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