/
blas.go
283 lines (253 loc) · 16.7 KB
/
blas.go
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// 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)
}