+++ /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"
-)
-
-// Dlabrd reduces the first NB rows and columns of a real general m×n matrix
-// A to upper or lower bidiagonal form by an orthogonal transformation
-// Q**T * A * P
-// If m >= n, A is reduced to upper bidiagonal form and upon exit the elements
-// on and below the diagonal in the first nb columns represent the elementary
-// reflectors, and the elements above the diagonal in the first nb rows represent
-// the matrix P. If m < n, A is reduced to lower bidiagonal form and the elements
-// P is instead stored above the diagonal.
-//
-// The reduction to bidiagonal form is stored in d and e, where d are the diagonal
-// elements, and e are the off-diagonal elements.
-//
-// The matrices Q and P are products of elementary reflectors
-// Q = H_0 * H_1 * ... * H_{nb-1}
-// P = G_0 * G_1 * ... * G_{nb-1}
-// where
-// H_i = I - tauQ[i] * v_i * v_i^T
-// G_i = I - tauP[i] * u_i * u_i^T
-//
-// As an example, on exit the entries of A when m = 6, n = 5, and nb = 2
-// [ 1 1 u1 u1 u1]
-// [v1 1 1 u2 u2]
-// [v1 v2 a a a]
-// [v1 v2 a a a]
-// [v1 v2 a a a]
-// [v1 v2 a a a]
-// and when m = 5, n = 6, and nb = 2
-// [ 1 u1 u1 u1 u1 u1]
-// [ 1 1 u2 u2 u2 u2]
-// [v1 1 a a a a]
-// [v1 v2 a a a a]
-// [v1 v2 a a a a]
-//
-// Dlabrd also returns the matrices X and Y which are used with U and V to
-// apply the transformation to the unreduced part of the matrix
-// A := A - V*Y^T - X*U^T
-// and returns the matrices X and Y which are needed to apply the
-// transformation to the unreduced part of A.
-//
-// X is an m×nb matrix, Y is an n×nb matrix. d, e, taup, and tauq must all have
-// length at least nb. Dlabrd will panic if these size constraints are violated.
-//
-// Dlabrd is an internal routine. It is exported for testing purposes.
-func (impl Implementation) Dlabrd(m, n, nb int, a []float64, lda int, d, e, tauQ, tauP, x []float64, ldx int, y []float64, ldy int) {
- checkMatrix(m, n, a, lda)
- checkMatrix(m, nb, x, ldx)
- checkMatrix(n, nb, y, ldy)
- if len(d) < nb {
- panic(badD)
- }
- if len(e) < nb {
- panic(badE)
- }
- if len(tauQ) < nb {
- panic(badTauQ)
- }
- if len(tauP) < nb {
- panic(badTauP)
- }
- if m <= 0 || n <= 0 {
- return
- }
- bi := blas64.Implementation()
- if m >= n {
- // Reduce to upper bidiagonal form.
- for i := 0; i < nb; i++ {
- bi.Dgemv(blas.NoTrans, m-i, i, -1, a[i*lda:], lda, y[i*ldy:], 1, 1, a[i*lda+i:], lda)
- bi.Dgemv(blas.NoTrans, m-i, i, -1, x[i*ldx:], ldx, a[i:], lda, 1, a[i*lda+i:], lda)
-
- a[i*lda+i], tauQ[i] = impl.Dlarfg(m-i, a[i*lda+i], a[min(i+1, m-1)*lda+i:], lda)
- d[i] = a[i*lda+i]
- if i < n-1 {
- // Compute Y[i+1:n, i].
- a[i*lda+i] = 1
- bi.Dgemv(blas.Trans, m-i, n-i-1, 1, a[i*lda+i+1:], lda, a[i*lda+i:], lda, 0, y[(i+1)*ldy+i:], ldy)
- bi.Dgemv(blas.Trans, m-i, i, 1, a[i*lda:], lda, a[i*lda+i:], lda, 0, y[i:], ldy)
- bi.Dgemv(blas.NoTrans, n-i-1, i, -1, y[(i+1)*ldy:], ldy, y[i:], ldy, 1, y[(i+1)*ldy+i:], ldy)
- bi.Dgemv(blas.Trans, m-i, i, 1, x[i*ldx:], ldx, a[i*lda+i:], lda, 0, y[i:], ldy)
- bi.Dgemv(blas.Trans, i, n-i-1, -1, a[i+1:], lda, y[i:], ldy, 1, y[(i+1)*ldy+i:], ldy)
- bi.Dscal(n-i-1, tauQ[i], y[(i+1)*ldy+i:], ldy)
-
- // Update A[i, i+1:n].
- bi.Dgemv(blas.NoTrans, n-i-1, i+1, -1, y[(i+1)*ldy:], ldy, a[i*lda:], 1, 1, a[i*lda+i+1:], 1)
- bi.Dgemv(blas.Trans, i, n-i-1, -1, a[i+1:], lda, x[i*ldx:], 1, 1, a[i*lda+i+1:], 1)
-
- // Generate reflection P[i] to annihilate A[i, i+2:n].
- a[i*lda+i+1], tauP[i] = impl.Dlarfg(n-i-1, a[i*lda+i+1], a[i*lda+min(i+2, n-1):], 1)
- e[i] = a[i*lda+i+1]
- a[i*lda+i+1] = 1
-
- // Compute X[i+1:m, i].
- bi.Dgemv(blas.NoTrans, m-i-1, n-i-1, 1, a[(i+1)*lda+i+1:], lda, a[i*lda+i+1:], 1, 0, x[(i+1)*ldx+i:], ldx)
- bi.Dgemv(blas.Trans, n-i-1, i+1, 1, y[(i+1)*ldy:], ldy, a[i*lda+i+1:], 1, 0, x[i:], ldx)
- bi.Dgemv(blas.NoTrans, m-i-1, i+1, -1, a[(i+1)*lda:], lda, x[i:], ldx, 1, x[(i+1)*ldx+i:], ldx)
- bi.Dgemv(blas.NoTrans, i, n-i-1, 1, a[i+1:], lda, a[i*lda+i+1:], 1, 0, x[i:], ldx)
- bi.Dgemv(blas.NoTrans, m-i-1, i, -1, x[(i+1)*ldx:], ldx, x[i:], ldx, 1, x[(i+1)*ldx+i:], ldx)
- bi.Dscal(m-i-1, tauP[i], x[(i+1)*ldx+i:], ldx)
- }
- }
- return
- }
- // Reduce to lower bidiagonal form.
- for i := 0; i < nb; i++ {
- // Update A[i,i:n]
- bi.Dgemv(blas.NoTrans, n-i, i, -1, y[i*ldy:], ldy, a[i*lda:], 1, 1, a[i*lda+i:], 1)
- bi.Dgemv(blas.Trans, i, n-i, -1, a[i:], lda, x[i*ldx:], 1, 1, a[i*lda+i:], 1)
-
- // Generate reflection P[i] to annihilate A[i, i+1:n]
- a[i*lda+i], tauP[i] = impl.Dlarfg(n-i, a[i*lda+i], a[i*lda+min(i+1, n-1):], 1)
- d[i] = a[i*lda+i]
- if i < m-1 {
- a[i*lda+i] = 1
- // Compute X[i+1:m, i].
- bi.Dgemv(blas.NoTrans, m-i-1, n-i, 1, a[(i+1)*lda+i:], lda, a[i*lda+i:], 1, 0, x[(i+1)*ldx+i:], ldx)
- bi.Dgemv(blas.Trans, n-i, i, 1, y[i*ldy:], ldy, a[i*lda+i:], 1, 0, x[i:], ldx)
- bi.Dgemv(blas.NoTrans, m-i-1, i, -1, a[(i+1)*lda:], lda, x[i:], ldx, 1, x[(i+1)*ldx+i:], ldx)
- bi.Dgemv(blas.NoTrans, i, n-i, 1, a[i:], lda, a[i*lda+i:], 1, 0, x[i:], ldx)
- bi.Dgemv(blas.NoTrans, m-i-1, i, -1, x[(i+1)*ldx:], ldx, x[i:], ldx, 1, x[(i+1)*ldx+i:], ldx)
- bi.Dscal(m-i-1, tauP[i], x[(i+1)*ldx+i:], ldx)
-
- // Update A[i+1:m, i].
- bi.Dgemv(blas.NoTrans, m-i-1, i, -1, a[(i+1)*lda:], lda, y[i*ldy:], 1, 1, a[(i+1)*lda+i:], lda)
- bi.Dgemv(blas.NoTrans, m-i-1, i+1, -1, x[(i+1)*ldx:], ldx, a[i:], lda, 1, a[(i+1)*lda+i:], lda)
-
- // Generate reflection Q[i] to annihilate A[i+2:m, i].
- a[(i+1)*lda+i], tauQ[i] = impl.Dlarfg(m-i-1, a[(i+1)*lda+i], a[min(i+2, m-1)*lda+i:], lda)
- e[i] = a[(i+1)*lda+i]
- a[(i+1)*lda+i] = 1
-
- // Compute Y[i+1:n, i].
- bi.Dgemv(blas.Trans, m-i-1, n-i-1, 1, a[(i+1)*lda+i+1:], lda, a[(i+1)*lda+i:], lda, 0, y[(i+1)*ldy+i:], ldy)
- bi.Dgemv(blas.Trans, m-i-1, i, 1, a[(i+1)*lda:], lda, a[(i+1)*lda+i:], lda, 0, y[i:], ldy)
- bi.Dgemv(blas.NoTrans, n-i-1, i, -1, y[(i+1)*ldy:], ldy, y[i:], ldy, 1, y[(i+1)*ldy+i:], ldy)
- bi.Dgemv(blas.Trans, m-i-1, i+1, 1, x[(i+1)*ldx:], ldx, a[(i+1)*lda+i:], lda, 0, y[i:], ldy)
- bi.Dgemv(blas.Trans, i+1, n-i-1, -1, a[i+1:], lda, y[i:], ldy, 1, y[(i+1)*ldy+i:], ldy)
- bi.Dscal(n-i-1, tauQ[i], y[(i+1)*ldy+i:], ldy)
- }
- }
-}
OSDN Git Service
