mirror of https://github.com/k3s-io/k3s
533 lines
17 KiB
Go
533 lines
17 KiB
Go
// Copyright ©2015 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package cblas128
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import (
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/blas/gonum"
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)
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var cblas128 blas.Complex128 = gonum.Implementation{}
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// Use sets the BLAS complex128 implementation to be used by subsequent BLAS calls.
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// The default implementation is
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// gonum.org/v1/gonum/blas/gonum.Implementation.
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func Use(b blas.Complex128) {
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cblas128 = b
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}
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// Implementation returns the current BLAS complex128 implementation.
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//
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// Implementation allows direct calls to the current the BLAS complex128 implementation
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// giving finer control of parameters.
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func Implementation() blas.Complex128 {
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return cblas128
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}
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// Vector represents a vector with an associated element increment.
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type Vector struct {
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N int
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Inc int
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Data []complex128
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}
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// General represents a matrix using the conventional storage scheme.
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type General struct {
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Rows, Cols int
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Stride int
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Data []complex128
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}
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// Band represents a band matrix using the band storage scheme.
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type Band struct {
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Rows, Cols int
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KL, KU int
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Stride int
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Data []complex128
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}
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// Triangular represents a triangular matrix using the conventional storage scheme.
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type Triangular struct {
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N int
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Stride int
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Data []complex128
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Uplo blas.Uplo
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Diag blas.Diag
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}
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// TriangularBand represents a triangular matrix using the band storage scheme.
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type TriangularBand struct {
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N, K int
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Stride int
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Data []complex128
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Uplo blas.Uplo
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Diag blas.Diag
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}
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// TriangularPacked represents a triangular matrix using the packed storage scheme.
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type TriangularPacked struct {
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N int
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Data []complex128
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Uplo blas.Uplo
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Diag blas.Diag
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}
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// Symmetric represents a symmetric matrix using the conventional storage scheme.
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type Symmetric struct {
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N int
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Stride int
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Data []complex128
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Uplo blas.Uplo
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}
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// SymmetricBand represents a symmetric matrix using the band storage scheme.
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type SymmetricBand struct {
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N, K int
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Stride int
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Data []complex128
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Uplo blas.Uplo
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}
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// SymmetricPacked represents a symmetric matrix using the packed storage scheme.
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type SymmetricPacked struct {
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N int
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Data []complex128
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Uplo blas.Uplo
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}
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// Hermitian represents an Hermitian matrix using the conventional storage scheme.
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type Hermitian Symmetric
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// HermitianBand represents an Hermitian matrix using the band storage scheme.
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type HermitianBand SymmetricBand
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// HermitianPacked represents an Hermitian matrix using the packed storage scheme.
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type HermitianPacked SymmetricPacked
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// Level 1
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const (
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negInc = "cblas128: negative vector increment"
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badLength = "cblas128: vector length mismatch"
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)
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// Dotu computes the dot product of the two vectors without
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// complex conjugation:
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// xᵀ * y.
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// Dotu will panic if the lengths of x and y do not match.
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func Dotu(x, y Vector) complex128 {
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if x.N != y.N {
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panic(badLength)
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}
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return cblas128.Zdotu(x.N, x.Data, x.Inc, y.Data, y.Inc)
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}
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// Dotc computes the dot product of the two vectors with
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// complex conjugation:
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// xᴴ * y.
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// Dotc will panic if the lengths of x and y do not match.
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func Dotc(x, y Vector) complex128 {
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if x.N != y.N {
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panic(badLength)
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}
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return cblas128.Zdotc(x.N, x.Data, x.Inc, y.Data, y.Inc)
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}
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// Nrm2 computes the Euclidean norm of the vector x:
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// sqrt(\sum_i x[i] * x[i]).
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//
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// Nrm2 will panic if the vector increment is negative.
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func Nrm2(x Vector) float64 {
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if x.Inc < 0 {
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panic(negInc)
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}
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return cblas128.Dznrm2(x.N, x.Data, x.Inc)
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}
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// Asum computes the sum of magnitudes of the real and imaginary parts of
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// elements of the vector x:
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// \sum_i (|Re x[i]| + |Im x[i]|).
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//
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// Asum will panic if the vector increment is negative.
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func Asum(x Vector) float64 {
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if x.Inc < 0 {
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panic(negInc)
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}
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return cblas128.Dzasum(x.N, x.Data, x.Inc)
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}
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// Iamax returns the index of an element of x with the largest sum of
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// magnitudes of the real and imaginary parts (|Re x[i]|+|Im x[i]|).
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// If there are multiple such indices, the earliest is returned.
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//
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// Iamax returns -1 if n == 0.
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//
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// Iamax will panic if the vector increment is negative.
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func Iamax(x Vector) int {
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if x.Inc < 0 {
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panic(negInc)
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}
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return cblas128.Izamax(x.N, x.Data, x.Inc)
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}
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// Swap exchanges the elements of two vectors:
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// x[i], y[i] = y[i], x[i] for all i.
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// Swap will panic if the lengths of x and y do not match.
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func Swap(x, y Vector) {
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if x.N != y.N {
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panic(badLength)
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}
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cblas128.Zswap(x.N, x.Data, x.Inc, y.Data, y.Inc)
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}
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// Copy copies the elements of x into the elements of y:
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// y[i] = x[i] for all i.
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// Copy will panic if the lengths of x and y do not match.
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func Copy(x, y Vector) {
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if x.N != y.N {
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panic(badLength)
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}
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cblas128.Zcopy(x.N, x.Data, x.Inc, y.Data, y.Inc)
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}
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// Axpy computes
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// y = alpha * x + y,
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// where x and y are vectors, and alpha is a scalar.
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// Axpy will panic if the lengths of x and y do not match.
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func Axpy(alpha complex128, x, y Vector) {
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if x.N != y.N {
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panic(badLength)
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}
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cblas128.Zaxpy(x.N, alpha, x.Data, x.Inc, y.Data, y.Inc)
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}
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// Scal computes
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// x = alpha * x,
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// where x is a vector, and alpha is a scalar.
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//
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// Scal will panic if the vector increment is negative.
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func Scal(alpha complex128, x Vector) {
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if x.Inc < 0 {
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panic(negInc)
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}
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cblas128.Zscal(x.N, alpha, x.Data, x.Inc)
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}
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// Dscal computes
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// x = alpha * x,
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// where x is a vector, and alpha is a real scalar.
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//
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// Dscal will panic if the vector increment is negative.
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func Dscal(alpha float64, x Vector) {
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if x.Inc < 0 {
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panic(negInc)
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}
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cblas128.Zdscal(x.N, alpha, x.Data, x.Inc)
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}
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// Level 2
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// Gemv computes
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// y = alpha * A * x + beta * y if t == blas.NoTrans,
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// y = alpha * Aᵀ * x + beta * y if t == blas.Trans,
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// y = alpha * Aᴴ * x + beta * y if t == blas.ConjTrans,
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// where A is an m×n dense matrix, x and y are vectors, and alpha and beta are
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// scalars.
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func Gemv(t blas.Transpose, alpha complex128, a General, x Vector, beta complex128, y Vector) {
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cblas128.Zgemv(t, a.Rows, a.Cols, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
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}
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// Gbmv computes
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// y = alpha * A * x + beta * y if t == blas.NoTrans,
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// y = alpha * Aᵀ * x + beta * y if t == blas.Trans,
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// y = alpha * Aᴴ * x + beta * y if t == blas.ConjTrans,
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// where A is an m×n band matrix, x and y are vectors, and alpha and beta are
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// scalars.
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func Gbmv(t blas.Transpose, alpha complex128, a Band, x Vector, beta complex128, y Vector) {
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cblas128.Zgbmv(t, a.Rows, a.Cols, a.KL, a.KU, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
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}
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// Trmv computes
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// x = A * x if t == blas.NoTrans,
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// x = Aᵀ * x if t == blas.Trans,
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// x = Aᴴ * x if t == blas.ConjTrans,
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// where A is an n×n triangular matrix, and x is a vector.
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func Trmv(t blas.Transpose, a Triangular, x Vector) {
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cblas128.Ztrmv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
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}
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// Tbmv computes
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// x = A * x if t == blas.NoTrans,
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// x = Aᵀ * x if t == blas.Trans,
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// x = Aᴴ * x if t == blas.ConjTrans,
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// where A is an n×n triangular band matrix, and x is a vector.
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func Tbmv(t blas.Transpose, a TriangularBand, x Vector) {
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cblas128.Ztbmv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
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}
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// Tpmv computes
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// x = A * x if t == blas.NoTrans,
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// x = Aᵀ * x if t == blas.Trans,
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// x = Aᴴ * x if t == blas.ConjTrans,
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// where A is an n×n triangular matrix in packed format, and x is a vector.
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func Tpmv(t blas.Transpose, a TriangularPacked, x Vector) {
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cblas128.Ztpmv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
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}
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// Trsv solves
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// A * x = b if t == blas.NoTrans,
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// Aᵀ * x = b if t == blas.Trans,
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// Aᴴ * x = b if t == blas.ConjTrans,
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// where A is an n×n triangular matrix and x is a vector.
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//
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// At entry to the function, x contains the values of b, and the result is
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// stored in-place into x.
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//
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// No test for singularity or near-singularity is included in this
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// routine. Such tests must be performed before calling this routine.
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func Trsv(t blas.Transpose, a Triangular, x Vector) {
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cblas128.Ztrsv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
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}
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// Tbsv solves
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// A * x = b if t == blas.NoTrans,
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// Aᵀ * x = b if t == blas.Trans,
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// Aᴴ * x = b if t == blas.ConjTrans,
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// where A is an n×n triangular band matrix, and x is a vector.
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//
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// At entry to the function, x contains the values of b, and the result is
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// stored in-place into x.
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//
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// No test for singularity or near-singularity is included in this
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// routine. Such tests must be performed before calling this routine.
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func Tbsv(t blas.Transpose, a TriangularBand, x Vector) {
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cblas128.Ztbsv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
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}
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// Tpsv solves
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// A * x = b if t == blas.NoTrans,
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// Aᵀ * x = b if t == blas.Trans,
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// Aᴴ * x = b if t == blas.ConjTrans,
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// where A is an n×n triangular matrix in packed format and x is a vector.
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//
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// At entry to the function, x contains the values of b, and the result is
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// stored in-place into x.
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//
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// No test for singularity or near-singularity is included in this
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// routine. Such tests must be performed before calling this routine.
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func Tpsv(t blas.Transpose, a TriangularPacked, x Vector) {
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cblas128.Ztpsv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
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}
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// Hemv computes
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// y = alpha * A * x + beta * y,
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// where A is an n×n Hermitian matrix, x and y are vectors, and alpha and
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// beta are scalars.
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func Hemv(alpha complex128, a Hermitian, x Vector, beta complex128, y Vector) {
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cblas128.Zhemv(a.Uplo, a.N, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
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}
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// Hbmv performs
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// y = alpha * A * x + beta * y,
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// where A is an n×n Hermitian band matrix, x and y are vectors, and alpha
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// and beta are scalars.
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func Hbmv(alpha complex128, a HermitianBand, x Vector, beta complex128, y Vector) {
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cblas128.Zhbmv(a.Uplo, a.N, a.K, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
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}
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// Hpmv performs
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// y = alpha * A * x + beta * y,
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// where A is an n×n Hermitian matrix in packed format, x and y are vectors,
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// and alpha and beta are scalars.
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func Hpmv(alpha complex128, a HermitianPacked, x Vector, beta complex128, y Vector) {
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cblas128.Zhpmv(a.Uplo, a.N, alpha, a.Data, x.Data, x.Inc, beta, y.Data, y.Inc)
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}
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// Geru performs a rank-1 update
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// A += alpha * x * yᵀ,
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// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
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func Geru(alpha complex128, x, y Vector, a General) {
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cblas128.Zgeru(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
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}
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// Gerc performs a rank-1 update
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// A += alpha * x * yᴴ,
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// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
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func Gerc(alpha complex128, x, y Vector, a General) {
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cblas128.Zgerc(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
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}
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// Her performs a rank-1 update
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// A += alpha * x * yᵀ,
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// where A is an m×n Hermitian matrix, x and y are vectors, and alpha is a scalar.
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func Her(alpha float64, x Vector, a Hermitian) {
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cblas128.Zher(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data, a.Stride)
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}
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// Hpr performs a rank-1 update
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// A += alpha * x * xᴴ,
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// where A is an n×n Hermitian matrix in packed format, x is a vector, and
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// alpha is a scalar.
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func Hpr(alpha float64, x Vector, a HermitianPacked) {
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cblas128.Zhpr(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data)
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}
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// Her2 performs a rank-2 update
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// A += alpha * x * yᴴ + conj(alpha) * y * xᴴ,
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// where A is an n×n Hermitian matrix, x and y are vectors, and alpha is a scalar.
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func Her2(alpha complex128, x, y Vector, a Hermitian) {
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cblas128.Zher2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
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}
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// Hpr2 performs a rank-2 update
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// A += alpha * x * yᴴ + conj(alpha) * y * xᴴ,
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// where A is an n×n Hermitian matrix in packed format, x and y are vectors,
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// and alpha is a scalar.
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func Hpr2(alpha complex128, x, y Vector, a HermitianPacked) {
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cblas128.Zhpr2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data)
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}
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// Level 3
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// Gemm computes
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// C = alpha * A * B + beta * C,
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// where A, B, and C are dense matrices, and alpha and beta are scalars.
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// tA and tB specify whether A or B are transposed or conjugated.
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func Gemm(tA, tB blas.Transpose, alpha complex128, a, b General, beta complex128, c General) {
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var m, n, k int
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if tA == blas.NoTrans {
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m, k = a.Rows, a.Cols
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} else {
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m, k = a.Cols, a.Rows
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}
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if tB == blas.NoTrans {
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n = b.Cols
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} else {
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n = b.Rows
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}
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cblas128.Zgemm(tA, tB, m, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
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}
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// Symm performs
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// C = alpha * A * B + beta * C if s == blas.Left,
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// C = alpha * B * A + beta * C if s == blas.Right,
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// where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and
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// alpha and beta are scalars.
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func Symm(s blas.Side, alpha complex128, a Symmetric, b General, beta complex128, c General) {
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var m, n int
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if s == blas.Left {
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m, n = a.N, b.Cols
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} else {
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m, n = b.Rows, a.N
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}
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cblas128.Zsymm(s, a.Uplo, m, n, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
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}
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// Syrk performs a symmetric rank-k update
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// C = alpha * A * Aᵀ + beta * C if t == blas.NoTrans,
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// C = alpha * Aᵀ * A + beta * C if t == blas.Trans,
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// where C is an n×n symmetric matrix, A is an n×k matrix if t == blas.NoTrans
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// and a k×n matrix otherwise, and alpha and beta are scalars.
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func Syrk(t blas.Transpose, alpha complex128, a General, beta complex128, c Symmetric) {
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var n, k int
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if t == blas.NoTrans {
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n, k = a.Rows, a.Cols
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} else {
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n, k = a.Cols, a.Rows
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}
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cblas128.Zsyrk(c.Uplo, t, n, k, alpha, a.Data, a.Stride, beta, c.Data, c.Stride)
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}
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// Syr2k performs a symmetric rank-2k update
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// C = alpha * A * Bᵀ + alpha * B * Aᵀ + beta * C if t == blas.NoTrans,
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// C = alpha * Aᵀ * B + alpha * Bᵀ * A + beta * C if t == blas.Trans,
|
||
// where C is an n×n symmetric matrix, A and B are n×k matrices if
|
||
// t == blas.NoTrans and k×n otherwise, and alpha and beta are scalars.
|
||
func Syr2k(t blas.Transpose, alpha complex128, a, b General, beta complex128, c Symmetric) {
|
||
var n, k int
|
||
if t == blas.NoTrans {
|
||
n, k = a.Rows, a.Cols
|
||
} else {
|
||
n, k = a.Cols, a.Rows
|
||
}
|
||
cblas128.Zsyr2k(c.Uplo, t, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
|
||
}
|
||
|
||
// Trmm performs
|
||
// B = alpha * A * B if tA == blas.NoTrans and s == blas.Left,
|
||
// B = alpha * Aᵀ * B if tA == blas.Trans and s == blas.Left,
|
||
// B = alpha * Aᴴ * B if tA == blas.ConjTrans and s == blas.Left,
|
||
// B = alpha * B * A if tA == blas.NoTrans and s == blas.Right,
|
||
// B = alpha * B * Aᵀ if tA == blas.Trans and s == blas.Right,
|
||
// B = alpha * B * Aᴴ if tA == blas.ConjTrans and s == 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 Trmm(s blas.Side, tA blas.Transpose, alpha complex128, a Triangular, b General) {
|
||
cblas128.Ztrmm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
|
||
}
|
||
|
||
// Trsm solves
|
||
// A * X = alpha * B if tA == blas.NoTrans and s == blas.Left,
|
||
// Aᵀ * X = alpha * B if tA == blas.Trans and s == blas.Left,
|
||
// Aᴴ * X = alpha * B if tA == blas.ConjTrans and s == blas.Left,
|
||
// X * A = alpha * B if tA == blas.NoTrans and s == blas.Right,
|
||
// X * Aᵀ = alpha * B if tA == blas.Trans and s == blas.Right,
|
||
// X * Aᴴ = alpha * B if tA == blas.ConjTrans and s == 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, b contains the values of B, and the result is
|
||
// stored in-place into b.
|
||
//
|
||
// No check is made that A is invertible.
|
||
func Trsm(s blas.Side, tA blas.Transpose, alpha complex128, a Triangular, b General) {
|
||
cblas128.Ztrsm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
|
||
}
|
||
|
||
// Hemm performs
|
||
// C = alpha * A * B + beta * C if s == blas.Left,
|
||
// C = alpha * B * A + beta * C if s == blas.Right,
|
||
// where A is an n×n or m×m Hermitian matrix, B and C are m×n matrices, and
|
||
// alpha and beta are scalars.
|
||
func Hemm(s blas.Side, alpha complex128, a Hermitian, b General, beta complex128, c General) {
|
||
var m, n int
|
||
if s == blas.Left {
|
||
m, n = a.N, b.Cols
|
||
} else {
|
||
m, n = b.Rows, a.N
|
||
}
|
||
cblas128.Zhemm(s, a.Uplo, m, n, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
|
||
}
|
||
|
||
// Herk performs the Hermitian rank-k update
|
||
// C = alpha * A * Aᴴ + beta*C if t == blas.NoTrans,
|
||
// C = alpha * Aᴴ * A + beta*C if t == blas.ConjTrans,
|
||
// where C is an n×n Hermitian matrix, A is an n×k matrix if t == blas.NoTrans
|
||
// and a k×n matrix otherwise, and alpha and beta are scalars.
|
||
func Herk(t blas.Transpose, alpha float64, a General, beta float64, c Hermitian) {
|
||
var n, k int
|
||
if t == blas.NoTrans {
|
||
n, k = a.Rows, a.Cols
|
||
} else {
|
||
n, k = a.Cols, a.Rows
|
||
}
|
||
cblas128.Zherk(c.Uplo, t, n, k, alpha, a.Data, a.Stride, beta, c.Data, c.Stride)
|
||
}
|
||
|
||
// Her2k performs the Hermitian rank-2k update
|
||
// C = alpha * A * Bᴴ + conj(alpha) * B * Aᴴ + beta * C if t == blas.NoTrans,
|
||
// C = alpha * Aᴴ * B + conj(alpha) * Bᴴ * A + beta * C if t == blas.ConjTrans,
|
||
// where C is an n×n Hermitian matrix, A and B are n×k matrices if t == NoTrans
|
||
// and k×n matrices otherwise, and alpha and beta are scalars.
|
||
func Her2k(t blas.Transpose, alpha complex128, a, b General, beta float64, c Hermitian) {
|
||
var n, k int
|
||
if t == blas.NoTrans {
|
||
n, k = a.Rows, a.Cols
|
||
} else {
|
||
n, k = a.Cols, a.Rows
|
||
}
|
||
cblas128.Zher2k(c.Uplo, t, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
|
||
}
|