 1 - } - kacc22 := C.int(kacc22) - n := C.int(n) - ktop := C.int(ktop + 1) - kbot := C.int(kbot + 1) - nshfts := C.int(nshfts) - ldh := C.int(ldh) - iloz := C.int(iloz + 1) - ihiz := C.int(ihiz + 1) - ldz := C.int(ldz) - ldv := C.int(ldv) - ldu := C.int(ldu) - nh := C.int(nh) - ldwh := C.int(ldwh) - nv := C.int(nv) - ldwv := C.int(ldwv) - C.dlaqr5_((*C.int)(&wt), (*C.int)(&wz), (*C.int)(&kacc22), - (*C.int)(&n), (*C.int)(&ktop), (*C.int)(&kbot), - (*C.int)(&nshfts), (*C.double)(&sr[0]), (*C.double)(&si[0]), - (*C.double)(&h[0]), (*C.int)(&ldh), - (*C.int)(&iloz), (*C.int)(&ihiz), (*C.double)(&z[0]), (*C.int)(&ldz), - (*C.double)(&v[0]), (*C.int)(&ldv), - (*C.double)(&u[0]), (*C.int)(&ldu), - (*C.int)(&nh), (*C.double)(&wh[0]), (*C.int)(&ldwh), - (*C.int)(&nv), (*C.double)(&wv[0]), (*C.int)(&ldwv)) - }() +type Dlaqr5Test struct { + WantT bool + N int + NShifts int + KTop, KBot int + ShiftR, ShiftI []float64 + H []float64 + + HWant []float64 + ZWant []float64 } func main() { - const tmpl = "wantt%v_n%v_nshfts%v_ktop%v_kbot%v.txt" - - file, err := os.Create("dlaqr5data.zip") + file, err := os.Create(filepath.FromSlash("../../../testlapack/testdata/dlaqr5data.json.gz")) if err != nil { log.Fatal(err) } defer file.Close() - zipfile := zip.NewWriter(file) + w := gzip.NewWriter(file) rnd := rand.New(rand.NewSource(1)) + var tests []Dlaqr5Test for _, wantt := range []bool{true, false} { for _, n := range []int{2, 3, 4, 5, 6, 7, 11} { for k := 0; k <= min(5, n); k++ { @@ -89,14 +57,13 @@ func main() { sr, si := shiftpairs(npairs, rnd) nshfts := len(sr) - v := make([]float64, nshfts/2*3) - u := make([]float64, (3*nshfts-3)*(3*nshfts-3)) + v := genrand(nshfts/2, 3, rnd) + u := genrand(3*nshfts-3, 3*nshfts-3, rnd) + wh := genrand(3*nshfts-3, n, rnd) nh := n - wh := make([]float64, (3*nshfts-3)*n) + wv := genrand(n, 3*nshfts-3, rnd) nv := n - wv := make([]float64, n*(3*nshfts-3)) - z := eye(n) h := hessrand(n, rnd) if ktop > 0 { h[ktop+(ktop-1)*n] = 0 @@ -104,34 +71,54 @@ func main() { if kbot < n-1 { h[kbot+1+kbot*n] = 0 } + hin := make([]float64, len(h)) + copy(hin, h) + z := eye(n) - w, err := zipfile.Create(fmt.Sprintf(tmpl, wantt, n, nshfts, ktop, kbot)) - if err != nil { - log.Fatal(err) - } - writeCase(w, wantt, n, nshfts, ktop, kbot, sr, si, h) - fortranDlaqr5(wantt, true, 2, - n, ktop, kbot, + netlib.Dlaqr5(wantt, true, 2, + n, ktop+1, kbot+1, nshfts, sr, si, h, n, - 0, n-1, z, n, + 1, n, z, n, v, 3, u, 3*nshfts-3, nh, wh, nh, nv, wv, 3*nshfts-3) - writeCaseWant(w, n, h, z) + + tests = append(tests, Dlaqr5Test{ + WantT: wantt, + N: n, + NShifts: nshfts, + KTop: ktop, + KBot: kbot, + ShiftR: sr, + ShiftI: si, + H: rowMajor(n, n, hin), + HWant: rowMajor(n, n, h), + ZWant: rowMajor(n, n, z), + }) } } } } } + json.NewEncoder(w).Encode(tests) - err = zipfile.Close() + err = w.Close() if err != nil { log.Fatal(err) } } +// genrand returns a general r×c matrix with random entries. +func genrand(r, c int, rnd *rand.Rand) []float64 { + m := make([]float64, r*c) + for i := range m { + m[i] = rnd.NormFloat64() + } + return m +} + // eye returns an identity matrix of order n. func eye(n int) []float64 { m := make([]float64, n*n) @@ -176,36 +163,18 @@ func shiftpairs(k int, rnd *rand.Rand) (sr, si []float64) { return sr, si } -// writeCase writes into w given data with one value per line. h is assumed in -// column-major order and is written in row-major. -func writeCase(w io.Writer, wantt bool, n, nshfts, ktop, kbot int, sr, si, h []float64) { - fmt.Fprintln(w, wantt, n, nshfts, ktop, kbot) - for _, v := range sr { - fmt.Fprintln(w, v) +// rowMajor returns the given r×c column-major matrix a in row-major format. +func rowMajor(r, c int, a []float64) []float64 { + if len(a) != r*c { + panic("testdata: slice length mismatch") } - for _, v := range si { - fmt.Fprintln(w, v) - } - for i := 0; i < n; i++ { - for j := 0; j < n; j++ { - fmt.Fprintln(w, h[i+j*n]) - } - } -} - -// writeCaseWant writes into w given data with one value per line. h and z are -// assumed in column-major order and are written in row-major. -func writeCaseWant(w io.Writer, n int, h, z []float64) { - for i := 0; i < n; i++ { - for j := 0; j < n; j++ { - fmt.Fprintln(w, h[i+j*n]) - } - } - for i := 0; i < n; i++ { - for j := 0; j < n; j++ { - fmt.Fprintln(w, z[i+j*n]) + m := make([]float64, len(a)) + for i := 0; i < r; i++ { + for j := 0; j < c; j++ { + m[i*c+j] = a[i+j*r] } } + return m } func min(a, b int) int { diff --git a/internal/testdata/dlaqr5test/run.bash b/internal/testdata/dlaqr5test/run.bash deleted file mode 100755 index 6cf6ed74..00000000 --- a/internal/testdata/dlaqr5test/run.bash +++ /dev/null @@ -1,5 +0,0 @@ -#!/usr/bin/env bash - -go build -./dlaqr5test -rm -f dlaqr5test diff --git a/internal/testdata/dlaqr5test/xerbla.f b/internal/testdata/dlaqr5test/xerbla.f deleted file mode 100644 index eb1c037d..00000000 --- a/internal/testdata/dlaqr5test/xerbla.f +++ /dev/null @@ -1,89 +0,0 @@ -*> \brief \b XERBLA -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* 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 aux_blas -* -* ===================================================================== - SUBROUTINE XERBLA( SRNAME, INFO ) -* -* -- 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 .. - 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 diff --git a/internal/testdata/dlaqr5test/dlabad.f b/internal/testdata/netlib/dlabad.f similarity index 100% rename from internal/testdata/dlaqr5test/dlabad.f rename to internal/testdata/netlib/dlabad.f diff --git a/internal/testdata/dlaqr5test/dlaqr1.f b/internal/testdata/netlib/dlaqr1.f similarity index 100% rename from internal/testdata/dlaqr5test/dlaqr1.f rename to internal/testdata/netlib/dlaqr1.f diff --git a/internal/testdata/dlaqr5test/dlaqr5.f b/internal/testdata/netlib/dlaqr5.f similarity index 100% rename from internal/testdata/dlaqr5test/dlaqr5.f rename to internal/testdata/netlib/dlaqr5.f diff --git a/internal/testdata/dlaqr5test/dlaset.f b/internal/testdata/netlib/dlaset.f similarity index 100% rename from internal/testdata/dlaqr5test/dlaset.f rename to internal/testdata/netlib/dlaset.f diff --git a/internal/testdata/netlib/netlib.go b/internal/testdata/netlib/netlib.go index 01173873..182e074a 100644 --- a/internal/testdata/netlib/netlib.go +++ b/internal/testdata/netlib/netlib.go @@ -5,6 +5,11 @@ package netlib // void dlahr2_(int* n, int* k, int* nb, double* a, int* lda, double* tau, double* t, int* ldt, double* y, int* ldy); +// +// void dlaqr5_(int* wantt, int* wantz, int* kacc22, int* n, int* ktop, int* kbot, int* nshfts, +// double* sr, double* si, double* h, int* ldh, int* iloz, int* ihiz, +// double* z, int* ldz, double* v, int* ldv, double* u, int* ldu, +// int* nv, double* wv, int* ldwv, int* nh, double* wh, int* ldwh); import "C" func Dlahr2(n, k, nb int, a []float64, lda int, tau, t []float64, ldt int, y []float64, ldy int) { @@ -22,3 +27,42 @@ func Dlahr2(n, k, nb int, a []float64, lda int, tau, t []float64, ldt int, y []f (*C.double)(&y[0]), (*C.int)(&ldy)) }() } + +func Dlaqr5(wantt, wantz bool, kacc22 int, n, ktop, kbot int, nshfts int, sr, si []float64, h []float64, + ldh int, iloz, ihiz int, z []float64, ldz int, v []float64, ldv int, + u []float64, ldu int, nh int, wh []float64, ldwh int, nv int, wv []float64, ldwv int) { + func() { + wt := C.int(0) + if wantt { + wt = 1 + } + wz := C.int(0) + if wantz { + wz = 1 + } + kacc22 := C.int(kacc22) + n := C.int(n) + ktop := C.int(ktop) + kbot := C.int(kbot) + nshfts := C.int(nshfts) + ldh := C.int(ldh) + iloz := C.int(iloz) + ihiz := C.int(ihiz) + ldz := C.int(ldz) + ldv := C.int(ldv) + ldu := C.int(ldu) + nh := C.int(nh) + ldwh := C.int(ldwh) + nv := C.int(nv) + ldwv := C.int(ldwv) + C.dlaqr5_((*C.int)(&wt), (*C.int)(&wz), (*C.int)(&kacc22), + (*C.int)(&n), (*C.int)(&ktop), (*C.int)(&kbot), + (*C.int)(&nshfts), (*C.double)(&sr[0]), (*C.double)(&si[0]), + (*C.double)(&h[0]), (*C.int)(&ldh), + (*C.int)(&iloz), (*C.int)(&ihiz), (*C.double)(&z[0]), (*C.int)(&ldz), + (*C.double)(&v[0]), (*C.int)(&ldv), + (*C.double)(&u[0]), (*C.int)(&ldu), + (*C.int)(&nh), (*C.double)(&wh[0]), (*C.int)(&ldwh), + (*C.int)(&nv), (*C.double)(&wv[0]), (*C.int)(&ldwv)) + }() +} diff --git a/testlapack/dlaqr5.go b/testlapack/dlaqr5.go index 176738e1..8365a1ef 100644 --- a/testlapack/dlaqr5.go +++ b/testlapack/dlaqr5.go @@ -5,115 +5,210 @@ package testlapack import ( - "archive/zip" + "compress/gzip" + "encoding/json" "fmt" - "io" "log" + "math" + "math/rand" + "os" + "path/filepath" "testing" + + "github.com/gonum/blas" + "github.com/gonum/blas/blas64" ) type Dlaqr5er interface { Dlaqr5(wantt, wantz bool, kacc22 int, n, ktop, kbot, nshfts int, sr, si []float64, h []float64, ldh int, iloz, ihiz int, z []float64, ldz int, v []float64, ldv int, u []float64, ldu int, nh int, wh []float64, ldwh int, nv int, wv []float64, ldwv int) } +type Dlaqr5test struct { + WantT bool + N int + NShifts int + KTop, KBot int + ShiftR, ShiftI []float64 + H []float64 + + HWant []float64 + ZWant []float64 +} + func Dlaqr5Test(t *testing.T, impl Dlaqr5er) { - r, err := zip.OpenReader("../internal/testdata/dlaqr5test/dlaqr5data.zip") + // Test without using reference data. + rnd := rand.New(rand.NewSource(1)) + for _, n := range []int{1, 2, 3, 4, 5, 6, 10, 30} { + for _, extra := range []int{0, 1, 20} { + for _, kacc22 := range []int{0, 1, 2} { + for cas := 0; cas < 100; cas++ { + testDlaqr5(t, impl, n, extra, kacc22, rnd) + } + } + } + } + + // Test using reference data computed by the reference netlib + // implementation. + file, err := os.Open(filepath.FromSlash("../testlapack/testdata/dlaqr5data.json.gz")) + if err != nil { + log.Fatal(err) + } + defer file.Close() + r, err := gzip.NewReader(file) if err != nil { log.Fatal(err) } defer r.Close() - for _, f := range r.File { - tc, err := f.Open() - if err != nil { - log.Fatal(err) - } - wantt, n, nshfts, ktop, kbot, sr, si, hOrig, hwant, zwant := readDlaqr5Case(tc) - tc.Close() + var tests []Dlaqr5test + json.NewDecoder(r).Decode(&tests) + for _, test := range tests { + wantt := test.WantT + n := test.N + nshfts := test.NShifts + ktop := test.KTop + kbot := test.KBot + sr := test.ShiftR + si := test.ShiftI - v := make([]float64, nshfts/2*3) - u := make([]float64, (3*nshfts-3)*(3*nshfts-3)) - nh := n - wh := make([]float64, (3*nshfts-3)*n) - nv := n - wv := make([]float64, n*(3*nshfts-3)) + for _, extra := range []int{0, 1, 10} { + v := randomGeneral(nshfts/2, 3, 3+extra, rnd) + u := randomGeneral(3*nshfts-3, 3*nshfts-3, 3*nshfts-3+extra, rnd) + nh := n + wh := randomGeneral(3*nshfts-3, n, n+extra, rnd) + nv := n + wv := randomGeneral(n, 3*nshfts-3, 3*nshfts-3+extra, rnd) + + h := nanGeneral(n, n, n+extra) - for _, ldh := range []int{n, n + 1, n + 10} { - h := make([]float64, (n-1)*ldh+n) for _, kacc22 := range []int{0, 1, 2} { - copyMatrix(n, n, h, ldh, hOrig) - z := eye(n, ldh) + copyMatrix(n, n, h.Data, h.Stride, test.H) + z := eye(n, n+extra) impl.Dlaqr5(wantt, true, kacc22, n, ktop, kbot, nshfts, sr, si, - h, ldh, - 0, n-1, z, ldh, - v, 3, - u, 3*nshfts-3, - nh, wh, nh, - nv, wv, 3*nshfts-3) + h.Data, h.Stride, + 0, n-1, z.Data, z.Stride, + v.Data, v.Stride, + u.Data, u.Stride, + nh, wh.Data, wh.Stride, + nv, wv.Data, wv.Stride) - if !equalApprox(n, n, h, ldh, hwant, 1e-13) { - t.Errorf("Case %v, kacc22=%v: unexpected matrix H\nh =%v\nhwant=%v", f.Name, kacc22, h, hwant) + prefix := fmt.Sprintf("wantt=%v, n=%v, nshfts=%v, ktop=%v, kbot=%v, extra=%v, kacc22=%v", + wantt, n, nshfts, ktop, kbot, extra, kacc22) + if !equalApprox(n, n, h.Data, h.Stride, test.HWant, 1e-13) { + t.Errorf("Case %v: unexpected matrix H\nh =%v\nhwant=%v", prefix, h.Data, test.HWant) } - if !equalApprox(n, n, z, ldh, zwant, 1e-13) { - t.Errorf("Case %v, kacc22=%v: unexpected matrix Z\nz =%v\nzwant=%v", f.Name, kacc22, z, zwant) + if !equalApprox(n, n, z.Data, z.Stride, test.ZWant, 1e-13) { + t.Errorf("Case %v: unexpected matrix Z\nz =%v\nzwant=%v", prefix, z.Data, test.ZWant) } } } } } -// readDlaqr5Case reads and returns test data written by internal/testdata/dlaqr5test/main.go. -func readDlaqr5Case(r io.Reader) (wantt bool, n, nshfts, ktop, kbot int, sr, si []float64, h, hwant, zwant []float64) { - _, err := fmt.Fscanln(r, &wantt, &n, &nshfts, &ktop, &kbot) - if err != nil { - log.Fatal(err) - } - - sr = make([]float64, nshfts) - si = make([]float64, nshfts) - h = make([]float64, n*n) - hwant = make([]float64, n*n) - zwant = make([]float64, n*n) - - for i := range sr { - _, err = fmt.Fscanln(r, &sr[i]) - if err != nil { - log.Fatal(err) - } - } - for i := range si { - _, err = fmt.Fscanln(r, &si[i]) - if err != nil { - log.Fatal(err) - } - } +func testDlaqr5(t *testing.T, impl Dlaqr5er, n, extra, kacc22 int, rnd *rand.Rand) { + wantt := true + wantz := true + nshfts := 2 * n + sr := make([]float64, nshfts) + si := make([]float64, nshfts) for i := 0; i < n; i++ { - for j := 0; j < n; j++ { - _, err = fmt.Fscanln(r, &h[i*n+j]) - if err != nil { - log.Fatal(err) + re := rnd.NormFloat64() + im := rnd.NormFloat64() + sr[2*i], sr[2*i+1] = re, re + si[2*i], si[2*i+1] = im, -im + } + ktop := rnd.Intn(n) + kbot := rnd.Intn(n) + if kbot < ktop { + ktop, kbot = kbot, ktop + } + + v := randomGeneral(nshfts/2, 3, 3+extra, rnd) + u := randomGeneral(3*nshfts-3, 3*nshfts-3, 3*nshfts-3+extra, rnd) + nh := n + wh := randomGeneral(3*nshfts-3, n, n+extra, rnd) + nv := n + wv := randomGeneral(n, 3*nshfts-3, 3*nshfts-3+extra, rnd) + + h := randomHessenberg(n, n+extra, rnd) + if ktop > 0 { + h.Data[ktop*h.Stride+ktop-1] = 0 + } + if kbot < n-1 { + h.Data[(kbot+1)*h.Stride+kbot] = 0 + } + hCopy := h + hCopy.Data = make([]float64, len(h.Data)) + copy(hCopy.Data, h.Data) + + z := eye(n, n+extra) + + impl.Dlaqr5(wantt, wantz, kacc22, + n, ktop, kbot, + nshfts, sr, si, + h.Data, h.Stride, + 0, n-1, z.Data, z.Stride, + v.Data, v.Stride, + u.Data, u.Stride, + nh, wh.Data, wh.Stride, + nv, wv.Data, wv.Stride) + + prefix := fmt.Sprintf("Case n=%v, extra=%v, kacc22=%v", n, extra, kacc22) + + if !generalOutsideAllNaN(h) { + t.Errorf("%v: out-of-range write to H\n%v", prefix, h.Data) + } + if !generalOutsideAllNaN(z) { + t.Errorf("%v: out-of-range write to Z\n%v", prefix, z.Data) + } + if !generalOutsideAllNaN(u) { + t.Errorf("%v: out-of-range write to U\n%v", prefix, u.Data) + } + if !generalOutsideAllNaN(v) { + t.Errorf("%v: out-of-range write to V\n%v", prefix, v.Data) + } + if !generalOutsideAllNaN(wh) { + t.Errorf("%v: out-of-range write to WH\n%v", prefix, wh.Data) + } + if !generalOutsideAllNaN(wv) { + t.Errorf("%v: out-of-range write to WV\n%v", prefix, wv.Data) + } + + for i := 0; i < n; i++ { + for j := 0; j < i-1; j++ { + if h.Data[i*h.Stride+j] != 0 { + t.Errorf("%v: H is not Hessenberg, H[%v,%v]!=0", prefix, i, j) } } } + if !isOrthonormal(z) { + t.Errorf("%v: Z is not orthogonal", prefix) + } + // Construct Z^T * HOrig * Z and check that it is equal to H from Dlaqr5. + hz := blas64.General{ + Rows: n, + Cols: n, + Stride: n, + Data: make([]float64, n*n), + } + blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, hCopy, z, 0, hz) + zhz := blas64.General{ + Rows: n, + Cols: n, + Stride: n, + Data: make([]float64, n*n), + } + blas64.Gemm(blas.Trans, blas.NoTrans, 1, z, hz, 0, zhz) for i := 0; i < n; i++ { for j := 0; j < n; j++ { - _, err = fmt.Fscanln(r, &hwant[i*n+j]) - if err != nil { - log.Fatal(err) + diff := zhz.Data[i*zhz.Stride+j] - h.Data[i*h.Stride+j] + if math.Abs(diff) > 1e-13 { + t.Errorf("%v: Z^T*HOrig*Z and H are not equal, diff at [%v,%v]=%v", prefix, i, j, diff) } } } - for i := 0; i < n; i++ { - for j := 0; j < n; j++ { - _, err = fmt.Fscanln(r, &zwant[i*n+j]) - if err != nil { - log.Fatal(err) - } - } - } - - return wantt, n, nshfts, ktop, kbot, sr, si, h, hwant, zwant } diff --git a/testlapack/general.go b/testlapack/general.go index 5d4dbcc8..e5639ee6 100644 --- a/testlapack/general.go +++ b/testlapack/general.go @@ -60,6 +60,22 @@ func randomGeneral(r, c, stride int, rnd *rand.Rand) blas64.General { return ans } +// randomHessenberg allocates a new n×n Hessenberg matrix filled with zeros +// under the first subdiagonal and with random numbers elsewhere. Out-of-range +// elements are filled with NaN values. +func randomHessenberg(n, stride int, rnd *rand.Rand) blas64.General { + ans := nanGeneral(n, n, stride) + for i := 0; i < n; i++ { + for j := 0; j < i-1; j++ { + ans.Data[i*ans.Stride+j] = 0 + } + for j := max(0, i-1); j < n; j++ { + ans.Data[i*ans.Stride+j] = rnd.NormFloat64() + } + } + return ans +} + // nanTriangular allocates a new r×c triangular matrix filled with NaN values. func nanTriangular(uplo blas.Uplo, n, stride int) blas64.Triangular { return blas64.Triangular{ @@ -751,11 +767,14 @@ func equalApproxTriangular(upper bool, n int, a []float64, lda int, b []float64, return true } -// eye returns an identity matrix of order n and stride ld. -func eye(n, ld int) []float64 { - m := make([]float64, (n-1)*ld+n) +// eye returns an identity matrix of given order and stride. +func eye(n, stride int) blas64.General { + ans := nanGeneral(n, n, stride) for i := 0; i < n; i++ { - m[i*ld+i] = 1 + for j := 0; j < n; j++ { + ans.Data[i*ans.Stride+j] = 0 + } + ans.Data[i*ans.Stride+i] = 1 } - return m + return ans } diff --git a/testlapack/testdata/dlaqr5data.json.gz b/testlapack/testdata/dlaqr5data.json.gz new file mode 100644 index 00000000..9e629480 Binary files /dev/null and b/testlapack/testdata/dlaqr5data.json.gz differ