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109 lines
3.1 KiB
Go
109 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 gonum
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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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// Dgeqrf computes the QR factorization of the m×n matrix A using a blocked
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// algorithm. See the documentation for Dgeqr2 for a description of the
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// parameters at entry and exit.
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//
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// work is temporary storage, and lwork specifies the usable memory length.
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// The length of work must be at least max(1, lwork) and lwork must be -1
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// or at least n, otherwise this function will panic.
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// Dgeqrf is a blocked QR factorization, but the block size is limited
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// by the temporary space available. If lwork == -1, instead of performing Dgeqrf,
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// the optimal work length will be stored into work[0].
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//
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// tau must have length at least min(m,n), and this function will panic otherwise.
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func (impl Implementation) Dgeqrf(m, n int, a []float64, lda int, tau, work []float64, lwork int) {
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switch {
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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 lda < max(1, n):
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panic(badLdA)
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case lwork < max(1, n) && 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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// Quick return if possible.
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k := min(m, n)
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if k == 0 {
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work[0] = 1
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return
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}
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// nb is the optimal blocksize, i.e. the number of columns transformed at a time.
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nb := impl.Ilaenv(1, "DGEQRF", " ", m, n, -1, -1)
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if lwork == -1 {
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work[0] = float64(n * nb)
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return
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}
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if len(a) < (m-1)*lda+n {
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panic("lapack: insufficient length of a")
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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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nbmin := 2 // Minimal block size.
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var nx int // Use unblocked (unless changed in the next for loop)
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iws := n
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ldwork := nb
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// Only consider blocked if the suggested block size is > 1 and the
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// number of rows or columns is sufficiently large.
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if 1 < nb && nb < k {
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// nx is the block size at which the code switches from blocked
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// to unblocked.
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nx = max(0, impl.Ilaenv(3, "DGEQRF", " ", m, n, -1, -1))
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if k > nx {
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iws = ldwork * n
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if lwork < iws {
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// Not enough workspace to use the optimal block
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// size. Get the minimum block size instead.
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nb = lwork / n
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nbmin = max(2, impl.Ilaenv(2, "DGEQRF", " ", m, n, -1, -1))
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}
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}
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}
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// Compute QR using a blocked algorithm.
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var i int
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if nbmin <= nb && nb < k && nx < k {
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for i = 0; i < k-nx; i += nb {
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ib := min(k-i, nb)
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// Compute the QR factorization of the current block.
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impl.Dgeqr2(m-i, ib, a[i*lda+i:], lda, tau[i:], work)
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if i+ib < n {
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// Form the triangular factor of the block reflector and apply H^T
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// In Dlarft, work becomes the T matrix.
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impl.Dlarft(lapack.Forward, lapack.ColumnWise, 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.Trans, 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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}
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}
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// Call unblocked code on the remaining columns.
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if i < k {
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impl.Dgeqr2(m-i, n-i, a[i*lda+i:], lda, tau[i:], work)
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}
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work[0] = float64(iws)
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}
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