mirror of
https://github.com/TECHNOFAB11/zfs-localpv.git
synced 2025-12-16 16:23:52 +01:00
feat(modules): migrate to go modules and bump go version 1.14.4
- migrate to go module - bump go version 1.14.4 Signed-off-by: prateekpandey14 <prateek.pandey@mayadata.io>
This commit is contained in:
prateekpandey14
Pawan Prakash Sharma
parent
f5ae3ff476
commit
fa76b346a0
837 changed files with 104140 additions and 158314 deletions
314
vendor/gonum.org/v1/gonum/blas/gonum/dgemm.go
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vendored
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314
vendor/gonum.org/v1/gonum/blas/gonum/dgemm.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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"runtime"
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"sync"
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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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// Dgemm performs one of the matrix-matrix operations
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// C = alpha * A * B + beta * C
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// C = alpha * A^T * B + beta * C
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// C = alpha * A * B^T + beta * C
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// C = alpha * A^T * B^T + beta * C
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// where A is an m×k or k×m dense matrix, B is an n×k or k×n dense matrix, C is
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// an m×n matrix, and alpha and beta are scalars. tA and tB specify whether A or
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// B are transposed.
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func (Implementation) Dgemm(tA, tB blas.Transpose, m, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int) {
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switch tA {
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default:
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panic(badTranspose)
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case blas.NoTrans, blas.Trans, blas.ConjTrans:
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}
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switch tB {
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default:
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panic(badTranspose)
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case blas.NoTrans, blas.Trans, blas.ConjTrans:
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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 k < 0 {
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panic(kLT0)
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}
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aTrans := tA == blas.Trans || tA == blas.ConjTrans
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if aTrans {
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if lda < max(1, m) {
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panic(badLdA)
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}
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} else {
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if lda < max(1, k) {
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panic(badLdA)
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}
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}
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bTrans := tB == blas.Trans || tB == blas.ConjTrans
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if bTrans {
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if ldb < max(1, k) {
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panic(badLdB)
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}
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} else {
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if ldb < max(1, n) {
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panic(badLdB)
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}
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}
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if ldc < max(1, n) {
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panic(badLdC)
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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 aTrans {
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if len(a) < (k-1)*lda+m {
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panic(shortA)
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}
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} else {
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if len(a) < (m-1)*lda+k {
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panic(shortA)
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}
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}
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if bTrans {
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if len(b) < (n-1)*ldb+k {
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panic(shortB)
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}
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} else {
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if len(b) < (k-1)*ldb+n {
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panic(shortB)
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}
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}
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if len(c) < (m-1)*ldc+n {
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panic(shortC)
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}
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// Quick return if possible.
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if (alpha == 0 || k == 0) && beta == 1 {
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return
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}
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// scale c
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if beta != 1 {
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if beta == 0 {
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for i := 0; i < m; i++ {
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ctmp := c[i*ldc : i*ldc+n]
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for j := range ctmp {
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ctmp[j] = 0
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}
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}
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} else {
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for i := 0; i < m; i++ {
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ctmp := c[i*ldc : i*ldc+n]
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for j := range ctmp {
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ctmp[j] *= beta
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}
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}
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}
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}
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dgemmParallel(aTrans, bTrans, m, n, k, a, lda, b, ldb, c, ldc, alpha)
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}
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func dgemmParallel(aTrans, bTrans bool, m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
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// dgemmParallel computes a parallel matrix multiplication by partitioning
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// a and b into sub-blocks, and updating c with the multiplication of the sub-block
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// In all cases,
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// A = [ A_11 A_12 ... A_1j
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// A_21 A_22 ... A_2j
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// ...
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// A_i1 A_i2 ... A_ij]
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//
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// and same for B. All of the submatrix sizes are blockSize×blockSize except
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// at the edges.
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//
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// In all cases, there is one dimension for each matrix along which
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// C must be updated sequentially.
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// Cij = \sum_k Aik Bki, (A * B)
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// Cij = \sum_k Aki Bkj, (A^T * B)
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// Cij = \sum_k Aik Bjk, (A * B^T)
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// Cij = \sum_k Aki Bjk, (A^T * B^T)
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//
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// This code computes one {i, j} block sequentially along the k dimension,
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// and computes all of the {i, j} blocks concurrently. This
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// partitioning allows Cij to be updated in-place without race-conditions.
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// Instead of launching a goroutine for each possible concurrent computation,
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// a number of worker goroutines are created and channels are used to pass
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// available and completed cases.
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//
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// http://alexkr.com/docs/matrixmult.pdf is a good reference on matrix-matrix
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// multiplies, though this code does not copy matrices to attempt to eliminate
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// cache misses.
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maxKLen := k
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parBlocks := blocks(m, blockSize) * blocks(n, blockSize)
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if parBlocks < minParBlock {
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// The matrix multiplication is small in the dimensions where it can be
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// computed concurrently. Just do it in serial.
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dgemmSerial(aTrans, bTrans, m, n, k, a, lda, b, ldb, c, ldc, alpha)
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return
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}
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nWorkers := runtime.GOMAXPROCS(0)
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if parBlocks < nWorkers {
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nWorkers = parBlocks
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}
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// There is a tradeoff between the workers having to wait for work
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// and a large buffer making operations slow.
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buf := buffMul * nWorkers
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if buf > parBlocks {
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buf = parBlocks
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}
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sendChan := make(chan subMul, buf)
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// Launch workers. A worker receives an {i, j} submatrix of c, and computes
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// A_ik B_ki (or the transposed version) storing the result in c_ij. When the
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// channel is finally closed, it signals to the waitgroup that it has finished
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// computing.
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var wg sync.WaitGroup
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for i := 0; i < nWorkers; i++ {
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wg.Add(1)
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go func() {
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defer wg.Done()
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for sub := range sendChan {
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i := sub.i
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j := sub.j
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leni := blockSize
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if i+leni > m {
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leni = m - i
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}
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lenj := blockSize
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if j+lenj > n {
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lenj = n - j
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}
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cSub := sliceView64(c, ldc, i, j, leni, lenj)
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// Compute A_ik B_kj for all k
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for k := 0; k < maxKLen; k += blockSize {
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lenk := blockSize
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if k+lenk > maxKLen {
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lenk = maxKLen - k
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}
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var aSub, bSub []float64
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if aTrans {
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aSub = sliceView64(a, lda, k, i, lenk, leni)
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} else {
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aSub = sliceView64(a, lda, i, k, leni, lenk)
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}
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if bTrans {
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bSub = sliceView64(b, ldb, j, k, lenj, lenk)
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} else {
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bSub = sliceView64(b, ldb, k, j, lenk, lenj)
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}
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dgemmSerial(aTrans, bTrans, leni, lenj, lenk, aSub, lda, bSub, ldb, cSub, ldc, alpha)
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}
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}
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}()
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}
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// Send out all of the {i, j} subblocks for computation.
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for i := 0; i < m; i += blockSize {
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for j := 0; j < n; j += blockSize {
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sendChan <- subMul{
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i: i,
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j: j,
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}
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}
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}
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close(sendChan)
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wg.Wait()
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}
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// dgemmSerial is serial matrix multiply
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func dgemmSerial(aTrans, bTrans bool, m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
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switch {
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case !aTrans && !bTrans:
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dgemmSerialNotNot(m, n, k, a, lda, b, ldb, c, ldc, alpha)
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return
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case aTrans && !bTrans:
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dgemmSerialTransNot(m, n, k, a, lda, b, ldb, c, ldc, alpha)
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return
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case !aTrans && bTrans:
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dgemmSerialNotTrans(m, n, k, a, lda, b, ldb, c, ldc, alpha)
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return
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case aTrans && bTrans:
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dgemmSerialTransTrans(m, n, k, a, lda, b, ldb, c, ldc, alpha)
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return
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default:
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panic("unreachable")
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}
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}
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// dgemmSerial where neither a nor b are transposed
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func dgemmSerialNotNot(m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
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// This style is used instead of the literal [i*stride +j]) is used because
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// approximately 5 times faster as of go 1.3.
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for i := 0; i < m; i++ {
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ctmp := c[i*ldc : i*ldc+n]
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for l, v := range a[i*lda : i*lda+k] {
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tmp := alpha * v
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if tmp != 0 {
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f64.AxpyUnitary(tmp, b[l*ldb:l*ldb+n], ctmp)
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}
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}
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}
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}
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// dgemmSerial where neither a is transposed and b is not
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func dgemmSerialTransNot(m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
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// This style is used instead of the literal [i*stride +j]) is used because
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// approximately 5 times faster as of go 1.3.
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for l := 0; l < k; l++ {
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btmp := b[l*ldb : l*ldb+n]
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for i, v := range a[l*lda : l*lda+m] {
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tmp := alpha * v
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if tmp != 0 {
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ctmp := c[i*ldc : i*ldc+n]
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f64.AxpyUnitary(tmp, btmp, ctmp)
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}
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}
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}
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}
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// dgemmSerial where neither a is not transposed and b is
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func dgemmSerialNotTrans(m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
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// This style is used instead of the literal [i*stride +j]) is used because
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// approximately 5 times faster as of go 1.3.
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for i := 0; i < m; i++ {
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atmp := a[i*lda : i*lda+k]
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ctmp := c[i*ldc : i*ldc+n]
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for j := 0; j < n; j++ {
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ctmp[j] += alpha * f64.DotUnitary(atmp, b[j*ldb:j*ldb+k])
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}
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}
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}
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// dgemmSerial where both are transposed
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func dgemmSerialTransTrans(m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
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// This style is used instead of the literal [i*stride +j]) is used because
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// approximately 5 times faster as of go 1.3.
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for l := 0; l < k; l++ {
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for i, v := range a[l*lda : l*lda+m] {
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tmp := alpha * v
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if tmp != 0 {
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ctmp := c[i*ldc : i*ldc+n]
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f64.AxpyInc(tmp, b[l:], ctmp, uintptr(n), uintptr(ldb), 1, 0, 0)
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}
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}
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}
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}
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func sliceView64(a []float64, lda, i, j, r, c int) []float64 {
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return a[i*lda+j : (i+r-1)*lda+j+c]
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}
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88
vendor/gonum.org/v1/gonum/blas/gonum/doc.go
generated
vendored
Normal file
88
vendor/gonum.org/v1/gonum/blas/gonum/doc.go
generated
vendored
Normal file
|
|
@ -0,0 +1,88 @@
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|||
// 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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// Ensure changes made to blas/native are reflected in blas/cgo where relevant.
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/*
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Package gonum is a Go implementation of the BLAS API. This implementation
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panics when the input arguments are invalid as per the standard, for example
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if a vector increment is zero. Note that the treatment of NaN values
|
||||
is not specified, and differs among the BLAS implementations.
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gonum.org/v1/gonum/blas/blas64 provides helpful wrapper functions to the BLAS
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interface. The rest of this text describes the layout of the data for the input types.
|
||||
|
||||
Note that in the function documentation, x[i] refers to the i^th element
|
||||
of the vector, which will be different from the i^th element of the slice if
|
||||
incX != 1.
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||||
|
||||
See http://www.netlib.org/lapack/explore-html/d4/de1/_l_i_c_e_n_s_e_source.html
|
||||
for more license information.
|
||||
|
||||
Vector arguments are effectively strided slices. They have two input arguments,
|
||||
a number of elements, n, and an increment, incX. The increment specifies the
|
||||
distance between elements of the vector. The actual Go slice may be longer
|
||||
than necessary.
|
||||
The increment may be positive or negative, except in functions with only
|
||||
a single vector argument where the increment may only be positive. If the increment
|
||||
is negative, s[0] is the last element in the slice. Note that this is not the same
|
||||
as counting backward from the end of the slice, as len(s) may be longer than
|
||||
necessary. So, for example, if n = 5 and incX = 3, the elements of s are
|
||||
[0 * * 1 * * 2 * * 3 * * 4 * * * ...]
|
||||
where ∗ elements are never accessed. If incX = -3, the same elements are
|
||||
accessed, just in reverse order (4, 3, 2, 1, 0).
|
||||
|
||||
Dense matrices are specified by a number of rows, a number of columns, and a stride.
|
||||
The stride specifies the number of entries in the slice between the first element
|
||||
of successive rows. The stride must be at least as large as the number of columns
|
||||
but may be longer.
|
||||
[a00 ... a0n a0* ... a1stride-1 a21 ... amn am* ... amstride-1]
|
||||
Thus, dense[i*ld + j] refers to the {i, j}th element of the matrix.
|
||||
|
||||
Symmetric and triangular matrices (non-packed) are stored identically to Dense,
|
||||
except that only elements in one triangle of the matrix are accessed.
|
||||
|
||||
Packed symmetric and packed triangular matrices are laid out with the entries
|
||||
condensed such that all of the unreferenced elements are removed. So, the upper triangular
|
||||
matrix
|
||||
[
|
||||
1 2 3
|
||||
0 4 5
|
||||
0 0 6
|
||||
]
|
||||
and the lower-triangular matrix
|
||||
[
|
||||
1 0 0
|
||||
2 3 0
|
||||
4 5 6
|
||||
]
|
||||
will both be compacted as [1 2 3 4 5 6]. The (i, j) element of the original
|
||||
dense matrix can be found at element i*n - (i-1)*i/2 + j for upper triangular,
|
||||
and at element i * (i+1) /2 + j for lower triangular.
|
||||
|
||||
Banded matrices are laid out in a compact format, constructed by removing the
|
||||
zeros in the rows and aligning the diagonals. For example, the matrix
|
||||
[
|
||||
1 2 3 0 0 0
|
||||
4 5 6 7 0 0
|
||||
0 8 9 10 11 0
|
||||
0 0 12 13 14 15
|
||||
0 0 0 16 17 18
|
||||
0 0 0 0 19 20
|
||||
]
|
||||
|
||||
implicitly becomes (∗ entries are never accessed)
|
||||
[
|
||||
* 1 2 3
|
||||
4 5 6 7
|
||||
8 9 10 11
|
||||
12 13 14 15
|
||||
16 17 18 *
|
||||
19 20 * *
|
||||
]
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||||
which is given to the BLAS routine as [∗ 1 2 3 4 ...].
|
||||
|
||||
See http://www.crest.iu.edu/research/mtl/reference/html/banded.html
|
||||
for more information
|
||||
*/
|
||||
package gonum // import "gonum.org/v1/gonum/blas/gonum"
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||||
35
vendor/gonum.org/v1/gonum/blas/gonum/errors.go
generated
vendored
Normal file
35
vendor/gonum.org/v1/gonum/blas/gonum/errors.go
generated
vendored
Normal file
|
|
@ -0,0 +1,35 @@
|
|||
// 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
|
||||
|
||||
// Panic strings used during parameter checks.
|
||||
// This list is duplicated in netlib/blas/netlib. Keep in sync.
|
||||
const (
|
||||
zeroIncX = "blas: zero x index increment"
|
||||
zeroIncY = "blas: zero y index increment"
|
||||
|
||||
mLT0 = "blas: m < 0"
|
||||
nLT0 = "blas: n < 0"
|
||||
kLT0 = "blas: k < 0"
|
||||
kLLT0 = "blas: kL < 0"
|
||||
kULT0 = "blas: kU < 0"
|
||||
|
||||
badUplo = "blas: illegal triangle"
|
||||
badTranspose = "blas: illegal transpose"
|
||||
badDiag = "blas: illegal diagonal"
|
||||
badSide = "blas: illegal side"
|
||||
badFlag = "blas: illegal rotm flag"
|
||||
|
||||
badLdA = "blas: bad leading dimension of A"
|
||||
badLdB = "blas: bad leading dimension of B"
|
||||
badLdC = "blas: bad leading dimension of C"
|
||||
|
||||
shortX = "blas: insufficient length of x"
|
||||
shortY = "blas: insufficient length of y"
|
||||
shortAP = "blas: insufficient length of ap"
|
||||
shortA = "blas: insufficient length of a"
|
||||
shortB = "blas: insufficient length of b"
|
||||
shortC = "blas: insufficient length of c"
|
||||
)
|
||||
190
vendor/gonum.org/v1/gonum/blas/gonum/gemv.go
generated
vendored
Normal file
190
vendor/gonum.org/v1/gonum/blas/gonum/gemv.go
generated
vendored
Normal file
|
|
@ -0,0 +1,190 @@
|
|||
// Copyright ©2018 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/internal/asm/f32"
|
||||
"gonum.org/v1/gonum/internal/asm/f64"
|
||||
)
|
||||
|
||||
// TODO(Kunde21): Merge these methods back into level2double/level2single when Sgemv assembly kernels are merged into f32.
|
||||
|
||||
// Dgemv computes
|
||||
// y = alpha * A * x + beta * y if tA = blas.NoTrans
|
||||
// y = alpha * A^T * x + beta * y if tA = blas.Trans or blas.ConjTrans
|
||||
// where A is an m×n dense matrix, x and y are vectors, and alpha and beta are scalars.
|
||||
func (Implementation) Dgemv(tA blas.Transpose, m, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int) {
|
||||
if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
|
||||
panic(badTranspose)
|
||||
}
|
||||
if m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if lda < max(1, n) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
// Set up indexes
|
||||
lenX := m
|
||||
lenY := n
|
||||
if tA == blas.NoTrans {
|
||||
lenX = n
|
||||
lenY = m
|
||||
}
|
||||
|
||||
// Quick return if possible
|
||||
if m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
if (incX > 0 && (lenX-1)*incX >= len(x)) || (incX < 0 && (1-lenX)*incX >= len(x)) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && (lenY-1)*incY >= len(y)) || (incY < 0 && (1-lenY)*incY >= len(y)) {
|
||||
panic(shortY)
|
||||
}
|
||||
if len(a) < lda*(m-1)+n {
|
||||
panic(shortA)
|
||||
}
|
||||
|
||||
// Quick return if possible
|
||||
if alpha == 0 && beta == 1 {
|
||||
return
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
// First form y = beta * y
|
||||
if incY > 0 {
|
||||
Implementation{}.Dscal(lenY, beta, y, incY)
|
||||
} else {
|
||||
Implementation{}.Dscal(lenY, beta, y, -incY)
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// Form y = alpha * A * x + y
|
||||
if tA == blas.NoTrans {
|
||||
f64.GemvN(uintptr(m), uintptr(n), alpha, a, uintptr(lda), x, uintptr(incX), beta, y, uintptr(incY))
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
f64.GemvT(uintptr(m), uintptr(n), alpha, a, uintptr(lda), x, uintptr(incX), beta, y, uintptr(incY))
|
||||
}
|
||||
|
||||
// Sgemv computes
|
||||
// y = alpha * A * x + beta * y if tA = blas.NoTrans
|
||||
// y = alpha * A^T * x + beta * y if tA = blas.Trans or blas.ConjTrans
|
||||
// where A is an m×n dense matrix, x and y are vectors, and alpha and beta are scalars.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Sgemv(tA blas.Transpose, m, n int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int) {
|
||||
if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
|
||||
panic(badTranspose)
|
||||
}
|
||||
if m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
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 m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// Set up indexes
|
||||
lenX := m
|
||||
lenY := n
|
||||
if tA == blas.NoTrans {
|
||||
lenX = n
|
||||
lenY = m
|
||||
}
|
||||
if (incX > 0 && (lenX-1)*incX >= len(x)) || (incX < 0 && (1-lenX)*incX >= len(x)) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && (lenY-1)*incY >= len(y)) || (incY < 0 && (1-lenY)*incY >= len(y)) {
|
||||
panic(shortY)
|
||||
}
|
||||
if len(a) < lda*(m-1)+n {
|
||||
panic(shortA)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if alpha == 0 && beta == 1 {
|
||||
return
|
||||
}
|
||||
|
||||
// First form y = beta * y
|
||||
if incY > 0 {
|
||||
Implementation{}.Sscal(lenY, beta, y, incY)
|
||||
} else {
|
||||
Implementation{}.Sscal(lenY, beta, y, -incY)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
var kx, ky int
|
||||
if incX < 0 {
|
||||
kx = -(lenX - 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
ky = -(lenY - 1) * incY
|
||||
}
|
||||
|
||||
// Form y = alpha * A * x + y
|
||||
if tA == blas.NoTrans {
|
||||
if incX == 1 && incY == 1 {
|
||||
for i := 0; i < m; i++ {
|
||||
y[i] += alpha * f32.DotUnitary(a[lda*i:lda*i+n], x[:n])
|
||||
}
|
||||
return
|
||||
}
|
||||
iy := ky
|
||||
for i := 0; i < m; i++ {
|
||||
y[iy] += alpha * f32.DotInc(x, a[lda*i:lda*i+n], uintptr(n), uintptr(incX), 1, uintptr(kx), 0)
|
||||
iy += incY
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if incX == 1 && incY == 1 {
|
||||
for i := 0; i < m; i++ {
|
||||
tmp := alpha * x[i]
|
||||
if tmp != 0 {
|
||||
f32.AxpyUnitaryTo(y, tmp, a[lda*i:lda*i+n], y[:n])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
ix := kx
|
||||
for i := 0; i < m; i++ {
|
||||
tmp := alpha * x[ix]
|
||||
if tmp != 0 {
|
||||
f32.AxpyInc(tmp, a[lda*i:lda*i+n], y, uintptr(n), 1, uintptr(incY), 0, uintptr(ky))
|
||||
}
|
||||
ix += incX
|
||||
}
|
||||
}
|
||||
58
vendor/gonum.org/v1/gonum/blas/gonum/gonum.go
generated
vendored
Normal file
58
vendor/gonum.org/v1/gonum/blas/gonum/gonum.go
generated
vendored
Normal file
|
|
@ -0,0 +1,58 @@
|
|||
// 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.
|
||||
|
||||
//go:generate ./single_precision.bash
|
||||
|
||||
package gonum
|
||||
|
||||
import (
|
||||
"math"
|
||||
|
||||
"gonum.org/v1/gonum/internal/math32"
|
||||
)
|
||||
|
||||
type Implementation struct{}
|
||||
|
||||
// [SD]gemm behavior constants. These are kept here to keep them out of the
|
||||
// way during single precision code genration.
|
||||
const (
|
||||
blockSize = 64 // b x b matrix
|
||||
minParBlock = 4 // minimum number of blocks needed to go parallel
|
||||
buffMul = 4 // how big is the buffer relative to the number of workers
|
||||
)
|
||||
|
||||
// subMul is a common type shared by [SD]gemm.
|
||||
type subMul struct {
|
||||
i, j int // index of block
|
||||
}
|
||||
|
||||
func max(a, b int) int {
|
||||
if a > b {
|
||||
return a
|
||||
}
|
||||
return b
|
||||
}
|
||||
|
||||
func min(a, b int) int {
|
||||
if a > b {
|
||||
return b
|
||||
}
|
||||
return a
|
||||
}
|
||||
|
||||
// blocks returns the number of divisions of the dimension length with the given
|
||||
// block size.
|
||||
func blocks(dim, bsize int) int {
|
||||
return (dim + bsize - 1) / bsize
|
||||
}
|
||||
|
||||
// dcabs1 returns |real(z)|+|imag(z)|.
|
||||
func dcabs1(z complex128) float64 {
|
||||
return math.Abs(real(z)) + math.Abs(imag(z))
|
||||
}
|
||||
|
||||
// scabs1 returns |real(z)|+|imag(z)|.
|
||||
func scabs1(z complex64) float32 {
|
||||
return math32.Abs(real(z)) + math32.Abs(imag(z))
|
||||
}
|
||||
445
vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx128.go
generated
vendored
Normal file
445
vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx128.go
generated
vendored
Normal file
|
|
@ -0,0 +1,445 @@
|
|||
// Copyright ©2017 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 (
|
||||
"math"
|
||||
|
||||
"gonum.org/v1/gonum/blas"
|
||||
"gonum.org/v1/gonum/internal/asm/c128"
|
||||
)
|
||||
|
||||
var _ blas.Complex128Level1 = Implementation{}
|
||||
|
||||
// Dzasum returns the sum of the absolute values of the elements of x
|
||||
// \sum_i |Re(x[i])| + |Im(x[i])|
|
||||
// Dzasum returns 0 if incX is negative.
|
||||
func (Implementation) Dzasum(n int, x []complex128, incX int) float64 {
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return 0
|
||||
}
|
||||
var sum float64
|
||||
if incX == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
for _, v := range x[:n] {
|
||||
sum += dcabs1(v)
|
||||
}
|
||||
return sum
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
v := x[i*incX]
|
||||
sum += dcabs1(v)
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// Dznrm2 computes the Euclidean norm of the complex vector x,
|
||||
// ‖x‖_2 = sqrt(\sum_i x[i] * conj(x[i])).
|
||||
// This function returns 0 if incX is negative.
|
||||
func (Implementation) Dznrm2(n int, x []complex128, incX int) float64 {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return 0
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
var (
|
||||
scale float64
|
||||
ssq float64 = 1
|
||||
)
|
||||
if incX == 1 {
|
||||
for _, v := range x[:n] {
|
||||
re, im := math.Abs(real(v)), math.Abs(imag(v))
|
||||
if re != 0 {
|
||||
if re > scale {
|
||||
ssq = 1 + ssq*(scale/re)*(scale/re)
|
||||
scale = re
|
||||
} else {
|
||||
ssq += (re / scale) * (re / scale)
|
||||
}
|
||||
}
|
||||
if im != 0 {
|
||||
if im > scale {
|
||||
ssq = 1 + ssq*(scale/im)*(scale/im)
|
||||
scale = im
|
||||
} else {
|
||||
ssq += (im / scale) * (im / scale)
|
||||
}
|
||||
}
|
||||
}
|
||||
if math.IsInf(scale, 1) {
|
||||
return math.Inf(1)
|
||||
}
|
||||
return scale * math.Sqrt(ssq)
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
re, im := math.Abs(real(x[ix])), math.Abs(imag(x[ix]))
|
||||
if re != 0 {
|
||||
if re > scale {
|
||||
ssq = 1 + ssq*(scale/re)*(scale/re)
|
||||
scale = re
|
||||
} else {
|
||||
ssq += (re / scale) * (re / scale)
|
||||
}
|
||||
}
|
||||
if im != 0 {
|
||||
if im > scale {
|
||||
ssq = 1 + ssq*(scale/im)*(scale/im)
|
||||
scale = im
|
||||
} else {
|
||||
ssq += (im / scale) * (im / scale)
|
||||
}
|
||||
}
|
||||
}
|
||||
if math.IsInf(scale, 1) {
|
||||
return math.Inf(1)
|
||||
}
|
||||
return scale * math.Sqrt(ssq)
|
||||
}
|
||||
|
||||
// Izamax returns the index of the first element of x having largest |Re(·)|+|Im(·)|.
|
||||
// Izamax returns -1 if n is 0 or incX is negative.
|
||||
func (Implementation) Izamax(n int, x []complex128, incX int) int {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
// Return invalid index.
|
||||
return -1
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
// Return invalid index.
|
||||
return -1
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if len(x) <= (n-1)*incX {
|
||||
panic(shortX)
|
||||
}
|
||||
idx := 0
|
||||
max := dcabs1(x[0])
|
||||
if incX == 1 {
|
||||
for i, v := range x[1:n] {
|
||||
absV := dcabs1(v)
|
||||
if absV > max {
|
||||
max = absV
|
||||
idx = i + 1
|
||||
}
|
||||
}
|
||||
return idx
|
||||
}
|
||||
ix := incX
|
||||
for i := 1; i < n; i++ {
|
||||
absV := dcabs1(x[ix])
|
||||
if absV > max {
|
||||
max = absV
|
||||
idx = i
|
||||
}
|
||||
ix += incX
|
||||
}
|
||||
return idx
|
||||
}
|
||||
|
||||
// Zaxpy adds alpha times x to y:
|
||||
// y[i] += alpha * x[i] for all i
|
||||
func (Implementation) Zaxpy(n int, alpha complex128, x []complex128, incX int, y []complex128, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
|
||||
panic(shortY)
|
||||
}
|
||||
if alpha == 0 {
|
||||
return
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
c128.AxpyUnitary(alpha, x[:n], y[:n])
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (1 - n) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (1 - n) * incY
|
||||
}
|
||||
c128.AxpyInc(alpha, x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
|
||||
// Zcopy copies the vector x to vector y.
|
||||
func (Implementation) Zcopy(n int, x []complex128, incX int, y []complex128, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
|
||||
panic(shortY)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
copy(y[:n], x[:n])
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
y[iy] = x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// Zdotc computes the dot product
|
||||
// x^H · y
|
||||
// of two complex vectors x and y.
|
||||
func (Implementation) Zdotc(n int, x []complex128, incX int, y []complex128, incY int) complex128 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
if len(y) < n {
|
||||
panic(shortY)
|
||||
}
|
||||
return c128.DotcUnitary(x[:n], y[:n])
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
if ix >= len(x) || (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if iy >= len(y) || (n-1)*incY >= len(y) {
|
||||
panic(shortY)
|
||||
}
|
||||
return c128.DotcInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
|
||||
// Zdotu computes the dot product
|
||||
// x^T · y
|
||||
// of two complex vectors x and y.
|
||||
func (Implementation) Zdotu(n int, x []complex128, incX int, y []complex128, incY int) complex128 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
if len(y) < n {
|
||||
panic(shortY)
|
||||
}
|
||||
return c128.DotuUnitary(x[:n], y[:n])
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
if ix >= len(x) || (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if iy >= len(y) || (n-1)*incY >= len(y) {
|
||||
panic(shortY)
|
||||
}
|
||||
return c128.DotuInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
|
||||
// Zdscal scales the vector x by a real scalar alpha.
|
||||
// Zdscal has no effect if incX < 0.
|
||||
func (Implementation) Zdscal(n int, alpha float64, x []complex128, incX int) {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if alpha == 0 {
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for i := range x {
|
||||
x[i] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
x[ix] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for i, v := range x {
|
||||
x[i] = complex(alpha*real(v), alpha*imag(v))
|
||||
}
|
||||
return
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
v := x[ix]
|
||||
x[ix] = complex(alpha*real(v), alpha*imag(v))
|
||||
}
|
||||
}
|
||||
|
||||
// Zscal scales the vector x by a complex scalar alpha.
|
||||
// Zscal has no effect if incX < 0.
|
||||
func (Implementation) Zscal(n int, alpha complex128, x []complex128, incX int) {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if alpha == 0 {
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for i := range x {
|
||||
x[i] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
x[ix] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
if incX == 1 {
|
||||
c128.ScalUnitary(alpha, x[:n])
|
||||
return
|
||||
}
|
||||
c128.ScalInc(alpha, x, uintptr(n), uintptr(incX))
|
||||
}
|
||||
|
||||
// Zswap exchanges the elements of two complex vectors x and y.
|
||||
func (Implementation) Zswap(n int, x []complex128, incX int, y []complex128, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
|
||||
panic(shortY)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, v := range x {
|
||||
x[i], y[i] = y[i], v
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
x[ix], y[iy] = y[iy], x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
467
vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx64.go
generated
vendored
Normal file
467
vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx64.go
generated
vendored
Normal file
|
|
@ -0,0 +1,467 @@
|
|||
// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
|
||||
|
||||
// Copyright ©2017 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 (
|
||||
math "gonum.org/v1/gonum/internal/math32"
|
||||
|
||||
"gonum.org/v1/gonum/blas"
|
||||
"gonum.org/v1/gonum/internal/asm/c64"
|
||||
)
|
||||
|
||||
var _ blas.Complex64Level1 = Implementation{}
|
||||
|
||||
// Scasum returns the sum of the absolute values of the elements of x
|
||||
// \sum_i |Re(x[i])| + |Im(x[i])|
|
||||
// Scasum returns 0 if incX is negative.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Scasum(n int, x []complex64, incX int) float32 {
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return 0
|
||||
}
|
||||
var sum float32
|
||||
if incX == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
for _, v := range x[:n] {
|
||||
sum += scabs1(v)
|
||||
}
|
||||
return sum
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
v := x[i*incX]
|
||||
sum += scabs1(v)
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// Scnrm2 computes the Euclidean norm of the complex vector x,
|
||||
// ‖x‖_2 = sqrt(\sum_i x[i] * conj(x[i])).
|
||||
// This function returns 0 if incX is negative.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Scnrm2(n int, x []complex64, incX int) float32 {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return 0
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
var (
|
||||
scale float32
|
||||
ssq float32 = 1
|
||||
)
|
||||
if incX == 1 {
|
||||
for _, v := range x[:n] {
|
||||
re, im := math.Abs(real(v)), math.Abs(imag(v))
|
||||
if re != 0 {
|
||||
if re > scale {
|
||||
ssq = 1 + ssq*(scale/re)*(scale/re)
|
||||
scale = re
|
||||
} else {
|
||||
ssq += (re / scale) * (re / scale)
|
||||
}
|
||||
}
|
||||
if im != 0 {
|
||||
if im > scale {
|
||||
ssq = 1 + ssq*(scale/im)*(scale/im)
|
||||
scale = im
|
||||
} else {
|
||||
ssq += (im / scale) * (im / scale)
|
||||
}
|
||||
}
|
||||
}
|
||||
if math.IsInf(scale, 1) {
|
||||
return math.Inf(1)
|
||||
}
|
||||
return scale * math.Sqrt(ssq)
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
re, im := math.Abs(real(x[ix])), math.Abs(imag(x[ix]))
|
||||
if re != 0 {
|
||||
if re > scale {
|
||||
ssq = 1 + ssq*(scale/re)*(scale/re)
|
||||
scale = re
|
||||
} else {
|
||||
ssq += (re / scale) * (re / scale)
|
||||
}
|
||||
}
|
||||
if im != 0 {
|
||||
if im > scale {
|
||||
ssq = 1 + ssq*(scale/im)*(scale/im)
|
||||
scale = im
|
||||
} else {
|
||||
ssq += (im / scale) * (im / scale)
|
||||
}
|
||||
}
|
||||
}
|
||||
if math.IsInf(scale, 1) {
|
||||
return math.Inf(1)
|
||||
}
|
||||
return scale * math.Sqrt(ssq)
|
||||
}
|
||||
|
||||
// Icamax returns the index of the first element of x having largest |Re(·)|+|Im(·)|.
|
||||
// Icamax returns -1 if n is 0 or incX is negative.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Icamax(n int, x []complex64, incX int) int {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
// Return invalid index.
|
||||
return -1
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
// Return invalid index.
|
||||
return -1
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if len(x) <= (n-1)*incX {
|
||||
panic(shortX)
|
||||
}
|
||||
idx := 0
|
||||
max := scabs1(x[0])
|
||||
if incX == 1 {
|
||||
for i, v := range x[1:n] {
|
||||
absV := scabs1(v)
|
||||
if absV > max {
|
||||
max = absV
|
||||
idx = i + 1
|
||||
}
|
||||
}
|
||||
return idx
|
||||
}
|
||||
ix := incX
|
||||
for i := 1; i < n; i++ {
|
||||
absV := scabs1(x[ix])
|
||||
if absV > max {
|
||||
max = absV
|
||||
idx = i
|
||||
}
|
||||
ix += incX
|
||||
}
|
||||
return idx
|
||||
}
|
||||
|
||||
// Caxpy adds alpha times x to y:
|
||||
// y[i] += alpha * x[i] for all i
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Caxpy(n int, alpha complex64, x []complex64, incX int, y []complex64, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
|
||||
panic(shortY)
|
||||
}
|
||||
if alpha == 0 {
|
||||
return
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
c64.AxpyUnitary(alpha, x[:n], y[:n])
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (1 - n) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (1 - n) * incY
|
||||
}
|
||||
c64.AxpyInc(alpha, x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
|
||||
// Ccopy copies the vector x to vector y.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Ccopy(n int, x []complex64, incX int, y []complex64, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
|
||||
panic(shortY)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
copy(y[:n], x[:n])
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
y[iy] = x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// Cdotc computes the dot product
|
||||
// x^H · y
|
||||
// of two complex vectors x and y.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Cdotc(n int, x []complex64, incX int, y []complex64, incY int) complex64 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
if len(y) < n {
|
||||
panic(shortY)
|
||||
}
|
||||
return c64.DotcUnitary(x[:n], y[:n])
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
if ix >= len(x) || (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if iy >= len(y) || (n-1)*incY >= len(y) {
|
||||
panic(shortY)
|
||||
}
|
||||
return c64.DotcInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
|
||||
// Cdotu computes the dot product
|
||||
// x^T · y
|
||||
// of two complex vectors x and y.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Cdotu(n int, x []complex64, incX int, y []complex64, incY int) complex64 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
if len(y) < n {
|
||||
panic(shortY)
|
||||
}
|
||||
return c64.DotuUnitary(x[:n], y[:n])
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
if ix >= len(x) || (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if iy >= len(y) || (n-1)*incY >= len(y) {
|
||||
panic(shortY)
|
||||
}
|
||||
return c64.DotuInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
|
||||
// Csscal scales the vector x by a real scalar alpha.
|
||||
// Csscal has no effect if incX < 0.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Csscal(n int, alpha float32, x []complex64, incX int) {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if alpha == 0 {
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for i := range x {
|
||||
x[i] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
x[ix] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for i, v := range x {
|
||||
x[i] = complex(alpha*real(v), alpha*imag(v))
|
||||
}
|
||||
return
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
v := x[ix]
|
||||
x[ix] = complex(alpha*real(v), alpha*imag(v))
|
||||
}
|
||||
}
|
||||
|
||||
// Cscal scales the vector x by a complex scalar alpha.
|
||||
// Cscal has no effect if incX < 0.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Cscal(n int, alpha complex64, x []complex64, incX int) {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if alpha == 0 {
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for i := range x {
|
||||
x[i] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
x[ix] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
if incX == 1 {
|
||||
c64.ScalUnitary(alpha, x[:n])
|
||||
return
|
||||
}
|
||||
c64.ScalInc(alpha, x, uintptr(n), uintptr(incX))
|
||||
}
|
||||
|
||||
// Cswap exchanges the elements of two complex vectors x and y.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Cswap(n int, x []complex64, incX int, y []complex64, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
|
||||
panic(shortY)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, v := range x {
|
||||
x[i], y[i] = y[i], v
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
x[ix], y[iy] = y[iy], x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
644
vendor/gonum.org/v1/gonum/blas/gonum/level1float32.go
generated
vendored
Normal file
644
vendor/gonum.org/v1/gonum/blas/gonum/level1float32.go
generated
vendored
Normal file
|
|
@ -0,0 +1,644 @@
|
|||
// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
|
||||
|
||||
// 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 (
|
||||
math "gonum.org/v1/gonum/internal/math32"
|
||||
|
||||
"gonum.org/v1/gonum/blas"
|
||||
"gonum.org/v1/gonum/internal/asm/f32"
|
||||
)
|
||||
|
||||
var _ blas.Float32Level1 = Implementation{}
|
||||
|
||||
// Snrm2 computes the Euclidean norm of a vector,
|
||||
// sqrt(\sum_i x[i] * x[i]).
|
||||
// This function returns 0 if incX is negative.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Snrm2(n int, x []float32, incX int) float32 {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return 0
|
||||
}
|
||||
if len(x) <= (n-1)*incX {
|
||||
panic(shortX)
|
||||
}
|
||||
if n < 2 {
|
||||
if n == 1 {
|
||||
return math.Abs(x[0])
|
||||
}
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
var (
|
||||
scale float32 = 0
|
||||
sumSquares float32 = 1
|
||||
)
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for _, v := range x {
|
||||
if v == 0 {
|
||||
continue
|
||||
}
|
||||
absxi := math.Abs(v)
|
||||
if math.IsNaN(absxi) {
|
||||
return math.NaN()
|
||||
}
|
||||
if scale < absxi {
|
||||
sumSquares = 1 + sumSquares*(scale/absxi)*(scale/absxi)
|
||||
scale = absxi
|
||||
} else {
|
||||
sumSquares = sumSquares + (absxi/scale)*(absxi/scale)
|
||||
}
|
||||
}
|
||||
if math.IsInf(scale, 1) {
|
||||
return math.Inf(1)
|
||||
}
|
||||
return scale * math.Sqrt(sumSquares)
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
val := x[ix]
|
||||
if val == 0 {
|
||||
continue
|
||||
}
|
||||
absxi := math.Abs(val)
|
||||
if math.IsNaN(absxi) {
|
||||
return math.NaN()
|
||||
}
|
||||
if scale < absxi {
|
||||
sumSquares = 1 + sumSquares*(scale/absxi)*(scale/absxi)
|
||||
scale = absxi
|
||||
} else {
|
||||
sumSquares = sumSquares + (absxi/scale)*(absxi/scale)
|
||||
}
|
||||
}
|
||||
if math.IsInf(scale, 1) {
|
||||
return math.Inf(1)
|
||||
}
|
||||
return scale * math.Sqrt(sumSquares)
|
||||
}
|
||||
|
||||
// Sasum computes the sum of the absolute values of the elements of x.
|
||||
// \sum_i |x[i]|
|
||||
// Sasum returns 0 if incX is negative.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Sasum(n int, x []float32, incX int) float32 {
|
||||
var sum float32
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return 0
|
||||
}
|
||||
if len(x) <= (n-1)*incX {
|
||||
panic(shortX)
|
||||
}
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for _, v := range x {
|
||||
sum += math.Abs(v)
|
||||
}
|
||||
return sum
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
sum += math.Abs(x[i*incX])
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// Isamax returns the index of an element of x with the largest absolute value.
|
||||
// If there are multiple such indices the earliest is returned.
|
||||
// Isamax returns -1 if n == 0.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Isamax(n int, x []float32, incX int) int {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return -1
|
||||
}
|
||||
if len(x) <= (n-1)*incX {
|
||||
panic(shortX)
|
||||
}
|
||||
if n < 2 {
|
||||
if n == 1 {
|
||||
return 0
|
||||
}
|
||||
if n == 0 {
|
||||
return -1 // Netlib returns invalid index when n == 0.
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
idx := 0
|
||||
max := math.Abs(x[0])
|
||||
if incX == 1 {
|
||||
for i, v := range x[:n] {
|
||||
absV := math.Abs(v)
|
||||
if absV > max {
|
||||
max = absV
|
||||
idx = i
|
||||
}
|
||||
}
|
||||
return idx
|
||||
}
|
||||
ix := incX
|
||||
for i := 1; i < n; i++ {
|
||||
v := x[ix]
|
||||
absV := math.Abs(v)
|
||||
if absV > max {
|
||||
max = absV
|
||||
idx = i
|
||||
}
|
||||
ix += incX
|
||||
}
|
||||
return idx
|
||||
}
|
||||
|
||||
// Sswap exchanges the elements of two vectors.
|
||||
// x[i], y[i] = y[i], x[i] for all i
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Sswap(n int, x []float32, incX int, y []float32, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
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 incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, v := range x {
|
||||
x[i], y[i] = y[i], v
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
x[ix], y[iy] = y[iy], x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// Scopy copies the elements of x into the elements of y.
|
||||
// y[i] = x[i] for all i
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Scopy(n int, x []float32, incX int, y []float32, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
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 incX == 1 && incY == 1 {
|
||||
copy(y[:n], x[:n])
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
y[iy] = x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// Saxpy adds alpha times x to y
|
||||
// y[i] += alpha * x[i] for all i
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Saxpy(n int, alpha float32, x []float32, incX int, y []float32, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
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 alpha == 0 {
|
||||
return
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
f32.AxpyUnitary(alpha, x[:n], y[:n])
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
f32.AxpyInc(alpha, x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
|
||||
// Srotg computes the plane rotation
|
||||
// _ _ _ _ _ _
|
||||
// | c s | | a | | r |
|
||||
// | -s c | * | b | = | 0 |
|
||||
// ‾ ‾ ‾ ‾ ‾ ‾
|
||||
// where
|
||||
// r = ±√(a^2 + b^2)
|
||||
// c = a/r, the cosine of the plane rotation
|
||||
// s = b/r, the sine of the plane rotation
|
||||
//
|
||||
// NOTE: There is a discrepancy between the reference implementation and the BLAS
|
||||
// technical manual regarding the sign for r when a or b are zero.
|
||||
// Srotg agrees with the definition in the manual and other
|
||||
// common BLAS implementations.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Srotg(a, b float32) (c, s, r, z float32) {
|
||||
if b == 0 && a == 0 {
|
||||
return 1, 0, a, 0
|
||||
}
|
||||
absA := math.Abs(a)
|
||||
absB := math.Abs(b)
|
||||
aGTb := absA > absB
|
||||
r = math.Hypot(a, b)
|
||||
if aGTb {
|
||||
r = math.Copysign(r, a)
|
||||
} else {
|
||||
r = math.Copysign(r, b)
|
||||
}
|
||||
c = a / r
|
||||
s = b / r
|
||||
if aGTb {
|
||||
z = s
|
||||
} else if c != 0 { // r == 0 case handled above
|
||||
z = 1 / c
|
||||
} else {
|
||||
z = 1
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// Srotmg computes the modified Givens rotation. See
|
||||
// http://www.netlib.org/lapack/explore-html/df/deb/drotmg_8f.html
|
||||
// for more details.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Srotmg(d1, d2, x1, y1 float32) (p blas.SrotmParams, rd1, rd2, rx1 float32) {
|
||||
// The implementation of Drotmg used here is taken from Hopkins 1997
|
||||
// Appendix A: https://doi.org/10.1145/289251.289253
|
||||
// with the exception of the gam constants below.
|
||||
|
||||
const (
|
||||
gam = 4096.0
|
||||
gamsq = gam * gam
|
||||
rgamsq = 1.0 / gamsq
|
||||
)
|
||||
|
||||
if d1 < 0 {
|
||||
p.Flag = blas.Rescaling // Error state.
|
||||
return p, 0, 0, 0
|
||||
}
|
||||
|
||||
if d2 == 0 || y1 == 0 {
|
||||
p.Flag = blas.Identity
|
||||
return p, d1, d2, x1
|
||||
}
|
||||
|
||||
var h11, h12, h21, h22 float32
|
||||
if (d1 == 0 || x1 == 0) && d2 > 0 {
|
||||
p.Flag = blas.Diagonal
|
||||
h12 = 1
|
||||
h21 = -1
|
||||
x1 = y1
|
||||
d1, d2 = d2, d1
|
||||
} else {
|
||||
p2 := d2 * y1
|
||||
p1 := d1 * x1
|
||||
q2 := p2 * y1
|
||||
q1 := p1 * x1
|
||||
if math.Abs(q1) > math.Abs(q2) {
|
||||
p.Flag = blas.OffDiagonal
|
||||
h11 = 1
|
||||
h22 = 1
|
||||
h21 = -y1 / x1
|
||||
h12 = p2 / p1
|
||||
u := 1 - h12*h21
|
||||
if u <= 0 {
|
||||
p.Flag = blas.Rescaling // Error state.
|
||||
return p, 0, 0, 0
|
||||
}
|
||||
|
||||
d1 /= u
|
||||
d2 /= u
|
||||
x1 *= u
|
||||
} else {
|
||||
if q2 < 0 {
|
||||
p.Flag = blas.Rescaling // Error state.
|
||||
return p, 0, 0, 0
|
||||
}
|
||||
|
||||
p.Flag = blas.Diagonal
|
||||
h21 = -1
|
||||
h12 = 1
|
||||
h11 = p1 / p2
|
||||
h22 = x1 / y1
|
||||
u := 1 + h11*h22
|
||||
d1, d2 = d2/u, d1/u
|
||||
x1 = y1 * u
|
||||
}
|
||||
}
|
||||
|
||||
for d1 <= rgamsq && d1 != 0 {
|
||||
p.Flag = blas.Rescaling
|
||||
d1 = (d1 * gam) * gam
|
||||
x1 /= gam
|
||||
h11 /= gam
|
||||
h12 /= gam
|
||||
}
|
||||
for d1 > gamsq {
|
||||
p.Flag = blas.Rescaling
|
||||
d1 = (d1 / gam) / gam
|
||||
x1 *= gam
|
||||
h11 *= gam
|
||||
h12 *= gam
|
||||
}
|
||||
|
||||
for math.Abs(d2) <= rgamsq && d2 != 0 {
|
||||
p.Flag = blas.Rescaling
|
||||
d2 = (d2 * gam) * gam
|
||||
h21 /= gam
|
||||
h22 /= gam
|
||||
}
|
||||
for math.Abs(d2) > gamsq {
|
||||
p.Flag = blas.Rescaling
|
||||
d2 = (d2 / gam) / gam
|
||||
h21 *= gam
|
||||
h22 *= gam
|
||||
}
|
||||
|
||||
switch p.Flag {
|
||||
case blas.Diagonal:
|
||||
p.H = [4]float32{0: h11, 3: h22}
|
||||
case blas.OffDiagonal:
|
||||
p.H = [4]float32{1: h21, 2: h12}
|
||||
case blas.Rescaling:
|
||||
p.H = [4]float32{h11, h21, h12, h22}
|
||||
default:
|
||||
panic(badFlag)
|
||||
}
|
||||
|
||||
return p, d1, d2, x1
|
||||
}
|
||||
|
||||
// Srot applies a plane transformation.
|
||||
// x[i] = c * x[i] + s * y[i]
|
||||
// y[i] = c * y[i] - s * x[i]
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Srot(n int, x []float32, incX int, y []float32, incY int, c float32, s float32) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
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 incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, vx := range x {
|
||||
vy := y[i]
|
||||
x[i], y[i] = c*vx+s*vy, c*vy-s*vx
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
vx := x[ix]
|
||||
vy := y[iy]
|
||||
x[ix], y[iy] = c*vx+s*vy, c*vy-s*vx
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// Srotm applies the modified Givens rotation to the 2×n matrix.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Srotm(n int, x []float32, incX int, y []float32, incY int, p blas.SrotmParams) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
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 p.Flag == blas.Identity {
|
||||
return
|
||||
}
|
||||
|
||||
switch p.Flag {
|
||||
case blas.Rescaling:
|
||||
h11 := p.H[0]
|
||||
h12 := p.H[2]
|
||||
h21 := p.H[1]
|
||||
h22 := p.H[3]
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, vx := range x {
|
||||
vy := y[i]
|
||||
x[i], y[i] = vx*h11+vy*h12, vx*h21+vy*h22
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
vx := x[ix]
|
||||
vy := y[iy]
|
||||
x[ix], y[iy] = vx*h11+vy*h12, vx*h21+vy*h22
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
case blas.OffDiagonal:
|
||||
h12 := p.H[2]
|
||||
h21 := p.H[1]
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, vx := range x {
|
||||
vy := y[i]
|
||||
x[i], y[i] = vx+vy*h12, vx*h21+vy
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
vx := x[ix]
|
||||
vy := y[iy]
|
||||
x[ix], y[iy] = vx+vy*h12, vx*h21+vy
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
case blas.Diagonal:
|
||||
h11 := p.H[0]
|
||||
h22 := p.H[3]
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, vx := range x {
|
||||
vy := y[i]
|
||||
x[i], y[i] = vx*h11+vy, -vx+vy*h22
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
vx := x[ix]
|
||||
vy := y[iy]
|
||||
x[ix], y[iy] = vx*h11+vy, -vx+vy*h22
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Sscal scales x by alpha.
|
||||
// x[i] *= alpha
|
||||
// Sscal has no effect if incX < 0.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Sscal(n int, alpha float32, x []float32, incX int) {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if alpha == 0 {
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for i := range x {
|
||||
x[i] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
x[ix] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
if incX == 1 {
|
||||
f32.ScalUnitary(alpha, x[:n])
|
||||
return
|
||||
}
|
||||
f32.ScalInc(alpha, x, uintptr(n), uintptr(incX))
|
||||
}
|
||||
53
vendor/gonum.org/v1/gonum/blas/gonum/level1float32_dsdot.go
generated
vendored
Normal file
53
vendor/gonum.org/v1/gonum/blas/gonum/level1float32_dsdot.go
generated
vendored
Normal file
|
|
@ -0,0 +1,53 @@
|
|||
// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
|
||||
|
||||
// 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/internal/asm/f32"
|
||||
)
|
||||
|
||||
// Dsdot computes the dot product of the two vectors
|
||||
// \sum_i x[i]*y[i]
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Dsdot(n int, x []float32, incX int, y []float32, incY int) float64 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
if len(y) < n {
|
||||
panic(shortY)
|
||||
}
|
||||
return f32.DdotUnitary(x[:n], y[:n])
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
if ix >= len(x) || ix+(n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if iy >= len(y) || iy+(n-1)*incY >= len(y) {
|
||||
panic(shortY)
|
||||
}
|
||||
return f32.DdotInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
53
vendor/gonum.org/v1/gonum/blas/gonum/level1float32_sdot.go
generated
vendored
Normal file
53
vendor/gonum.org/v1/gonum/blas/gonum/level1float32_sdot.go
generated
vendored
Normal file
|
|
@ -0,0 +1,53 @@
|
|||
// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
|
||||
|
||||
// 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/internal/asm/f32"
|
||||
)
|
||||
|
||||
// Sdot computes the dot product of the two vectors
|
||||
// \sum_i x[i]*y[i]
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Sdot(n int, x []float32, incX int, y []float32, incY int) float32 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
if len(y) < n {
|
||||
panic(shortY)
|
||||
}
|
||||
return f32.DotUnitary(x[:n], y[:n])
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
if ix >= len(x) || ix+(n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if iy >= len(y) || iy+(n-1)*incY >= len(y) {
|
||||
panic(shortY)
|
||||
}
|
||||
return f32.DotInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
53
vendor/gonum.org/v1/gonum/blas/gonum/level1float32_sdsdot.go
generated
vendored
Normal file
53
vendor/gonum.org/v1/gonum/blas/gonum/level1float32_sdsdot.go
generated
vendored
Normal file
|
|
@ -0,0 +1,53 @@
|
|||
// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
|
||||
|
||||
// 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/internal/asm/f32"
|
||||
)
|
||||
|
||||
// Sdsdot computes the dot product of the two vectors plus a constant
|
||||
// alpha + \sum_i x[i]*y[i]
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Sdsdot(n int, alpha float32, x []float32, incX int, y []float32, incY int) float32 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
if len(y) < n {
|
||||
panic(shortY)
|
||||
}
|
||||
return alpha + float32(f32.DdotUnitary(x[:n], y[:n]))
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
if ix >= len(x) || ix+(n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if iy >= len(y) || iy+(n-1)*incY >= len(y) {
|
||||
panic(shortY)
|
||||
}
|
||||
return alpha + float32(f32.DdotInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy)))
|
||||
}
|
||||
620
vendor/gonum.org/v1/gonum/blas/gonum/level1float64.go
generated
vendored
Normal file
620
vendor/gonum.org/v1/gonum/blas/gonum/level1float64.go
generated
vendored
Normal file
|
|
@ -0,0 +1,620 @@
|
|||
// 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 (
|
||||
"math"
|
||||
|
||||
"gonum.org/v1/gonum/blas"
|
||||
"gonum.org/v1/gonum/internal/asm/f64"
|
||||
)
|
||||
|
||||
var _ blas.Float64Level1 = Implementation{}
|
||||
|
||||
// Dnrm2 computes the Euclidean norm of a vector,
|
||||
// sqrt(\sum_i x[i] * x[i]).
|
||||
// This function returns 0 if incX is negative.
|
||||
func (Implementation) Dnrm2(n int, x []float64, incX int) float64 {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return 0
|
||||
}
|
||||
if len(x) <= (n-1)*incX {
|
||||
panic(shortX)
|
||||
}
|
||||
if n < 2 {
|
||||
if n == 1 {
|
||||
return math.Abs(x[0])
|
||||
}
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
var (
|
||||
scale float64 = 0
|
||||
sumSquares float64 = 1
|
||||
)
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for _, v := range x {
|
||||
if v == 0 {
|
||||
continue
|
||||
}
|
||||
absxi := math.Abs(v)
|
||||
if math.IsNaN(absxi) {
|
||||
return math.NaN()
|
||||
}
|
||||
if scale < absxi {
|
||||
sumSquares = 1 + sumSquares*(scale/absxi)*(scale/absxi)
|
||||
scale = absxi
|
||||
} else {
|
||||
sumSquares = sumSquares + (absxi/scale)*(absxi/scale)
|
||||
}
|
||||
}
|
||||
if math.IsInf(scale, 1) {
|
||||
return math.Inf(1)
|
||||
}
|
||||
return scale * math.Sqrt(sumSquares)
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
val := x[ix]
|
||||
if val == 0 {
|
||||
continue
|
||||
}
|
||||
absxi := math.Abs(val)
|
||||
if math.IsNaN(absxi) {
|
||||
return math.NaN()
|
||||
}
|
||||
if scale < absxi {
|
||||
sumSquares = 1 + sumSquares*(scale/absxi)*(scale/absxi)
|
||||
scale = absxi
|
||||
} else {
|
||||
sumSquares = sumSquares + (absxi/scale)*(absxi/scale)
|
||||
}
|
||||
}
|
||||
if math.IsInf(scale, 1) {
|
||||
return math.Inf(1)
|
||||
}
|
||||
return scale * math.Sqrt(sumSquares)
|
||||
}
|
||||
|
||||
// Dasum computes the sum of the absolute values of the elements of x.
|
||||
// \sum_i |x[i]|
|
||||
// Dasum returns 0 if incX is negative.
|
||||
func (Implementation) Dasum(n int, x []float64, incX int) float64 {
|
||||
var sum float64
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return 0
|
||||
}
|
||||
if len(x) <= (n-1)*incX {
|
||||
panic(shortX)
|
||||
}
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for _, v := range x {
|
||||
sum += math.Abs(v)
|
||||
}
|
||||
return sum
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
sum += math.Abs(x[i*incX])
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// Idamax returns the index of an element of x with the largest absolute value.
|
||||
// If there are multiple such indices the earliest is returned.
|
||||
// Idamax returns -1 if n == 0.
|
||||
func (Implementation) Idamax(n int, x []float64, incX int) int {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return -1
|
||||
}
|
||||
if len(x) <= (n-1)*incX {
|
||||
panic(shortX)
|
||||
}
|
||||
if n < 2 {
|
||||
if n == 1 {
|
||||
return 0
|
||||
}
|
||||
if n == 0 {
|
||||
return -1 // Netlib returns invalid index when n == 0.
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
idx := 0
|
||||
max := math.Abs(x[0])
|
||||
if incX == 1 {
|
||||
for i, v := range x[:n] {
|
||||
absV := math.Abs(v)
|
||||
if absV > max {
|
||||
max = absV
|
||||
idx = i
|
||||
}
|
||||
}
|
||||
return idx
|
||||
}
|
||||
ix := incX
|
||||
for i := 1; i < n; i++ {
|
||||
v := x[ix]
|
||||
absV := math.Abs(v)
|
||||
if absV > max {
|
||||
max = absV
|
||||
idx = i
|
||||
}
|
||||
ix += incX
|
||||
}
|
||||
return idx
|
||||
}
|
||||
|
||||
// Dswap exchanges the elements of two vectors.
|
||||
// x[i], y[i] = y[i], x[i] for all i
|
||||
func (Implementation) Dswap(n int, x []float64, incX int, y []float64, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
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 incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, v := range x {
|
||||
x[i], y[i] = y[i], v
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
x[ix], y[iy] = y[iy], x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// Dcopy copies the elements of x into the elements of y.
|
||||
// y[i] = x[i] for all i
|
||||
func (Implementation) Dcopy(n int, x []float64, incX int, y []float64, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
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 incX == 1 && incY == 1 {
|
||||
copy(y[:n], x[:n])
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
y[iy] = x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// Daxpy adds alpha times x to y
|
||||
// y[i] += alpha * x[i] for all i
|
||||
func (Implementation) Daxpy(n int, alpha float64, x []float64, incX int, y []float64, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
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 alpha == 0 {
|
||||
return
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
f64.AxpyUnitary(alpha, x[:n], y[:n])
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
f64.AxpyInc(alpha, x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
|
||||
// Drotg computes the plane rotation
|
||||
// _ _ _ _ _ _
|
||||
// | c s | | a | | r |
|
||||
// | -s c | * | b | = | 0 |
|
||||
// ‾ ‾ ‾ ‾ ‾ ‾
|
||||
// where
|
||||
// r = ±√(a^2 + b^2)
|
||||
// c = a/r, the cosine of the plane rotation
|
||||
// s = b/r, the sine of the plane rotation
|
||||
//
|
||||
// NOTE: There is a discrepancy between the reference implementation and the BLAS
|
||||
// technical manual regarding the sign for r when a or b are zero.
|
||||
// Drotg agrees with the definition in the manual and other
|
||||
// common BLAS implementations.
|
||||
func (Implementation) Drotg(a, b float64) (c, s, r, z float64) {
|
||||
if b == 0 && a == 0 {
|
||||
return 1, 0, a, 0
|
||||
}
|
||||
absA := math.Abs(a)
|
||||
absB := math.Abs(b)
|
||||
aGTb := absA > absB
|
||||
r = math.Hypot(a, b)
|
||||
if aGTb {
|
||||
r = math.Copysign(r, a)
|
||||
} else {
|
||||
r = math.Copysign(r, b)
|
||||
}
|
||||
c = a / r
|
||||
s = b / r
|
||||
if aGTb {
|
||||
z = s
|
||||
} else if c != 0 { // r == 0 case handled above
|
||||
z = 1 / c
|
||||
} else {
|
||||
z = 1
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// Drotmg computes the modified Givens rotation. See
|
||||
// http://www.netlib.org/lapack/explore-html/df/deb/drotmg_8f.html
|
||||
// for more details.
|
||||
func (Implementation) Drotmg(d1, d2, x1, y1 float64) (p blas.DrotmParams, rd1, rd2, rx1 float64) {
|
||||
// The implementation of Drotmg used here is taken from Hopkins 1997
|
||||
// Appendix A: https://doi.org/10.1145/289251.289253
|
||||
// with the exception of the gam constants below.
|
||||
|
||||
const (
|
||||
gam = 4096.0
|
||||
gamsq = gam * gam
|
||||
rgamsq = 1.0 / gamsq
|
||||
)
|
||||
|
||||
if d1 < 0 {
|
||||
p.Flag = blas.Rescaling // Error state.
|
||||
return p, 0, 0, 0
|
||||
}
|
||||
|
||||
if d2 == 0 || y1 == 0 {
|
||||
p.Flag = blas.Identity
|
||||
return p, d1, d2, x1
|
||||
}
|
||||
|
||||
var h11, h12, h21, h22 float64
|
||||
if (d1 == 0 || x1 == 0) && d2 > 0 {
|
||||
p.Flag = blas.Diagonal
|
||||
h12 = 1
|
||||
h21 = -1
|
||||
x1 = y1
|
||||
d1, d2 = d2, d1
|
||||
} else {
|
||||
p2 := d2 * y1
|
||||
p1 := d1 * x1
|
||||
q2 := p2 * y1
|
||||
q1 := p1 * x1
|
||||
if math.Abs(q1) > math.Abs(q2) {
|
||||
p.Flag = blas.OffDiagonal
|
||||
h11 = 1
|
||||
h22 = 1
|
||||
h21 = -y1 / x1
|
||||
h12 = p2 / p1
|
||||
u := 1 - h12*h21
|
||||
if u <= 0 {
|
||||
p.Flag = blas.Rescaling // Error state.
|
||||
return p, 0, 0, 0
|
||||
}
|
||||
|
||||
d1 /= u
|
||||
d2 /= u
|
||||
x1 *= u
|
||||
} else {
|
||||
if q2 < 0 {
|
||||
p.Flag = blas.Rescaling // Error state.
|
||||
return p, 0, 0, 0
|
||||
}
|
||||
|
||||
p.Flag = blas.Diagonal
|
||||
h21 = -1
|
||||
h12 = 1
|
||||
h11 = p1 / p2
|
||||
h22 = x1 / y1
|
||||
u := 1 + h11*h22
|
||||
d1, d2 = d2/u, d1/u
|
||||
x1 = y1 * u
|
||||
}
|
||||
}
|
||||
|
||||
for d1 <= rgamsq && d1 != 0 {
|
||||
p.Flag = blas.Rescaling
|
||||
d1 = (d1 * gam) * gam
|
||||
x1 /= gam
|
||||
h11 /= gam
|
||||
h12 /= gam
|
||||
}
|
||||
for d1 > gamsq {
|
||||
p.Flag = blas.Rescaling
|
||||
d1 = (d1 / gam) / gam
|
||||
x1 *= gam
|
||||
h11 *= gam
|
||||
h12 *= gam
|
||||
}
|
||||
|
||||
for math.Abs(d2) <= rgamsq && d2 != 0 {
|
||||
p.Flag = blas.Rescaling
|
||||
d2 = (d2 * gam) * gam
|
||||
h21 /= gam
|
||||
h22 /= gam
|
||||
}
|
||||
for math.Abs(d2) > gamsq {
|
||||
p.Flag = blas.Rescaling
|
||||
d2 = (d2 / gam) / gam
|
||||
h21 *= gam
|
||||
h22 *= gam
|
||||
}
|
||||
|
||||
switch p.Flag {
|
||||
case blas.Diagonal:
|
||||
p.H = [4]float64{0: h11, 3: h22}
|
||||
case blas.OffDiagonal:
|
||||
p.H = [4]float64{1: h21, 2: h12}
|
||||
case blas.Rescaling:
|
||||
p.H = [4]float64{h11, h21, h12, h22}
|
||||
default:
|
||||
panic(badFlag)
|
||||
}
|
||||
|
||||
return p, d1, d2, x1
|
||||
}
|
||||
|
||||
// Drot applies a plane transformation.
|
||||
// x[i] = c * x[i] + s * y[i]
|
||||
// y[i] = c * y[i] - s * x[i]
|
||||
func (Implementation) Drot(n int, x []float64, incX int, y []float64, incY int, c float64, s float64) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
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 incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, vx := range x {
|
||||
vy := y[i]
|
||||
x[i], y[i] = c*vx+s*vy, c*vy-s*vx
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
vx := x[ix]
|
||||
vy := y[iy]
|
||||
x[ix], y[iy] = c*vx+s*vy, c*vy-s*vx
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// Drotm applies the modified Givens rotation to the 2×n matrix.
|
||||
func (Implementation) Drotm(n int, x []float64, incX int, y []float64, incY int, p blas.DrotmParams) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
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 p.Flag == blas.Identity {
|
||||
return
|
||||
}
|
||||
|
||||
switch p.Flag {
|
||||
case blas.Rescaling:
|
||||
h11 := p.H[0]
|
||||
h12 := p.H[2]
|
||||
h21 := p.H[1]
|
||||
h22 := p.H[3]
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, vx := range x {
|
||||
vy := y[i]
|
||||
x[i], y[i] = vx*h11+vy*h12, vx*h21+vy*h22
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
vx := x[ix]
|
||||
vy := y[iy]
|
||||
x[ix], y[iy] = vx*h11+vy*h12, vx*h21+vy*h22
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
case blas.OffDiagonal:
|
||||
h12 := p.H[2]
|
||||
h21 := p.H[1]
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, vx := range x {
|
||||
vy := y[i]
|
||||
x[i], y[i] = vx+vy*h12, vx*h21+vy
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
vx := x[ix]
|
||||
vy := y[iy]
|
||||
x[ix], y[iy] = vx+vy*h12, vx*h21+vy
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
case blas.Diagonal:
|
||||
h11 := p.H[0]
|
||||
h22 := p.H[3]
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, vx := range x {
|
||||
vy := y[i]
|
||||
x[i], y[i] = vx*h11+vy, -vx+vy*h22
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
vx := x[ix]
|
||||
vy := y[iy]
|
||||
x[ix], y[iy] = vx*h11+vy, -vx+vy*h22
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Dscal scales x by alpha.
|
||||
// x[i] *= alpha
|
||||
// Dscal has no effect if incX < 0.
|
||||
func (Implementation) Dscal(n int, alpha float64, x []float64, incX int) {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if alpha == 0 {
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for i := range x {
|
||||
x[i] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
x[ix] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
if incX == 1 {
|
||||
f64.ScalUnitary(alpha, x[:n])
|
||||
return
|
||||
}
|
||||
f64.ScalInc(alpha, x, uintptr(n), uintptr(incX))
|
||||
}
|
||||
49
vendor/gonum.org/v1/gonum/blas/gonum/level1float64_ddot.go
generated
vendored
Normal file
49
vendor/gonum.org/v1/gonum/blas/gonum/level1float64_ddot.go
generated
vendored
Normal file
|
|
@ -0,0 +1,49 @@
|
|||
// 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/internal/asm/f64"
|
||||
)
|
||||
|
||||
// Ddot computes the dot product of the two vectors
|
||||
// \sum_i x[i]*y[i]
|
||||
func (Implementation) Ddot(n int, x []float64, incX int, y []float64, incY int) float64 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
if len(y) < n {
|
||||
panic(shortY)
|
||||
}
|
||||
return f64.DotUnitary(x[:n], y[:n])
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
if ix >= len(x) || ix+(n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if iy >= len(y) || iy+(n-1)*incY >= len(y) {
|
||||
panic(shortY)
|
||||
}
|
||||
return f64.DotInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
2906
vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx128.go
generated
vendored
Normal file
2906
vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx128.go
generated
vendored
Normal file
File diff suppressed because it is too large
Load diff
2942
vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx64.go
generated
vendored
Normal file
2942
vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx64.go
generated
vendored
Normal file
File diff suppressed because it is too large
Load diff
2296
vendor/gonum.org/v1/gonum/blas/gonum/level2float32.go
generated
vendored
Normal file
2296
vendor/gonum.org/v1/gonum/blas/gonum/level2float32.go
generated
vendored
Normal file
File diff suppressed because it is too large
Load diff
2264
vendor/gonum.org/v1/gonum/blas/gonum/level2float64.go
generated
vendored
Normal file
2264
vendor/gonum.org/v1/gonum/blas/gonum/level2float64.go
generated
vendored
Normal file
File diff suppressed because it is too large
Load diff
1715
vendor/gonum.org/v1/gonum/blas/gonum/level3cmplx128.go
generated
vendored
Normal file
1715
vendor/gonum.org/v1/gonum/blas/gonum/level3cmplx128.go
generated
vendored
Normal file
File diff suppressed because it is too large
Load diff
1735
vendor/gonum.org/v1/gonum/blas/gonum/level3cmplx64.go
generated
vendored
Normal file
1735
vendor/gonum.org/v1/gonum/blas/gonum/level3cmplx64.go
generated
vendored
Normal file
File diff suppressed because it is too large
Load diff
876
vendor/gonum.org/v1/gonum/blas/gonum/level3float32.go
generated
vendored
Normal file
876
vendor/gonum.org/v1/gonum/blas/gonum/level3float32.go
generated
vendored
Normal file
|
|
@ -0,0 +1,876 @@
|
|||
// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
|
||||
|
||||
// Copyright ©2014 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/internal/asm/f32"
|
||||
)
|
||||
|
||||
var _ blas.Float32Level3 = Implementation{}
|
||||
|
||||
// Strsm solves one of the matrix equations
|
||||
// A * X = alpha * B if tA == blas.NoTrans and side == blas.Left
|
||||
// A^T * X = alpha * B if tA == blas.Trans or blas.ConjTrans, and side == blas.Left
|
||||
// X * A = alpha * B if tA == blas.NoTrans and side == blas.Right
|
||||
// X * A^T = alpha * B if tA == blas.Trans or blas.ConjTrans, and side == blas.Right
|
||||
// where A is an n×n or m×m triangular matrix, X and B are m×n matrices, and alpha is a
|
||||
// scalar.
|
||||
//
|
||||
// At entry to the function, X contains the values of B, and the result is
|
||||
// stored in-place into X.
|
||||
//
|
||||
// No check is made that A is invertible.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Strsm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int) {
|
||||
if s != blas.Left && s != blas.Right {
|
||||
panic(badSide)
|
||||
}
|
||||
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 m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
k := n
|
||||
if s == blas.Left {
|
||||
k = m
|
||||
}
|
||||
if lda < max(1, k) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldb < max(1, n) {
|
||||
panic(badLdB)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(k-1)+k {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(b) < ldb*(m-1)+n {
|
||||
panic(shortB)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := range btmp {
|
||||
btmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
nonUnit := d == blas.NonUnit
|
||||
if s == blas.Left {
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := m - 1; i >= 0; i-- {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if alpha != 1 {
|
||||
f32.ScalUnitary(alpha, btmp)
|
||||
}
|
||||
for ka, va := range a[i*lda+i+1 : i*lda+m] {
|
||||
if va != 0 {
|
||||
k := ka + i + 1
|
||||
f32.AxpyUnitary(-va, b[k*ldb:k*ldb+n], btmp)
|
||||
}
|
||||
}
|
||||
if nonUnit {
|
||||
tmp := 1 / a[i*lda+i]
|
||||
f32.ScalUnitary(tmp, btmp)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if alpha != 1 {
|
||||
f32.ScalUnitary(alpha, btmp)
|
||||
}
|
||||
for k, va := range a[i*lda : i*lda+i] {
|
||||
if va != 0 {
|
||||
f32.AxpyUnitary(-va, b[k*ldb:k*ldb+n], btmp)
|
||||
}
|
||||
}
|
||||
if nonUnit {
|
||||
tmp := 1 / a[i*lda+i]
|
||||
f32.ScalUnitary(tmp, btmp)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed
|
||||
if ul == blas.Upper {
|
||||
for k := 0; k < m; k++ {
|
||||
btmpk := b[k*ldb : k*ldb+n]
|
||||
if nonUnit {
|
||||
tmp := 1 / a[k*lda+k]
|
||||
f32.ScalUnitary(tmp, btmpk)
|
||||
}
|
||||
for ia, va := range a[k*lda+k+1 : k*lda+m] {
|
||||
if va != 0 {
|
||||
i := ia + k + 1
|
||||
f32.AxpyUnitary(-va, btmpk, b[i*ldb:i*ldb+n])
|
||||
}
|
||||
}
|
||||
if alpha != 1 {
|
||||
f32.ScalUnitary(alpha, btmpk)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for k := m - 1; k >= 0; k-- {
|
||||
btmpk := b[k*ldb : k*ldb+n]
|
||||
if nonUnit {
|
||||
tmp := 1 / a[k*lda+k]
|
||||
f32.ScalUnitary(tmp, btmpk)
|
||||
}
|
||||
for i, va := range a[k*lda : k*lda+k] {
|
||||
if va != 0 {
|
||||
f32.AxpyUnitary(-va, btmpk, b[i*ldb:i*ldb+n])
|
||||
}
|
||||
}
|
||||
if alpha != 1 {
|
||||
f32.ScalUnitary(alpha, btmpk)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is to the right of X.
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if alpha != 1 {
|
||||
f32.ScalUnitary(alpha, btmp)
|
||||
}
|
||||
for k, vb := range btmp {
|
||||
if vb == 0 {
|
||||
continue
|
||||
}
|
||||
if nonUnit {
|
||||
btmp[k] /= a[k*lda+k]
|
||||
}
|
||||
f32.AxpyUnitary(-btmp[k], a[k*lda+k+1:k*lda+n], btmp[k+1:n])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if alpha != 1 {
|
||||
f32.ScalUnitary(alpha, btmp)
|
||||
}
|
||||
for k := n - 1; k >= 0; k-- {
|
||||
if btmp[k] == 0 {
|
||||
continue
|
||||
}
|
||||
if nonUnit {
|
||||
btmp[k] /= a[k*lda+k]
|
||||
}
|
||||
f32.AxpyUnitary(-btmp[k], a[k*lda:k*lda+k], btmp[:k])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := n - 1; j >= 0; j-- {
|
||||
tmp := alpha*btmp[j] - f32.DotUnitary(a[j*lda+j+1:j*lda+n], btmp[j+1:])
|
||||
if nonUnit {
|
||||
tmp /= a[j*lda+j]
|
||||
}
|
||||
btmp[j] = tmp
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := 0; j < n; j++ {
|
||||
tmp := alpha*btmp[j] - f32.DotUnitary(a[j*lda:j*lda+j], btmp[:j])
|
||||
if nonUnit {
|
||||
tmp /= a[j*lda+j]
|
||||
}
|
||||
btmp[j] = tmp
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Ssymm performs one of the matrix-matrix operations
|
||||
// C = alpha * A * B + beta * C if side == blas.Left
|
||||
// C = alpha * B * A + beta * C if side == blas.Right
|
||||
// where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and alpha
|
||||
// is a scalar.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Ssymm(s blas.Side, ul blas.Uplo, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int) {
|
||||
if s != blas.Right && s != blas.Left {
|
||||
panic(badSide)
|
||||
}
|
||||
if ul != blas.Lower && ul != blas.Upper {
|
||||
panic(badUplo)
|
||||
}
|
||||
if m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
k := n
|
||||
if s == blas.Left {
|
||||
k = m
|
||||
}
|
||||
if lda < max(1, k) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldb < max(1, n) {
|
||||
panic(badLdB)
|
||||
}
|
||||
if ldc < max(1, n) {
|
||||
panic(badLdC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(k-1)+k {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(b) < ldb*(m-1)+n {
|
||||
panic(shortB)
|
||||
}
|
||||
if len(c) < ldc*(m-1)+n {
|
||||
panic(shortC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if alpha == 0 && beta == 1 {
|
||||
return
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
if beta == 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := 0; j < n; j++ {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
isUpper := ul == blas.Upper
|
||||
if s == blas.Left {
|
||||
for i := 0; i < m; i++ {
|
||||
atmp := alpha * a[i*lda+i]
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j, v := range btmp {
|
||||
ctmp[j] *= beta
|
||||
ctmp[j] += atmp * v
|
||||
}
|
||||
|
||||
for k := 0; k < i; k++ {
|
||||
var atmp float32
|
||||
if isUpper {
|
||||
atmp = a[k*lda+i]
|
||||
} else {
|
||||
atmp = a[i*lda+k]
|
||||
}
|
||||
atmp *= alpha
|
||||
f32.AxpyUnitary(atmp, b[k*ldb:k*ldb+n], ctmp)
|
||||
}
|
||||
for k := i + 1; k < m; k++ {
|
||||
var atmp float32
|
||||
if isUpper {
|
||||
atmp = a[i*lda+k]
|
||||
} else {
|
||||
atmp = a[k*lda+i]
|
||||
}
|
||||
atmp *= alpha
|
||||
f32.AxpyUnitary(atmp, b[k*ldb:k*ldb+n], ctmp)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if isUpper {
|
||||
for i := 0; i < m; i++ {
|
||||
for j := n - 1; j >= 0; j-- {
|
||||
tmp := alpha * b[i*ldb+j]
|
||||
var tmp2 float32
|
||||
atmp := a[j*lda+j+1 : j*lda+n]
|
||||
btmp := b[i*ldb+j+1 : i*ldb+n]
|
||||
ctmp := c[i*ldc+j+1 : i*ldc+n]
|
||||
for k, v := range atmp {
|
||||
ctmp[k] += tmp * v
|
||||
tmp2 += btmp[k] * v
|
||||
}
|
||||
c[i*ldc+j] *= beta
|
||||
c[i*ldc+j] += tmp*a[j*lda+j] + alpha*tmp2
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
for j := 0; j < n; j++ {
|
||||
tmp := alpha * b[i*ldb+j]
|
||||
var tmp2 float32
|
||||
atmp := a[j*lda : j*lda+j]
|
||||
btmp := b[i*ldb : i*ldb+j]
|
||||
ctmp := c[i*ldc : i*ldc+j]
|
||||
for k, v := range atmp {
|
||||
ctmp[k] += tmp * v
|
||||
tmp2 += btmp[k] * v
|
||||
}
|
||||
c[i*ldc+j] *= beta
|
||||
c[i*ldc+j] += tmp*a[j*lda+j] + alpha*tmp2
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Ssyrk performs one of the symmetric rank-k operations
|
||||
// C = alpha * A * A^T + beta * C if tA == blas.NoTrans
|
||||
// C = alpha * A^T * A + beta * C if tA == blas.Trans or tA == blas.ConjTrans
|
||||
// where A is an n×k or k×n matrix, C is an n×n symmetric matrix, and alpha and
|
||||
// beta are scalars.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Ssyrk(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float32, a []float32, lda int, beta float32, c []float32, ldc int) {
|
||||
if ul != blas.Lower && ul != blas.Upper {
|
||||
panic(badUplo)
|
||||
}
|
||||
if tA != blas.Trans && tA != blas.NoTrans && tA != blas.ConjTrans {
|
||||
panic(badTranspose)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if k < 0 {
|
||||
panic(kLT0)
|
||||
}
|
||||
row, col := k, n
|
||||
if tA == blas.NoTrans {
|
||||
row, col = n, k
|
||||
}
|
||||
if lda < max(1, col) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldc < max(1, n) {
|
||||
panic(badLdC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(row-1)+col {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(c) < ldc*(n-1)+n {
|
||||
panic(shortC)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
if beta == 0 {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
if beta == 0 {
|
||||
for jc := range ctmp {
|
||||
j := jc + i
|
||||
ctmp[jc] = alpha * f32.DotUnitary(atmp, a[j*lda:j*lda+k])
|
||||
}
|
||||
} else {
|
||||
for jc, vc := range ctmp {
|
||||
j := jc + i
|
||||
ctmp[jc] = vc*beta + alpha*f32.DotUnitary(atmp, a[j*lda:j*lda+k])
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
if beta == 0 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] = alpha * f32.DotUnitary(a[j*lda:j*lda+k], atmp)
|
||||
}
|
||||
} else {
|
||||
for j, vc := range ctmp {
|
||||
ctmp[j] = vc*beta + alpha*f32.DotUnitary(a[j*lda:j*lda+k], atmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
if beta == 0 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
} else if beta != 1 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
for l := 0; l < k; l++ {
|
||||
tmp := alpha * a[l*lda+i]
|
||||
if tmp != 0 {
|
||||
f32.AxpyUnitary(tmp, a[l*lda+i:l*lda+n], ctmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
if beta != 1 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
for l := 0; l < k; l++ {
|
||||
tmp := alpha * a[l*lda+i]
|
||||
if tmp != 0 {
|
||||
f32.AxpyUnitary(tmp, a[l*lda:l*lda+i+1], ctmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Ssyr2k performs one of the symmetric rank 2k operations
|
||||
// C = alpha * A * B^T + alpha * B * A^T + beta * C if tA == blas.NoTrans
|
||||
// C = alpha * A^T * B + alpha * B^T * A + beta * C if tA == blas.Trans or tA == blas.ConjTrans
|
||||
// where A and B are n×k or k×n matrices, C is an n×n symmetric matrix, and
|
||||
// alpha and beta are scalars.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Ssyr2k(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int) {
|
||||
if ul != blas.Lower && ul != blas.Upper {
|
||||
panic(badUplo)
|
||||
}
|
||||
if tA != blas.Trans && tA != blas.NoTrans && tA != blas.ConjTrans {
|
||||
panic(badTranspose)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if k < 0 {
|
||||
panic(kLT0)
|
||||
}
|
||||
row, col := k, n
|
||||
if tA == blas.NoTrans {
|
||||
row, col = n, k
|
||||
}
|
||||
if lda < max(1, col) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldb < max(1, col) {
|
||||
panic(badLdB)
|
||||
}
|
||||
if ldc < max(1, n) {
|
||||
panic(badLdC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(row-1)+col {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(b) < ldb*(row-1)+col {
|
||||
panic(shortB)
|
||||
}
|
||||
if len(c) < ldc*(n-1)+n {
|
||||
panic(shortC)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
if beta == 0 {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
btmp := b[i*ldb : i*ldb+k]
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for jc := range ctmp {
|
||||
j := i + jc
|
||||
var tmp1, tmp2 float32
|
||||
binner := b[j*ldb : j*ldb+k]
|
||||
for l, v := range a[j*lda : j*lda+k] {
|
||||
tmp1 += v * btmp[l]
|
||||
tmp2 += atmp[l] * binner[l]
|
||||
}
|
||||
ctmp[jc] *= beta
|
||||
ctmp[jc] += alpha * (tmp1 + tmp2)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
btmp := b[i*ldb : i*ldb+k]
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := 0; j <= i; j++ {
|
||||
var tmp1, tmp2 float32
|
||||
binner := b[j*ldb : j*ldb+k]
|
||||
for l, v := range a[j*lda : j*lda+k] {
|
||||
tmp1 += v * btmp[l]
|
||||
tmp2 += atmp[l] * binner[l]
|
||||
}
|
||||
ctmp[j] *= beta
|
||||
ctmp[j] += alpha * (tmp1 + tmp2)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
if beta != 1 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
for l := 0; l < k; l++ {
|
||||
tmp1 := alpha * b[l*ldb+i]
|
||||
tmp2 := alpha * a[l*lda+i]
|
||||
btmp := b[l*ldb+i : l*ldb+n]
|
||||
if tmp1 != 0 || tmp2 != 0 {
|
||||
for j, v := range a[l*lda+i : l*lda+n] {
|
||||
ctmp[j] += v*tmp1 + btmp[j]*tmp2
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
if beta != 1 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
for l := 0; l < k; l++ {
|
||||
tmp1 := alpha * b[l*ldb+i]
|
||||
tmp2 := alpha * a[l*lda+i]
|
||||
btmp := b[l*ldb : l*ldb+i+1]
|
||||
if tmp1 != 0 || tmp2 != 0 {
|
||||
for j, v := range a[l*lda : l*lda+i+1] {
|
||||
ctmp[j] += v*tmp1 + btmp[j]*tmp2
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Strmm performs one of the matrix-matrix operations
|
||||
// B = alpha * A * B if tA == blas.NoTrans and side == blas.Left
|
||||
// B = alpha * A^T * B if tA == blas.Trans or blas.ConjTrans, and side == blas.Left
|
||||
// B = alpha * B * A if tA == blas.NoTrans and side == blas.Right
|
||||
// B = alpha * B * A^T if tA == blas.Trans or blas.ConjTrans, and side == blas.Right
|
||||
// where A is an n×n or m×m triangular matrix, B is an m×n matrix, and alpha is a scalar.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Strmm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int) {
|
||||
if s != blas.Left && s != blas.Right {
|
||||
panic(badSide)
|
||||
}
|
||||
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 m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
k := n
|
||||
if s == blas.Left {
|
||||
k = m
|
||||
}
|
||||
if lda < max(1, k) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldb < max(1, n) {
|
||||
panic(badLdB)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(k-1)+k {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(b) < ldb*(m-1)+n {
|
||||
panic(shortB)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := range btmp {
|
||||
btmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
nonUnit := d == blas.NonUnit
|
||||
if s == blas.Left {
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
tmp := alpha
|
||||
if nonUnit {
|
||||
tmp *= a[i*lda+i]
|
||||
}
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
f32.ScalUnitary(tmp, btmp)
|
||||
for ka, va := range a[i*lda+i+1 : i*lda+m] {
|
||||
k := ka + i + 1
|
||||
if va != 0 {
|
||||
f32.AxpyUnitary(alpha*va, b[k*ldb:k*ldb+n], btmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := m - 1; i >= 0; i-- {
|
||||
tmp := alpha
|
||||
if nonUnit {
|
||||
tmp *= a[i*lda+i]
|
||||
}
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
f32.ScalUnitary(tmp, btmp)
|
||||
for k, va := range a[i*lda : i*lda+i] {
|
||||
if va != 0 {
|
||||
f32.AxpyUnitary(alpha*va, b[k*ldb:k*ldb+n], btmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if ul == blas.Upper {
|
||||
for k := m - 1; k >= 0; k-- {
|
||||
btmpk := b[k*ldb : k*ldb+n]
|
||||
for ia, va := range a[k*lda+k+1 : k*lda+m] {
|
||||
i := ia + k + 1
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if va != 0 {
|
||||
f32.AxpyUnitary(alpha*va, btmpk, btmp)
|
||||
}
|
||||
}
|
||||
tmp := alpha
|
||||
if nonUnit {
|
||||
tmp *= a[k*lda+k]
|
||||
}
|
||||
if tmp != 1 {
|
||||
f32.ScalUnitary(tmp, btmpk)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for k := 0; k < m; k++ {
|
||||
btmpk := b[k*ldb : k*ldb+n]
|
||||
for i, va := range a[k*lda : k*lda+k] {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if va != 0 {
|
||||
f32.AxpyUnitary(alpha*va, btmpk, btmp)
|
||||
}
|
||||
}
|
||||
tmp := alpha
|
||||
if nonUnit {
|
||||
tmp *= a[k*lda+k]
|
||||
}
|
||||
if tmp != 1 {
|
||||
f32.ScalUnitary(tmp, btmpk)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is on the right
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for k := n - 1; k >= 0; k-- {
|
||||
tmp := alpha * btmp[k]
|
||||
if tmp == 0 {
|
||||
continue
|
||||
}
|
||||
btmp[k] = tmp
|
||||
if nonUnit {
|
||||
btmp[k] *= a[k*lda+k]
|
||||
}
|
||||
f32.AxpyUnitary(tmp, a[k*lda+k+1:k*lda+n], btmp[k+1:n])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for k := 0; k < n; k++ {
|
||||
tmp := alpha * btmp[k]
|
||||
if tmp == 0 {
|
||||
continue
|
||||
}
|
||||
btmp[k] = tmp
|
||||
if nonUnit {
|
||||
btmp[k] *= a[k*lda+k]
|
||||
}
|
||||
f32.AxpyUnitary(tmp, a[k*lda:k*lda+k], btmp[:k])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j, vb := range btmp {
|
||||
tmp := vb
|
||||
if nonUnit {
|
||||
tmp *= a[j*lda+j]
|
||||
}
|
||||
tmp += f32.DotUnitary(a[j*lda+j+1:j*lda+n], btmp[j+1:n])
|
||||
btmp[j] = alpha * tmp
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := n - 1; j >= 0; j-- {
|
||||
tmp := btmp[j]
|
||||
if nonUnit {
|
||||
tmp *= a[j*lda+j]
|
||||
}
|
||||
tmp += f32.DotUnitary(a[j*lda:j*lda+j], btmp[:j])
|
||||
btmp[j] = alpha * tmp
|
||||
}
|
||||
}
|
||||
}
|
||||
864
vendor/gonum.org/v1/gonum/blas/gonum/level3float64.go
generated
vendored
Normal file
864
vendor/gonum.org/v1/gonum/blas/gonum/level3float64.go
generated
vendored
Normal file
|
|
@ -0,0 +1,864 @@
|
|||
// Copyright ©2014 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/internal/asm/f64"
|
||||
)
|
||||
|
||||
var _ blas.Float64Level3 = Implementation{}
|
||||
|
||||
// Dtrsm solves one of the matrix equations
|
||||
// A * X = alpha * B if tA == blas.NoTrans and side == blas.Left
|
||||
// A^T * X = alpha * B if tA == blas.Trans or blas.ConjTrans, and side == blas.Left
|
||||
// X * A = alpha * B if tA == blas.NoTrans and side == blas.Right
|
||||
// X * A^T = alpha * B if tA == blas.Trans or blas.ConjTrans, and side == blas.Right
|
||||
// where A is an n×n or m×m triangular matrix, X and B are m×n matrices, and alpha is a
|
||||
// scalar.
|
||||
//
|
||||
// At entry to the function, X contains the values of B, and the result is
|
||||
// stored in-place into X.
|
||||
//
|
||||
// No check is made that A is invertible.
|
||||
func (Implementation) Dtrsm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int) {
|
||||
if s != blas.Left && s != blas.Right {
|
||||
panic(badSide)
|
||||
}
|
||||
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 m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
k := n
|
||||
if s == blas.Left {
|
||||
k = m
|
||||
}
|
||||
if lda < max(1, k) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldb < max(1, n) {
|
||||
panic(badLdB)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(k-1)+k {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(b) < ldb*(m-1)+n {
|
||||
panic(shortB)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := range btmp {
|
||||
btmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
nonUnit := d == blas.NonUnit
|
||||
if s == blas.Left {
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := m - 1; i >= 0; i-- {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if alpha != 1 {
|
||||
f64.ScalUnitary(alpha, btmp)
|
||||
}
|
||||
for ka, va := range a[i*lda+i+1 : i*lda+m] {
|
||||
if va != 0 {
|
||||
k := ka + i + 1
|
||||
f64.AxpyUnitary(-va, b[k*ldb:k*ldb+n], btmp)
|
||||
}
|
||||
}
|
||||
if nonUnit {
|
||||
tmp := 1 / a[i*lda+i]
|
||||
f64.ScalUnitary(tmp, btmp)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if alpha != 1 {
|
||||
f64.ScalUnitary(alpha, btmp)
|
||||
}
|
||||
for k, va := range a[i*lda : i*lda+i] {
|
||||
if va != 0 {
|
||||
f64.AxpyUnitary(-va, b[k*ldb:k*ldb+n], btmp)
|
||||
}
|
||||
}
|
||||
if nonUnit {
|
||||
tmp := 1 / a[i*lda+i]
|
||||
f64.ScalUnitary(tmp, btmp)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed
|
||||
if ul == blas.Upper {
|
||||
for k := 0; k < m; k++ {
|
||||
btmpk := b[k*ldb : k*ldb+n]
|
||||
if nonUnit {
|
||||
tmp := 1 / a[k*lda+k]
|
||||
f64.ScalUnitary(tmp, btmpk)
|
||||
}
|
||||
for ia, va := range a[k*lda+k+1 : k*lda+m] {
|
||||
if va != 0 {
|
||||
i := ia + k + 1
|
||||
f64.AxpyUnitary(-va, btmpk, b[i*ldb:i*ldb+n])
|
||||
}
|
||||
}
|
||||
if alpha != 1 {
|
||||
f64.ScalUnitary(alpha, btmpk)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for k := m - 1; k >= 0; k-- {
|
||||
btmpk := b[k*ldb : k*ldb+n]
|
||||
if nonUnit {
|
||||
tmp := 1 / a[k*lda+k]
|
||||
f64.ScalUnitary(tmp, btmpk)
|
||||
}
|
||||
for i, va := range a[k*lda : k*lda+k] {
|
||||
if va != 0 {
|
||||
f64.AxpyUnitary(-va, btmpk, b[i*ldb:i*ldb+n])
|
||||
}
|
||||
}
|
||||
if alpha != 1 {
|
||||
f64.ScalUnitary(alpha, btmpk)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is to the right of X.
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if alpha != 1 {
|
||||
f64.ScalUnitary(alpha, btmp)
|
||||
}
|
||||
for k, vb := range btmp {
|
||||
if vb == 0 {
|
||||
continue
|
||||
}
|
||||
if nonUnit {
|
||||
btmp[k] /= a[k*lda+k]
|
||||
}
|
||||
f64.AxpyUnitary(-btmp[k], a[k*lda+k+1:k*lda+n], btmp[k+1:n])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if alpha != 1 {
|
||||
f64.ScalUnitary(alpha, btmp)
|
||||
}
|
||||
for k := n - 1; k >= 0; k-- {
|
||||
if btmp[k] == 0 {
|
||||
continue
|
||||
}
|
||||
if nonUnit {
|
||||
btmp[k] /= a[k*lda+k]
|
||||
}
|
||||
f64.AxpyUnitary(-btmp[k], a[k*lda:k*lda+k], btmp[:k])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := n - 1; j >= 0; j-- {
|
||||
tmp := alpha*btmp[j] - f64.DotUnitary(a[j*lda+j+1:j*lda+n], btmp[j+1:])
|
||||
if nonUnit {
|
||||
tmp /= a[j*lda+j]
|
||||
}
|
||||
btmp[j] = tmp
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := 0; j < n; j++ {
|
||||
tmp := alpha*btmp[j] - f64.DotUnitary(a[j*lda:j*lda+j], btmp[:j])
|
||||
if nonUnit {
|
||||
tmp /= a[j*lda+j]
|
||||
}
|
||||
btmp[j] = tmp
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Dsymm performs one of the matrix-matrix operations
|
||||
// C = alpha * A * B + beta * C if side == blas.Left
|
||||
// C = alpha * B * A + beta * C if side == blas.Right
|
||||
// where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and alpha
|
||||
// is a scalar.
|
||||
func (Implementation) Dsymm(s blas.Side, ul blas.Uplo, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int) {
|
||||
if s != blas.Right && s != blas.Left {
|
||||
panic(badSide)
|
||||
}
|
||||
if ul != blas.Lower && ul != blas.Upper {
|
||||
panic(badUplo)
|
||||
}
|
||||
if m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
k := n
|
||||
if s == blas.Left {
|
||||
k = m
|
||||
}
|
||||
if lda < max(1, k) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldb < max(1, n) {
|
||||
panic(badLdB)
|
||||
}
|
||||
if ldc < max(1, n) {
|
||||
panic(badLdC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(k-1)+k {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(b) < ldb*(m-1)+n {
|
||||
panic(shortB)
|
||||
}
|
||||
if len(c) < ldc*(m-1)+n {
|
||||
panic(shortC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if alpha == 0 && beta == 1 {
|
||||
return
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
if beta == 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := 0; j < n; j++ {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
isUpper := ul == blas.Upper
|
||||
if s == blas.Left {
|
||||
for i := 0; i < m; i++ {
|
||||
atmp := alpha * a[i*lda+i]
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j, v := range btmp {
|
||||
ctmp[j] *= beta
|
||||
ctmp[j] += atmp * v
|
||||
}
|
||||
|
||||
for k := 0; k < i; k++ {
|
||||
var atmp float64
|
||||
if isUpper {
|
||||
atmp = a[k*lda+i]
|
||||
} else {
|
||||
atmp = a[i*lda+k]
|
||||
}
|
||||
atmp *= alpha
|
||||
f64.AxpyUnitary(atmp, b[k*ldb:k*ldb+n], ctmp)
|
||||
}
|
||||
for k := i + 1; k < m; k++ {
|
||||
var atmp float64
|
||||
if isUpper {
|
||||
atmp = a[i*lda+k]
|
||||
} else {
|
||||
atmp = a[k*lda+i]
|
||||
}
|
||||
atmp *= alpha
|
||||
f64.AxpyUnitary(atmp, b[k*ldb:k*ldb+n], ctmp)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if isUpper {
|
||||
for i := 0; i < m; i++ {
|
||||
for j := n - 1; j >= 0; j-- {
|
||||
tmp := alpha * b[i*ldb+j]
|
||||
var tmp2 float64
|
||||
atmp := a[j*lda+j+1 : j*lda+n]
|
||||
btmp := b[i*ldb+j+1 : i*ldb+n]
|
||||
ctmp := c[i*ldc+j+1 : i*ldc+n]
|
||||
for k, v := range atmp {
|
||||
ctmp[k] += tmp * v
|
||||
tmp2 += btmp[k] * v
|
||||
}
|
||||
c[i*ldc+j] *= beta
|
||||
c[i*ldc+j] += tmp*a[j*lda+j] + alpha*tmp2
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
for j := 0; j < n; j++ {
|
||||
tmp := alpha * b[i*ldb+j]
|
||||
var tmp2 float64
|
||||
atmp := a[j*lda : j*lda+j]
|
||||
btmp := b[i*ldb : i*ldb+j]
|
||||
ctmp := c[i*ldc : i*ldc+j]
|
||||
for k, v := range atmp {
|
||||
ctmp[k] += tmp * v
|
||||
tmp2 += btmp[k] * v
|
||||
}
|
||||
c[i*ldc+j] *= beta
|
||||
c[i*ldc+j] += tmp*a[j*lda+j] + alpha*tmp2
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Dsyrk performs one of the symmetric rank-k operations
|
||||
// C = alpha * A * A^T + beta * C if tA == blas.NoTrans
|
||||
// C = alpha * A^T * A + beta * C if tA == blas.Trans or tA == blas.ConjTrans
|
||||
// where A is an n×k or k×n matrix, C is an n×n symmetric matrix, and alpha and
|
||||
// beta are scalars.
|
||||
func (Implementation) Dsyrk(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float64, a []float64, lda int, beta float64, c []float64, ldc int) {
|
||||
if ul != blas.Lower && ul != blas.Upper {
|
||||
panic(badUplo)
|
||||
}
|
||||
if tA != blas.Trans && tA != blas.NoTrans && tA != blas.ConjTrans {
|
||||
panic(badTranspose)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if k < 0 {
|
||||
panic(kLT0)
|
||||
}
|
||||
row, col := k, n
|
||||
if tA == blas.NoTrans {
|
||||
row, col = n, k
|
||||
}
|
||||
if lda < max(1, col) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldc < max(1, n) {
|
||||
panic(badLdC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(row-1)+col {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(c) < ldc*(n-1)+n {
|
||||
panic(shortC)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
if beta == 0 {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
if beta == 0 {
|
||||
for jc := range ctmp {
|
||||
j := jc + i
|
||||
ctmp[jc] = alpha * f64.DotUnitary(atmp, a[j*lda:j*lda+k])
|
||||
}
|
||||
} else {
|
||||
for jc, vc := range ctmp {
|
||||
j := jc + i
|
||||
ctmp[jc] = vc*beta + alpha*f64.DotUnitary(atmp, a[j*lda:j*lda+k])
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
if beta == 0 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] = alpha * f64.DotUnitary(a[j*lda:j*lda+k], atmp)
|
||||
}
|
||||
} else {
|
||||
for j, vc := range ctmp {
|
||||
ctmp[j] = vc*beta + alpha*f64.DotUnitary(a[j*lda:j*lda+k], atmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
if beta == 0 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
} else if beta != 1 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
for l := 0; l < k; l++ {
|
||||
tmp := alpha * a[l*lda+i]
|
||||
if tmp != 0 {
|
||||
f64.AxpyUnitary(tmp, a[l*lda+i:l*lda+n], ctmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
if beta != 1 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
for l := 0; l < k; l++ {
|
||||
tmp := alpha * a[l*lda+i]
|
||||
if tmp != 0 {
|
||||
f64.AxpyUnitary(tmp, a[l*lda:l*lda+i+1], ctmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Dsyr2k performs one of the symmetric rank 2k operations
|
||||
// C = alpha * A * B^T + alpha * B * A^T + beta * C if tA == blas.NoTrans
|
||||
// C = alpha * A^T * B + alpha * B^T * A + beta * C if tA == blas.Trans or tA == blas.ConjTrans
|
||||
// where A and B are n×k or k×n matrices, C is an n×n symmetric matrix, and
|
||||
// alpha and beta are scalars.
|
||||
func (Implementation) Dsyr2k(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int) {
|
||||
if ul != blas.Lower && ul != blas.Upper {
|
||||
panic(badUplo)
|
||||
}
|
||||
if tA != blas.Trans && tA != blas.NoTrans && tA != blas.ConjTrans {
|
||||
panic(badTranspose)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if k < 0 {
|
||||
panic(kLT0)
|
||||
}
|
||||
row, col := k, n
|
||||
if tA == blas.NoTrans {
|
||||
row, col = n, k
|
||||
}
|
||||
if lda < max(1, col) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldb < max(1, col) {
|
||||
panic(badLdB)
|
||||
}
|
||||
if ldc < max(1, n) {
|
||||
panic(badLdC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(row-1)+col {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(b) < ldb*(row-1)+col {
|
||||
panic(shortB)
|
||||
}
|
||||
if len(c) < ldc*(n-1)+n {
|
||||
panic(shortC)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
if beta == 0 {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
btmp := b[i*ldb : i*ldb+k]
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for jc := range ctmp {
|
||||
j := i + jc
|
||||
var tmp1, tmp2 float64
|
||||
binner := b[j*ldb : j*ldb+k]
|
||||
for l, v := range a[j*lda : j*lda+k] {
|
||||
tmp1 += v * btmp[l]
|
||||
tmp2 += atmp[l] * binner[l]
|
||||
}
|
||||
ctmp[jc] *= beta
|
||||
ctmp[jc] += alpha * (tmp1 + tmp2)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
btmp := b[i*ldb : i*ldb+k]
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := 0; j <= i; j++ {
|
||||
var tmp1, tmp2 float64
|
||||
binner := b[j*ldb : j*ldb+k]
|
||||
for l, v := range a[j*lda : j*lda+k] {
|
||||
tmp1 += v * btmp[l]
|
||||
tmp2 += atmp[l] * binner[l]
|
||||
}
|
||||
ctmp[j] *= beta
|
||||
ctmp[j] += alpha * (tmp1 + tmp2)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
if beta != 1 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
for l := 0; l < k; l++ {
|
||||
tmp1 := alpha * b[l*ldb+i]
|
||||
tmp2 := alpha * a[l*lda+i]
|
||||
btmp := b[l*ldb+i : l*ldb+n]
|
||||
if tmp1 != 0 || tmp2 != 0 {
|
||||
for j, v := range a[l*lda+i : l*lda+n] {
|
||||
ctmp[j] += v*tmp1 + btmp[j]*tmp2
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
if beta != 1 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
for l := 0; l < k; l++ {
|
||||
tmp1 := alpha * b[l*ldb+i]
|
||||
tmp2 := alpha * a[l*lda+i]
|
||||
btmp := b[l*ldb : l*ldb+i+1]
|
||||
if tmp1 != 0 || tmp2 != 0 {
|
||||
for j, v := range a[l*lda : l*lda+i+1] {
|
||||
ctmp[j] += v*tmp1 + btmp[j]*tmp2
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Dtrmm performs one of the matrix-matrix operations
|
||||
// B = alpha * A * B if tA == blas.NoTrans and side == blas.Left
|
||||
// B = alpha * A^T * B if tA == blas.Trans or blas.ConjTrans, and side == blas.Left
|
||||
// B = alpha * B * A if tA == blas.NoTrans and side == blas.Right
|
||||
// B = alpha * B * A^T if tA == blas.Trans or blas.ConjTrans, and side == blas.Right
|
||||
// where A is an n×n or m×m triangular matrix, B is an m×n matrix, and alpha is a scalar.
|
||||
func (Implementation) Dtrmm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int) {
|
||||
if s != blas.Left && s != blas.Right {
|
||||
panic(badSide)
|
||||
}
|
||||
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 m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
k := n
|
||||
if s == blas.Left {
|
||||
k = m
|
||||
}
|
||||
if lda < max(1, k) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldb < max(1, n) {
|
||||
panic(badLdB)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(k-1)+k {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(b) < ldb*(m-1)+n {
|
||||
panic(shortB)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := range btmp {
|
||||
btmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
nonUnit := d == blas.NonUnit
|
||||
if s == blas.Left {
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
tmp := alpha
|
||||
if nonUnit {
|
||||
tmp *= a[i*lda+i]
|
||||
}
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
f64.ScalUnitary(tmp, btmp)
|
||||
for ka, va := range a[i*lda+i+1 : i*lda+m] {
|
||||
k := ka + i + 1
|
||||
if va != 0 {
|
||||
f64.AxpyUnitary(alpha*va, b[k*ldb:k*ldb+n], btmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := m - 1; i >= 0; i-- {
|
||||
tmp := alpha
|
||||
if nonUnit {
|
||||
tmp *= a[i*lda+i]
|
||||
}
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
f64.ScalUnitary(tmp, btmp)
|
||||
for k, va := range a[i*lda : i*lda+i] {
|
||||
if va != 0 {
|
||||
f64.AxpyUnitary(alpha*va, b[k*ldb:k*ldb+n], btmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if ul == blas.Upper {
|
||||
for k := m - 1; k >= 0; k-- {
|
||||
btmpk := b[k*ldb : k*ldb+n]
|
||||
for ia, va := range a[k*lda+k+1 : k*lda+m] {
|
||||
i := ia + k + 1
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if va != 0 {
|
||||
f64.AxpyUnitary(alpha*va, btmpk, btmp)
|
||||
}
|
||||
}
|
||||
tmp := alpha
|
||||
if nonUnit {
|
||||
tmp *= a[k*lda+k]
|
||||
}
|
||||
if tmp != 1 {
|
||||
f64.ScalUnitary(tmp, btmpk)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for k := 0; k < m; k++ {
|
||||
btmpk := b[k*ldb : k*ldb+n]
|
||||
for i, va := range a[k*lda : k*lda+k] {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if va != 0 {
|
||||
f64.AxpyUnitary(alpha*va, btmpk, btmp)
|
||||
}
|
||||
}
|
||||
tmp := alpha
|
||||
if nonUnit {
|
||||
tmp *= a[k*lda+k]
|
||||
}
|
||||
if tmp != 1 {
|
||||
f64.ScalUnitary(tmp, btmpk)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is on the right
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for k := n - 1; k >= 0; k-- {
|
||||
tmp := alpha * btmp[k]
|
||||
if tmp == 0 {
|
||||
continue
|
||||
}
|
||||
btmp[k] = tmp
|
||||
if nonUnit {
|
||||
btmp[k] *= a[k*lda+k]
|
||||
}
|
||||
f64.AxpyUnitary(tmp, a[k*lda+k+1:k*lda+n], btmp[k+1:n])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for k := 0; k < n; k++ {
|
||||
tmp := alpha * btmp[k]
|
||||
if tmp == 0 {
|
||||
continue
|
||||
}
|
||||
btmp[k] = tmp
|
||||
if nonUnit {
|
||||
btmp[k] *= a[k*lda+k]
|
||||
}
|
||||
f64.AxpyUnitary(tmp, a[k*lda:k*lda+k], btmp[:k])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j, vb := range btmp {
|
||||
tmp := vb
|
||||
if nonUnit {
|
||||
tmp *= a[j*lda+j]
|
||||
}
|
||||
tmp += f64.DotUnitary(a[j*lda+j+1:j*lda+n], btmp[j+1:n])
|
||||
btmp[j] = alpha * tmp
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := n - 1; j >= 0; j-- {
|
||||
tmp := btmp[j]
|
||||
if nonUnit {
|
||||
tmp *= a[j*lda+j]
|
||||
}
|
||||
tmp += f64.DotUnitary(a[j*lda:j*lda+j], btmp[:j])
|
||||
btmp[j] = alpha * tmp
|
||||
}
|
||||
}
|
||||
}
|
||||
318
vendor/gonum.org/v1/gonum/blas/gonum/sgemm.go
generated
vendored
Normal file
318
vendor/gonum.org/v1/gonum/blas/gonum/sgemm.go
generated
vendored
Normal file
|
|
@ -0,0 +1,318 @@
|
|||
// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
|
||||
|
||||
// Copyright ©2014 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 (
|
||||
"runtime"
|
||||
"sync"
|
||||
|
||||
"gonum.org/v1/gonum/blas"
|
||||
"gonum.org/v1/gonum/internal/asm/f32"
|
||||
)
|
||||
|
||||
// Sgemm performs one of the matrix-matrix operations
|
||||
// C = alpha * A * B + beta * C
|
||||
// C = alpha * A^T * B + beta * C
|
||||
// C = alpha * A * B^T + beta * C
|
||||
// C = alpha * A^T * B^T + beta * C
|
||||
// where A is an m×k or k×m dense matrix, B is an n×k or k×n dense matrix, C is
|
||||
// an m×n matrix, and alpha and beta are scalars. tA and tB specify whether A or
|
||||
// B are transposed.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Sgemm(tA, tB blas.Transpose, m, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int) {
|
||||
switch tA {
|
||||
default:
|
||||
panic(badTranspose)
|
||||
case blas.NoTrans, blas.Trans, blas.ConjTrans:
|
||||
}
|
||||
switch tB {
|
||||
default:
|
||||
panic(badTranspose)
|
||||
case blas.NoTrans, blas.Trans, blas.ConjTrans:
|
||||
}
|
||||
if m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if k < 0 {
|
||||
panic(kLT0)
|
||||
}
|
||||
aTrans := tA == blas.Trans || tA == blas.ConjTrans
|
||||
if aTrans {
|
||||
if lda < max(1, m) {
|
||||
panic(badLdA)
|
||||
}
|
||||
} else {
|
||||
if lda < max(1, k) {
|
||||
panic(badLdA)
|
||||
}
|
||||
}
|
||||
bTrans := tB == blas.Trans || tB == blas.ConjTrans
|
||||
if bTrans {
|
||||
if ldb < max(1, k) {
|
||||
panic(badLdB)
|
||||
}
|
||||
} else {
|
||||
if ldb < max(1, n) {
|
||||
panic(badLdB)
|
||||
}
|
||||
}
|
||||
if ldc < max(1, n) {
|
||||
panic(badLdC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if aTrans {
|
||||
if len(a) < (k-1)*lda+m {
|
||||
panic(shortA)
|
||||
}
|
||||
} else {
|
||||
if len(a) < (m-1)*lda+k {
|
||||
panic(shortA)
|
||||
}
|
||||
}
|
||||
if bTrans {
|
||||
if len(b) < (n-1)*ldb+k {
|
||||
panic(shortB)
|
||||
}
|
||||
} else {
|
||||
if len(b) < (k-1)*ldb+n {
|
||||
panic(shortB)
|
||||
}
|
||||
}
|
||||
if len(c) < (m-1)*ldc+n {
|
||||
panic(shortC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if (alpha == 0 || k == 0) && beta == 1 {
|
||||
return
|
||||
}
|
||||
|
||||
// scale c
|
||||
if beta != 1 {
|
||||
if beta == 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
} else {
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
sgemmParallel(aTrans, bTrans, m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
}
|
||||
|
||||
func sgemmParallel(aTrans, bTrans bool, m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
|
||||
// dgemmParallel computes a parallel matrix multiplication by partitioning
|
||||
// a and b into sub-blocks, and updating c with the multiplication of the sub-block
|
||||
// In all cases,
|
||||
// A = [ A_11 A_12 ... A_1j
|
||||
// A_21 A_22 ... A_2j
|
||||
// ...
|
||||
// A_i1 A_i2 ... A_ij]
|
||||
//
|
||||
// and same for B. All of the submatrix sizes are blockSize×blockSize except
|
||||
// at the edges.
|
||||
//
|
||||
// In all cases, there is one dimension for each matrix along which
|
||||
// C must be updated sequentially.
|
||||
// Cij = \sum_k Aik Bki, (A * B)
|
||||
// Cij = \sum_k Aki Bkj, (A^T * B)
|
||||
// Cij = \sum_k Aik Bjk, (A * B^T)
|
||||
// Cij = \sum_k Aki Bjk, (A^T * B^T)
|
||||
//
|
||||
// This code computes one {i, j} block sequentially along the k dimension,
|
||||
// and computes all of the {i, j} blocks concurrently. This
|
||||
// partitioning allows Cij to be updated in-place without race-conditions.
|
||||
// Instead of launching a goroutine for each possible concurrent computation,
|
||||
// a number of worker goroutines are created and channels are used to pass
|
||||
// available and completed cases.
|
||||
//
|
||||
// http://alexkr.com/docs/matrixmult.pdf is a good reference on matrix-matrix
|
||||
// multiplies, though this code does not copy matrices to attempt to eliminate
|
||||
// cache misses.
|
||||
|
||||
maxKLen := k
|
||||
parBlocks := blocks(m, blockSize) * blocks(n, blockSize)
|
||||
if parBlocks < minParBlock {
|
||||
// The matrix multiplication is small in the dimensions where it can be
|
||||
// computed concurrently. Just do it in serial.
|
||||
sgemmSerial(aTrans, bTrans, m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
return
|
||||
}
|
||||
|
||||
nWorkers := runtime.GOMAXPROCS(0)
|
||||
if parBlocks < nWorkers {
|
||||
nWorkers = parBlocks
|
||||
}
|
||||
// There is a tradeoff between the workers having to wait for work
|
||||
// and a large buffer making operations slow.
|
||||
buf := buffMul * nWorkers
|
||||
if buf > parBlocks {
|
||||
buf = parBlocks
|
||||
}
|
||||
|
||||
sendChan := make(chan subMul, buf)
|
||||
|
||||
// Launch workers. A worker receives an {i, j} submatrix of c, and computes
|
||||
// A_ik B_ki (or the transposed version) storing the result in c_ij. When the
|
||||
// channel is finally closed, it signals to the waitgroup that it has finished
|
||||
// computing.
|
||||
var wg sync.WaitGroup
|
||||
for i := 0; i < nWorkers; i++ {
|
||||
wg.Add(1)
|
||||
go func() {
|
||||
defer wg.Done()
|
||||
for sub := range sendChan {
|
||||
i := sub.i
|
||||
j := sub.j
|
||||
leni := blockSize
|
||||
if i+leni > m {
|
||||
leni = m - i
|
||||
}
|
||||
lenj := blockSize
|
||||
if j+lenj > n {
|
||||
lenj = n - j
|
||||
}
|
||||
|
||||
cSub := sliceView32(c, ldc, i, j, leni, lenj)
|
||||
|
||||
// Compute A_ik B_kj for all k
|
||||
for k := 0; k < maxKLen; k += blockSize {
|
||||
lenk := blockSize
|
||||
if k+lenk > maxKLen {
|
||||
lenk = maxKLen - k
|
||||
}
|
||||
var aSub, bSub []float32
|
||||
if aTrans {
|
||||
aSub = sliceView32(a, lda, k, i, lenk, leni)
|
||||
} else {
|
||||
aSub = sliceView32(a, lda, i, k, leni, lenk)
|
||||
}
|
||||
if bTrans {
|
||||
bSub = sliceView32(b, ldb, j, k, lenj, lenk)
|
||||
} else {
|
||||
bSub = sliceView32(b, ldb, k, j, lenk, lenj)
|
||||
}
|
||||
sgemmSerial(aTrans, bTrans, leni, lenj, lenk, aSub, lda, bSub, ldb, cSub, ldc, alpha)
|
||||
}
|
||||
}
|
||||
}()
|
||||
}
|
||||
|
||||
// Send out all of the {i, j} subblocks for computation.
|
||||
for i := 0; i < m; i += blockSize {
|
||||
for j := 0; j < n; j += blockSize {
|
||||
sendChan <- subMul{
|
||||
i: i,
|
||||
j: j,
|
||||
}
|
||||
}
|
||||
}
|
||||
close(sendChan)
|
||||
wg.Wait()
|
||||
}
|
||||
|
||||
// sgemmSerial is serial matrix multiply
|
||||
func sgemmSerial(aTrans, bTrans bool, m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
|
||||
switch {
|
||||
case !aTrans && !bTrans:
|
||||
sgemmSerialNotNot(m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
return
|
||||
case aTrans && !bTrans:
|
||||
sgemmSerialTransNot(m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
return
|
||||
case !aTrans && bTrans:
|
||||
sgemmSerialNotTrans(m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
return
|
||||
case aTrans && bTrans:
|
||||
sgemmSerialTransTrans(m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
return
|
||||
default:
|
||||
panic("unreachable")
|
||||
}
|
||||
}
|
||||
|
||||
// sgemmSerial where neither a nor b are transposed
|
||||
func sgemmSerialNotNot(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
|
||||
// This style is used instead of the literal [i*stride +j]) is used because
|
||||
// approximately 5 times faster as of go 1.3.
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for l, v := range a[i*lda : i*lda+k] {
|
||||
tmp := alpha * v
|
||||
if tmp != 0 {
|
||||
f32.AxpyUnitary(tmp, b[l*ldb:l*ldb+n], ctmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// sgemmSerial where neither a is transposed and b is not
|
||||
func sgemmSerialTransNot(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
|
||||
// This style is used instead of the literal [i*stride +j]) is used because
|
||||
// approximately 5 times faster as of go 1.3.
|
||||
for l := 0; l < k; l++ {
|
||||
btmp := b[l*ldb : l*ldb+n]
|
||||
for i, v := range a[l*lda : l*lda+m] {
|
||||
tmp := alpha * v
|
||||
if tmp != 0 {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
f32.AxpyUnitary(tmp, btmp, ctmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// sgemmSerial where neither a is not transposed and b is
|
||||
func sgemmSerialNotTrans(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
|
||||
// This style is used instead of the literal [i*stride +j]) is used because
|
||||
// approximately 5 times faster as of go 1.3.
|
||||
for i := 0; i < m; i++ {
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := 0; j < n; j++ {
|
||||
ctmp[j] += alpha * f32.DotUnitary(atmp, b[j*ldb:j*ldb+k])
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// sgemmSerial where both are transposed
|
||||
func sgemmSerialTransTrans(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
|
||||
// This style is used instead of the literal [i*stride +j]) is used because
|
||||
// approximately 5 times faster as of go 1.3.
|
||||
for l := 0; l < k; l++ {
|
||||
for i, v := range a[l*lda : l*lda+m] {
|
||||
tmp := alpha * v
|
||||
if tmp != 0 {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
f32.AxpyInc(tmp, b[l:], ctmp, uintptr(n), uintptr(ldb), 1, 0, 0)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func sliceView32(a []float32, lda, i, j, r, c int) []float32 {
|
||||
return a[i*lda+j : (i+r-1)*lda+j+c]
|
||||
}
|
||||
218
vendor/gonum.org/v1/gonum/blas/gonum/single_precision.bash
generated
vendored
Normal file
218
vendor/gonum.org/v1/gonum/blas/gonum/single_precision.bash
generated
vendored
Normal file
|
|
@ -0,0 +1,218 @@
|
|||
#!/usr/bin/env bash
|
||||
|
||||
# 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.
|
||||
|
||||
WARNINGF32='//\
|
||||
// Float32 implementations are autogenerated and not directly tested.\
|
||||
'
|
||||
WARNINGC64='//\
|
||||
// Complex64 implementations are autogenerated and not directly tested.\
|
||||
'
|
||||
|
||||
# Level1 routines.
|
||||
|
||||
echo Generating level1float32.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level1float32.go
|
||||
cat level1float64.go \
|
||||
| gofmt -r 'blas.Float64Level1 -> blas.Float32Level1' \
|
||||
\
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
| gofmt -r 'blas.DrotmParams -> blas.SrotmParams' \
|
||||
\
|
||||
| gofmt -r 'f64.AxpyInc -> f32.AxpyInc' \
|
||||
| gofmt -r 'f64.AxpyUnitary -> f32.AxpyUnitary' \
|
||||
| gofmt -r 'f64.DotUnitary -> f32.DotUnitary' \
|
||||
| gofmt -r 'f64.ScalInc -> f32.ScalInc' \
|
||||
| gofmt -r 'f64.ScalUnitary -> f32.ScalUnitary' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNINGF32\1S\2_" \
|
||||
-e 's_^// D_// S_' \
|
||||
-e "s_^\(func (Implementation) \)Id\(.*\)\$_$WARNINGF32\1Is\2_" \
|
||||
-e 's_^// Id_// Is_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
|
||||
-e 's_"math"_math "gonum.org/v1/gonum/internal/math32"_' \
|
||||
>> level1float32.go
|
||||
|
||||
echo Generating level1cmplx64.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level1cmplx64.go
|
||||
cat level1cmplx128.go \
|
||||
| gofmt -r 'blas.Complex128Level1 -> blas.Complex64Level1' \
|
||||
\
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
| gofmt -r 'complex128 -> complex64' \
|
||||
\
|
||||
| gofmt -r 'c128.AxpyInc -> c64.AxpyInc' \
|
||||
| gofmt -r 'c128.AxpyUnitary -> c64.AxpyUnitary' \
|
||||
| gofmt -r 'c128.DotcInc -> c64.DotcInc' \
|
||||
| gofmt -r 'c128.DotcUnitary -> c64.DotcUnitary' \
|
||||
| gofmt -r 'c128.DotuInc -> c64.DotuInc' \
|
||||
| gofmt -r 'c128.DotuUnitary -> c64.DotuUnitary' \
|
||||
| gofmt -r 'c128.ScalInc -> c64.ScalInc' \
|
||||
| gofmt -r 'c128.ScalUnitary -> c64.ScalUnitary' \
|
||||
| gofmt -r 'dcabs1 -> scabs1' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)Zdot\(.*\)\$_$WARNINGC64\1Cdot\2_" \
|
||||
-e 's_^// Zdot_// Cdot_' \
|
||||
-e "s_^\(func (Implementation) \)Zdscal\(.*\)\$_$WARNINGC64\1Csscal\2_" \
|
||||
-e 's_^// Zdscal_// Csscal_' \
|
||||
-e "s_^\(func (Implementation) \)Z\(.*\)\$_$WARNINGC64\1C\2_" \
|
||||
-e 's_^// Z_// C_' \
|
||||
-e "s_^\(func (Implementation) \)Iz\(.*\)\$_$WARNINGC64\1Ic\2_" \
|
||||
-e 's_^// Iz_// Ic_' \
|
||||
-e "s_^\(func (Implementation) \)Dz\(.*\)\$_$WARNINGC64\1Sc\2_" \
|
||||
-e 's_^// Dz_// Sc_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/c128"_"gonum.org/v1/gonum/internal/asm/c64"_' \
|
||||
-e 's_"math"_math "gonum.org/v1/gonum/internal/math32"_' \
|
||||
>> level1cmplx64.go
|
||||
|
||||
echo Generating level1float32_sdot.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level1float32_sdot.go
|
||||
cat level1float64_ddot.go \
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
\
|
||||
| gofmt -r 'f64.DotInc -> f32.DotInc' \
|
||||
| gofmt -r 'f64.DotUnitary -> f32.DotUnitary' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNINGF32\1S\2_" \
|
||||
-e 's_^// D_// S_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
|
||||
>> level1float32_sdot.go
|
||||
|
||||
echo Generating level1float32_dsdot.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level1float32_dsdot.go
|
||||
cat level1float64_ddot.go \
|
||||
| gofmt -r '[]float64 -> []float32' \
|
||||
\
|
||||
| gofmt -r 'f64.DotInc -> f32.DdotInc' \
|
||||
| gofmt -r 'f64.DotUnitary -> f32.DdotUnitary' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNINGF32\1Ds\2_" \
|
||||
-e 's_^// D_// Ds_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
|
||||
>> level1float32_dsdot.go
|
||||
|
||||
echo Generating level1float32_sdsdot.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level1float32_sdsdot.go
|
||||
cat level1float64_ddot.go \
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
\
|
||||
| gofmt -r 'f64.DotInc(x, y, f(n), f(incX), f(incY), f(ix), f(iy)) -> alpha + float32(f32.DdotInc(x, y, f(n), f(incX), f(incY), f(ix), f(iy)))' \
|
||||
| gofmt -r 'f64.DotUnitary(a, b) -> alpha + float32(f32.DdotUnitary(a, b))' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNINGF32\1Sds\2_" \
|
||||
-e 's_^// D\(.*\)$_// Sds\1 plus a constant_' \
|
||||
-e 's_\\sum_alpha + \\sum_' \
|
||||
-e 's/n int/n int, alpha float32/' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
|
||||
>> level1float32_sdsdot.go
|
||||
|
||||
|
||||
# Level2 routines.
|
||||
|
||||
echo Generating level2float32.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level2float32.go
|
||||
cat level2float64.go \
|
||||
| gofmt -r 'blas.Float64Level2 -> blas.Float32Level2' \
|
||||
\
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
\
|
||||
| gofmt -r 'f64.AxpyInc -> f32.AxpyInc' \
|
||||
| gofmt -r 'f64.AxpyIncTo -> f32.AxpyIncTo' \
|
||||
| gofmt -r 'f64.AxpyUnitary -> f32.AxpyUnitary' \
|
||||
| gofmt -r 'f64.AxpyUnitaryTo -> f32.AxpyUnitaryTo' \
|
||||
| gofmt -r 'f64.DotInc -> f32.DotInc' \
|
||||
| gofmt -r 'f64.DotUnitary -> f32.DotUnitary' \
|
||||
| gofmt -r 'f64.ScalInc -> f32.ScalInc' \
|
||||
| gofmt -r 'f64.ScalUnitary -> f32.ScalUnitary' \
|
||||
| gofmt -r 'f64.Ger -> f32.Ger' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNINGF32\1S\2_" \
|
||||
-e 's_^// D_// S_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
|
||||
>> level2float32.go
|
||||
|
||||
echo Generating level2cmplx64.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level2cmplx64.go
|
||||
cat level2cmplx128.go \
|
||||
| gofmt -r 'blas.Complex128Level2 -> blas.Complex64Level2' \
|
||||
\
|
||||
| gofmt -r 'complex128 -> complex64' \
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
\
|
||||
| gofmt -r 'c128.AxpyInc -> c64.AxpyInc' \
|
||||
| gofmt -r 'c128.AxpyUnitary -> c64.AxpyUnitary' \
|
||||
| gofmt -r 'c128.DotuInc -> c64.DotuInc' \
|
||||
| gofmt -r 'c128.DotuUnitary -> c64.DotuUnitary' \
|
||||
| gofmt -r 'c128.ScalInc -> c64.ScalInc' \
|
||||
| gofmt -r 'c128.ScalUnitary -> c64.ScalUnitary' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)Z\(.*\)\$_$WARNINGC64\1C\2_" \
|
||||
-e 's_^// Z_// C_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/c128"_"gonum.org/v1/gonum/internal/asm/c64"_' \
|
||||
-e 's_"math/cmplx"_cmplx "gonum.org/v1/gonum/internal/cmplx64"_' \
|
||||
>> level2cmplx64.go
|
||||
|
||||
# Level3 routines.
|
||||
|
||||
echo Generating level3float32.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level3float32.go
|
||||
cat level3float64.go \
|
||||
| gofmt -r 'blas.Float64Level3 -> blas.Float32Level3' \
|
||||
\
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
\
|
||||
| gofmt -r 'f64.AxpyUnitaryTo -> f32.AxpyUnitaryTo' \
|
||||
| gofmt -r 'f64.AxpyUnitary -> f32.AxpyUnitary' \
|
||||
| gofmt -r 'f64.DotUnitary -> f32.DotUnitary' \
|
||||
| gofmt -r 'f64.ScalUnitary -> f32.ScalUnitary' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNINGF32\1S\2_" \
|
||||
-e 's_^// D_// S_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
|
||||
>> level3float32.go
|
||||
|
||||
echo Generating sgemm.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > sgemm.go
|
||||
cat dgemm.go \
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
| gofmt -r 'sliceView64 -> sliceView32' \
|
||||
\
|
||||
| gofmt -r 'dgemmParallel -> sgemmParallel' \
|
||||
| gofmt -r 'computeNumBlocks64 -> computeNumBlocks32' \
|
||||
| gofmt -r 'dgemmSerial -> sgemmSerial' \
|
||||
| gofmt -r 'dgemmSerialNotNot -> sgemmSerialNotNot' \
|
||||
| gofmt -r 'dgemmSerialTransNot -> sgemmSerialTransNot' \
|
||||
| gofmt -r 'dgemmSerialNotTrans -> sgemmSerialNotTrans' \
|
||||
| gofmt -r 'dgemmSerialTransTrans -> sgemmSerialTransTrans' \
|
||||
\
|
||||
| gofmt -r 'f64.AxpyInc -> f32.AxpyInc' \
|
||||
| gofmt -r 'f64.AxpyUnitary -> f32.AxpyUnitary' \
|
||||
| gofmt -r 'f64.DotUnitary -> f32.DotUnitary' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNINGF32\1S\2_" \
|
||||
-e 's_^// D_// S_' \
|
||||
-e 's_^// d_// s_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
|
||||
>> sgemm.go
|
||||
|
||||
echo Generating level3cmplx64.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level3cmplx64.go
|
||||
cat level3cmplx128.go \
|
||||
| gofmt -r 'blas.Complex128Level3 -> blas.Complex64Level3' \
|
||||
\
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
| gofmt -r 'complex128 -> complex64' \
|
||||
\
|
||||
| gofmt -r 'c128.ScalUnitary -> c64.ScalUnitary' \
|
||||
| gofmt -r 'c128.DscalUnitary -> c64.SscalUnitary' \
|
||||
| gofmt -r 'c128.DotcUnitary -> c64.DotcUnitary' \
|
||||
| gofmt -r 'c128.AxpyUnitary -> c64.AxpyUnitary' \
|
||||
| gofmt -r 'c128.DotuUnitary -> c64.DotuUnitary' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)Z\(.*\)\$_$WARNINGC64\1C\2_" \
|
||||
-e 's_^// Z_// C_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/c128"_"gonum.org/v1/gonum/internal/asm/c64"_' \
|
||||
-e 's_"math/cmplx"_cmplx "gonum.org/v1/gonum/internal/cmplx64"_' \
|
||||
>> level3cmplx64.go
|
||||
Loading…
Add table
Add a link
Reference in a new issue