mirror of
https://github.com/gonum/gonum.git
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17ea55aedb
Apply (with manual curation after the fact):
* s/^T/U+1d40/g
* s/^H/U+1d34/g
* s/, {2,3}if / $1/g
Some additional manual editing of odd formatting.
130 lines
3.9 KiB
Go
130 lines
3.9 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 gonum
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import "gonum.org/v1/gonum/blas"
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// Dormhr multiplies an m×n general matrix C with an nq×nq orthogonal matrix Q
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// Q * C if side == blas.Left and trans == blas.NoTrans,
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// Qᵀ * C if side == blas.Left and trans == blas.Trans,
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// C * Q if side == blas.Right and trans == blas.NoTrans,
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// C * Qᵀ if side == blas.Right and trans == blas.Trans,
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// where nq == m if side == blas.Left and nq == n if side == blas.Right.
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//
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// Q is defined implicitly as the product of ihi-ilo elementary reflectors, as
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// returned by Dgehrd:
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// Q = H_{ilo} H_{ilo+1} ... H_{ihi-1}.
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// Q is 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 < m if m > 0 and side == blas.Left,
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// ilo = 0 and ihi = -1 if m = 0 and side == blas.Left,
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// 0 <= ilo <= ihi < n if n > 0 and side == blas.Right,
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// ilo = 0 and ihi = -1 if n = 0 and side == blas.Right.
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//
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// a and lda represent an m×m matrix if side == blas.Left and an n×n matrix if
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// side == blas.Right. The matrix contains vectors which define the elementary
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// reflectors, as returned by Dgehrd.
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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 m-1 if side == blas.Left and n-1 if side ==
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// blas.Right.
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//
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// c and ldc represent the m×n matrix C. On return, c is overwritten by the
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// product with Q.
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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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// max(1,n), if side == blas.Left, and max(1,m), if side == blas.Right. For
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// optimum performance lwork should be at least n*nb if side == blas.Left and
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// m*nb if side == blas.Right, where nb is the optimal block size. On return,
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// work[0] will contain the optimal value of lwork.
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//
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// If lwork == -1, instead of performing Dormhr, only the optimal value of lwork
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// will be stored in work[0].
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//
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// If any requirement on input sizes is not met, Dormhr will panic.
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//
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// Dormhr is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dormhr(side blas.Side, trans blas.Transpose, m, n, ilo, ihi int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int) {
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nq := n // The order of Q.
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nw := m // The minimum length of work.
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if side == blas.Left {
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nq = m
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nw = n
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}
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switch {
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case side != blas.Left && side != blas.Right:
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panic(badSide)
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case trans != blas.NoTrans && trans != blas.Trans:
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panic(badTrans)
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case m < 0:
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panic(mLT0)
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case n < 0:
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panic(nLT0)
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case ilo < 0 || max(1, nq) <= ilo:
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panic(badIlo)
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case ihi < min(ilo, nq-1) || nq <= ihi:
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panic(badIhi)
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case lda < max(1, nq):
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panic(badLdA)
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case lwork < max(1, nw) && lwork != -1:
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panic(badLWork)
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case len(work) < max(1, lwork):
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panic(shortWork)
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}
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// Quick return if possible.
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if m == 0 || n == 0 {
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work[0] = 1
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return
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}
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nh := ihi - ilo
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var nb int
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if side == blas.Left {
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opts := "LN"
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if trans == blas.Trans {
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opts = "LT"
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}
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nb = impl.Ilaenv(1, "DORMQR", opts, nh, n, nh, -1)
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} else {
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opts := "RN"
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if trans == blas.Trans {
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opts = "RT"
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}
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nb = impl.Ilaenv(1, "DORMQR", opts, m, nh, nh, -1)
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}
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lwkopt := max(1, nw) * nb
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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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if nh == 0 {
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work[0] = 1
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return
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}
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switch {
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case len(a) < (nq-1)*lda+nq:
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panic(shortA)
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case len(c) < (m-1)*ldc+n:
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panic(shortC)
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case len(tau) != nq-1:
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panic(badLenTau)
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}
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if side == blas.Left {
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impl.Dormqr(side, trans, nh, n, nh, a[(ilo+1)*lda+ilo:], lda,
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tau[ilo:ihi], c[(ilo+1)*ldc:], ldc, work, lwork)
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} else {
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impl.Dormqr(side, trans, m, nh, nh, a[(ilo+1)*lda+ilo:], lda,
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tau[ilo:ihi], c[ilo+1:], ldc, work, lwork)
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}
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work[0] = float64(lwkopt)
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}
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