cblas128.go

// 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 cblas128 provides a simple interface to the complex128 BLAS API.
package cblas128

import (
	"github.com/gonum/blas"
	"github.com/gonum/blas/cgo"
)

// TODO(kortschak): Change this and the comment below to native.Implementation
// when blas/native covers the complex BLAS API.
var cblas128 blas.Complex128 = cgo.Implementation{}

// Use sets the BLAS complex128 implementation to be used by subsequent BLAS calls.
// The default implementation is cgo.Implementation.
func Use(b blas.Complex128) {
	cblas128 = b
}

// Implementation returns the current BLAS complex128 implementation.
//
// Implementation allows direct calls to the current the BLAS complex128 implementation
// giving finer control of parameters.
func Implementation() blas.Complex128 {
	return cblas128
}

// Vector represents a vector with an associated element increment.
type Vector struct {
	Inc  int
	Data []complex128
}

// General represents a matrix using the conventional storage scheme.
type General struct {
	Rows, Cols int
	Stride     int
	Data       []complex128
}

// Band represents a band matrix using the band storage scheme.
type Band struct {
	Rows, Cols int
	KL, KU     int
	Stride     int
	Data       []complex128
}

// Triangular represents a triangular matrix using the conventional storage scheme.
type Triangular struct {
	N      int
	Stride int
	Data   []complex128
	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   []complex128
	Uplo   blas.Uplo
	Diag   blas.Diag
}

// TriangularPacked represents a triangular matrix using the packed storage scheme.
type TriangularPacked struct {
	N    int
	Data []complex128
	Uplo blas.Uplo
	Diag blas.Diag
}

// Symmetric represents a symmetric matrix using the conventional storage scheme.
type Symmetric struct {
	N      int
	Stride int
	Data   []complex128
	Uplo   blas.Uplo
}

// SymmetricBand represents a symmetric matrix using the band storage scheme.
type SymmetricBand struct {
	N, K   int
	Stride int
	Data   []complex128
	Uplo   blas.Uplo
}

// SymmetricPacked represents a symmetric matrix using the packed storage scheme.
type SymmetricPacked struct {
	N    int
	Data []complex128
	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 = "cblas128: 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) complex128 {
	return cblas128.Zdotu(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) complex128 {
	return cblas128.Zdotc(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) float64 {
	if x.Inc < 0 {
		panic(negInc)
	}
	return cblas128.Dznrm2(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) float64 {
	if x.Inc < 0 {
		panic(negInc)
	}
	return cblas128.Dzasum(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 cblas128.Izamax(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) {
	cblas128.Zswap(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) {
	cblas128.Zcopy(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 complex128, x, y Vector) {
	cblas128.Zaxpy(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 complex128, x Vector) {
	if x.Inc < 0 {
		panic(negInc)
	}
	cblas128.Zscal(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 float64, x Vector) {
	if x.Inc < 0 {
		panic(negInc)
	}
	cblas128.Zdscal(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 complex128, a General, x Vector, beta complex128, y Vector) {
	cblas128.Zgemv(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 complex128, a Band, x Vector, beta complex128, y Vector) {
	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)
}

// 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) {
	cblas128.Ztrmv(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) {
	cblas128.Ztbmv(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) {
	cblas128.Ztpmv(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) {
	cblas128.Ztrsv(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) {
	cblas128.Ztbsv(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) {
	cblas128.Ztpsv(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 complex128, a Hermitian, x Vector, beta complex128, y Vector) {
	cblas128.Zhemv(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 complex128, a HermitianBand, x Vector, beta complex128, y Vector) {
	cblas128.Zhbmv(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 complex128, a HermitianPacked, x Vector, beta complex128, y Vector) {
	cblas128.Zhpmv(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 complex128, x, y Vector, a General) {
	cblas128.Zgeru(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 complex128, x, y Vector, a General) {
	cblas128.Zgerc(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 float64, x Vector, a Hermitian) {
	cblas128.Zher(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 float64, x Vector, a HermitianPacked) {
	cblas128.Zhpr(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 complex128, x, y Vector, a Hermitian) {
	cblas128.Zher2(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 complex128, x, y Vector, a HermitianPacked) {
	cblas128.Zhpr2(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 complex128, a, b General, beta complex128, 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
	}
	cblas128.Zgemm(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 complex128, a Symmetric, 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.Zsymm(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 complex128, a 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.Zsyrk(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 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 * 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 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,
//  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 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 * 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 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 * 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 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)
}