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Pull from master
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btracey
@@ -14,6 +14,7 @@ import (
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// Copied from lapack/native. Keep in sync.
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const (
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absIncNotOne = "lapack: increment not one or negative one"
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badDiag = "lapack: bad diag"
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badDirect = "lapack: bad direct"
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badIpiv = "lapack: insufficient permutation length"
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badLdA = "lapack: index of a out of range"
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119
native/dlacn2.go
Normal file
119
native/dlacn2.go
Normal file
@@ -0,0 +1,119 @@
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package native
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import (
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"math"
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"github.com/gonum/blas/blas64"
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)
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// Dlacn2 estimates the 1-norm of an n×n matrix A using sequential updates with
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// matrix-vector products provided externally.
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//
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// Dlacn2 is called sequentially. In between calls, x should be overwritten by
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// A * X if kase == 1
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// A^T * X if kase == 2
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// all other prameters should be unchanged during sequential calls, and the updated
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// values of est and kase should be used. On the final return (when kase is returned
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// as 0), V = A * W, where est = norm(V) / norm(W).
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//
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// isign, v, and x must all have length n and will panic otherwise. isave is used
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// for temporary storage.
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func (impl Implementation) Dlacn2(n int, v, x []float64, isgn []int, est float64, kase int, isave [3]int) (float64, int) {
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checkVector(n, x, 1)
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checkVector(n, v, 1)
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if len(isgn) < n {
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panic("lapack: insufficient isgn length")
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}
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if isave[0] < 1 || isave[0] > 5 {
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panic("lapack: bad isave value")
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}
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itmax := 5
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bi := blas64.Implementation()
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if kase == 0 {
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for i := 0; i < n; i++ {
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x[i] = 1 / float64(n)
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}
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kase = 1
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isave[0] = 1
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return est, kase
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}
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switch isave[0] {
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default:
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panic("unknown case")
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case 1:
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if n == 1 {
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v[0] = x[0]
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est = math.Abs(v[0])
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kase = 0
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return est, kase
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}
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est = bi.Dasum(n, x, 1)
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for i := 0; i < n; i++ {
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x[i] = math.Copysign(1, x[i])
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isgn[i] = int(x[i])
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}
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kase = 2
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isave[0] = 2
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return est, kase
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case 2:
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isave[1] = bi.Idamax(n, x, 1)
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isave[2] = 2
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for i := 0; i < n; i++ {
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x[i] = 0
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}
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x[isave[1]] = 1
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kase = 1
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isave[0] = 3
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return est, kase
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case 3:
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bi.Dcopy(n, x, 1, v, 1)
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estold := est
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est = bi.Dasum(n, v, 1)
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sameSigns := true
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for i := 0; i < n; i++ {
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if int(math.Copysign(1, x[i])) != isgn[i] {
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sameSigns = false
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break
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}
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}
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if !sameSigns && est > estold {
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for i := 0; i < n; i++ {
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x[i] = math.Copysign(1, x[i])
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isgn[i] = int(x[i])
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}
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kase = 2
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isave[0] = 4
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return est, kase
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}
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case 4:
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jlast := isave[1]
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isave[1] = bi.Idamax(n, x, 1)
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if x[jlast] != math.Abs(x[isave[1]]) && isave[2] < itmax {
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isave[2] += 1
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for i := 0; i < n; i++ {
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x[i] = 0
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}
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x[isave[1]] = 1
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kase = 1
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isave[0] = 3
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return est, kase
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}
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case 5:
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tmp := 2 * (bi.Dasum(n, x, 1)) / float64(3*n)
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if tmp > est {
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bi.Dcopy(n, x, 1, v, 1)
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est = tmp
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}
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kase = 0
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return est, kase
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}
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// Iteration complete. Final stage
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altsgn := 1.0
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for i := 0; i < n; i++ {
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x[i] = altsgn * (1 + float64(i)/float64(n-1))
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altsgn *= -1
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}
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kase = 1
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isave[0] = 5
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return est, kase
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}
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334
native/dlatrs.go
Normal file
334
native/dlatrs.go
Normal file
@@ -0,0 +1,334 @@
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package native
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import (
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"math"
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"github.com/gonum/blas"
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"github.com/gonum/blas/blas64"
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)
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// Dlatrs solves a triangular system of equations scaled to prevent overflow. It
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// solves
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// A * x = scale * b if trans == blas.NoTrans
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// A^T * x = scale * b if trans == blas.Trans
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// where the scale s is set for numeric stability.
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//
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// A is an n×n triangular matrix. On entry, the slice x contains the values of
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// of b, and on exit it contains the solution vector x.
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//
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// If normin == true, cnorm is an input and cnorm[j] contains the norm of the off-diagonal
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// part of the j^th column of A. If trans == blas.NoTrans, cnorm[j] must be greater
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// than or equal to the infinity norm, and greater than or equal to the one-norm
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// otherwise. If normin == false, then cnorm is treated as an output, and is set
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// to contain the 1-norm of the off-diagonal part of the j^th column of A.
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func (impl Implementation) Dlatrs(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, normin bool, n int, a []float64, lda int, x []float64, cnorm []float64) (scale float64) {
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if uplo != blas.Upper && uplo != blas.Lower {
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panic(badUplo)
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}
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if trans != blas.Trans && trans != blas.NoTrans {
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panic(badTrans)
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}
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if diag != blas.Unit && diag != blas.NonUnit {
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panic(badDiag)
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}
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upper := uplo == blas.Upper
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noTrans := trans == blas.NoTrans
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nonUnit := diag == blas.NonUnit
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if n < 0 {
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panic(nLT0)
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}
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checkMatrix(n, n, a, lda)
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checkVector(n, x, 1)
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checkVector(n, cnorm, 1)
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if n == 0 {
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return
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}
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scale = 1
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bi := blas64.Implementation()
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if !normin {
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if upper {
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for j := 0; j < n; j++ {
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cnorm[j] = bi.Dasum(j, a[j:], lda)
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}
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} else {
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for j := 0; j < n-1; j++ {
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cnorm[j] = bi.Dasum(n-j-1, a[(j+1)*lda+j:], lda)
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}
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cnorm[n-1] = 0
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}
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}
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// Scale the column norms by tscal if the maximum element in cnorm is greater than bignum.
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imax := bi.Idamax(n, cnorm, 1)
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tmax := cnorm[imax]
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var tscal float64
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if tmax <= bignum {
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tscal = 1
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} else {
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tscal = 1 / (smlnum * tmax)
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bi.Dscal(n, tscal, cnorm, 1)
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}
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// Compute a bound on the computed solution vector to see if bi.Dtrsv can be used.
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j := bi.Idamax(n, x, 1)
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xmax := math.Abs(x[j])
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xbnd := xmax
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var grow float64
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var jfirst, jlast, jinc int
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if noTrans {
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if upper {
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jfirst = n - 1
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jlast = 0
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jinc = -1
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} else {
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jfirst = 0
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jlast = n - 1
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jinc = 1
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}
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// Compute the growth in A * x = b.
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if tscal != 1 {
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grow = 0
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goto Finish
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}
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if nonUnit {
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grow = 1 / math.Max(xbnd, smlnum)
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xbnd = grow
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for j := jfirst; j != jlast; j += jinc {
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if grow <= smlnum {
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goto Finish
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}
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tjj := math.Abs(a[j*lda+j])
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xbnd = math.Min(xbnd, math.Min(1, tjj)*grow)
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if tjj+cnorm[j] >= smlnum {
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grow *= tjj / (tjj + cnorm[j])
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} else {
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grow = 0
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}
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}
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grow = xbnd
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} else {
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grow = math.Min(1, 1/math.Max(xbnd, smlnum))
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for j := jfirst; j != jlast; j += jinc {
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if grow <= smlnum {
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goto Finish
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}
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grow *= 1 / (1 + cnorm[j])
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}
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}
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} else {
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if upper {
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jfirst = 0
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jlast = n - 1
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jinc = 1
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} else {
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jfirst = n - 1
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jlast = 0
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jinc = -1
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}
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if tscal != 1 {
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grow = 0
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goto Finish
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}
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if nonUnit {
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grow = 1 / (math.Max(xbnd, smlnum))
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xbnd = grow
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for j := jfirst; j != jlast; j += jinc {
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if grow <= smlnum {
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goto Finish
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}
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xj := 1 + cnorm[j]
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grow = math.Min(grow, xbnd/xj)
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tjj := math.Abs(a[j*lda+j])
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if xj > tjj {
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xbnd *= tjj / xj
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}
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}
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grow = math.Min(grow, xbnd)
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} else {
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grow = math.Min(1, 1/math.Max(xbnd, smlnum))
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for j := jfirst; j != jlast; j += jinc {
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if grow <= smlnum {
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goto Finish
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}
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xj := 1 + cnorm[j]
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grow /= xj
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}
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}
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}
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|
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Finish:
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if grow*tscal > smlnum {
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bi.Dtrsv(uplo, trans, diag, n, a, lda, x, 1)
|
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// TODO(btracey): check if this else is everything
|
||||
} else {
|
||||
if xmax > bignum {
|
||||
scale = bignum / xmax
|
||||
bi.Dscal(n, scale, x, 1)
|
||||
xmax = bignum
|
||||
}
|
||||
if noTrans {
|
||||
for j := jfirst; j != jlast; j += jinc {
|
||||
xj := math.Abs(x[j])
|
||||
var tjjs float64
|
||||
if nonUnit {
|
||||
tjjs = a[j*lda+j] * tscal
|
||||
} else {
|
||||
tjjs = tscal
|
||||
if tscal == 1 {
|
||||
break
|
||||
}
|
||||
}
|
||||
tjj := math.Abs(tjjs)
|
||||
if tjj > smlnum {
|
||||
if tjj < 1 {
|
||||
if xj > tjj*bignum {
|
||||
rec := 1 / xj
|
||||
bi.Dscal(n, rec, x, 1)
|
||||
scale *= rec
|
||||
xmax *= rec
|
||||
}
|
||||
}
|
||||
x[j] /= tjjs
|
||||
xj = math.Abs(x[j])
|
||||
} else if tjj > 0 {
|
||||
if xj > tjj*bignum {
|
||||
rec := (tjj * bignum) / xj
|
||||
if cnorm[j] > 1 {
|
||||
rec /= cnorm[j]
|
||||
}
|
||||
bi.Dscal(n, rec, x, 1)
|
||||
scale *= rec
|
||||
xmax *= rec
|
||||
}
|
||||
x[j] /= tjjs
|
||||
xj = math.Abs(x[j])
|
||||
} else {
|
||||
for i := 0; i < n; i++ {
|
||||
x[i] = 0
|
||||
}
|
||||
x[j] = 1
|
||||
xj = 1
|
||||
scale = 0
|
||||
xmax = 0
|
||||
}
|
||||
if xj > 1 {
|
||||
rec := 1 / xj
|
||||
if cnorm[j] > (bignum-xmax)*rec {
|
||||
rec *= 0.5
|
||||
bi.Dscal(n, rec, x, 1)
|
||||
scale *= rec
|
||||
}
|
||||
} else if xj*cnorm[j] > bignum-xmax {
|
||||
bi.Dscal(n, 0.5, x, 1)
|
||||
scale *= 0.5
|
||||
}
|
||||
if upper {
|
||||
if j > 0 {
|
||||
bi.Daxpy(j, -x[j]*tscal, a[j:], lda, x, 1)
|
||||
i := bi.Idamax(j, x, 1)
|
||||
xmax = math.Abs(x[i])
|
||||
}
|
||||
} else {
|
||||
if j < n-1 {
|
||||
bi.Daxpy(n-j-1, -x[j]*tscal, a[(j+1)*lda+j:], lda, x[j+1:], 1)
|
||||
i := j + bi.Idamax(n-j-1, x[j+1:], 1)
|
||||
xmax = math.Abs(x[i])
|
||||
}
|
||||
}
|
||||
}
|
||||
} else {
|
||||
for j := jfirst; j != jlast; j += jinc {
|
||||
xj := math.Abs(x[j])
|
||||
uscal := tscal
|
||||
rec := 1 / math.Max(xmax, 1)
|
||||
var tjjs float64
|
||||
if cnorm[j] > (bignum-xj)*rec {
|
||||
rec *= 0.5
|
||||
if nonUnit {
|
||||
tjjs = a[j*lda+j] * tscal
|
||||
} else {
|
||||
tjjs = tscal
|
||||
}
|
||||
tjj := math.Abs(tjjs)
|
||||
if tjj > 1 {
|
||||
rec = math.Min(1, rec*tjj)
|
||||
uscal /= tjjs
|
||||
}
|
||||
if rec < 1 {
|
||||
bi.Dscal(n, rec, x, 1)
|
||||
scale *= rec
|
||||
xmax *= rec
|
||||
}
|
||||
}
|
||||
var sumj float64
|
||||
if uscal == 1 {
|
||||
if upper {
|
||||
sumj = bi.Ddot(j, a[j:], lda, x, 1)
|
||||
} else if j < n-1 {
|
||||
sumj = bi.Ddot(n-j-1, a[(j+1)*lda+j:], lda, x[j+1:], 1)
|
||||
}
|
||||
} else {
|
||||
if upper {
|
||||
for i := 0; i < j; i++ {
|
||||
sumj += (a[i*lda+j] * uscal) * x[i]
|
||||
}
|
||||
} else if j < n {
|
||||
for i := j + 1; i < n; i++ {
|
||||
sumj += (a[i*lda+j] * uscal) * x[i]
|
||||
}
|
||||
}
|
||||
}
|
||||
if uscal == tscal {
|
||||
x[j] -= sumj
|
||||
xj := math.Abs(x[j])
|
||||
var tjjs float64
|
||||
if nonUnit {
|
||||
tjjs = a[j*lda+j] * tscal
|
||||
} else {
|
||||
tjjs = tscal
|
||||
if tscal == 1 {
|
||||
goto Out2
|
||||
}
|
||||
}
|
||||
tjj := math.Abs(tjjs)
|
||||
if tjj > smlnum {
|
||||
if tjj < 1 {
|
||||
if xj > tjj*bignum {
|
||||
rec = 1 / xj
|
||||
bi.Dscal(n, rec, x, 1)
|
||||
scale *= rec
|
||||
xmax *= rec
|
||||
}
|
||||
}
|
||||
x[j] /= tjjs
|
||||
} else if tjj > 0 {
|
||||
if xj > tjj*bignum {
|
||||
rec = (tjj * bignum) / xj
|
||||
bi.Dscal(n, rec, x, 1)
|
||||
scale *= rec
|
||||
xmax *= rec
|
||||
}
|
||||
x[j] /= tjjs
|
||||
} else {
|
||||
for i := 0; i < n; i++ {
|
||||
x[i] = 0
|
||||
}
|
||||
x[j] = 1
|
||||
scale = 0
|
||||
xmax = 0
|
||||
}
|
||||
} else {
|
||||
x[j] = x[j]/tjjs - sumj
|
||||
}
|
||||
Out2:
|
||||
xmax = math.Max(xmax, math.Abs(x[j]))
|
||||
}
|
||||
}
|
||||
scale /= tscal
|
||||
}
|
||||
if tscal != 1 {
|
||||
bi.Dscal(n, 1/tscal, cnorm, 1)
|
||||
}
|
||||
return scale
|
||||
}
|
||||
@@ -20,6 +20,7 @@ var _ lapack.Float64 = Implementation{}
|
||||
// This list is duplicated in lapack/cgo. Keep in sync.
|
||||
const (
|
||||
absIncNotOne = "lapack: increment not one or negative one"
|
||||
badDiag = "lapack: bad diag"
|
||||
badDirect = "lapack: bad direct"
|
||||
badIpiv = "lapack: insufficient permutation length"
|
||||
badLdA = "lapack: index of a out of range"
|
||||
@@ -74,10 +75,6 @@ func max(a, b int) int {
|
||||
return b
|
||||
}
|
||||
|
||||
// dlamch is a function in fortran, but since go forces IEEE-754 these are all
|
||||
// fixed values. Probably a way to get them as constants.
|
||||
// TODO(btracey): Is there a better way to find the smallest number such that 1+E > 1
|
||||
|
||||
var (
|
||||
// dlamchE is the machine epsilon. For IEEE this is 2^-53.
|
||||
dlamchE = math.Float64frombits(0x3ca0000000000000)
|
||||
@@ -89,4 +86,7 @@ var (
|
||||
// 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)
|
||||
|
||||
smlnum = dlamchS / dlamchP
|
||||
bignum = 1 / smlnum
|
||||
)
|
||||
|
||||
Reference in New Issue
Block a user