+++ /dev/null
-// Copyright ©2015 The Gonum Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package gonum
-
-import (
- "gonum.org/v1/gonum/blas"
- "gonum.org/v1/gonum/lapack"
-)
-
-// Dormlq multiplies the matrix C by the orthogonal matrix Q defined by the
-// slices a and tau. A and tau are as returned from Dgelqf.
-// C = Q * C if side == blas.Left and trans == blas.NoTrans
-// C = Q^T * C if side == blas.Left and trans == blas.Trans
-// C = C * Q if side == blas.Right and trans == blas.NoTrans
-// C = C * Q^T if side == blas.Right and trans == blas.Trans
-// If side == blas.Left, A is a matrix of side k×m, and if side == blas.Right
-// A is of size k×n. This uses a blocked algorithm.
-//
-// work is temporary storage, and lwork specifies the usable memory length.
-// At minimum, lwork >= m if side == blas.Left and lwork >= n if side == blas.Right,
-// and this function will panic otherwise.
-// Dormlq uses a block algorithm, but the block size is limited
-// by the temporary space available. If lwork == -1, instead of performing Dormlq,
-// the optimal work length will be stored into work[0].
-//
-// tau contains the Householder scales and must have length at least k, and
-// this function will panic otherwise.
-func (impl Implementation) Dormlq(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int) {
- if side != blas.Left && side != blas.Right {
- panic(badSide)
- }
- if trans != blas.Trans && trans != blas.NoTrans {
- panic(badTrans)
- }
- left := side == blas.Left
- if left {
- checkMatrix(k, m, a, lda)
- } else {
- checkMatrix(k, n, a, lda)
- }
- checkMatrix(m, n, c, ldc)
- if len(tau) < k {
- panic(badTau)
- }
- if len(work) < lwork {
- panic(shortWork)
- }
- nw := m
- if left {
- nw = n
- }
- if lwork < max(1, nw) && lwork != -1 {
- panic(badWork)
- }
-
- if m == 0 || n == 0 || k == 0 {
- work[0] = 1
- return
- }
-
- const (
- nbmax = 64
- ldt = nbmax
- tsize = nbmax * ldt
- )
- opts := string(side) + string(trans)
- nb := min(nbmax, impl.Ilaenv(1, "DORMLQ", opts, m, n, k, -1))
- lworkopt := max(1, nw)*nb + tsize
- if lwork == -1 {
- work[0] = float64(lworkopt)
- return
- }
-
- nbmin := 2
- if 1 < nb && nb < k {
- iws := nw*nb + tsize
- if lwork < iws {
- nb = (lwork - tsize) / nw
- nbmin = max(2, impl.Ilaenv(2, "DORMLQ", opts, m, n, k, -1))
- }
- }
- if nb < nbmin || k <= nb {
- // Call unblocked code.
- impl.Dorml2(side, trans, m, n, k, a, lda, tau, c, ldc, work)
- work[0] = float64(lworkopt)
- return
- }
-
- t := work[:tsize]
- wrk := work[tsize:]
- ldwrk := nb
-
- notran := trans == blas.NoTrans
- transt := blas.NoTrans
- if notran {
- transt = blas.Trans
- }
-
- switch {
- case left && notran:
- for i := 0; i < k; i += nb {
- ib := min(nb, k-i)
- impl.Dlarft(lapack.Forward, lapack.RowWise, m-i, ib,
- a[i*lda+i:], lda,
- tau[i:],
- t, ldt)
- impl.Dlarfb(side, transt, lapack.Forward, lapack.RowWise, m-i, n, ib,
- a[i*lda+i:], lda,
- t, ldt,
- c[i*ldc:], ldc,
- wrk, ldwrk)
- }
-
- case left && !notran:
- for i := ((k - 1) / nb) * nb; i >= 0; i -= nb {
- ib := min(nb, k-i)
- impl.Dlarft(lapack.Forward, lapack.RowWise, m-i, ib,
- a[i*lda+i:], lda,
- tau[i:],
- t, ldt)
- impl.Dlarfb(side, transt, lapack.Forward, lapack.RowWise, m-i, n, ib,
- a[i*lda+i:], lda,
- t, ldt,
- c[i*ldc:], ldc,
- wrk, ldwrk)
- }
-
- case !left && notran:
- for i := ((k - 1) / nb) * nb; i >= 0; i -= nb {
- ib := min(nb, k-i)
- impl.Dlarft(lapack.Forward, lapack.RowWise, n-i, ib,
- a[i*lda+i:], lda,
- tau[i:],
- t, ldt)
- impl.Dlarfb(side, transt, lapack.Forward, lapack.RowWise, m, n-i, ib,
- a[i*lda+i:], lda,
- t, ldt,
- c[i:], ldc,
- wrk, ldwrk)
- }
-
- case !left && !notran:
- for i := 0; i < k; i += nb {
- ib := min(nb, k-i)
- impl.Dlarft(lapack.Forward, lapack.RowWise, n-i, ib,
- a[i*lda+i:], lda,
- tau[i:],
- t, ldt)
- impl.Dlarfb(side, transt, lapack.Forward, lapack.RowWise, m, n-i, ib,
- a[i*lda+i:], lda,
- t, ldt,
- c[i:], ldc,
- wrk, ldwrk)
- }
- }
- work[0] = float64(lworkopt)
-}
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