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 // 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 * Pᵀ 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) { switch { case side != blas.Left && side != blas.Right: panic(badSide) case pivot != lapack.Variable && pivot != lapack.Top && pivot != lapack.Bottom: panic(badPivot) case direct != lapack.Forward && direct != lapack.Backward: panic(badDirect) case m < 0: panic(mLT0) case n < 0: panic(nLT0) case lda < max(1, n): panic(badLdA) } // Quick return if possible. if m == 0 || n == 0 { return } if side == blas.Left { if len(c) < m-1 { panic(shortC) } if len(s) < m-1 { panic(shortS) } } else { if len(c) < n-1 { panic(shortC) } if len(s) < n-1 { panic(shortS) } } if len(a) < (m-1)*lda+n { panic(shortA) } 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 } } } }