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gonum/blas/cblas64/cblas64.go
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// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Package cblas64 provides a simple interface to the complex64 BLAS API.
package cblas64 // import "gonum.org/v1/gonum/blas/cblas64"
import (
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/gonum"
)
var cblas64 blas.Complex64 = gonum.Implementation{}
// Use sets the BLAS complex64 implementation to be used by subsequent BLAS calls.
// The default implementation is cgo.Implementation.
func Use(b blas.Complex64) {
cblas64 = b
}
// Implementation returns the current BLAS complex64 implementation.
//
// Implementation allows direct calls to the current the BLAS complex64 implementation
// giving finer control of parameters.
func Implementation() blas.Complex64 {
return cblas64
}
// Vector represents a vector with an associated element increment.
type Vector struct {
Inc int
Data []complex64
}
// General represents a matrix using the conventional storage scheme.
type General struct {
Rows, Cols int
Stride int
Data []complex64
}
// Band represents a band matrix using the band storage scheme.
type Band struct {
Rows, Cols int
KL, KU int
Stride int
Data []complex64
}
// Triangular represents a triangular matrix using the conventional storage scheme.
type Triangular struct {
N int
Stride int
Data []complex64
Uplo blas.Uplo
Diag blas.Diag
}
// TriangularBand represents a triangular matrix using the band storage scheme.
type TriangularBand struct {
N, K int
Stride int
Data []complex64
Uplo blas.Uplo
Diag blas.Diag
}
// TriangularPacked represents a triangular matrix using the packed storage scheme.
type TriangularPacked struct {
N int
Data []complex64
Uplo blas.Uplo
Diag blas.Diag
}
// Symmetric represents a symmetric matrix using the conventional storage scheme.
type Symmetric struct {
N int
Stride int
Data []complex64
Uplo blas.Uplo
}
// SymmetricBand represents a symmetric matrix using the band storage scheme.
type SymmetricBand struct {
N, K int
Stride int
Data []complex64
Uplo blas.Uplo
}
// SymmetricPacked represents a symmetric matrix using the packed storage scheme.
type SymmetricPacked struct {
N int
Data []complex64
Uplo blas.Uplo
}
// Hermitian represents an Hermitian matrix using the conventional storage scheme.
type Hermitian Symmetric
// HermitianBand represents an Hermitian matrix using the band storage scheme.
type HermitianBand SymmetricBand
// HermitianPacked represents an Hermitian matrix using the packed storage scheme.
type HermitianPacked SymmetricPacked
// Level 1
const negInc = "cblas64: negative vector increment"
// Dotu computes the dot product of the two vectors without
// complex conjugation:
// x^T * y
func Dotu(n int, x, y Vector) complex64 {
return cblas64.Cdotu(n, x.Data, x.Inc, y.Data, y.Inc)
}
// Dotc computes the dot product of the two vectors with
// complex conjugation:
// x^H * y.
func Dotc(n int, x, y Vector) complex64 {
return cblas64.Cdotc(n, x.Data, x.Inc, y.Data, y.Inc)
}
// Nrm2 computes the Euclidean norm of the vector x:
// sqrt(\sum_i x[i] * x[i]).
//
// Nrm2 will panic if the vector increment is negative.
func Nrm2(n int, x Vector) float32 {
if x.Inc < 0 {
panic(negInc)
}
return cblas64.Scnrm2(n, x.Data, x.Inc)
}
// Asum computes the sum of magnitudes of the real and imaginary parts of
// elements of the vector x:
// \sum_i (|Re x[i]| + |Im x[i]|).
//
// Asum will panic if the vector increment is negative.
func Asum(n int, x Vector) float32 {
if x.Inc < 0 {
panic(negInc)
}
return cblas64.Scasum(n, x.Data, x.Inc)
}
// Iamax returns the index of an element of x with the largest sum of
// magnitudes of the real and imaginary parts (|Re x[i]|+|Im x[i]|).
// If there are multiple such indices, the earliest is returned.
//
// Iamax returns -1 if n == 0.
//
// Iamax will panic if the vector increment is negative.
func Iamax(n int, x Vector) int {
if x.Inc < 0 {
panic(negInc)
}
return cblas64.Icamax(n, x.Data, x.Inc)
}
// Swap exchanges the elements of two vectors:
// x[i], y[i] = y[i], x[i] for all i.
func Swap(n int, x, y Vector) {
cblas64.Cswap(n, x.Data, x.Inc, y.Data, y.Inc)
}
// Copy copies the elements of x into the elements of y:
// y[i] = x[i] for all i.
func Copy(n int, x, y Vector) {
cblas64.Ccopy(n, x.Data, x.Inc, y.Data, y.Inc)
}
// Axpy computes
// y = alpha * x + y,
// where x and y are vectors, and alpha is a scalar.
func Axpy(n int, alpha complex64, x, y Vector) {
cblas64.Caxpy(n, alpha, x.Data, x.Inc, y.Data, y.Inc)
}
// Scal computes
// x = alpha * x,
// where x is a vector, and alpha is a scalar.
//
// Scal will panic if the vector increment is negative.
func Scal(n int, alpha complex64, x Vector) {
if x.Inc < 0 {
panic(negInc)
}
cblas64.Cscal(n, alpha, x.Data, x.Inc)
}
// Dscal computes
// x = alpha * x,
// where x is a vector, and alpha is a real scalar.
//
// Dscal will panic if the vector increment is negative.
func Dscal(n int, alpha float32, x Vector) {
if x.Inc < 0 {
panic(negInc)
}
cblas64.Csscal(n, alpha, x.Data, x.Inc)
}
// Level 2
// Gemv computes
// y = alpha * A * x + beta * y, if t == blas.NoTrans,
// y = alpha * A^T * x + beta * y, if t == blas.Trans,
// y = alpha * A^H * x + beta * y, if t == blas.ConjTrans,
// where A is an m×n dense matrix, x and y are vectors, and alpha and beta are
// scalars.
func Gemv(t blas.Transpose, alpha complex64, a General, x Vector, beta complex64, y Vector) {
cblas64.Cgemv(t, a.Rows, a.Cols, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
}
// Gbmv computes
// y = alpha * A * x + beta * y, if t == blas.NoTrans,
// y = alpha * A^T * x + beta * y, if t == blas.Trans,
// y = alpha * A^H * x + beta * y, if t == blas.ConjTrans,
// where A is an m×n band matrix, x and y are vectors, and alpha and beta are
// scalars.
func Gbmv(t blas.Transpose, alpha complex64, a Band, x Vector, beta complex64, y Vector) {
cblas64.Cgbmv(t, a.Rows, a.Cols, a.KL, a.KU, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
}
// Trmv computes
// x = A * x, if t == blas.NoTrans,
// x = A^T * x, if t == blas.Trans,
// x = A^H * x, if t == blas.ConjTrans,
// where A is an n×n triangular matrix, and x is a vector.
func Trmv(t blas.Transpose, a Triangular, x Vector) {
cblas64.Ctrmv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
}
// Tbmv computes
// x = A * x, if t == blas.NoTrans,
// x = A^T * x, if t == blas.Trans,
// x = A^H * x, if t == blas.ConjTrans,
// where A is an n×n triangular band matrix, and x is a vector.
func Tbmv(t blas.Transpose, a TriangularBand, x Vector) {
cblas64.Ctbmv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
}
// Tpmv computes
// x = A * x, if t == blas.NoTrans,
// x = A^T * x, if t == blas.Trans,
// x = A^H * x, if t == blas.ConjTrans,
// where A is an n×n triangular matrix in packed format, and x is a vector.
func Tpmv(t blas.Transpose, a TriangularPacked, x Vector) {
cblas64.Ctpmv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
}
// Trsv solves
// A * x = b, if t == blas.NoTrans,
// A^T * x = b, if t == blas.Trans,
// A^H * x = b, if t == blas.ConjTrans,
// where A is an n×n triangular matrix and x is a vector.
//
// At entry to the function, x contains the values of b, and the result is
// stored in-place into x.
//
// No test for singularity or near-singularity is included in this
// routine. Such tests must be performed before calling this routine.
func Trsv(t blas.Transpose, a Triangular, x Vector) {
cblas64.Ctrsv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
}
// Tbsv solves
// A * x = b, if t == blas.NoTrans,
// A^T * x = b, if t == blas.Trans,
// A^H * x = b, if t == blas.ConjTrans,
// where A is an n×n triangular band matrix, and x is a vector.
//
// At entry to the function, x contains the values of b, and the result is
// stored in-place into x.
//
// No test for singularity or near-singularity is included in this
// routine. Such tests must be performed before calling this routine.
func Tbsv(t blas.Transpose, a TriangularBand, x Vector) {
cblas64.Ctbsv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
}
// Tpsv solves
// A * x = b, if t == blas.NoTrans,
// A^T * x = b, if t == blas.Trans,
// A^H * x = b, if t == blas.ConjTrans,
// where A is an n×n triangular matrix in packed format and x is a vector.
//
// At entry to the function, x contains the values of b, and the result is
// stored in-place into x.
//
// No test for singularity or near-singularity is included in this
// routine. Such tests must be performed before calling this routine.
func Tpsv(t blas.Transpose, a TriangularPacked, x Vector) {
cblas64.Ctpsv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
}
// Hemv computes
// y = alpha * A * x + beta * y,
// where A is an n×n Hermitian matrix, x and y are vectors, and alpha and
// beta are scalars.
func Hemv(alpha complex64, a Hermitian, x Vector, beta complex64, y Vector) {
cblas64.Chemv(a.Uplo, a.N, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
}
// Hbmv performs
// y = alpha * A * x + beta * y,
// where A is an n×n Hermitian band matrix, x and y are vectors, and alpha
// and beta are scalars.
func Hbmv(alpha complex64, a HermitianBand, x Vector, beta complex64, y Vector) {
cblas64.Chbmv(a.Uplo, a.N, a.K, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
}
// Hpmv performs
// y = alpha * A * x + beta * y,
// where A is an n×n Hermitian matrix in packed format, x and y are vectors,
// and alpha and beta are scalars.
func Hpmv(alpha complex64, a HermitianPacked, x Vector, beta complex64, y Vector) {
cblas64.Chpmv(a.Uplo, a.N, alpha, a.Data, x.Data, x.Inc, beta, y.Data, y.Inc)
}
// Geru performs a rank-1 update
// A += alpha * x * y^T,
// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
func Geru(alpha complex64, x, y Vector, a General) {
cblas64.Cgeru(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
}
// Gerc performs a rank-1 update
// A += alpha * x * y^H,
// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
func Gerc(alpha complex64, x, y Vector, a General) {
cblas64.Cgerc(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
}
// Her performs a rank-1 update
// A += alpha * x * y^T,
// where A is an m×n Hermitian matrix, x and y are vectors, and alpha is a scalar.
func Her(alpha float32, x Vector, a Hermitian) {
cblas64.Cher(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data, a.Stride)
}
// Hpr performs a rank-1 update
// A += alpha * x * x^H,
// where A is an n×n Hermitian matrix in packed format, x is a vector, and
// alpha is a scalar.
func Hpr(alpha float32, x Vector, a HermitianPacked) {
cblas64.Chpr(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data)
}
// Her2 performs a rank-2 update
// A += alpha * x * y^H + conj(alpha) * y * x^H,
// where A is an n×n Hermitian matrix, x and y are vectors, and alpha is a scalar.
func Her2(alpha complex64, x, y Vector, a Hermitian) {
cblas64.Cher2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
}
// Hpr2 performs a rank-2 update
// A += alpha * x * y^H + conj(alpha) * y * x^H,
// where A is an n×n Hermitian matrix in packed format, x and y are vectors,
// and alpha is a scalar.
func Hpr2(alpha complex64, x, y Vector, a HermitianPacked) {
cblas64.Chpr2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data)
}
// Level 3
// Gemm computes
// C = alpha * A * B + beta * C,
// where A, B, and C are dense matrices, and alpha and beta are scalars.
// tA and tB specify whether A or B are transposed or conjugated.
func Gemm(tA, tB blas.Transpose, alpha complex64, a, b General, beta complex64, c General) {
var m, n, k int
if tA == blas.NoTrans {
m, k = a.Rows, a.Cols
} else {
m, k = a.Cols, a.Rows
}
if tB == blas.NoTrans {
n = b.Cols
} else {
n = b.Rows
}
cblas64.Cgemm(tA, tB, m, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
}
// Symm 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 symmetric matrix, B and C are m×n matrices, and
// alpha and beta are scalars.
func Symm(s blas.Side, alpha complex64, a Symmetric, b General, beta complex64, c General) {
var m, n int
if s == blas.Left {
m, n = a.N, b.Cols
} else {
m, n = b.Rows, a.N
}
cblas64.Csymm(s, a.Uplo, m, n, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
}
// Syrk performs a symmetric rank-k update
// C = alpha * A * A^T + beta * C, if t == blas.NoTrans,
// C = alpha * A^T * A + beta * C, if t == blas.Trans,
// where C is an n×n symmetric matrix, A is an n×k matrix if t == blas.NoTrans
// and a k×n matrix otherwise, and alpha and beta are scalars.
func Syrk(t blas.Transpose, alpha complex64, a General, beta complex64, c Symmetric) {
var n, k int
if t == blas.NoTrans {
n, k = a.Rows, a.Cols
} else {
n, k = a.Cols, a.Rows
}
cblas64.Csyrk(c.Uplo, t, n, k, alpha, a.Data, a.Stride, beta, c.Data, c.Stride)
}
// Syr2k performs a symmetric rank-2k update
// C = alpha * A * B^T + alpha * B * A^T + beta * C, if t == blas.NoTrans,
// C = alpha * A^T * B + alpha * B^T * 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 complex64, a, b General, beta complex64, c Symmetric) {
var n, k int
if t == blas.NoTrans {
n, k = a.Rows, a.Cols
} else {
n, k = a.Cols, a.Rows
}
cblas64.Csyr2k(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 * A^T * B, if tA == blas.Trans and s == blas.Left,
// B = alpha * A^H * B, if tA == blas.ConjTrans and s == blas.Left,
// B = alpha * B * A, if tA == blas.NoTrans and s == blas.Right,
// B = alpha * B * A^T, if tA == blas.Trans and s == blas.Right,
// B = alpha * B * A^H, 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 complex64, a Triangular, b General) {
cblas64.Ctrmm(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,
// A^T * X = alpha * B, if tA == blas.Trans and s == blas.Left,
// A^H * X = alpha * B, if tA == blas.ConjTrans and s == blas.Left,
// X * A = alpha * B, if tA == blas.NoTrans and s == blas.Right,
// X * A^T = alpha * B, if tA == blas.Trans and s == blas.Right,
// X * A^H = 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 complex64, a Triangular, b General) {
cblas64.Ctrsm(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 complex64, a Hermitian, b General, beta complex64, c General) {
var m, n int
if s == blas.Left {
m, n = a.N, b.Cols
} else {
m, n = b.Rows, a.N
}
cblas64.Chemm(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 * A^H + beta*C, if t == blas.NoTrans,
// C = alpha * A^H * 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 float32, a General, beta float32, c Hermitian) {
var n, k int
if t == blas.NoTrans {
n, k = a.Rows, a.Cols
} else {
n, k = a.Cols, a.Rows
}
cblas64.Cherk(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 * B^H + conj(alpha) * B * A^H + beta * C, if t == blas.NoTrans,
// C = alpha * A^H * B + conj(alpha) * B^H * 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 complex64, a, b General, beta float32, c Hermitian) {
var n, k int
if t == blas.NoTrans {
n, k = a.Rows, a.Cols
} else {
n, k = a.Cols, a.Rows
}
cblas64.Cher2k(c.Uplo, t, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
}