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blas/gonum: add Zsyrk with test

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This commit is contained in:
Vladimir Chalupecky
2019-01-06 21:49:07 +01:00
committed by Vladimír Chalupecký
parent 73c94a2aff
commit 20d2a2bc77
6 changed files with 335 additions and 16 deletions
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3
blas/gonum/cmplx.go
View File

@@ -138,9 +138,6 @@ func (Implementation) Cher2k(ul blas.Uplo, t blas.Transpose, n, k int, alpha com
func (Implementation) Zsymm(s blas.Side, ul blas.Uplo, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int) {
panic(noComplex)
}
func (Implementation) Zsyrk(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex128, a []complex128, lda int, beta complex128, c []complex128, ldc int) {
panic(noComplex)
}
func (Implementation) Zsyr2k(ul blas.Uplo, t blas.Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int) {
panic(noComplex)
}

144
blas/gonum/level3cmplx128.go
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@@ -8,6 +8,7 @@ import (
"math/cmplx"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/internal/asm/c128"
)
var _ blas.Complex128Level3 = Implementation{}
@@ -252,3 +253,146 @@ func (Implementation) Zgemm(tA, tB blas.Transpose, m, n, k int, alpha complex128
}
}
}
// Zsyrk performs one of the symmetric rank-k operations
// C = alpha*A*A^T + beta*C if trans == blas.NoTrans
// C = alpha*A^T*A + beta*C if trans == blas.Trans
// where alpha and beta are scalars, C is an n×n symmetric matrix and A is
// an n×k matrix in the first case and a k×n matrix in the second case.
func (Implementation) Zsyrk(uplo blas.Uplo, trans blas.Transpose, n, k int, alpha complex128, a []complex128, lda int, beta complex128, c []complex128, ldc int) {
var rowA, colA int
switch trans {
default:
panic(badTranspose)
case blas.NoTrans:
rowA, colA = n, k
case blas.Trans:
rowA, colA = k, n
}
switch {
case uplo != blas.Lower && uplo != blas.Upper:
panic(badUplo)
case n < 0:
panic(nLT0)
case k < 0:
panic(kLT0)
case lda < max(1, colA):
panic(badLdA)
case 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) < (rowA-1)*lda+colA {
panic(shortA)
}
if len(c) < (n-1)*ldc+n {
panic(shortC)
}
// Quick return if possible.
if (alpha == 0 || k == 0) && beta == 1 {
return
}
if alpha == 0 {
if uplo == blas.Upper {
if beta == 0 {
for i := 0; i < n; i++ {
ci := c[i*ldc+i : i*ldc+n]
for j := range ci {
ci[j] = 0
}
}
} else {
for i := 0; i < n; i++ {
ci := c[i*ldc+i : i*ldc+n]
c128.ScalUnitary(beta, ci)
}
}
} else {
if beta == 0 {
for i := 0; i < n; i++ {
ci := c[i*ldc : i*ldc+i+1]
for j := range ci {
ci[j] = 0
}
}
} else {
for i := 0; i < n; i++ {
ci := c[i*ldc : i*ldc+i+1]
c128.ScalUnitary(beta, ci)
}
}
}
return
}
if trans == blas.NoTrans {
// Form C = alpha*A*A^T + beta*C.
if uplo == blas.Upper {
for i := 0; i < n; i++ {
ci := c[i*ldc+i : i*ldc+n]
ai := a[i*lda : i*lda+k]
for jc, cij := range ci {
j := i + jc
ci[jc] = beta*cij + alpha*c128.DotuUnitary(ai, a[j*lda:j*lda+k])
}
}
} else {
for i := 0; i < n; i++ {
ci := c[i*ldc : i*ldc+i+1]
ai := a[i*lda : i*lda+k]
for j, cij := range ci {
ci[j] = beta*cij + alpha*c128.DotuUnitary(ai, a[j*lda:j*lda+k])
}
}
}
} else {
// Form C = alpha*A^T*A + beta*C.
if uplo == blas.Upper {
for i := 0; i < n; i++ {
ci := c[i*ldc+i : i*ldc+n]
if beta == 0 {
for jc := range ci {
ci[jc] = 0
}
} else if beta != 1 {
for jc := range ci {
ci[jc] *= beta
}
}
for j := 0; j < k; j++ {
aji := a[j*lda+i]
if aji != 0 {
c128.AxpyUnitary(alpha*aji, a[j*lda+i:j*lda+n], ci)
}
}
}
} else {
for i := 0; i < n; i++ {
ci := c[i*ldc : i*ldc+i+1]
if beta == 0 {
for j := range ci {
ci[j] = 0
}
} else if beta != 1 {
for j := range ci {
ci[j] *= beta
}
}
for j := 0; j < k; j++ {
aji := a[j*lda+i]
if aji != 0 {
c128.AxpyUnitary(alpha*aji, a[j*lda:j*lda+i+1], ci)
}
}
}
}
}
}

4
blas/gonum/level3cmplx128_test.go
View File

@@ -13,3 +13,7 @@ import (
func TestZgemm(t *testing.T) {
testblas.ZgemmTest(t, impl)
}
func TestZsyrk(t *testing.T) {
testblas.ZsyrkTest(t, impl)
}

52
blas/testblas/common.go
View File

@@ -652,3 +652,55 @@ func zmm(tA, tB blas.Transpose, m, n, k int, alpha complex128, a []complex128, l
}
return r
}
// transString returns a string representation of blas.Transpose.
func transString(t blas.Transpose) string {
switch t {
case blas.NoTrans:
return "NoTrans"
case blas.Trans:
return "Trans"
case blas.ConjTrans:
return "ConjTrans"
}
return "unknown trans"
}
// uploString returns a string representation of blas.Uplo.
func uploString(uplo blas.Uplo) string {
switch uplo {
case blas.Lower:
return "Lower"
case blas.Upper:
return "Upper"
}
return "unknown uplo"
}
// zSameLowerTri returns whether n×n matrices A and B are same under the diagonal.
func zSameLowerTri(n int, a []complex128, lda int, b []complex128, ldb int) bool {
for i := 1; i < n; i++ {
for j := 0; j < i; j++ {
aij := a[i*lda+j]
bij := b[i*ldb+j]
if !sameComplex128(aij, bij) {
return false
}
}
}
return true
}
// zSameUpperTri returns whether n×n matrices A and B are same above the diagonal.
func zSameUpperTri(n int, a []complex128, lda int, b []complex128, ldb int) bool {
for i := 0; i < n-1; i++ {
for j := i + 1; j < n; j++ {
aij := a[i*lda+j]
bij := b[i*ldb+j]
if !sameComplex128(aij, bij) {
return false
}
}
}
return true
}

13
blas/testblas/zgemm.go
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@@ -33,19 +33,6 @@ func ZgemmTest(t *testing.T, impl Zgemmer) {
}
}
// transString returns a string representation of blas.Transpose.
func transString(t blas.Transpose) string {
switch t {
case blas.NoTrans:
return "NoTrans"
case blas.Trans:
return "Trans"
case blas.ConjTrans:
return "ConjTrans"
}
return "unknown trans"
}
func zgemmTest(t *testing.T, impl Zgemmer, tA, tB blas.Transpose, m, n, k int) {
const tol = 1e-13

135
blas/testblas/zsyrk.go Normal file
View File

@@ -0,0 +1,135 @@
// Copyright ©2019 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 testblas
import (
"fmt"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
)
type Zsyrker interface {
Zsyrk(uplo blas.Uplo, trans blas.Transpose, n, k int, alpha complex128, a []complex128, lda int, beta complex128, c []complex128, ldc int)
}
func ZsyrkTest(t *testing.T, impl Zsyrker) {
for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
name := uploString(uplo) + "-" + transString(trans)
t.Run(name, func(t *testing.T) {
for _, n := range []int{0, 1, 2, 3, 4, 5} {
for _, k := range []int{0, 1, 2, 3, 4, 5, 7} {
zsyrkTest(t, impl, uplo, trans, n, k)
}
}
})
}
}
}
func zsyrkTest(t *testing.T, impl Zsyrker, uplo blas.Uplo, trans blas.Transpose, n, k int) {
const tol = 1e-13
rnd := rand.New(rand.NewSource(1))
rowA, colA := n, k
if trans == blas.Trans {
rowA, colA = k, n
}
for _, lda := range []int{max(1, colA), colA + 2} {
for _, ldc := range []int{max(1, n), n + 4} {
for _, alpha := range []complex128{0, 1, complex(0.7, -0.9)} {
for _, beta := range []complex128{0, 1, complex(1.3, -1.1)} {
// Allocate the matrix A and fill it with random numbers.
a := make([]complex128, rowA*lda)
for i := range a {
a[i] = rndComplex128(rnd)
}
// Create a copy of A for checking that
// Zsyrk does not modify A.
aCopy := make([]complex128, len(a))
copy(aCopy, a)
// Allocate the matrix C and fill it with random numbers.
c := make([]complex128, n*ldc)
for i := range c {
c[i] = rndComplex128(rnd)
}
// Create a copy of C for checking that
// Zsyrk does not modify its triangle
// opposite to uplo.
cCopy := make([]complex128, len(c))
copy(cCopy, c)
// Create a copy of C expanded into a
// full symmetric matrix for computing
// the expected result using zmm.
cSym := make([]complex128, len(c))
copy(cSym, c)
if uplo == blas.Upper {
for i := 0; i < n-1; i++ {
for j := i + 1; j < n; j++ {
cSym[j*ldc+i] = cSym[i*ldc+j]
}
}
} else {
for i := 1; i < n; i++ {
for j := 0; j < i; j++ {
cSym[j*ldc+i] = cSym[i*ldc+j]
}
}
}
// Compute the expected result using an internal Zgemm implementation.
var want []complex128
if trans == blas.NoTrans {
want = zmm(blas.NoTrans, blas.Trans, n, n, k, alpha, a, lda, a, lda, beta, cSym, ldc)
} else {
want = zmm(blas.Trans, blas.NoTrans, n, n, k, alpha, a, lda, a, lda, beta, cSym, ldc)
}
// Compute the result using Zsyrk.
impl.Zsyrk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
prefix := fmt.Sprintf("n=%v,k=%v,lda=%v,ldc=%v,alpha=%v,beta=%v", n, k, lda, ldc, alpha, beta)
if !zsame(a, aCopy) {
t.Errorf("%v: unexpected modification of A", prefix)
continue
}
if uplo == blas.Upper && !zSameLowerTri(n, c, ldc, cCopy, ldc) {
t.Errorf("%v: unexpected modification in lower triangle of C", prefix)
continue
}
if uplo == blas.Lower && !zSameUpperTri(n, c, ldc, cCopy, ldc) {
t.Errorf("%v: unexpected modification in upper triangle of C", prefix)
continue
}
// Expand C into a full symmetric matrix
// for comparison with the result from zmm.
if uplo == blas.Upper {
for i := 0; i < n-1; i++ {
for j := i + 1; j < n; j++ {
c[j*ldc+i] = c[i*ldc+j]
}
}
} else {
for i := 1; i < n; i++ {
for j := 0; j < i; j++ {
c[j*ldc+i] = c[i*ldc+j]
}
}
}
if !zEqualApprox(c, want, tol) {
t.Errorf("%v: unexpected result", prefix)
}
}
}
}
}
}