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98 lines
2.5 KiB
Go
98 lines
2.5 KiB
Go
// Copyright ©2015 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package gonum
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import (
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"math"
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"gonum.org/v1/gonum/blas/blas64"
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"gonum.org/v1/gonum/lapack"
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)
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// Dlasq1 computes the singular values of an n×n bidiagonal matrix with diagonal
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// d and off-diagonal e. On exit, d contains the singular values in decreasing
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// order, and e is overwritten. d must have length at least n, e must have
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// length at least n-1, and the input work must have length at least 4*n. Dlasq1
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// will panic if these conditions are not met.
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//
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// Dlasq1 is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dlasq1(n int, d, e, work []float64) (info int) {
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// TODO(btracey): replace info with an error.
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if n < 0 {
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panic(nLT0)
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}
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if len(work) < 4*n {
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panic(badWork)
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}
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if len(d) < n {
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panic("lapack: length of d less than n")
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}
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if len(e) < n-1 {
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panic("lapack: length of e less than n-1")
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}
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if n == 0 {
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return info
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}
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if n == 1 {
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d[0] = math.Abs(d[0])
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return info
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}
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if n == 2 {
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d[1], d[0] = impl.Dlas2(d[0], e[0], d[1])
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return info
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}
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// Estimate the largest singular value.
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var sigmx float64
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for i := 0; i < n-1; i++ {
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d[i] = math.Abs(d[i])
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sigmx = math.Max(sigmx, math.Abs(e[i]))
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}
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d[n-1] = math.Abs(d[n-1])
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// Early return if sigmx is zero (matrix is already diagonal).
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if sigmx == 0 {
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impl.Dlasrt(lapack.SortDecreasing, n, d)
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return info
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}
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for i := 0; i < n; i++ {
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sigmx = math.Max(sigmx, d[i])
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}
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// Copy D and E into WORK (in the Z format) and scale (squaring the
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// input data makes scaling by a power of the radix pointless).
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eps := dlamchP
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safmin := dlamchS
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scale := math.Sqrt(eps / safmin)
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bi := blas64.Implementation()
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bi.Dcopy(n, d, 1, work, 2)
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bi.Dcopy(n-1, e, 1, work[1:], 2)
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impl.Dlascl(lapack.General, 0, 0, sigmx, scale, 2*n-1, 1, work, 1)
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// Compute the q's and e's.
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for i := 0; i < 2*n-1; i++ {
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work[i] *= work[i]
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}
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work[2*n-1] = 0
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info = impl.Dlasq2(n, work)
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if info == 0 {
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for i := 0; i < n; i++ {
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d[i] = math.Sqrt(work[i])
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}
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impl.Dlascl(lapack.General, 0, 0, scale, sigmx, n, 1, d, 1)
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} else if info == 2 {
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// Maximum number of iterations exceeded. Move data from work
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// into D and E so the calling subroutine can try to finish.
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for i := 0; i < n; i++ {
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d[i] = math.Sqrt(work[2*i])
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e[i] = math.Sqrt(work[2*i+1])
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}
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impl.Dlascl(lapack.General, 0, 0, scale, sigmx, n, 1, d, 1)
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impl.Dlascl(lapack.General, 0, 0, scale, sigmx, n, 1, e, 1)
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}
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return info
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}
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