+++ /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"
-)
-
-// Dlasr applies a sequence of plane rotations to the m×n matrix A. This series
-// of plane rotations is implicitly represented by a matrix P. P is multiplied
-// by a depending on the value of side -- A = P * A if side == lapack.Left,
-// A = A * P^T if side == lapack.Right.
-//
-//The exact value of P depends on the value of pivot, but in all cases P is
-// implicitly represented by a series of 2×2 rotation matrices. The entries of
-// rotation matrix k are defined by s[k] and c[k]
-// R(k) = [ c[k] s[k]]
-// [-s[k] s[k]]
-// If direct == lapack.Forward, the rotation matrices are applied as
-// P = P(z-1) * ... * P(2) * P(1), while if direct == lapack.Backward they are
-// applied as P = P(1) * P(2) * ... * P(n).
-//
-// pivot defines the mapping of the elements in R(k) to P(k).
-// If pivot == lapack.Variable, the rotation is performed for the (k, k+1) plane.
-// P(k) = [1 ]
-// [ ... ]
-// [ 1 ]
-// [ c[k] s[k] ]
-// [ -s[k] c[k] ]
-// [ 1 ]
-// [ ... ]
-// [ 1]
-// if pivot == lapack.Top, the rotation is performed for the (1, k+1) plane,
-// P(k) = [c[k] s[k] ]
-// [ 1 ]
-// [ ... ]
-// [ 1 ]
-// [-s[k] c[k] ]
-// [ 1 ]
-// [ ... ]
-// [ 1]
-// and if pivot == lapack.Bottom, the rotation is performed for the (k, z) plane.
-// P(k) = [1 ]
-// [ ... ]
-// [ 1 ]
-// [ c[k] s[k]]
-// [ 1 ]
-// [ ... ]
-// [ 1 ]
-// [ -s[k] c[k]]
-// s and c have length m - 1 if side == blas.Left, and n - 1 if side == blas.Right.
-//
-// Dlasr is an internal routine. It is exported for testing purposes.
-func (impl Implementation) Dlasr(side blas.Side, pivot lapack.Pivot, direct lapack.Direct, m, n int, c, s, a []float64, lda int) {
- checkMatrix(m, n, a, lda)
- if side != blas.Left && side != blas.Right {
- panic(badSide)
- }
- if pivot != lapack.Variable && pivot != lapack.Top && pivot != lapack.Bottom {
- panic(badPivot)
- }
- if direct != lapack.Forward && direct != lapack.Backward {
- panic(badDirect)
- }
- if side == blas.Left {
- if len(c) < m-1 {
- panic(badSlice)
- }
- if len(s) < m-1 {
- panic(badSlice)
- }
- } else {
- if len(c) < n-1 {
- panic(badSlice)
- }
- if len(s) < n-1 {
- panic(badSlice)
- }
- }
- if m == 0 || n == 0 {
- return
- }
- if side == blas.Left {
- if pivot == lapack.Variable {
- if direct == lapack.Forward {
- for j := 0; j < m-1; j++ {
- ctmp := c[j]
- stmp := s[j]
- if ctmp != 1 || stmp != 0 {
- for i := 0; i < n; i++ {
- tmp2 := a[j*lda+i]
- tmp := a[(j+1)*lda+i]
- a[(j+1)*lda+i] = ctmp*tmp - stmp*tmp2
- a[j*lda+i] = stmp*tmp + ctmp*tmp2
- }
- }
- }
- return
- }
- for j := m - 2; j >= 0; j-- {
- ctmp := c[j]
- stmp := s[j]
- if ctmp != 1 || stmp != 0 {
- for i := 0; i < n; i++ {
- tmp2 := a[j*lda+i]
- tmp := a[(j+1)*lda+i]
- a[(j+1)*lda+i] = ctmp*tmp - stmp*tmp2
- a[j*lda+i] = stmp*tmp + ctmp*tmp2
- }
- }
- }
- return
- } else if pivot == lapack.Top {
- if direct == lapack.Forward {
- for j := 1; j < m; j++ {
- ctmp := c[j-1]
- stmp := s[j-1]
- if ctmp != 1 || stmp != 0 {
- for i := 0; i < n; i++ {
- tmp := a[j*lda+i]
- tmp2 := a[i]
- a[j*lda+i] = ctmp*tmp - stmp*tmp2
- a[i] = stmp*tmp + ctmp*tmp2
- }
- }
- }
- return
- }
- for j := m - 1; j >= 1; j-- {
- ctmp := c[j-1]
- stmp := s[j-1]
- if ctmp != 1 || stmp != 0 {
- for i := 0; i < n; i++ {
- ctmp := c[j-1]
- stmp := s[j-1]
- if ctmp != 1 || stmp != 0 {
- for i := 0; i < n; i++ {
- tmp := a[j*lda+i]
- tmp2 := a[i]
- a[j*lda+i] = ctmp*tmp - stmp*tmp2
- a[i] = stmp*tmp + ctmp*tmp2
- }
- }
- }
- }
- }
- return
- }
- if direct == lapack.Forward {
- for j := 0; j < m-1; j++ {
- ctmp := c[j]
- stmp := s[j]
- if ctmp != 1 || stmp != 0 {
- for i := 0; i < n; i++ {
- tmp := a[j*lda+i]
- tmp2 := a[(m-1)*lda+i]
- a[j*lda+i] = stmp*tmp2 + ctmp*tmp
- a[(m-1)*lda+i] = ctmp*tmp2 - stmp*tmp
- }
- }
- }
- return
- }
- for j := m - 2; j >= 0; j-- {
- ctmp := c[j]
- stmp := s[j]
- if ctmp != 1 || stmp != 0 {
- for i := 0; i < n; i++ {
- tmp := a[j*lda+i]
- tmp2 := a[(m-1)*lda+i]
- a[j*lda+i] = stmp*tmp2 + ctmp*tmp
- a[(m-1)*lda+i] = ctmp*tmp2 - stmp*tmp
- }
- }
- }
- return
- }
- if pivot == lapack.Variable {
- if direct == lapack.Forward {
- for j := 0; j < n-1; j++ {
- ctmp := c[j]
- stmp := s[j]
- if ctmp != 1 || stmp != 0 {
- for i := 0; i < m; i++ {
- tmp := a[i*lda+j+1]
- tmp2 := a[i*lda+j]
- a[i*lda+j+1] = ctmp*tmp - stmp*tmp2
- a[i*lda+j] = stmp*tmp + ctmp*tmp2
- }
- }
- }
- return
- }
- for j := n - 2; j >= 0; j-- {
- ctmp := c[j]
- stmp := s[j]
- if ctmp != 1 || stmp != 0 {
- for i := 0; i < m; i++ {
- tmp := a[i*lda+j+1]
- tmp2 := a[i*lda+j]
- a[i*lda+j+1] = ctmp*tmp - stmp*tmp2
- a[i*lda+j] = stmp*tmp + ctmp*tmp2
- }
- }
- }
- return
- } else if pivot == lapack.Top {
- if direct == lapack.Forward {
- for j := 1; j < n; j++ {
- ctmp := c[j-1]
- stmp := s[j-1]
- if ctmp != 1 || stmp != 0 {
- for i := 0; i < m; i++ {
- tmp := a[i*lda+j]
- tmp2 := a[i*lda]
- a[i*lda+j] = ctmp*tmp - stmp*tmp2
- a[i*lda] = stmp*tmp + ctmp*tmp2
- }
- }
- }
- return
- }
- for j := n - 1; j >= 1; j-- {
- ctmp := c[j-1]
- stmp := s[j-1]
- if ctmp != 1 || stmp != 0 {
- for i := 0; i < m; i++ {
- tmp := a[i*lda+j]
- tmp2 := a[i*lda]
- a[i*lda+j] = ctmp*tmp - stmp*tmp2
- a[i*lda] = stmp*tmp + ctmp*tmp2
- }
- }
- }
- return
- }
- if direct == lapack.Forward {
- for j := 0; j < n-1; j++ {
- ctmp := c[j]
- stmp := s[j]
- if ctmp != 1 || stmp != 0 {
- for i := 0; i < m; i++ {
- tmp := a[i*lda+j]
- tmp2 := a[i*lda+n-1]
- a[i*lda+j] = stmp*tmp2 + ctmp*tmp
- a[i*lda+n-1] = ctmp*tmp2 - stmp*tmp
- }
-
- }
- }
- return
- }
- for j := n - 2; j >= 0; j-- {
- ctmp := c[j]
- stmp := s[j]
- if ctmp != 1 || stmp != 0 {
- for i := 0; i < m; i++ {
- tmp := a[i*lda+j]
- tmp2 := a[i*lda+n-1]
- a[i*lda+j] = stmp*tmp2 + ctmp*tmp
- a[i*lda+n-1] = ctmp*tmp2 - stmp*tmp
- }
- }
- }
-}
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