blas/blas.go

// Copyright ©2013 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 ./conversions.bash

package blas

// Flag constants indicate Givens transformation H matrix state.
type Flag int

const (
	Identity    Flag = -2 // H is the identity matrix; no rotation is needed.
	Rescaling   Flag = -1 // H specifies rescaling.
	OffDiagonal Flag = 0  // Off-diagonal elements of H are non-unit.
	Diagonal    Flag = 1  // Diagonal elements of H are non-unit.
)

// SrotmParams contains Givens transformation parameters returned
// by the Float32 Srotm method.
type SrotmParams struct {
	Flag
	H [4]float32 // Column-major 2 by 2 matrix.
}

// DrotmParams contains Givens transformation parameters returned
// by the Float64 Drotm method.
type DrotmParams struct {
	Flag
	H [4]float64 // Column-major 2 by 2 matrix.
}

// Transpose specifies the transposition operation of a matrix.
type Transpose byte

const (
	NoTrans   Transpose = 'N'
	Trans     Transpose = 'T'
	ConjTrans Transpose = 'C'
)

// Uplo specifies whether a matrix is upper or lower triangular.
type Uplo byte

const (
	Upper Uplo = 'U'
	Lower Uplo = 'L'
	All   Uplo = 'A'
)

// Diag specifies whether a matrix is unit triangular.
type Diag byte

const (
	NonUnit Diag = 'N'
	Unit    Diag = 'U'
)

// Side specifies from which side a multiplication operation is performed.
type Side byte

const (
	Left  Side = 'L'
	Right Side = 'R'
)

// Float32 implements the single precision real BLAS routines.
type Float32 interface {
	Float32Level1
	Float32Level2
	Float32Level3
}

// Float32Level1 implements the single precision real BLAS Level 1 routines.
type Float32Level1 interface {
	Sdsdot(n int, alpha float32, x []float32, incX int, y []float32, incY int) float32
	Dsdot(n int, x []float32, incX int, y []float32, incY int) float64
	Sdot(n int, x []float32, incX int, y []float32, incY int) float32
	Snrm2(n int, x []float32, incX int) float32
	Sasum(n int, x []float32, incX int) float32
	Isamax(n int, x []float32, incX int) int
	Sswap(n int, x []float32, incX int, y []float32, incY int)
	Scopy(n int, x []float32, incX int, y []float32, incY int)
	Saxpy(n int, alpha float32, x []float32, incX int, y []float32, incY int)
	Srotg(a, b float32) (c, s, r, z float32)
	Srotmg(d1, d2, b1, b2 float32) (p SrotmParams, rd1, rd2, rb1 float32)
	Srot(n int, x []float32, incX int, y []float32, incY int, c, s float32)
	Srotm(n int, x []float32, incX int, y []float32, incY int, p SrotmParams)
	Sscal(n int, alpha float32, x []float32, incX int)
}

// Float32Level2 implements the single precision real BLAS Level 2 routines.
type Float32Level2 interface {
	Sgemv(tA Transpose, m, n int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)
	Sgbmv(tA Transpose, m, n, kL, kU int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)
	Strmv(ul Uplo, tA Transpose, d Diag, n int, a []float32, lda int, x []float32, incX int)
	Stbmv(ul Uplo, tA Transpose, d Diag, n, k int, a []float32, lda int, x []float32, incX int)
	Stpmv(ul Uplo, tA Transpose, d Diag, n int, ap []float32, x []float32, incX int)
	Strsv(ul Uplo, tA Transpose, d Diag, n int, a []float32, lda int, x []float32, incX int)
	Stbsv(ul Uplo, tA Transpose, d Diag, n, k int, a []float32, lda int, x []float32, incX int)
	Stpsv(ul Uplo, tA Transpose, d Diag, n int, ap []float32, x []float32, incX int)
	Ssymv(ul Uplo, n int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)
	Ssbmv(ul Uplo, n, k int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)
	Sspmv(ul Uplo, n int, alpha float32, ap []float32, x []float32, incX int, beta float32, y []float32, incY int)
	Sger(m, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32, lda int)
	Ssyr(ul Uplo, n int, alpha float32, x []float32, incX int, a []float32, lda int)
	Sspr(ul Uplo, n int, alpha float32, x []float32, incX int, ap []float32)
	Ssyr2(ul Uplo, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32, lda int)
	Sspr2(ul Uplo, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32)
}

// Float32Level3 implements the single precision real BLAS Level 3 routines.
type Float32Level3 interface {
	Sgemm(tA, tB Transpose, m, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int)
	Ssymm(s Side, ul Uplo, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int)
	Ssyrk(ul Uplo, t Transpose, n, k int, alpha float32, a []float32, lda int, beta float32, c []float32, ldc int)
	Ssyr2k(ul Uplo, t Transpose, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int)
	Strmm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int)
	Strsm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int)
}

// Float64 implements the single precision real BLAS routines.
type Float64 interface {
	Float64Level1
	Float64Level2
	Float64Level3
}

// Float64Level1 implements the double precision real BLAS Level 1 routines.
type Float64Level1 interface {
	Ddot(n int, x []float64, incX int, y []float64, incY int) float64
	Dnrm2(n int, x []float64, incX int) float64
	Dasum(n int, x []float64, incX int) float64
	Idamax(n int, x []float64, incX int) int
	Dswap(n int, x []float64, incX int, y []float64, incY int)
	Dcopy(n int, x []float64, incX int, y []float64, incY int)
	Daxpy(n int, alpha float64, x []float64, incX int, y []float64, incY int)
	Drotg(a, b float64) (c, s, r, z float64)
	Drotmg(d1, d2, b1, b2 float64) (p DrotmParams, rd1, rd2, rb1 float64)
	Drot(n int, x []float64, incX int, y []float64, incY int, c float64, s float64)
	Drotm(n int, x []float64, incX int, y []float64, incY int, p DrotmParams)
	Dscal(n int, alpha float64, x []float64, incX int)
}

// Float64Level2 implements the double precision real BLAS Level 2 routines.
type Float64Level2 interface {
	Dgemv(tA Transpose, m, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)
	Dgbmv(tA Transpose, m, n, kL, kU int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)
	Dtrmv(ul Uplo, tA Transpose, d Diag, n int, a []float64, lda int, x []float64, incX int)
	Dtbmv(ul Uplo, tA Transpose, d Diag, n, k int, a []float64, lda int, x []float64, incX int)
	Dtpmv(ul Uplo, tA Transpose, d Diag, n int, ap []float64, x []float64, incX int)
	Dtrsv(ul Uplo, tA Transpose, d Diag, n int, a []float64, lda int, x []float64, incX int)
	Dtbsv(ul Uplo, tA Transpose, d Diag, n, k int, a []float64, lda int, x []float64, incX int)
	Dtpsv(ul Uplo, tA Transpose, d Diag, n int, ap []float64, x []float64, incX int)
	Dsymv(ul Uplo, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)
	Dsbmv(ul Uplo, n, k int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)
	Dspmv(ul Uplo, n int, alpha float64, ap []float64, x []float64, incX int, beta float64, y []float64, incY int)
	Dger(m, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int)
	Dsyr(ul Uplo, n int, alpha float64, x []float64, incX int, a []float64, lda int)
	Dspr(ul Uplo, n int, alpha float64, x []float64, incX int, ap []float64)
	Dsyr2(ul Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int)
	Dspr2(ul Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64)
}

// Float64Level3 implements the double precision real BLAS Level 3 routines.
type Float64Level3 interface {
	Dgemm(tA, tB Transpose, m, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)
	Dsymm(s Side, ul Uplo, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)
	Dsyrk(ul Uplo, t Transpose, n, k int, alpha float64, a []float64, lda int, beta float64, c []float64, ldc int)
	Dsyr2k(ul Uplo, t Transpose, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)
	Dtrmm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int)
	Dtrsm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int)
}

// Complex64 implements the single precision complex BLAS routines.
type Complex64 interface {
	Complex64Level1
	Complex64Level2
	Complex64Level3
}

// Complex64Level1 implements the single precision complex BLAS Level 1 routines.
type Complex64Level1 interface {
	Cdotu(n int, x []complex64, incX int, y []complex64, incY int) (dotu complex64)
	Cdotc(n int, x []complex64, incX int, y []complex64, incY int) (dotc complex64)
	Scnrm2(n int, x []complex64, incX int) float32
	Scasum(n int, x []complex64, incX int) float32
	Icamax(n int, x []complex64, incX int) int
	Cswap(n int, x []complex64, incX int, y []complex64, incY int)
	Ccopy(n int, x []complex64, incX int, y []complex64, incY int)
	Caxpy(n int, alpha complex64, x []complex64, incX int, y []complex64, incY int)
	Cscal(n int, alpha complex64, x []complex64, incX int)
	Csscal(n int, alpha float32, x []complex64, incX int)
}

// Complex64Level2 implements the single precision complex BLAS routines Level 2 routines.
type Complex64Level2 interface {
	Cgemv(tA Transpose, m, n int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)
	Cgbmv(tA Transpose, m, n, kL, kU int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)
	Ctrmv(ul Uplo, tA Transpose, d Diag, n int, a []complex64, lda int, x []complex64, incX int)
	Ctbmv(ul Uplo, tA Transpose, d Diag, n, k int, a []complex64, lda int, x []complex64, incX int)
	Ctpmv(ul Uplo, tA Transpose, d Diag, n int, ap []complex64, x []complex64, incX int)
	Ctrsv(ul Uplo, tA Transpose, d Diag, n int, a []complex64, lda int, x []complex64, incX int)
	Ctbsv(ul Uplo, tA Transpose, d Diag, n, k int, a []complex64, lda int, x []complex64, incX int)
	Ctpsv(ul Uplo, tA Transpose, d Diag, n int, ap []complex64, x []complex64, incX int)
	Chemv(ul Uplo, n int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)
	Chbmv(ul Uplo, n, k int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)
	Chpmv(ul Uplo, n int, alpha complex64, ap []complex64, x []complex64, incX int, beta complex64, y []complex64, incY int)
	Cgeru(m, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int)
	Cgerc(m, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int)
	Cher(ul Uplo, n int, alpha float32, x []complex64, incX int, a []complex64, lda int)
	Chpr(ul Uplo, n int, alpha float32, x []complex64, incX int, a []complex64)
	Cher2(ul Uplo, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int)
	Chpr2(ul Uplo, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, ap []complex64)
}

// Complex64Level3 implements the single precision complex BLAS Level 3 routines.
type Complex64Level3 interface {
	Cgemm(tA, tB Transpose, m, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)
	Csymm(s Side, ul Uplo, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)
	Csyrk(ul Uplo, t Transpose, n, k int, alpha complex64, a []complex64, lda int, beta complex64, c []complex64, ldc int)
	Csyr2k(ul Uplo, t Transpose, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)
	Ctrmm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int)
	Ctrsm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int)
	Chemm(s Side, ul Uplo, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)
	Cherk(ul Uplo, t Transpose, n, k int, alpha float32, a []complex64, lda int, beta float32, c []complex64, ldc int)
	Cher2k(ul Uplo, t Transpose, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta float32, c []complex64, ldc int)
}

// Complex128 implements the double precision complex BLAS routines.
type Complex128 interface {
	Complex128Level1
	Complex128Level2
	Complex128Level3
}

// Complex128Level1 implements the double precision complex BLAS Level 1 routines.
type Complex128Level1 interface {
	Zdotu(n int, x []complex128, incX int, y []complex128, incY int) (dotu complex128)
	Zdotc(n int, x []complex128, incX int, y []complex128, incY int) (dotc complex128)
	Dznrm2(n int, x []complex128, incX int) float64
	Dzasum(n int, x []complex128, incX int) float64
	Izamax(n int, x []complex128, incX int) int
	Zswap(n int, x []complex128, incX int, y []complex128, incY int)
	Zcopy(n int, x []complex128, incX int, y []complex128, incY int)
	Zaxpy(n int, alpha complex128, x []complex128, incX int, y []complex128, incY int)
	Zscal(n int, alpha complex128, x []complex128, incX int)
	Zdscal(n int, alpha float64, x []complex128, incX int)
}

// Complex128Level2 implements the double precision complex BLAS Level 2 routines.
type Complex128Level2 interface {
	Zgemv(tA Transpose, m, n int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)
	Zgbmv(tA Transpose, m, n int, kL int, kU int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)
	Ztrmv(ul Uplo, tA Transpose, d Diag, n int, a []complex128, lda int, x []complex128, incX int)
	Ztbmv(ul Uplo, tA Transpose, d Diag, n, k int, a []complex128, lda int, x []complex128, incX int)
	Ztpmv(ul Uplo, tA Transpose, d Diag, n int, ap []complex128, x []complex128, incX int)
	Ztrsv(ul Uplo, tA Transpose, d Diag, n int, a []complex128, lda int, x []complex128, incX int)
	Ztbsv(ul Uplo, tA Transpose, d Diag, n, k int, a []complex128, lda int, x []complex128, incX int)
	Ztpsv(ul Uplo, tA Transpose, d Diag, n int, ap []complex128, x []complex128, incX int)
	Zhemv(ul Uplo, n int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)
	Zhbmv(ul Uplo, n, k int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)
	Zhpmv(ul Uplo, n int, alpha complex128, ap []complex128, x []complex128, incX int, beta complex128, y []complex128, incY int)
	Zgeru(m, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)
	Zgerc(m, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)
	Zher(ul Uplo, n int, alpha float64, x []complex128, incX int, a []complex128, lda int)
	Zhpr(ul Uplo, n int, alpha float64, x []complex128, incX int, a []complex128)
	Zher2(ul Uplo, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)
	Zhpr2(ul Uplo, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, ap []complex128)
}

// Complex128Level3 implements the double precision complex BLAS Level 3 routines.
type Complex128Level3 interface {
	Zgemm(tA, tB Transpose, m, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)
	Zsymm(s Side, ul Uplo, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)
	Zsyrk(ul Uplo, t Transpose, n, k int, alpha complex128, a []complex128, lda int, beta complex128, c []complex128, ldc int)
	Zsyr2k(ul Uplo, t Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)
	Ztrmm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int)
	Ztrsm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int)
	Zhemm(s Side, ul Uplo, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)
	Zherk(ul Uplo, t Transpose, n, k int, alpha float64, a []complex128, lda int, beta float64, c []complex128, ldc int)
	Zher2k(ul Uplo, t Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta float64, c []complex128, ldc int)
}