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94 lines
2.7 KiB
Go
94 lines
2.7 KiB
Go
// Copyright ©2016 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 native
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// Dorghr generates an n×n orthogonal matrix Q which is defined as the product
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// of ihi-ilo elementary reflectors:
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// Q = H_{ilo} H_{ilo+1} ... H_{ihi-1}.
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//
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// a and lda represent an n×n matrix that contains the elementary reflectors, as
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// returned by Dgehrd. On return, a is overwritten by the n×n orthogonal matrix
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// Q. Q will be equal to the identity matrix except in the submatrix
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// Q[ilo+1:ihi+1,ilo+1:ihi+1].
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//
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// ilo and ihi must have the same values as in the previous call of Dgehrd. It
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// must hold that
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// 0 <= ilo <= ihi < n, if n > 0,
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// ilo = 0, ihi = -1, if n == 0.
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//
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// tau contains the scalar factors of the elementary reflectors, as returned by
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// Dgehrd. tau must have length n-1.
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//
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// work must have length at least max(1,lwork) and lwork must be at least
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// ihi-ilo. For optimum performance lwork must be at least (ihi-ilo)*nb where nb
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// is the optimal blocksize. On return, work[0] will contain the optimal value
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// of lwork.
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//
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// If lwork == -1, instead of performing Dorghr, only the optimal value of lwork
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// will be stored into work[0].
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//
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// If any requirement on input sizes is not met, Dorghr will panic.
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//
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// Dorghr is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dorghr(n, ilo, ihi int, a []float64, lda int, tau, work []float64, lwork int) {
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checkMatrix(n, n, a, lda)
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nh := ihi - ilo
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switch {
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case ilo < 0 || max(1, n) <= ilo:
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panic(badIlo)
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case ihi < min(ilo, n-1) || n <= ihi:
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panic(badIhi)
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case lwork < max(1, nh) && lwork != -1:
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panic(badWork)
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case len(work) < max(1, lwork):
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panic(shortWork)
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}
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lwkopt := max(1, nh) * impl.Ilaenv(1, "DORGQR", " ", nh, nh, nh, -1)
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if lwork == -1 {
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work[0] = float64(lwkopt)
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return
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}
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// Quick return if possible.
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if n == 0 {
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work[0] = 1
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return
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}
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// Shift the vectors which define the elementary reflectors one column
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// to the right.
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for i := ilo + 2; i < ihi+1; i++ {
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copy(a[i*lda+ilo+1:i*lda+i], a[i*lda+ilo:i*lda+i-1])
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}
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// Set the first ilo+1 and the last n-ihi-1 rows and columns to those of
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// the identity matrix.
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for i := 0; i < ilo+1; i++ {
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for j := 0; j < n; j++ {
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a[i*lda+j] = 0
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}
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a[i*lda+i] = 1
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}
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for i := ilo + 1; i < ihi+1; i++ {
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for j := 0; j <= ilo; j++ {
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a[i*lda+j] = 0
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}
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for j := i; j < n; j++ {
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a[i*lda+j] = 0
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}
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}
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for i := ihi + 1; i < n; i++ {
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for j := 0; j < n; j++ {
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a[i*lda+j] = 0
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}
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a[i*lda+i] = 1
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}
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if nh > 0 {
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// Generate Q[ilo+1:ihi+1,ilo+1:ihi+1].
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impl.Dorgqr(nh, nh, nh, a[(ilo+1)*lda+ilo+1:], lda, tau[ilo:ihi], work, lwork)
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}
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work[0] = float64(lwkopt)
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}
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