2265 lines
42 KiB
Go
2265 lines
42 KiB
Go
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// Copyright ©2014 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 gonum
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import (
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/internal/asm/f64"
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)
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var _ blas.Float64Level2 = Implementation{}
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// Dger performs the rank-one operation
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// A += alpha * x * y^T
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// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
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func (Implementation) Dger(m, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int) {
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if m < 0 {
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panic(mLT0)
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}
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if n < 0 {
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panic(nLT0)
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}
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if lda < max(1, n) {
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panic(badLdA)
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}
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if incX == 0 {
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panic(zeroIncX)
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}
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if incY == 0 {
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panic(zeroIncY)
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}
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// Quick return if possible.
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if m == 0 || n == 0 {
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return
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}
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// For zero matrix size the following slice length checks are trivially satisfied.
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if (incX > 0 && len(x) <= (m-1)*incX) || (incX < 0 && len(x) <= (1-m)*incX) {
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panic(shortX)
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}
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if (incY > 0 && len(y) <= (n-1)*incY) || (incY < 0 && len(y) <= (1-n)*incY) {
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panic(shortY)
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}
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if len(a) < lda*(m-1)+n {
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panic(shortA)
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}
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// Quick return if possible.
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if alpha == 0 {
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return
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}
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f64.Ger(uintptr(m), uintptr(n),
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alpha,
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x, uintptr(incX),
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y, uintptr(incY),
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a, uintptr(lda))
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}
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// Dgbmv performs one of the matrix-vector operations
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// y = alpha * A * x + beta * y if tA == blas.NoTrans
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// y = alpha * A^T * x + beta * y if tA == blas.Trans or blas.ConjTrans
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// where A is an m×n band matrix with kL sub-diagonals and kU super-diagonals,
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// x and y are vectors, and alpha and beta are scalars.
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func (Implementation) Dgbmv(tA blas.Transpose, m, n, kL, kU int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int) {
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if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
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panic(badTranspose)
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}
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if m < 0 {
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panic(mLT0)
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}
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if n < 0 {
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panic(nLT0)
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}
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if kL < 0 {
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panic(kLLT0)
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}
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if kU < 0 {
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panic(kULT0)
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}
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if lda < kL+kU+1 {
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panic(badLdA)
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}
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if incX == 0 {
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panic(zeroIncX)
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}
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if incY == 0 {
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panic(zeroIncY)
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}
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// Quick return if possible.
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if m == 0 || n == 0 {
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return
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}
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// For zero matrix size the following slice length checks are trivially satisfied.
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if len(a) < lda*(min(m, n+kL)-1)+kL+kU+1 {
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panic(shortA)
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}
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lenX := m
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lenY := n
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if tA == blas.NoTrans {
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lenX = n
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lenY = m
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}
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if (incX > 0 && len(x) <= (lenX-1)*incX) || (incX < 0 && len(x) <= (1-lenX)*incX) {
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panic(shortX)
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}
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if (incY > 0 && len(y) <= (lenY-1)*incY) || (incY < 0 && len(y) <= (1-lenY)*incY) {
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panic(shortY)
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}
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// Quick return if possible.
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if alpha == 0 && beta == 1 {
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return
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}
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var kx, ky int
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if incX < 0 {
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kx = -(lenX - 1) * incX
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}
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if incY < 0 {
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ky = -(lenY - 1) * incY
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}
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// Form y = beta * y.
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if beta != 1 {
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if incY == 1 {
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if beta == 0 {
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for i := range y[:lenY] {
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y[i] = 0
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}
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} else {
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f64.ScalUnitary(beta, y[:lenY])
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}
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} else {
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iy := ky
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if beta == 0 {
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for i := 0; i < lenY; i++ {
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y[iy] = 0
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iy += incY
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}
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} else {
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if incY > 0 {
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f64.ScalInc(beta, y, uintptr(lenY), uintptr(incY))
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} else {
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f64.ScalInc(beta, y, uintptr(lenY), uintptr(-incY))
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}
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}
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}
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}
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if alpha == 0 {
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return
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}
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// i and j are indices of the compacted banded matrix.
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// off is the offset into the dense matrix (off + j = densej)
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nCol := kU + 1 + kL
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if tA == blas.NoTrans {
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iy := ky
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if incX == 1 {
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for i := 0; i < min(m, n+kL); i++ {
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l := max(0, kL-i)
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u := min(nCol, n+kL-i)
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off := max(0, i-kL)
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atmp := a[i*lda+l : i*lda+u]
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xtmp := x[off : off+u-l]
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var sum float64
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for j, v := range atmp {
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sum += xtmp[j] * v
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}
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y[iy] += sum * alpha
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iy += incY
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}
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return
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}
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for i := 0; i < min(m, n+kL); i++ {
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l := max(0, kL-i)
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u := min(nCol, n+kL-i)
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off := max(0, i-kL)
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atmp := a[i*lda+l : i*lda+u]
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jx := kx
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var sum float64
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for _, v := range atmp {
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sum += x[off*incX+jx] * v
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jx += incX
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}
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y[iy] += sum * alpha
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iy += incY
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}
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return
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}
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if incX == 1 {
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for i := 0; i < min(m, n+kL); i++ {
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l := max(0, kL-i)
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u := min(nCol, n+kL-i)
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off := max(0, i-kL)
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atmp := a[i*lda+l : i*lda+u]
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tmp := alpha * x[i]
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jy := ky
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for _, v := range atmp {
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y[jy+off*incY] += tmp * v
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jy += incY
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}
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}
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return
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}
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ix := kx
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for i := 0; i < min(m, n+kL); i++ {
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l := max(0, kL-i)
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u := min(nCol, n+kL-i)
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off := max(0, i-kL)
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atmp := a[i*lda+l : i*lda+u]
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tmp := alpha * x[ix]
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jy := ky
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for _, v := range atmp {
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y[jy+off*incY] += tmp * v
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jy += incY
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}
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ix += incX
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}
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}
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// Dtrmv performs one of the matrix-vector operations
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// x = A * x if tA == blas.NoTrans
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// x = A^T * x if tA == blas.Trans or blas.ConjTrans
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// where A is an n×n triangular matrix, and x is a vector.
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func (Implementation) Dtrmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float64, lda int, x []float64, incX int) {
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if ul != blas.Lower && ul != blas.Upper {
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panic(badUplo)
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}
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if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
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panic(badTranspose)
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}
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if d != blas.NonUnit && d != blas.Unit {
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panic(badDiag)
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}
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if n < 0 {
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panic(nLT0)
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}
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if lda < max(1, n) {
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panic(badLdA)
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}
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if incX == 0 {
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panic(zeroIncX)
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}
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// Quick return if possible.
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if n == 0 {
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return
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}
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// For zero matrix size the following slice length checks are trivially satisfied.
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if len(a) < lda*(n-1)+n {
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panic(shortA)
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}
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if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
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panic(shortX)
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}
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nonUnit := d != blas.Unit
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if n == 1 {
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if nonUnit {
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x[0] *= a[0]
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}
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return
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}
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var kx int
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if incX <= 0 {
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kx = -(n - 1) * incX
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}
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if tA == blas.NoTrans {
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if ul == blas.Upper {
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if incX == 1 {
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for i := 0; i < n; i++ {
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ilda := i * lda
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var tmp float64
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if nonUnit {
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tmp = a[ilda+i] * x[i]
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} else {
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tmp = x[i]
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}
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x[i] = tmp + f64.DotUnitary(a[ilda+i+1:ilda+n], x[i+1:n])
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}
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return
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}
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ix := kx
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for i := 0; i < n; i++ {
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ilda := i * lda
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var tmp float64
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if nonUnit {
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tmp = a[ilda+i] * x[ix]
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} else {
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tmp = x[ix]
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}
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x[ix] = tmp + f64.DotInc(x, a[ilda+i+1:ilda+n], uintptr(n-i-1), uintptr(incX), 1, uintptr(ix+incX), 0)
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ix += incX
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}
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return
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}
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if incX == 1 {
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for i := n - 1; i >= 0; i-- {
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ilda := i * lda
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var tmp float64
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if nonUnit {
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tmp += a[ilda+i] * x[i]
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} else {
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tmp = x[i]
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}
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x[i] = tmp + f64.DotUnitary(a[ilda:ilda+i], x[:i])
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}
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return
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}
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ix := kx + (n-1)*incX
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for i := n - 1; i >= 0; i-- {
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ilda := i * lda
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var tmp float64
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if nonUnit {
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tmp = a[ilda+i] * x[ix]
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} else {
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tmp = x[ix]
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}
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x[ix] = tmp + f64.DotInc(x, a[ilda:ilda+i], uintptr(i), uintptr(incX), 1, uintptr(kx), 0)
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ix -= incX
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}
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return
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|||
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}
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// Cases where a is transposed.
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if ul == blas.Upper {
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if incX == 1 {
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for i := n - 1; i >= 0; i-- {
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ilda := i * lda
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xi := x[i]
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f64.AxpyUnitary(xi, a[ilda+i+1:ilda+n], x[i+1:n])
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if nonUnit {
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x[i] *= a[ilda+i]
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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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ix := kx + (n-1)*incX
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for i := n - 1; i >= 0; i-- {
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ilda := i * lda
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xi := x[ix]
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f64.AxpyInc(xi, a[ilda+i+1:ilda+n], x, uintptr(n-i-1), 1, uintptr(incX), 0, uintptr(kx+(i+1)*incX))
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if nonUnit {
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|||
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x[ix] *= a[ilda+i]
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}
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|||
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ix -= incX
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|||
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}
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|||
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return
|
|||
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}
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
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ilda := i * lda
|
|||
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xi := x[i]
|
|||
|
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f64.AxpyUnitary(xi, a[ilda:ilda+i], x[:i])
|
|||
|
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if nonUnit {
|
|||
|
|
x[i] *= a[i*lda+i]
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
ilda := i * lda
|
|||
|
|
xi := x[ix]
|
|||
|
|
f64.AxpyInc(xi, a[ilda:ilda+i], x, uintptr(i), 1, uintptr(incX), 0, uintptr(kx))
|
|||
|
|
if nonUnit {
|
|||
|
|
x[ix] *= a[ilda+i]
|
|||
|
|
}
|
|||
|
|
ix += incX
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Dtrsv solves one of the systems of equations
|
|||
|
|
// A * x = b if tA == blas.NoTrans
|
|||
|
|
// A^T * x = b if tA == blas.Trans or blas.ConjTrans
|
|||
|
|
// where A is an n×n triangular matrix, and x and b are vectors.
|
|||
|
|
//
|
|||
|
|
// At entry to the function, x contains the values of b, and the result is
|
|||
|
|
// stored in-place into x.
|
|||
|
|
//
|
|||
|
|
// No test for singularity or near-singularity is included in this
|
|||
|
|
// routine. Such tests must be performed before calling this routine.
|
|||
|
|
func (Implementation) Dtrsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float64, lda int, x []float64, incX int) {
|
|||
|
|
if ul != blas.Lower && ul != blas.Upper {
|
|||
|
|
panic(badUplo)
|
|||
|
|
}
|
|||
|
|
if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
|
|||
|
|
panic(badTranspose)
|
|||
|
|
}
|
|||
|
|
if d != blas.NonUnit && d != blas.Unit {
|
|||
|
|
panic(badDiag)
|
|||
|
|
}
|
|||
|
|
if n < 0 {
|
|||
|
|
panic(nLT0)
|
|||
|
|
}
|
|||
|
|
if lda < max(1, n) {
|
|||
|
|
panic(badLdA)
|
|||
|
|
}
|
|||
|
|
if incX == 0 {
|
|||
|
|
panic(zeroIncX)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if n == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// For zero matrix size the following slice length checks are trivially satisfied.
|
|||
|
|
if len(a) < lda*(n-1)+n {
|
|||
|
|
panic(shortA)
|
|||
|
|
}
|
|||
|
|
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
|||
|
|
panic(shortX)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if n == 1 {
|
|||
|
|
if d == blas.NonUnit {
|
|||
|
|
x[0] /= a[0]
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
var kx int
|
|||
|
|
if incX < 0 {
|
|||
|
|
kx = -(n - 1) * incX
|
|||
|
|
}
|
|||
|
|
nonUnit := d == blas.NonUnit
|
|||
|
|
if tA == blas.NoTrans {
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
var sum float64
|
|||
|
|
atmp := a[i*lda+i+1 : i*lda+n]
|
|||
|
|
for j, v := range atmp {
|
|||
|
|
jv := i + j + 1
|
|||
|
|
sum += x[jv] * v
|
|||
|
|
}
|
|||
|
|
x[i] -= sum
|
|||
|
|
if nonUnit {
|
|||
|
|
x[i] /= a[i*lda+i]
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx + (n-1)*incX
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
var sum float64
|
|||
|
|
jx := ix + incX
|
|||
|
|
atmp := a[i*lda+i+1 : i*lda+n]
|
|||
|
|
for _, v := range atmp {
|
|||
|
|
sum += x[jx] * v
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
x[ix] -= sum
|
|||
|
|
if nonUnit {
|
|||
|
|
x[ix] /= a[i*lda+i]
|
|||
|
|
}
|
|||
|
|
ix -= incX
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
var sum float64
|
|||
|
|
atmp := a[i*lda : i*lda+i]
|
|||
|
|
for j, v := range atmp {
|
|||
|
|
sum += x[j] * v
|
|||
|
|
}
|
|||
|
|
x[i] -= sum
|
|||
|
|
if nonUnit {
|
|||
|
|
x[i] /= a[i*lda+i]
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
jx := kx
|
|||
|
|
var sum float64
|
|||
|
|
atmp := a[i*lda : i*lda+i]
|
|||
|
|
for _, v := range atmp {
|
|||
|
|
sum += x[jx] * v
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
x[ix] -= sum
|
|||
|
|
if nonUnit {
|
|||
|
|
x[ix] /= a[i*lda+i]
|
|||
|
|
}
|
|||
|
|
ix += incX
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
// Cases where a is transposed.
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
if nonUnit {
|
|||
|
|
x[i] /= a[i*lda+i]
|
|||
|
|
}
|
|||
|
|
xi := x[i]
|
|||
|
|
atmp := a[i*lda+i+1 : i*lda+n]
|
|||
|
|
for j, v := range atmp {
|
|||
|
|
jv := j + i + 1
|
|||
|
|
x[jv] -= v * xi
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
if nonUnit {
|
|||
|
|
x[ix] /= a[i*lda+i]
|
|||
|
|
}
|
|||
|
|
xi := x[ix]
|
|||
|
|
jx := kx + (i+1)*incX
|
|||
|
|
atmp := a[i*lda+i+1 : i*lda+n]
|
|||
|
|
for _, v := range atmp {
|
|||
|
|
x[jx] -= v * xi
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
ix += incX
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
if nonUnit {
|
|||
|
|
x[i] /= a[i*lda+i]
|
|||
|
|
}
|
|||
|
|
xi := x[i]
|
|||
|
|
atmp := a[i*lda : i*lda+i]
|
|||
|
|
for j, v := range atmp {
|
|||
|
|
x[j] -= v * xi
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx + (n-1)*incX
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
if nonUnit {
|
|||
|
|
x[ix] /= a[i*lda+i]
|
|||
|
|
}
|
|||
|
|
xi := x[ix]
|
|||
|
|
jx := kx
|
|||
|
|
atmp := a[i*lda : i*lda+i]
|
|||
|
|
for _, v := range atmp {
|
|||
|
|
x[jx] -= v * xi
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
ix -= incX
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Dsymv performs the matrix-vector operation
|
|||
|
|
// y = alpha * A * x + beta * y
|
|||
|
|
// where A is an n×n symmetric matrix, x and y are vectors, and alpha and
|
|||
|
|
// beta are scalars.
|
|||
|
|
func (Implementation) Dsymv(ul blas.Uplo, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int) {
|
|||
|
|
if ul != blas.Lower && ul != blas.Upper {
|
|||
|
|
panic(badUplo)
|
|||
|
|
}
|
|||
|
|
if n < 0 {
|
|||
|
|
panic(nLT0)
|
|||
|
|
}
|
|||
|
|
if lda < max(1, n) {
|
|||
|
|
panic(badLdA)
|
|||
|
|
}
|
|||
|
|
if incX == 0 {
|
|||
|
|
panic(zeroIncX)
|
|||
|
|
}
|
|||
|
|
if incY == 0 {
|
|||
|
|
panic(zeroIncY)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if n == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// For zero matrix size the following slice length checks are trivially satisfied.
|
|||
|
|
if len(a) < lda*(n-1)+n {
|
|||
|
|
panic(shortA)
|
|||
|
|
}
|
|||
|
|
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
|||
|
|
panic(shortX)
|
|||
|
|
}
|
|||
|
|
if (incY > 0 && len(y) <= (n-1)*incY) || (incY < 0 && len(y) <= (1-n)*incY) {
|
|||
|
|
panic(shortY)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if alpha == 0 && beta == 1 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Set up start points
|
|||
|
|
var kx, ky int
|
|||
|
|
if incX < 0 {
|
|||
|
|
kx = -(n - 1) * incX
|
|||
|
|
}
|
|||
|
|
if incY < 0 {
|
|||
|
|
ky = -(n - 1) * incY
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Form y = beta * y
|
|||
|
|
if beta != 1 {
|
|||
|
|
if incY == 1 {
|
|||
|
|
if beta == 0 {
|
|||
|
|
for i := range y[:n] {
|
|||
|
|
y[i] = 0
|
|||
|
|
}
|
|||
|
|
} else {
|
|||
|
|
f64.ScalUnitary(beta, y[:n])
|
|||
|
|
}
|
|||
|
|
} else {
|
|||
|
|
iy := ky
|
|||
|
|
if beta == 0 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
y[iy] = 0
|
|||
|
|
iy += incY
|
|||
|
|
}
|
|||
|
|
} else {
|
|||
|
|
if incY > 0 {
|
|||
|
|
f64.ScalInc(beta, y, uintptr(n), uintptr(incY))
|
|||
|
|
} else {
|
|||
|
|
f64.ScalInc(beta, y, uintptr(n), uintptr(-incY))
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if alpha == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if n == 1 {
|
|||
|
|
y[0] += alpha * a[0] * x[0]
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
if incX == 1 {
|
|||
|
|
iy := ky
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
xv := x[i] * alpha
|
|||
|
|
sum := x[i] * a[i*lda+i]
|
|||
|
|
jy := ky + (i+1)*incY
|
|||
|
|
atmp := a[i*lda+i+1 : i*lda+n]
|
|||
|
|
for j, v := range atmp {
|
|||
|
|
jp := j + i + 1
|
|||
|
|
sum += x[jp] * v
|
|||
|
|
y[jy] += xv * v
|
|||
|
|
jy += incY
|
|||
|
|
}
|
|||
|
|
y[iy] += alpha * sum
|
|||
|
|
iy += incY
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
iy := ky
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
xv := x[ix] * alpha
|
|||
|
|
sum := x[ix] * a[i*lda+i]
|
|||
|
|
jx := kx + (i+1)*incX
|
|||
|
|
jy := ky + (i+1)*incY
|
|||
|
|
atmp := a[i*lda+i+1 : i*lda+n]
|
|||
|
|
for _, v := range atmp {
|
|||
|
|
sum += x[jx] * v
|
|||
|
|
y[jy] += xv * v
|
|||
|
|
jx += incX
|
|||
|
|
jy += incY
|
|||
|
|
}
|
|||
|
|
y[iy] += alpha * sum
|
|||
|
|
ix += incX
|
|||
|
|
iy += incY
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
// Cases where a is lower triangular.
|
|||
|
|
if incX == 1 {
|
|||
|
|
iy := ky
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
jy := ky
|
|||
|
|
xv := alpha * x[i]
|
|||
|
|
atmp := a[i*lda : i*lda+i]
|
|||
|
|
var sum float64
|
|||
|
|
for j, v := range atmp {
|
|||
|
|
sum += x[j] * v
|
|||
|
|
y[jy] += xv * v
|
|||
|
|
jy += incY
|
|||
|
|
}
|
|||
|
|
sum += x[i] * a[i*lda+i]
|
|||
|
|
sum *= alpha
|
|||
|
|
y[iy] += sum
|
|||
|
|
iy += incY
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
iy := ky
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
jx := kx
|
|||
|
|
jy := ky
|
|||
|
|
xv := alpha * x[ix]
|
|||
|
|
atmp := a[i*lda : i*lda+i]
|
|||
|
|
var sum float64
|
|||
|
|
for _, v := range atmp {
|
|||
|
|
sum += x[jx] * v
|
|||
|
|
y[jy] += xv * v
|
|||
|
|
jx += incX
|
|||
|
|
jy += incY
|
|||
|
|
}
|
|||
|
|
sum += x[ix] * a[i*lda+i]
|
|||
|
|
sum *= alpha
|
|||
|
|
y[iy] += sum
|
|||
|
|
ix += incX
|
|||
|
|
iy += incY
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Dtbmv performs one of the matrix-vector operations
|
|||
|
|
// x = A * x if tA == blas.NoTrans
|
|||
|
|
// x = A^T * x if tA == blas.Trans or blas.ConjTrans
|
|||
|
|
// where A is an n×n triangular band matrix with k+1 diagonals, and x is a vector.
|
|||
|
|
func (Implementation) Dtbmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float64, lda int, x []float64, incX int) {
|
|||
|
|
if ul != blas.Lower && ul != blas.Upper {
|
|||
|
|
panic(badUplo)
|
|||
|
|
}
|
|||
|
|
if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
|
|||
|
|
panic(badTranspose)
|
|||
|
|
}
|
|||
|
|
if d != blas.NonUnit && d != blas.Unit {
|
|||
|
|
panic(badDiag)
|
|||
|
|
}
|
|||
|
|
if n < 0 {
|
|||
|
|
panic(nLT0)
|
|||
|
|
}
|
|||
|
|
if k < 0 {
|
|||
|
|
panic(kLT0)
|
|||
|
|
}
|
|||
|
|
if lda < k+1 {
|
|||
|
|
panic(badLdA)
|
|||
|
|
}
|
|||
|
|
if incX == 0 {
|
|||
|
|
panic(zeroIncX)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if n == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// For zero matrix size the following slice length checks are trivially satisfied.
|
|||
|
|
if len(a) < lda*(n-1)+k+1 {
|
|||
|
|
panic(shortA)
|
|||
|
|
}
|
|||
|
|
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
|||
|
|
panic(shortX)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
var kx int
|
|||
|
|
if incX < 0 {
|
|||
|
|
kx = -(n - 1) * incX
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
nonunit := d != blas.Unit
|
|||
|
|
|
|||
|
|
if tA == blas.NoTrans {
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
u := min(1+k, n-i)
|
|||
|
|
var sum float64
|
|||
|
|
atmp := a[i*lda:]
|
|||
|
|
xtmp := x[i:]
|
|||
|
|
for j := 1; j < u; j++ {
|
|||
|
|
sum += xtmp[j] * atmp[j]
|
|||
|
|
}
|
|||
|
|
if nonunit {
|
|||
|
|
sum += xtmp[0] * atmp[0]
|
|||
|
|
} else {
|
|||
|
|
sum += xtmp[0]
|
|||
|
|
}
|
|||
|
|
x[i] = sum
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
u := min(1+k, n-i)
|
|||
|
|
var sum float64
|
|||
|
|
atmp := a[i*lda:]
|
|||
|
|
jx := incX
|
|||
|
|
for j := 1; j < u; j++ {
|
|||
|
|
sum += x[ix+jx] * atmp[j]
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
if nonunit {
|
|||
|
|
sum += x[ix] * atmp[0]
|
|||
|
|
} else {
|
|||
|
|
sum += x[ix]
|
|||
|
|
}
|
|||
|
|
x[ix] = sum
|
|||
|
|
ix += incX
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
l := max(0, k-i)
|
|||
|
|
atmp := a[i*lda:]
|
|||
|
|
var sum float64
|
|||
|
|
for j := l; j < k; j++ {
|
|||
|
|
sum += x[i-k+j] * atmp[j]
|
|||
|
|
}
|
|||
|
|
if nonunit {
|
|||
|
|
sum += x[i] * atmp[k]
|
|||
|
|
} else {
|
|||
|
|
sum += x[i]
|
|||
|
|
}
|
|||
|
|
x[i] = sum
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx + (n-1)*incX
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
l := max(0, k-i)
|
|||
|
|
atmp := a[i*lda:]
|
|||
|
|
var sum float64
|
|||
|
|
jx := l * incX
|
|||
|
|
for j := l; j < k; j++ {
|
|||
|
|
sum += x[ix-k*incX+jx] * atmp[j]
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
if nonunit {
|
|||
|
|
sum += x[ix] * atmp[k]
|
|||
|
|
} else {
|
|||
|
|
sum += x[ix]
|
|||
|
|
}
|
|||
|
|
x[ix] = sum
|
|||
|
|
ix -= incX
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
u := k + 1
|
|||
|
|
if i < u {
|
|||
|
|
u = i + 1
|
|||
|
|
}
|
|||
|
|
var sum float64
|
|||
|
|
for j := 1; j < u; j++ {
|
|||
|
|
sum += x[i-j] * a[(i-j)*lda+j]
|
|||
|
|
}
|
|||
|
|
if nonunit {
|
|||
|
|
sum += x[i] * a[i*lda]
|
|||
|
|
} else {
|
|||
|
|
sum += x[i]
|
|||
|
|
}
|
|||
|
|
x[i] = sum
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx + (n-1)*incX
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
u := k + 1
|
|||
|
|
if i < u {
|
|||
|
|
u = i + 1
|
|||
|
|
}
|
|||
|
|
var sum float64
|
|||
|
|
jx := incX
|
|||
|
|
for j := 1; j < u; j++ {
|
|||
|
|
sum += x[ix-jx] * a[(i-j)*lda+j]
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
if nonunit {
|
|||
|
|
sum += x[ix] * a[i*lda]
|
|||
|
|
} else {
|
|||
|
|
sum += x[ix]
|
|||
|
|
}
|
|||
|
|
x[ix] = sum
|
|||
|
|
ix -= incX
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
u := k
|
|||
|
|
if i+k >= n {
|
|||
|
|
u = n - i - 1
|
|||
|
|
}
|
|||
|
|
var sum float64
|
|||
|
|
for j := 0; j < u; j++ {
|
|||
|
|
sum += x[i+j+1] * a[(i+j+1)*lda+k-j-1]
|
|||
|
|
}
|
|||
|
|
if nonunit {
|
|||
|
|
sum += x[i] * a[i*lda+k]
|
|||
|
|
} else {
|
|||
|
|
sum += x[i]
|
|||
|
|
}
|
|||
|
|
x[i] = sum
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
u := k
|
|||
|
|
if i+k >= n {
|
|||
|
|
u = n - i - 1
|
|||
|
|
}
|
|||
|
|
var (
|
|||
|
|
sum float64
|
|||
|
|
jx int
|
|||
|
|
)
|
|||
|
|
for j := 0; j < u; j++ {
|
|||
|
|
sum += x[ix+jx+incX] * a[(i+j+1)*lda+k-j-1]
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
if nonunit {
|
|||
|
|
sum += x[ix] * a[i*lda+k]
|
|||
|
|
} else {
|
|||
|
|
sum += x[ix]
|
|||
|
|
}
|
|||
|
|
x[ix] = sum
|
|||
|
|
ix += incX
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Dtpmv performs one of the matrix-vector operations
|
|||
|
|
// x = A * x if tA == blas.NoTrans
|
|||
|
|
// x = A^T * x if tA == blas.Trans or blas.ConjTrans
|
|||
|
|
// where A is an n×n triangular matrix in packed format, and x is a vector.
|
|||
|
|
func (Implementation) Dtpmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, ap []float64, x []float64, incX int) {
|
|||
|
|
if ul != blas.Lower && ul != blas.Upper {
|
|||
|
|
panic(badUplo)
|
|||
|
|
}
|
|||
|
|
if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
|
|||
|
|
panic(badTranspose)
|
|||
|
|
}
|
|||
|
|
if d != blas.NonUnit && d != blas.Unit {
|
|||
|
|
panic(badDiag)
|
|||
|
|
}
|
|||
|
|
if n < 0 {
|
|||
|
|
panic(nLT0)
|
|||
|
|
}
|
|||
|
|
if incX == 0 {
|
|||
|
|
panic(zeroIncX)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if n == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// For zero matrix size the following slice length checks are trivially satisfied.
|
|||
|
|
if len(ap) < n*(n+1)/2 {
|
|||
|
|
panic(shortAP)
|
|||
|
|
}
|
|||
|
|
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
|||
|
|
panic(shortX)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
var kx int
|
|||
|
|
if incX < 0 {
|
|||
|
|
kx = -(n - 1) * incX
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
nonUnit := d == blas.NonUnit
|
|||
|
|
var offset int // Offset is the index of (i,i)
|
|||
|
|
if tA == blas.NoTrans {
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
xi := x[i]
|
|||
|
|
if nonUnit {
|
|||
|
|
xi *= ap[offset]
|
|||
|
|
}
|
|||
|
|
atmp := ap[offset+1 : offset+n-i]
|
|||
|
|
xtmp := x[i+1:]
|
|||
|
|
for j, v := range atmp {
|
|||
|
|
xi += v * xtmp[j]
|
|||
|
|
}
|
|||
|
|
x[i] = xi
|
|||
|
|
offset += n - i
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
xix := x[ix]
|
|||
|
|
if nonUnit {
|
|||
|
|
xix *= ap[offset]
|
|||
|
|
}
|
|||
|
|
atmp := ap[offset+1 : offset+n-i]
|
|||
|
|
jx := kx + (i+1)*incX
|
|||
|
|
for _, v := range atmp {
|
|||
|
|
xix += v * x[jx]
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
x[ix] = xix
|
|||
|
|
offset += n - i
|
|||
|
|
ix += incX
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
if incX == 1 {
|
|||
|
|
offset = n*(n+1)/2 - 1
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
xi := x[i]
|
|||
|
|
if nonUnit {
|
|||
|
|
xi *= ap[offset]
|
|||
|
|
}
|
|||
|
|
atmp := ap[offset-i : offset]
|
|||
|
|
for j, v := range atmp {
|
|||
|
|
xi += v * x[j]
|
|||
|
|
}
|
|||
|
|
x[i] = xi
|
|||
|
|
offset -= i + 1
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx + (n-1)*incX
|
|||
|
|
offset = n*(n+1)/2 - 1
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
xix := x[ix]
|
|||
|
|
if nonUnit {
|
|||
|
|
xix *= ap[offset]
|
|||
|
|
}
|
|||
|
|
atmp := ap[offset-i : offset]
|
|||
|
|
jx := kx
|
|||
|
|
for _, v := range atmp {
|
|||
|
|
xix += v * x[jx]
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
x[ix] = xix
|
|||
|
|
offset -= i + 1
|
|||
|
|
ix -= incX
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
// Cases where ap is transposed.
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
if incX == 1 {
|
|||
|
|
offset = n*(n+1)/2 - 1
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
xi := x[i]
|
|||
|
|
atmp := ap[offset+1 : offset+n-i]
|
|||
|
|
xtmp := x[i+1:]
|
|||
|
|
for j, v := range atmp {
|
|||
|
|
xtmp[j] += v * xi
|
|||
|
|
}
|
|||
|
|
if nonUnit {
|
|||
|
|
x[i] *= ap[offset]
|
|||
|
|
}
|
|||
|
|
offset -= n - i + 1
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx + (n-1)*incX
|
|||
|
|
offset = n*(n+1)/2 - 1
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
xix := x[ix]
|
|||
|
|
jx := kx + (i+1)*incX
|
|||
|
|
atmp := ap[offset+1 : offset+n-i]
|
|||
|
|
for _, v := range atmp {
|
|||
|
|
x[jx] += v * xix
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
if nonUnit {
|
|||
|
|
x[ix] *= ap[offset]
|
|||
|
|
}
|
|||
|
|
offset -= n - i + 1
|
|||
|
|
ix -= incX
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
xi := x[i]
|
|||
|
|
atmp := ap[offset-i : offset]
|
|||
|
|
for j, v := range atmp {
|
|||
|
|
x[j] += v * xi
|
|||
|
|
}
|
|||
|
|
if nonUnit {
|
|||
|
|
x[i] *= ap[offset]
|
|||
|
|
}
|
|||
|
|
offset += i + 2
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
xix := x[ix]
|
|||
|
|
jx := kx
|
|||
|
|
atmp := ap[offset-i : offset]
|
|||
|
|
for _, v := range atmp {
|
|||
|
|
x[jx] += v * xix
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
if nonUnit {
|
|||
|
|
x[ix] *= ap[offset]
|
|||
|
|
}
|
|||
|
|
ix += incX
|
|||
|
|
offset += i + 2
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Dtbsv solves one of the systems of equations
|
|||
|
|
// A * x = b if tA == blas.NoTrans
|
|||
|
|
// A^T * x = b if tA == blas.Trans or tA == blas.ConjTrans
|
|||
|
|
// where A is an n×n triangular band matrix with k+1 diagonals,
|
|||
|
|
// and x and b are vectors.
|
|||
|
|
//
|
|||
|
|
// At entry to the function, x contains the values of b, and the result is
|
|||
|
|
// stored in-place into x.
|
|||
|
|
//
|
|||
|
|
// No test for singularity or near-singularity is included in this
|
|||
|
|
// routine. Such tests must be performed before calling this routine.
|
|||
|
|
func (Implementation) Dtbsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float64, lda int, x []float64, incX int) {
|
|||
|
|
if ul != blas.Lower && ul != blas.Upper {
|
|||
|
|
panic(badUplo)
|
|||
|
|
}
|
|||
|
|
if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
|
|||
|
|
panic(badTranspose)
|
|||
|
|
}
|
|||
|
|
if d != blas.NonUnit && d != blas.Unit {
|
|||
|
|
panic(badDiag)
|
|||
|
|
}
|
|||
|
|
if n < 0 {
|
|||
|
|
panic(nLT0)
|
|||
|
|
}
|
|||
|
|
if k < 0 {
|
|||
|
|
panic(kLT0)
|
|||
|
|
}
|
|||
|
|
if lda < k+1 {
|
|||
|
|
panic(badLdA)
|
|||
|
|
}
|
|||
|
|
if incX == 0 {
|
|||
|
|
panic(zeroIncX)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if n == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// For zero matrix size the following slice length checks are trivially satisfied.
|
|||
|
|
if len(a) < lda*(n-1)+k+1 {
|
|||
|
|
panic(shortA)
|
|||
|
|
}
|
|||
|
|
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
|||
|
|
panic(shortX)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
var kx int
|
|||
|
|
if incX < 0 {
|
|||
|
|
kx = -(n - 1) * incX
|
|||
|
|
}
|
|||
|
|
nonUnit := d == blas.NonUnit
|
|||
|
|
// Form x = A^-1 x.
|
|||
|
|
// Several cases below use subslices for speed improvement.
|
|||
|
|
// The incX != 1 cases usually do not because incX may be negative.
|
|||
|
|
if tA == blas.NoTrans {
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
bands := k
|
|||
|
|
if i+bands >= n {
|
|||
|
|
bands = n - i - 1
|
|||
|
|
}
|
|||
|
|
atmp := a[i*lda+1:]
|
|||
|
|
xtmp := x[i+1 : i+bands+1]
|
|||
|
|
var sum float64
|
|||
|
|
for j, v := range xtmp {
|
|||
|
|
sum += v * atmp[j]
|
|||
|
|
}
|
|||
|
|
x[i] -= sum
|
|||
|
|
if nonUnit {
|
|||
|
|
x[i] /= a[i*lda]
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx + (n-1)*incX
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
max := k + 1
|
|||
|
|
if i+max > n {
|
|||
|
|
max = n - i
|
|||
|
|
}
|
|||
|
|
atmp := a[i*lda:]
|
|||
|
|
var (
|
|||
|
|
jx int
|
|||
|
|
sum float64
|
|||
|
|
)
|
|||
|
|
for j := 1; j < max; j++ {
|
|||
|
|
jx += incX
|
|||
|
|
sum += x[ix+jx] * atmp[j]
|
|||
|
|
}
|
|||
|
|
x[ix] -= sum
|
|||
|
|
if nonUnit {
|
|||
|
|
x[ix] /= atmp[0]
|
|||
|
|
}
|
|||
|
|
ix -= incX
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
bands := k
|
|||
|
|
if i-k < 0 {
|
|||
|
|
bands = i
|
|||
|
|
}
|
|||
|
|
atmp := a[i*lda+k-bands:]
|
|||
|
|
xtmp := x[i-bands : i]
|
|||
|
|
var sum float64
|
|||
|
|
for j, v := range xtmp {
|
|||
|
|
sum += v * atmp[j]
|
|||
|
|
}
|
|||
|
|
x[i] -= sum
|
|||
|
|
if nonUnit {
|
|||
|
|
x[i] /= atmp[bands]
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
bands := k
|
|||
|
|
if i-k < 0 {
|
|||
|
|
bands = i
|
|||
|
|
}
|
|||
|
|
atmp := a[i*lda+k-bands:]
|
|||
|
|
var (
|
|||
|
|
sum float64
|
|||
|
|
jx int
|
|||
|
|
)
|
|||
|
|
for j := 0; j < bands; j++ {
|
|||
|
|
sum += x[ix-bands*incX+jx] * atmp[j]
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
x[ix] -= sum
|
|||
|
|
if nonUnit {
|
|||
|
|
x[ix] /= atmp[bands]
|
|||
|
|
}
|
|||
|
|
ix += incX
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
// Cases where a is transposed.
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
bands := k
|
|||
|
|
if i-k < 0 {
|
|||
|
|
bands = i
|
|||
|
|
}
|
|||
|
|
var sum float64
|
|||
|
|
for j := 0; j < bands; j++ {
|
|||
|
|
sum += x[i-bands+j] * a[(i-bands+j)*lda+bands-j]
|
|||
|
|
}
|
|||
|
|
x[i] -= sum
|
|||
|
|
if nonUnit {
|
|||
|
|
x[i] /= a[i*lda]
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
bands := k
|
|||
|
|
if i-k < 0 {
|
|||
|
|
bands = i
|
|||
|
|
}
|
|||
|
|
var (
|
|||
|
|
sum float64
|
|||
|
|
jx int
|
|||
|
|
)
|
|||
|
|
for j := 0; j < bands; j++ {
|
|||
|
|
sum += x[ix-bands*incX+jx] * a[(i-bands+j)*lda+bands-j]
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
x[ix] -= sum
|
|||
|
|
if nonUnit {
|
|||
|
|
x[ix] /= a[i*lda]
|
|||
|
|
}
|
|||
|
|
ix += incX
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
bands := k
|
|||
|
|
if i+bands >= n {
|
|||
|
|
bands = n - i - 1
|
|||
|
|
}
|
|||
|
|
var sum float64
|
|||
|
|
xtmp := x[i+1 : i+1+bands]
|
|||
|
|
for j, v := range xtmp {
|
|||
|
|
sum += v * a[(i+j+1)*lda+k-j-1]
|
|||
|
|
}
|
|||
|
|
x[i] -= sum
|
|||
|
|
if nonUnit {
|
|||
|
|
x[i] /= a[i*lda+k]
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx + (n-1)*incX
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
bands := k
|
|||
|
|
if i+bands >= n {
|
|||
|
|
bands = n - i - 1
|
|||
|
|
}
|
|||
|
|
var (
|
|||
|
|
sum float64
|
|||
|
|
jx int
|
|||
|
|
)
|
|||
|
|
for j := 0; j < bands; j++ {
|
|||
|
|
sum += x[ix+jx+incX] * a[(i+j+1)*lda+k-j-1]
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
x[ix] -= sum
|
|||
|
|
if nonUnit {
|
|||
|
|
x[ix] /= a[i*lda+k]
|
|||
|
|
}
|
|||
|
|
ix -= incX
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Dsbmv performs the matrix-vector operation
|
|||
|
|
// y = alpha * A * x + beta * y
|
|||
|
|
// where A is an n×n symmetric band matrix with k super-diagonals, x and y are
|
|||
|
|
// vectors, and alpha and beta are scalars.
|
|||
|
|
func (Implementation) Dsbmv(ul blas.Uplo, n, k int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int) {
|
|||
|
|
if ul != blas.Lower && ul != blas.Upper {
|
|||
|
|
panic(badUplo)
|
|||
|
|
}
|
|||
|
|
if n < 0 {
|
|||
|
|
panic(nLT0)
|
|||
|
|
}
|
|||
|
|
if k < 0 {
|
|||
|
|
panic(kLT0)
|
|||
|
|
}
|
|||
|
|
if lda < k+1 {
|
|||
|
|
panic(badLdA)
|
|||
|
|
}
|
|||
|
|
if incX == 0 {
|
|||
|
|
panic(zeroIncX)
|
|||
|
|
}
|
|||
|
|
if incY == 0 {
|
|||
|
|
panic(zeroIncY)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if n == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// For zero matrix size the following slice length checks are trivially satisfied.
|
|||
|
|
if len(a) < lda*(n-1)+k+1 {
|
|||
|
|
panic(shortA)
|
|||
|
|
}
|
|||
|
|
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
|||
|
|
panic(shortX)
|
|||
|
|
}
|
|||
|
|
if (incY > 0 && len(y) <= (n-1)*incY) || (incY < 0 && len(y) <= (1-n)*incY) {
|
|||
|
|
panic(shortY)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if alpha == 0 && beta == 1 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Set up indexes
|
|||
|
|
lenX := n
|
|||
|
|
lenY := n
|
|||
|
|
var kx, ky int
|
|||
|
|
if incX < 0 {
|
|||
|
|
kx = -(lenX - 1) * incX
|
|||
|
|
}
|
|||
|
|
if incY < 0 {
|
|||
|
|
ky = -(lenY - 1) * incY
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Form y = beta * y.
|
|||
|
|
if beta != 1 {
|
|||
|
|
if incY == 1 {
|
|||
|
|
if beta == 0 {
|
|||
|
|
for i := range y[:n] {
|
|||
|
|
y[i] = 0
|
|||
|
|
}
|
|||
|
|
} else {
|
|||
|
|
f64.ScalUnitary(beta, y[:n])
|
|||
|
|
}
|
|||
|
|
} else {
|
|||
|
|
iy := ky
|
|||
|
|
if beta == 0 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
y[iy] = 0
|
|||
|
|
iy += incY
|
|||
|
|
}
|
|||
|
|
} else {
|
|||
|
|
if incY > 0 {
|
|||
|
|
f64.ScalInc(beta, y, uintptr(n), uintptr(incY))
|
|||
|
|
} else {
|
|||
|
|
f64.ScalInc(beta, y, uintptr(n), uintptr(-incY))
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if alpha == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
if incX == 1 {
|
|||
|
|
iy := ky
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
atmp := a[i*lda:]
|
|||
|
|
tmp := alpha * x[i]
|
|||
|
|
sum := tmp * atmp[0]
|
|||
|
|
u := min(k, n-i-1)
|
|||
|
|
jy := incY
|
|||
|
|
for j := 1; j <= u; j++ {
|
|||
|
|
v := atmp[j]
|
|||
|
|
sum += alpha * x[i+j] * v
|
|||
|
|
y[iy+jy] += tmp * v
|
|||
|
|
jy += incY
|
|||
|
|
}
|
|||
|
|
y[iy] += sum
|
|||
|
|
iy += incY
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
iy := ky
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
atmp := a[i*lda:]
|
|||
|
|
tmp := alpha * x[ix]
|
|||
|
|
sum := tmp * atmp[0]
|
|||
|
|
u := min(k, n-i-1)
|
|||
|
|
jx := incX
|
|||
|
|
jy := incY
|
|||
|
|
for j := 1; j <= u; j++ {
|
|||
|
|
v := atmp[j]
|
|||
|
|
sum += alpha * x[ix+jx] * v
|
|||
|
|
y[iy+jy] += tmp * v
|
|||
|
|
jx += incX
|
|||
|
|
jy += incY
|
|||
|
|
}
|
|||
|
|
y[iy] += sum
|
|||
|
|
ix += incX
|
|||
|
|
iy += incY
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Casses where a has bands below the diagonal.
|
|||
|
|
if incX == 1 {
|
|||
|
|
iy := ky
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
l := max(0, k-i)
|
|||
|
|
tmp := alpha * x[i]
|
|||
|
|
jy := l * incY
|
|||
|
|
atmp := a[i*lda:]
|
|||
|
|
for j := l; j < k; j++ {
|
|||
|
|
v := atmp[j]
|
|||
|
|
y[iy] += alpha * v * x[i-k+j]
|
|||
|
|
y[iy-k*incY+jy] += tmp * v
|
|||
|
|
jy += incY
|
|||
|
|
}
|
|||
|
|
y[iy] += tmp * atmp[k]
|
|||
|
|
iy += incY
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
iy := ky
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
l := max(0, k-i)
|
|||
|
|
tmp := alpha * x[ix]
|
|||
|
|
jx := l * incX
|
|||
|
|
jy := l * incY
|
|||
|
|
atmp := a[i*lda:]
|
|||
|
|
for j := l; j < k; j++ {
|
|||
|
|
v := atmp[j]
|
|||
|
|
y[iy] += alpha * v * x[ix-k*incX+jx]
|
|||
|
|
y[iy-k*incY+jy] += tmp * v
|
|||
|
|
jx += incX
|
|||
|
|
jy += incY
|
|||
|
|
}
|
|||
|
|
y[iy] += tmp * atmp[k]
|
|||
|
|
ix += incX
|
|||
|
|
iy += incY
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Dsyr performs the symmetric rank-one update
|
|||
|
|
// A += alpha * x * x^T
|
|||
|
|
// where A is an n×n symmetric matrix, and x is a vector.
|
|||
|
|
func (Implementation) Dsyr(ul blas.Uplo, n int, alpha float64, x []float64, incX int, a []float64, lda int) {
|
|||
|
|
if ul != blas.Lower && ul != blas.Upper {
|
|||
|
|
panic(badUplo)
|
|||
|
|
}
|
|||
|
|
if n < 0 {
|
|||
|
|
panic(nLT0)
|
|||
|
|
}
|
|||
|
|
if lda < max(1, n) {
|
|||
|
|
panic(badLdA)
|
|||
|
|
}
|
|||
|
|
if incX == 0 {
|
|||
|
|
panic(zeroIncX)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if n == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// For zero matrix size the following slice length checks are trivially satisfied.
|
|||
|
|
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
|||
|
|
panic(shortX)
|
|||
|
|
}
|
|||
|
|
if len(a) < lda*(n-1)+n {
|
|||
|
|
panic(shortA)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if alpha == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
lenX := n
|
|||
|
|
var kx int
|
|||
|
|
if incX < 0 {
|
|||
|
|
kx = -(lenX - 1) * incX
|
|||
|
|
}
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
tmp := x[i] * alpha
|
|||
|
|
if tmp != 0 {
|
|||
|
|
atmp := a[i*lda+i : i*lda+n]
|
|||
|
|
xtmp := x[i:n]
|
|||
|
|
for j, v := range xtmp {
|
|||
|
|
atmp[j] += v * tmp
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
tmp := x[ix] * alpha
|
|||
|
|
if tmp != 0 {
|
|||
|
|
jx := ix
|
|||
|
|
atmp := a[i*lda:]
|
|||
|
|
for j := i; j < n; j++ {
|
|||
|
|
atmp[j] += x[jx] * tmp
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
ix += incX
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
// Cases where a is lower triangular.
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
tmp := x[i] * alpha
|
|||
|
|
if tmp != 0 {
|
|||
|
|
atmp := a[i*lda:]
|
|||
|
|
xtmp := x[:i+1]
|
|||
|
|
for j, v := range xtmp {
|
|||
|
|
atmp[j] += tmp * v
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
tmp := x[ix] * alpha
|
|||
|
|
if tmp != 0 {
|
|||
|
|
atmp := a[i*lda:]
|
|||
|
|
jx := kx
|
|||
|
|
for j := 0; j < i+1; j++ {
|
|||
|
|
atmp[j] += tmp * x[jx]
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
ix += incX
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Dsyr2 performs the symmetric rank-two update
|
|||
|
|
// A += alpha * x * y^T + alpha * y * x^T
|
|||
|
|
// where A is an n×n symmetric matrix, x and y are vectors, and alpha is a scalar.
|
|||
|
|
func (Implementation) Dsyr2(ul blas.Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int) {
|
|||
|
|
if ul != blas.Lower && ul != blas.Upper {
|
|||
|
|
panic(badUplo)
|
|||
|
|
}
|
|||
|
|
if n < 0 {
|
|||
|
|
panic(nLT0)
|
|||
|
|
}
|
|||
|
|
if lda < max(1, n) {
|
|||
|
|
panic(badLdA)
|
|||
|
|
}
|
|||
|
|
if incX == 0 {
|
|||
|
|
panic(zeroIncX)
|
|||
|
|
}
|
|||
|
|
if incY == 0 {
|
|||
|
|
panic(zeroIncY)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if n == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// For zero matrix size the following slice length checks are trivially satisfied.
|
|||
|
|
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
|||
|
|
panic(shortX)
|
|||
|
|
}
|
|||
|
|
if (incY > 0 && len(y) <= (n-1)*incY) || (incY < 0 && len(y) <= (1-n)*incY) {
|
|||
|
|
panic(shortY)
|
|||
|
|
}
|
|||
|
|
if len(a) < lda*(n-1)+n {
|
|||
|
|
panic(shortA)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if alpha == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
var ky, kx int
|
|||
|
|
if incY < 0 {
|
|||
|
|
ky = -(n - 1) * incY
|
|||
|
|
}
|
|||
|
|
if incX < 0 {
|
|||
|
|
kx = -(n - 1) * incX
|
|||
|
|
}
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
if incX == 1 && incY == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
xi := x[i]
|
|||
|
|
yi := y[i]
|
|||
|
|
atmp := a[i*lda:]
|
|||
|
|
for j := i; j < n; j++ {
|
|||
|
|
atmp[j] += alpha * (xi*y[j] + x[j]*yi)
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
iy := ky
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
jx := kx + i*incX
|
|||
|
|
jy := ky + i*incY
|
|||
|
|
xi := x[ix]
|
|||
|
|
yi := y[iy]
|
|||
|
|
atmp := a[i*lda:]
|
|||
|
|
for j := i; j < n; j++ {
|
|||
|
|
atmp[j] += alpha * (xi*y[jy] + x[jx]*yi)
|
|||
|
|
jx += incX
|
|||
|
|
jy += incY
|
|||
|
|
}
|
|||
|
|
ix += incX
|
|||
|
|
iy += incY
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
if incX == 1 && incY == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
xi := x[i]
|
|||
|
|
yi := y[i]
|
|||
|
|
atmp := a[i*lda:]
|
|||
|
|
for j := 0; j <= i; j++ {
|
|||
|
|
atmp[j] += alpha * (xi*y[j] + x[j]*yi)
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
iy := ky
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
jx := kx
|
|||
|
|
jy := ky
|
|||
|
|
xi := x[ix]
|
|||
|
|
yi := y[iy]
|
|||
|
|
atmp := a[i*lda:]
|
|||
|
|
for j := 0; j <= i; j++ {
|
|||
|
|
atmp[j] += alpha * (xi*y[jy] + x[jx]*yi)
|
|||
|
|
jx += incX
|
|||
|
|
jy += incY
|
|||
|
|
}
|
|||
|
|
ix += incX
|
|||
|
|
iy += incY
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Dtpsv solves one of the systems of equations
|
|||
|
|
// A * x = b if tA == blas.NoTrans
|
|||
|
|
// A^T * x = b if tA == blas.Trans or blas.ConjTrans
|
|||
|
|
// where A is an n×n triangular matrix in packed format, and x and b are vectors.
|
|||
|
|
//
|
|||
|
|
// At entry to the function, x contains the values of b, and the result is
|
|||
|
|
// stored in-place into x.
|
|||
|
|
//
|
|||
|
|
// No test for singularity or near-singularity is included in this
|
|||
|
|
// routine. Such tests must be performed before calling this routine.
|
|||
|
|
func (Implementation) Dtpsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, ap []float64, x []float64, incX int) {
|
|||
|
|
if ul != blas.Lower && ul != blas.Upper {
|
|||
|
|
panic(badUplo)
|
|||
|
|
}
|
|||
|
|
if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
|
|||
|
|
panic(badTranspose)
|
|||
|
|
}
|
|||
|
|
if d != blas.NonUnit && d != blas.Unit {
|
|||
|
|
panic(badDiag)
|
|||
|
|
}
|
|||
|
|
if n < 0 {
|
|||
|
|
panic(nLT0)
|
|||
|
|
}
|
|||
|
|
if incX == 0 {
|
|||
|
|
panic(zeroIncX)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if n == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// For zero matrix size the following slice length checks are trivially satisfied.
|
|||
|
|
if len(ap) < n*(n+1)/2 {
|
|||
|
|
panic(shortAP)
|
|||
|
|
}
|
|||
|
|
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
|||
|
|
panic(shortX)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
var kx int
|
|||
|
|
if incX < 0 {
|
|||
|
|
kx = -(n - 1) * incX
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
nonUnit := d == blas.NonUnit
|
|||
|
|
var offset int // Offset is the index of (i,i)
|
|||
|
|
if tA == blas.NoTrans {
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
offset = n*(n+1)/2 - 1
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
atmp := ap[offset+1 : offset+n-i]
|
|||
|
|
xtmp := x[i+1:]
|
|||
|
|
var sum float64
|
|||
|
|
for j, v := range atmp {
|
|||
|
|
sum += v * xtmp[j]
|
|||
|
|
}
|
|||
|
|
x[i] -= sum
|
|||
|
|
if nonUnit {
|
|||
|
|
x[i] /= ap[offset]
|
|||
|
|
}
|
|||
|
|
offset -= n - i + 1
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx + (n-1)*incX
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
atmp := ap[offset+1 : offset+n-i]
|
|||
|
|
jx := kx + (i+1)*incX
|
|||
|
|
var sum float64
|
|||
|
|
for _, v := range atmp {
|
|||
|
|
sum += v * x[jx]
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
x[ix] -= sum
|
|||
|
|
if nonUnit {
|
|||
|
|
x[ix] /= ap[offset]
|
|||
|
|
}
|
|||
|
|
ix -= incX
|
|||
|
|
offset -= n - i + 1
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
atmp := ap[offset-i : offset]
|
|||
|
|
var sum float64
|
|||
|
|
for j, v := range atmp {
|
|||
|
|
sum += v * x[j]
|
|||
|
|
}
|
|||
|
|
x[i] -= sum
|
|||
|
|
if nonUnit {
|
|||
|
|
x[i] /= ap[offset]
|
|||
|
|
}
|
|||
|
|
offset += i + 2
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
jx := kx
|
|||
|
|
atmp := ap[offset-i : offset]
|
|||
|
|
var sum float64
|
|||
|
|
for _, v := range atmp {
|
|||
|
|
sum += v * x[jx]
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
x[ix] -= sum
|
|||
|
|
if nonUnit {
|
|||
|
|
x[ix] /= ap[offset]
|
|||
|
|
}
|
|||
|
|
ix += incX
|
|||
|
|
offset += i + 2
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
// Cases where ap is transposed.
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
if nonUnit {
|
|||
|
|
x[i] /= ap[offset]
|
|||
|
|
}
|
|||
|
|
xi := x[i]
|
|||
|
|
atmp := ap[offset+1 : offset+n-i]
|
|||
|
|
xtmp := x[i+1:]
|
|||
|
|
for j, v := range atmp {
|
|||
|
|
xtmp[j] -= v * xi
|
|||
|
|
}
|
|||
|
|
offset += n - i
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
if nonUnit {
|
|||
|
|
x[ix] /= ap[offset]
|
|||
|
|
}
|
|||
|
|
xix := x[ix]
|
|||
|
|
atmp := ap[offset+1 : offset+n-i]
|
|||
|
|
jx := kx + (i+1)*incX
|
|||
|
|
for _, v := range atmp {
|
|||
|
|
x[jx] -= v * xix
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
ix += incX
|
|||
|
|
offset += n - i
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
if incX == 1 {
|
|||
|
|
offset = n*(n+1)/2 - 1
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
if nonUnit {
|
|||
|
|
x[i] /= ap[offset]
|
|||
|
|
}
|
|||
|
|
xi := x[i]
|
|||
|
|
atmp := ap[offset-i : offset]
|
|||
|
|
for j, v := range atmp {
|
|||
|
|
x[j] -= v * xi
|
|||
|
|
}
|
|||
|
|
offset -= i + 1
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx + (n-1)*incX
|
|||
|
|
offset = n*(n+1)/2 - 1
|
|||
|
|
for i := n - 1; i >= 0; i-- {
|
|||
|
|
if nonUnit {
|
|||
|
|
x[ix] /= ap[offset]
|
|||
|
|
}
|
|||
|
|
xix := x[ix]
|
|||
|
|
atmp := ap[offset-i : offset]
|
|||
|
|
jx := kx
|
|||
|
|
for _, v := range atmp {
|
|||
|
|
x[jx] -= v * xix
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
ix -= incX
|
|||
|
|
offset -= i + 1
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Dspmv performs the matrix-vector operation
|
|||
|
|
// y = alpha * A * x + beta * y
|
|||
|
|
// where A is an n×n symmetric matrix in packed format, x and y are vectors,
|
|||
|
|
// and alpha and beta are scalars.
|
|||
|
|
func (Implementation) Dspmv(ul blas.Uplo, n int, alpha float64, ap []float64, x []float64, incX int, beta float64, y []float64, incY int) {
|
|||
|
|
if ul != blas.Lower && ul != blas.Upper {
|
|||
|
|
panic(badUplo)
|
|||
|
|
}
|
|||
|
|
if n < 0 {
|
|||
|
|
panic(nLT0)
|
|||
|
|
}
|
|||
|
|
if incX == 0 {
|
|||
|
|
panic(zeroIncX)
|
|||
|
|
}
|
|||
|
|
if incY == 0 {
|
|||
|
|
panic(zeroIncY)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if n == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// For zero matrix size the following slice length checks are trivially satisfied.
|
|||
|
|
if len(ap) < n*(n+1)/2 {
|
|||
|
|
panic(shortAP)
|
|||
|
|
}
|
|||
|
|
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
|||
|
|
panic(shortX)
|
|||
|
|
}
|
|||
|
|
if (incY > 0 && len(y) <= (n-1)*incY) || (incY < 0 && len(y) <= (1-n)*incY) {
|
|||
|
|
panic(shortY)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if alpha == 0 && beta == 1 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Set up start points
|
|||
|
|
var kx, ky int
|
|||
|
|
if incX < 0 {
|
|||
|
|
kx = -(n - 1) * incX
|
|||
|
|
}
|
|||
|
|
if incY < 0 {
|
|||
|
|
ky = -(n - 1) * incY
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Form y = beta * y.
|
|||
|
|
if beta != 1 {
|
|||
|
|
if incY == 1 {
|
|||
|
|
if beta == 0 {
|
|||
|
|
for i := range y[:n] {
|
|||
|
|
y[i] = 0
|
|||
|
|
}
|
|||
|
|
} else {
|
|||
|
|
f64.ScalUnitary(beta, y[:n])
|
|||
|
|
}
|
|||
|
|
} else {
|
|||
|
|
iy := ky
|
|||
|
|
if beta == 0 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
y[iy] = 0
|
|||
|
|
iy += incY
|
|||
|
|
}
|
|||
|
|
} else {
|
|||
|
|
if incY > 0 {
|
|||
|
|
f64.ScalInc(beta, y, uintptr(n), uintptr(incY))
|
|||
|
|
} else {
|
|||
|
|
f64.ScalInc(beta, y, uintptr(n), uintptr(-incY))
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if alpha == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if n == 1 {
|
|||
|
|
y[0] += alpha * ap[0] * x[0]
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
var offset int // Offset is the index of (i,i).
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
if incX == 1 {
|
|||
|
|
iy := ky
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
xv := x[i] * alpha
|
|||
|
|
sum := ap[offset] * x[i]
|
|||
|
|
atmp := ap[offset+1 : offset+n-i]
|
|||
|
|
xtmp := x[i+1:]
|
|||
|
|
jy := ky + (i+1)*incY
|
|||
|
|
for j, v := range atmp {
|
|||
|
|
sum += v * xtmp[j]
|
|||
|
|
y[jy] += v * xv
|
|||
|
|
jy += incY
|
|||
|
|
}
|
|||
|
|
y[iy] += alpha * sum
|
|||
|
|
iy += incY
|
|||
|
|
offset += n - i
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
iy := ky
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
xv := x[ix] * alpha
|
|||
|
|
sum := ap[offset] * x[ix]
|
|||
|
|
atmp := ap[offset+1 : offset+n-i]
|
|||
|
|
jx := kx + (i+1)*incX
|
|||
|
|
jy := ky + (i+1)*incY
|
|||
|
|
for _, v := range atmp {
|
|||
|
|
sum += v * x[jx]
|
|||
|
|
y[jy] += v * xv
|
|||
|
|
jx += incX
|
|||
|
|
jy += incY
|
|||
|
|
}
|
|||
|
|
y[iy] += alpha * sum
|
|||
|
|
ix += incX
|
|||
|
|
iy += incY
|
|||
|
|
offset += n - i
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
if incX == 1 {
|
|||
|
|
iy := ky
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
xv := x[i] * alpha
|
|||
|
|
atmp := ap[offset-i : offset]
|
|||
|
|
jy := ky
|
|||
|
|
var sum float64
|
|||
|
|
for j, v := range atmp {
|
|||
|
|
sum += v * x[j]
|
|||
|
|
y[jy] += v * xv
|
|||
|
|
jy += incY
|
|||
|
|
}
|
|||
|
|
sum += ap[offset] * x[i]
|
|||
|
|
y[iy] += alpha * sum
|
|||
|
|
iy += incY
|
|||
|
|
offset += i + 2
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
iy := ky
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
xv := x[ix] * alpha
|
|||
|
|
atmp := ap[offset-i : offset]
|
|||
|
|
jx := kx
|
|||
|
|
jy := ky
|
|||
|
|
var sum float64
|
|||
|
|
for _, v := range atmp {
|
|||
|
|
sum += v * x[jx]
|
|||
|
|
y[jy] += v * xv
|
|||
|
|
jx += incX
|
|||
|
|
jy += incY
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
sum += ap[offset] * x[ix]
|
|||
|
|
y[iy] += alpha * sum
|
|||
|
|
ix += incX
|
|||
|
|
iy += incY
|
|||
|
|
offset += i + 2
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Dspr performs the symmetric rank-one operation
|
|||
|
|
// A += alpha * x * x^T
|
|||
|
|
// where A is an n×n symmetric matrix in packed format, x is a vector, and
|
|||
|
|
// alpha is a scalar.
|
|||
|
|
func (Implementation) Dspr(ul blas.Uplo, n int, alpha float64, x []float64, incX int, ap []float64) {
|
|||
|
|
if ul != blas.Lower && ul != blas.Upper {
|
|||
|
|
panic(badUplo)
|
|||
|
|
}
|
|||
|
|
if n < 0 {
|
|||
|
|
panic(nLT0)
|
|||
|
|
}
|
|||
|
|
if incX == 0 {
|
|||
|
|
panic(zeroIncX)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if n == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// For zero matrix size the following slice length checks are trivially satisfied.
|
|||
|
|
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
|||
|
|
panic(shortX)
|
|||
|
|
}
|
|||
|
|
if len(ap) < n*(n+1)/2 {
|
|||
|
|
panic(shortAP)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if alpha == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
lenX := n
|
|||
|
|
var kx int
|
|||
|
|
if incX < 0 {
|
|||
|
|
kx = -(lenX - 1) * incX
|
|||
|
|
}
|
|||
|
|
var offset int // Offset is the index of (i,i).
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
atmp := ap[offset:]
|
|||
|
|
xv := alpha * x[i]
|
|||
|
|
xtmp := x[i:n]
|
|||
|
|
for j, v := range xtmp {
|
|||
|
|
atmp[j] += xv * v
|
|||
|
|
}
|
|||
|
|
offset += n - i
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
jx := kx + i*incX
|
|||
|
|
atmp := ap[offset:]
|
|||
|
|
xv := alpha * x[ix]
|
|||
|
|
for j := 0; j < n-i; j++ {
|
|||
|
|
atmp[j] += xv * x[jx]
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
ix += incX
|
|||
|
|
offset += n - i
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
if incX == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
atmp := ap[offset-i:]
|
|||
|
|
xv := alpha * x[i]
|
|||
|
|
xtmp := x[:i+1]
|
|||
|
|
for j, v := range xtmp {
|
|||
|
|
atmp[j] += xv * v
|
|||
|
|
}
|
|||
|
|
offset += i + 2
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
jx := kx
|
|||
|
|
atmp := ap[offset-i:]
|
|||
|
|
xv := alpha * x[ix]
|
|||
|
|
for j := 0; j <= i; j++ {
|
|||
|
|
atmp[j] += xv * x[jx]
|
|||
|
|
jx += incX
|
|||
|
|
}
|
|||
|
|
ix += incX
|
|||
|
|
offset += i + 2
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Dspr2 performs the symmetric rank-2 update
|
|||
|
|
// A += alpha * x * y^T + alpha * y * x^T
|
|||
|
|
// where A is an n×n symmetric matrix in packed format, x and y are vectors,
|
|||
|
|
// and alpha is a scalar.
|
|||
|
|
func (Implementation) Dspr2(ul blas.Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, ap []float64) {
|
|||
|
|
if ul != blas.Lower && ul != blas.Upper {
|
|||
|
|
panic(badUplo)
|
|||
|
|
}
|
|||
|
|
if n < 0 {
|
|||
|
|
panic(nLT0)
|
|||
|
|
}
|
|||
|
|
if incX == 0 {
|
|||
|
|
panic(zeroIncX)
|
|||
|
|
}
|
|||
|
|
if incY == 0 {
|
|||
|
|
panic(zeroIncY)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if n == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// For zero matrix size the following slice length checks are trivially satisfied.
|
|||
|
|
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
|||
|
|
panic(shortX)
|
|||
|
|
}
|
|||
|
|
if (incY > 0 && len(y) <= (n-1)*incY) || (incY < 0 && len(y) <= (1-n)*incY) {
|
|||
|
|
panic(shortY)
|
|||
|
|
}
|
|||
|
|
if len(ap) < n*(n+1)/2 {
|
|||
|
|
panic(shortAP)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Quick return if possible.
|
|||
|
|
if alpha == 0 {
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
var ky, kx int
|
|||
|
|
if incY < 0 {
|
|||
|
|
ky = -(n - 1) * incY
|
|||
|
|
}
|
|||
|
|
if incX < 0 {
|
|||
|
|
kx = -(n - 1) * incX
|
|||
|
|
}
|
|||
|
|
var offset int // Offset is the index of (i,i).
|
|||
|
|
if ul == blas.Upper {
|
|||
|
|
if incX == 1 && incY == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
atmp := ap[offset:]
|
|||
|
|
xi := x[i]
|
|||
|
|
yi := y[i]
|
|||
|
|
xtmp := x[i:n]
|
|||
|
|
ytmp := y[i:n]
|
|||
|
|
for j, v := range xtmp {
|
|||
|
|
atmp[j] += alpha * (xi*ytmp[j] + v*yi)
|
|||
|
|
}
|
|||
|
|
offset += n - i
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
iy := ky
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
jx := kx + i*incX
|
|||
|
|
jy := ky + i*incY
|
|||
|
|
atmp := ap[offset:]
|
|||
|
|
xi := x[ix]
|
|||
|
|
yi := y[iy]
|
|||
|
|
for j := 0; j < n-i; j++ {
|
|||
|
|
atmp[j] += alpha * (xi*y[jy] + x[jx]*yi)
|
|||
|
|
jx += incX
|
|||
|
|
jy += incY
|
|||
|
|
}
|
|||
|
|
ix += incX
|
|||
|
|
iy += incY
|
|||
|
|
offset += n - i
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
if incX == 1 && incY == 1 {
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
atmp := ap[offset-i:]
|
|||
|
|
xi := x[i]
|
|||
|
|
yi := y[i]
|
|||
|
|
xtmp := x[:i+1]
|
|||
|
|
for j, v := range xtmp {
|
|||
|
|
atmp[j] += alpha * (xi*y[j] + v*yi)
|
|||
|
|
}
|
|||
|
|
offset += i + 2
|
|||
|
|
}
|
|||
|
|
return
|
|||
|
|
}
|
|||
|
|
ix := kx
|
|||
|
|
iy := ky
|
|||
|
|
for i := 0; i < n; i++ {
|
|||
|
|
jx := kx
|
|||
|
|
jy := ky
|
|||
|
|
atmp := ap[offset-i:]
|
|||
|
|
for j := 0; j <= i; j++ {
|
|||
|
|
atmp[j] += alpha * (x[ix]*y[jy] + x[jx]*y[iy])
|
|||
|
|
jx += incX
|
|||
|
|
jy += incY
|
|||
|
|
}
|
|||
|
|
ix += incX
|
|||
|
|
iy += incY
|
|||
|
|
offset += i + 2
|
|||
|
|
}
|
|||
|
|
}
|