+++ /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/blas/blas64"
- "gonum.org/v1/gonum/lapack"
-)
-
-// Dlarfb applies a block reflector to a matrix.
-//
-// In the call to Dlarfb, the mxn c is multiplied by the implicitly defined matrix h as follows:
-// c = h * c if side == Left and trans == NoTrans
-// c = c * h if side == Right and trans == NoTrans
-// c = h^T * c if side == Left and trans == Trans
-// c = c * h^T if side == Right and trans == Trans
-// h is a product of elementary reflectors. direct sets the direction of multiplication
-// h = h_1 * h_2 * ... * h_k if direct == Forward
-// h = h_k * h_k-1 * ... * h_1 if direct == Backward
-// The combination of direct and store defines the orientation of the elementary
-// reflectors. In all cases the ones on the diagonal are implicitly represented.
-//
-// If direct == lapack.Forward and store == lapack.ColumnWise
-// V = [ 1 ]
-// [v1 1 ]
-// [v1 v2 1]
-// [v1 v2 v3]
-// [v1 v2 v3]
-// If direct == lapack.Forward and store == lapack.RowWise
-// V = [ 1 v1 v1 v1 v1]
-// [ 1 v2 v2 v2]
-// [ 1 v3 v3]
-// If direct == lapack.Backward and store == lapack.ColumnWise
-// V = [v1 v2 v3]
-// [v1 v2 v3]
-// [ 1 v2 v3]
-// [ 1 v3]
-// [ 1]
-// If direct == lapack.Backward and store == lapack.RowWise
-// V = [v1 v1 1 ]
-// [v2 v2 v2 1 ]
-// [v3 v3 v3 v3 1]
-// An elementary reflector can be explicitly constructed by extracting the
-// corresponding elements of v, placing a 1 where the diagonal would be, and
-// placing zeros in the remaining elements.
-//
-// t is a k×k matrix containing the block reflector, and this function will panic
-// if t is not of sufficient size. See Dlarft for more information.
-//
-// work is a temporary storage matrix with stride ldwork.
-// work must be of size at least n×k side == Left and m×k if side == Right, and
-// this function will panic if this size is not met.
-//
-// Dlarfb is an internal routine. It is exported for testing purposes.
-func (Implementation) Dlarfb(side blas.Side, trans blas.Transpose, direct lapack.Direct, store lapack.StoreV, m, n, k int, v []float64, ldv int, t []float64, ldt int, c []float64, ldc int, work []float64, ldwork int) {
- if side != blas.Left && side != blas.Right {
- panic(badSide)
- }
- if trans != blas.Trans && trans != blas.NoTrans {
- panic(badTrans)
- }
- if direct != lapack.Forward && direct != lapack.Backward {
- panic(badDirect)
- }
- if store != lapack.ColumnWise && store != lapack.RowWise {
- panic(badStore)
- }
- checkMatrix(m, n, c, ldc)
- if k < 0 {
- panic(kLT0)
- }
- checkMatrix(k, k, t, ldt)
- nv := m
- nw := n
- if side == blas.Right {
- nv = n
- nw = m
- }
- if store == lapack.ColumnWise {
- checkMatrix(nv, k, v, ldv)
- } else {
- checkMatrix(k, nv, v, ldv)
- }
- checkMatrix(nw, k, work, ldwork)
-
- if m == 0 || n == 0 {
- return
- }
-
- bi := blas64.Implementation()
-
- transt := blas.Trans
- if trans == blas.Trans {
- transt = blas.NoTrans
- }
- // TODO(btracey): This follows the original Lapack code where the
- // elements are copied into the columns of the working array. The
- // loops should go in the other direction so the data is written
- // into the rows of work so the copy is not strided. A bigger change
- // would be to replace work with work^T, but benchmarks would be
- // needed to see if the change is merited.
- if store == lapack.ColumnWise {
- if direct == lapack.Forward {
- // V1 is the first k rows of C. V2 is the remaining rows.
- if side == blas.Left {
- // W = C^T V = C1^T V1 + C2^T V2 (stored in work).
-
- // W = C1.
- for j := 0; j < k; j++ {
- bi.Dcopy(n, c[j*ldc:], 1, work[j:], ldwork)
- }
- // W = W * V1.
- bi.Dtrmm(blas.Right, blas.Lower, blas.NoTrans, blas.Unit,
- n, k, 1,
- v, ldv,
- work, ldwork)
- if m > k {
- // W = W + C2^T V2.
- bi.Dgemm(blas.Trans, blas.NoTrans, n, k, m-k,
- 1, c[k*ldc:], ldc, v[k*ldv:], ldv,
- 1, work, ldwork)
- }
- // W = W * T^T or W * T.
- bi.Dtrmm(blas.Right, blas.Upper, transt, blas.NonUnit, n, k,
- 1, t, ldt,
- work, ldwork)
- // C -= V * W^T.
- if m > k {
- // C2 -= V2 * W^T.
- bi.Dgemm(blas.NoTrans, blas.Trans, m-k, n, k,
- -1, v[k*ldv:], ldv, work, ldwork,
- 1, c[k*ldc:], ldc)
- }
- // W *= V1^T.
- bi.Dtrmm(blas.Right, blas.Lower, blas.Trans, blas.Unit, n, k,
- 1, v, ldv,
- work, ldwork)
- // C1 -= W^T.
- // TODO(btracey): This should use blas.Axpy.
- for i := 0; i < n; i++ {
- for j := 0; j < k; j++ {
- c[j*ldc+i] -= work[i*ldwork+j]
- }
- }
- return
- }
- // Form C = C * H or C * H^T, where C = (C1 C2).
-
- // W = C1.
- for i := 0; i < k; i++ {
- bi.Dcopy(m, c[i:], ldc, work[i:], ldwork)
- }
- // W *= V1.
- bi.Dtrmm(blas.Right, blas.Lower, blas.NoTrans, blas.Unit, m, k,
- 1, v, ldv,
- work, ldwork)
- if n > k {
- bi.Dgemm(blas.NoTrans, blas.NoTrans, m, k, n-k,
- 1, c[k:], ldc, v[k*ldv:], ldv,
- 1, work, ldwork)
- }
- // W *= T or T^T.
- bi.Dtrmm(blas.Right, blas.Upper, trans, blas.NonUnit, m, k,
- 1, t, ldt,
- work, ldwork)
- if n > k {
- bi.Dgemm(blas.NoTrans, blas.Trans, m, n-k, k,
- -1, work, ldwork, v[k*ldv:], ldv,
- 1, c[k:], ldc)
- }
- // C -= W * V^T.
- bi.Dtrmm(blas.Right, blas.Lower, blas.Trans, blas.Unit, m, k,
- 1, v, ldv,
- work, ldwork)
- // C -= W.
- // TODO(btracey): This should use blas.Axpy.
- for i := 0; i < m; i++ {
- for j := 0; j < k; j++ {
- c[i*ldc+j] -= work[i*ldwork+j]
- }
- }
- return
- }
- // V = (V1)
- // = (V2) (last k rows)
- // Where V2 is unit upper triangular.
- if side == blas.Left {
- // Form H * C or
- // W = C^T V.
-
- // W = C2^T.
- for j := 0; j < k; j++ {
- bi.Dcopy(n, c[(m-k+j)*ldc:], 1, work[j:], ldwork)
- }
- // W *= V2.
- bi.Dtrmm(blas.Right, blas.Upper, blas.NoTrans, blas.Unit, n, k,
- 1, v[(m-k)*ldv:], ldv,
- work, ldwork)
- if m > k {
- // W += C1^T * V1.
- bi.Dgemm(blas.Trans, blas.NoTrans, n, k, m-k,
- 1, c, ldc, v, ldv,
- 1, work, ldwork)
- }
- // W *= T or T^T.
- bi.Dtrmm(blas.Right, blas.Lower, transt, blas.NonUnit, n, k,
- 1, t, ldt,
- work, ldwork)
- // C -= V * W^T.
- if m > k {
- bi.Dgemm(blas.NoTrans, blas.Trans, m-k, n, k,
- -1, v, ldv, work, ldwork,
- 1, c, ldc)
- }
- // W *= V2^T.
- bi.Dtrmm(blas.Right, blas.Upper, blas.Trans, blas.Unit, n, k,
- 1, v[(m-k)*ldv:], ldv,
- work, ldwork)
- // C2 -= W^T.
- // TODO(btracey): This should use blas.Axpy.
- for i := 0; i < n; i++ {
- for j := 0; j < k; j++ {
- c[(m-k+j)*ldc+i] -= work[i*ldwork+j]
- }
- }
- return
- }
- // Form C * H or C * H^T where C = (C1 C2).
- // W = C * V.
-
- // W = C2.
- for j := 0; j < k; j++ {
- bi.Dcopy(m, c[n-k+j:], ldc, work[j:], ldwork)
- }
-
- // W = W * V2.
- bi.Dtrmm(blas.Right, blas.Upper, blas.NoTrans, blas.Unit, m, k,
- 1, v[(n-k)*ldv:], ldv,
- work, ldwork)
- if n > k {
- bi.Dgemm(blas.NoTrans, blas.NoTrans, m, k, n-k,
- 1, c, ldc, v, ldv,
- 1, work, ldwork)
- }
- // W *= T or T^T.
- bi.Dtrmm(blas.Right, blas.Lower, trans, blas.NonUnit, m, k,
- 1, t, ldt,
- work, ldwork)
- // C -= W * V^T.
- if n > k {
- // C1 -= W * V1^T.
- bi.Dgemm(blas.NoTrans, blas.Trans, m, n-k, k,
- -1, work, ldwork, v, ldv,
- 1, c, ldc)
- }
- // W *= V2^T.
- bi.Dtrmm(blas.Right, blas.Upper, blas.Trans, blas.Unit, m, k,
- 1, v[(n-k)*ldv:], ldv,
- work, ldwork)
- // C2 -= W.
- // TODO(btracey): This should use blas.Axpy.
- for i := 0; i < m; i++ {
- for j := 0; j < k; j++ {
- c[i*ldc+n-k+j] -= work[i*ldwork+j]
- }
- }
- return
- }
- // Store = Rowwise.
- if direct == lapack.Forward {
- // V = (V1 V2) where v1 is unit upper triangular.
- if side == blas.Left {
- // Form H * C or H^T * C where C = (C1; C2).
- // W = C^T * V^T.
-
- // W = C1^T.
- for j := 0; j < k; j++ {
- bi.Dcopy(n, c[j*ldc:], 1, work[j:], ldwork)
- }
- // W *= V1^T.
- bi.Dtrmm(blas.Right, blas.Upper, blas.Trans, blas.Unit, n, k,
- 1, v, ldv,
- work, ldwork)
- if m > k {
- bi.Dgemm(blas.Trans, blas.Trans, n, k, m-k,
- 1, c[k*ldc:], ldc, v[k:], ldv,
- 1, work, ldwork)
- }
- // W *= T or T^T.
- bi.Dtrmm(blas.Right, blas.Upper, transt, blas.NonUnit, n, k,
- 1, t, ldt,
- work, ldwork)
- // C -= V^T * W^T.
- if m > k {
- bi.Dgemm(blas.Trans, blas.Trans, m-k, n, k,
- -1, v[k:], ldv, work, ldwork,
- 1, c[k*ldc:], ldc)
- }
- // W *= V1.
- bi.Dtrmm(blas.Right, blas.Upper, blas.NoTrans, blas.Unit, n, k,
- 1, v, ldv,
- work, ldwork)
- // C1 -= W^T.
- // TODO(btracey): This should use blas.Axpy.
- for i := 0; i < n; i++ {
- for j := 0; j < k; j++ {
- c[j*ldc+i] -= work[i*ldwork+j]
- }
- }
- return
- }
- // Form C * H or C * H^T where C = (C1 C2).
- // W = C * V^T.
-
- // W = C1.
- for j := 0; j < k; j++ {
- bi.Dcopy(m, c[j:], ldc, work[j:], ldwork)
- }
- // W *= V1^T.
- bi.Dtrmm(blas.Right, blas.Upper, blas.Trans, blas.Unit, m, k,
- 1, v, ldv,
- work, ldwork)
- if n > k {
- bi.Dgemm(blas.NoTrans, blas.Trans, m, k, n-k,
- 1, c[k:], ldc, v[k:], ldv,
- 1, work, ldwork)
- }
- // W *= T or T^T.
- bi.Dtrmm(blas.Right, blas.Upper, trans, blas.NonUnit, m, k,
- 1, t, ldt,
- work, ldwork)
- // C -= W * V.
- if n > k {
- bi.Dgemm(blas.NoTrans, blas.NoTrans, m, n-k, k,
- -1, work, ldwork, v[k:], ldv,
- 1, c[k:], ldc)
- }
- // W *= V1.
- bi.Dtrmm(blas.Right, blas.Upper, blas.NoTrans, blas.Unit, m, k,
- 1, v, ldv,
- work, ldwork)
- // C1 -= W.
- // TODO(btracey): This should use blas.Axpy.
- for i := 0; i < m; i++ {
- for j := 0; j < k; j++ {
- c[i*ldc+j] -= work[i*ldwork+j]
- }
- }
- return
- }
- // V = (V1 V2) where V2 is the last k columns and is lower unit triangular.
- if side == blas.Left {
- // Form H * C or H^T C where C = (C1 ; C2).
- // W = C^T * V^T.
-
- // W = C2^T.
- for j := 0; j < k; j++ {
- bi.Dcopy(n, c[(m-k+j)*ldc:], 1, work[j:], ldwork)
- }
- // W *= V2^T.
- bi.Dtrmm(blas.Right, blas.Lower, blas.Trans, blas.Unit, n, k,
- 1, v[m-k:], ldv,
- work, ldwork)
- if m > k {
- bi.Dgemm(blas.Trans, blas.Trans, n, k, m-k,
- 1, c, ldc, v, ldv,
- 1, work, ldwork)
- }
- // W *= T or T^T.
- bi.Dtrmm(blas.Right, blas.Lower, transt, blas.NonUnit, n, k,
- 1, t, ldt,
- work, ldwork)
- // C -= V^T * W^T.
- if m > k {
- bi.Dgemm(blas.Trans, blas.Trans, m-k, n, k,
- -1, v, ldv, work, ldwork,
- 1, c, ldc)
- }
- // W *= V2.
- bi.Dtrmm(blas.Right, blas.Lower, blas.NoTrans, blas.Unit, n, k,
- 1, v[m-k:], ldv,
- work, ldwork)
- // C2 -= W^T.
- // TODO(btracey): This should use blas.Axpy.
- for i := 0; i < n; i++ {
- for j := 0; j < k; j++ {
- c[(m-k+j)*ldc+i] -= work[i*ldwork+j]
- }
- }
- return
- }
- // Form C * H or C * H^T where C = (C1 C2).
- // W = C * V^T.
- // W = C2.
- for j := 0; j < k; j++ {
- bi.Dcopy(m, c[n-k+j:], ldc, work[j:], ldwork)
- }
- // W *= V2^T.
- bi.Dtrmm(blas.Right, blas.Lower, blas.Trans, blas.Unit, m, k,
- 1, v[n-k:], ldv,
- work, ldwork)
- if n > k {
- bi.Dgemm(blas.NoTrans, blas.Trans, m, k, n-k,
- 1, c, ldc, v, ldv,
- 1, work, ldwork)
- }
- // W *= T or T^T.
- bi.Dtrmm(blas.Right, blas.Lower, trans, blas.NonUnit, m, k,
- 1, t, ldt,
- work, ldwork)
- // C -= W * V.
- if n > k {
- bi.Dgemm(blas.NoTrans, blas.NoTrans, m, n-k, k,
- -1, work, ldwork, v, ldv,
- 1, c, ldc)
- }
- // W *= V2.
- bi.Dtrmm(blas.Right, blas.Lower, blas.NoTrans, blas.Unit, m, k,
- 1, v[n-k:], ldv,
- work, ldwork)
- // C1 -= W.
- // TODO(btracey): This should use blas.Axpy.
- for i := 0; i < m; i++ {
- for j := 0; j < k; j++ {
- c[i*ldc+n-k+j] -= work[i*ldwork+j]
- }
- }
-}