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121 lines
3.1 KiB
Go
121 lines
3.1 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 native
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import (
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/lapack"
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)
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// Dorgqr generates an m×n matrix Q with orthonormal columns defined by the
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// product of elementary reflectors
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// Q = H_0 * H_1 * ... * H_{k-1}
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// as computed by Dgeqrf.
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// Dorgqr is the blocked version of Dorg2r that makes greater use of level-3 BLAS
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// routines.
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//
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// The length of tau must be at least k, and the length of work must be at least n.
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// It also must be that 0 <= k <= n and 0 <= n <= m.
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//
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// work is temporary storage, and lwork specifies the usable memory length. At
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// minimum, lwork >= n, and the amount of blocking is limited by the usable
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// length. If lwork == -1, instead of computing Dorgqr the optimal work length
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// is stored into work[0].
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//
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// Dorgqr will panic if the conditions on input values are not met.
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//
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// Dorgqr is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dorgqr(m, n, k int, a []float64, lda int, tau, work []float64, lwork int) {
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nb := impl.Ilaenv(1, "DORGQR", " ", m, n, k, -1)
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// work is treated as an n×nb matrix
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if lwork == -1 {
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work[0] = float64(max(1, n) * nb)
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return
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}
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checkMatrix(m, n, a, lda)
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if k < 0 {
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panic(kLT0)
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}
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if k > n {
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panic(kGTN)
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}
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if n > m {
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panic(mLTN)
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}
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if len(tau) < k {
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panic(badTau)
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}
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if len(work) < lwork {
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panic(shortWork)
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}
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if lwork < n {
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panic(badWork)
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}
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if n == 0 {
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return
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}
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nbmin := 2 // Minimum number of blocks
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var nx int // Minimum number of rows
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iws := n // Length of work needed
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var ldwork int
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if nb > 1 && nb < k {
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nx = max(0, impl.Ilaenv(3, "DORGQR", " ", m, n, k, -1))
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if nx < k {
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ldwork = nb
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iws = n * ldwork
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if lwork < iws {
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nb = lwork / n
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ldwork = nb
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nbmin = max(2, impl.Ilaenv(2, "DORGQR", " ", m, n, k, -1))
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}
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}
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}
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var ki, kk int
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if nb >= nbmin && nb < k && nx < k {
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// The first kk columns are handled by the blocked method.
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// Note: lapack has nx here, but this means the last nx rows are handled
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// serially which could be quite different than nb.
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ki = ((k - nb - 1) / nb) * nb
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kk = min(k, ki+nb)
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for j := kk; j < n; j++ {
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for i := 0; i < kk; i++ {
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a[i*lda+j] = 0
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}
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}
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}
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if kk < n {
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// Perform the operation on colums kk to the end.
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impl.Dorg2r(m-kk, n-kk, k-kk, a[kk*lda+kk:], lda, tau[kk:], work)
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}
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if kk == 0 {
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return
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}
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// Perform the operation on column-blocks
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for i := ki; i >= 0; i -= nb {
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ib := min(nb, k-i)
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if i+ib < n {
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impl.Dlarft(lapack.Forward, lapack.ColumnWise,
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m-i, ib,
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a[i*lda+i:], lda,
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tau[i:],
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work, ldwork)
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impl.Dlarfb(blas.Left, blas.NoTrans, lapack.Forward, lapack.ColumnWise,
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m-i, n-i-ib, ib,
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a[i*lda+i:], lda,
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work, ldwork,
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a[i*lda+i+ib:], lda,
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work[ib*ldwork:], ldwork)
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}
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impl.Dorg2r(m-i, ib, ib, a[i*lda+i:], lda, tau[i:], work)
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// Set rows 0:i-1 of current block to zero
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for j := i; j < i+ib; j++ {
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for l := 0; l < i; l++ {
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a[l*lda+j] = 0
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}
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}
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}
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}
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