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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 blas32 provides a simple interface to the float32 BLAS API.
package blas32 // import "gonum.org/v1/gonum/blas/blas32"
import (
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/gonum"
)
var blas32 blas.Float32 = gonum.Implementation{}
// Use sets the BLAS float32 implementation to be used by subsequent BLAS calls.
// The default implementation is native.Implementation.
func Use(b blas.Float32) {
blas32 = b
}
// Implementation returns the current BLAS float32 implementation.
//
// Implementation allows direct calls to the current the BLAS float32 implementation
// giving finer control of parameters.
func Implementation() blas.Float32 {
return blas32
}
// Vector represents a vector with an associated element increment.
type Vector struct {
Inc int
Data []float32
}
// General represents a matrix using the conventional storage scheme.
type General struct {
Rows, Cols int
Stride int
Data []float32
}
// Band represents a band matrix using the band storage scheme.
type Band struct {
Rows, Cols int
KL, KU int
Stride int
Data []float32
}
// Triangular represents a triangular matrix using the conventional storage scheme.
type Triangular struct {
N int
Stride int
Data []float32
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 []float32
Uplo blas.Uplo
Diag blas.Diag
}
// TriangularPacked represents a triangular matrix using the packed storage scheme.
type TriangularPacked struct {
N int
Data []float32
Uplo blas.Uplo
Diag blas.Diag
}
// Symmetric represents a symmetric matrix using the conventional storage scheme.
type Symmetric struct {
N int
Stride int
Data []float32
Uplo blas.Uplo
}
// SymmetricBand represents a symmetric matrix using the band storage scheme.
type SymmetricBand struct {
N, K int
Stride int
Data []float32
Uplo blas.Uplo
}
// SymmetricPacked represents a symmetric matrix using the packed storage scheme.
type SymmetricPacked struct {
N int
Data []float32
Uplo blas.Uplo
}
// Level 1
const negInc = "blas32: negative vector increment"
// Dot computes the dot product of the two vectors:
// \sum_i x[i]*y[i].
func Dot(n int, x, y Vector) float32 {
return blas32.Sdot(n, x.Data, x.Inc, y.Data, y.Inc)
}
// DDot computes the dot product of the two vectors:
// \sum_i x[i]*y[i].
func DDot(n int, x, y Vector) float64 {
return blas32.Dsdot(n, x.Data, x.Inc, y.Data, y.Inc)
}
// SDDot computes the dot product of the two vectors adding a constant:
// alpha + \sum_i x[i]*y[i].
func SDDot(n int, alpha float32, x, y Vector) float32 {
return blas32.Sdsdot(n, alpha, 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 blas32.Snrm2(n, x.Data, x.Inc)
}
// Asum computes the sum of the absolute values of the elements of x:
// \sum_i |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 blas32.Sasum(n, x.Data, x.Inc)
}
// Iamax returns the index of an element of x with the largest absolute value.
// 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 blas32.Isamax(n, x.Data, x.Inc)
}
// Swap exchanges the elements of the two vectors:
// x[i], y[i] = y[i], x[i] for all i.
func Swap(n int, x, y Vector) {
blas32.Sswap(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) {
blas32.Scopy(n, x.Data, x.Inc, y.Data, y.Inc)
}
// Axpy adds x scaled by alpha to y:
// y[i] += alpha*x[i] for all i.
func Axpy(n int, alpha float32, x, y Vector) {
blas32.Saxpy(n, alpha, x.Data, x.Inc, y.Data, y.Inc)
}
// Rotg computes the parameters of a Givens plane rotation so that
// ⎡ c s⎤ ⎡a⎤ ⎡r⎤
// ⎣-s c⎦ * ⎣b⎦ = ⎣0⎦
// where a and b are the Cartesian coordinates of a given point.
// c, s, and r are defined as
// r = ±Sqrt(a^2 + b^2),
// c = a/r, the cosine of the rotation angle,
// s = a/r, the sine of the rotation angle,
// and z is defined such that
// if |a| > |b|, z = s,
// otherwise if c != 0, z = 1/c,
// otherwise z = 1.
func Rotg(a, b float32) (c, s, r, z float32) {
return blas32.Srotg(a, b)
}
// Rotmg computes the modified Givens rotation. See
// http://www.netlib.org/lapack/explore-html/df/deb/drotmg_8f.html
// for more details.
func Rotmg(d1, d2, b1, b2 float32) (p blas.SrotmParams, rd1, rd2, rb1 float32) {
return blas32.Srotmg(d1, d2, b1, b2)
}
// Rot applies a plane transformation to n points represented by the vectors x
// and y:
// x[i] = c*x[i] + s*y[i],
// y[i] = -s*x[i] + c*y[i], for all i.
func Rot(n int, x, y Vector, c, s float32) {
blas32.Srot(n, x.Data, x.Inc, y.Data, y.Inc, c, s)
}
// Rotm applies the modified Givens rotation to n points represented by the
// vectors x and y.
func Rotm(n int, x, y Vector, p blas.SrotmParams) {
blas32.Srotm(n, x.Data, x.Inc, y.Data, y.Inc, p)
}
// Scal scales the vector x by alpha:
// x[i] *= alpha for all i.
//
// Scal will panic if the vector increment is negative.
func Scal(n int, alpha float32, x Vector) {
if x.Inc < 0 {
panic(negInc)
}
blas32.Sscal(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 or 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 float32, a General, x Vector, beta float32, y Vector) {
blas32.Sgemv(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 or 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 float32, a Band, x Vector, beta float32, y Vector) {
blas32.Sgbmv(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 or blas.ConjTrans,
// where A is an n×n triangular matrix, and x is a vector.
func Trmv(t blas.Transpose, a Triangular, x Vector) {
blas32.Strmv(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 or 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) {
blas32.Stbmv(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 or 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) {
blas32.Stpmv(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 or blas.ConjTrans,
// where A is an n×n triangular matrix, and x and b are vectors.
//
// 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) {
blas32.Strsv(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 or blas.ConjTrans,
// where A is an n×n triangular band matrix, and x and b are vectors.
//
// 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) {
blas32.Stbsv(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 or blas.ConjTrans,
// where A is an n×n triangular matrix in packed format, and x and b are
// vectors.
//
// 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) {
blas32.Stpsv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
}
// Symv computes
// y = alpha * A * x + beta * y,
// where A is an n×n symmetric matrix, x and y are vectors, and alpha and
// beta are scalars.
func Symv(alpha float32, a Symmetric, x Vector, beta float32, y Vector) {
blas32.Ssymv(a.Uplo, a.N, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
}
// Sbmv performs
// y = alpha * A * x + beta * y,
// where A is an n×n symmetric band matrix, x and y are vectors, and alpha
// and beta are scalars.
func Sbmv(alpha float32, a SymmetricBand, x Vector, beta float32, y Vector) {
blas32.Ssbmv(a.Uplo, a.N, a.K, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
}
// Spmv performs
// y = alpha * A * x + beta * y,
// where A is an n×n symmetric matrix in packed format, x and y are vectors,
// and alpha and beta are scalars.
func Spmv(alpha float32, a SymmetricPacked, x Vector, beta float32, y Vector) {
blas32.Sspmv(a.Uplo, a.N, alpha, a.Data, x.Data, x.Inc, beta, y.Data, y.Inc)
}
// Ger 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 Ger(alpha float32, x, y Vector, a General) {
blas32.Sger(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
}
// Syr performs a rank-1 update
// A += alpha * x * x^T,
// where A is an n×n symmetric matrix, x is a vector, and alpha is a scalar.
func Syr(alpha float32, x Vector, a Symmetric) {
blas32.Ssyr(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data, a.Stride)
}
// Spr performs the rank-1 update
// A += alpha * x * x^T,
// where A is an n×n symmetric matrix in packed format, x is a vector, and
// alpha is a scalar.
func Spr(alpha float32, x Vector, a SymmetricPacked) {
blas32.Sspr(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data)
}
// Syr2 performs a rank-2 update
// A += alpha * x * y^T + alpha * y * x^T,
// where A is a symmetric n×n matrix, x and y are vectors, and alpha is a scalar.
func Syr2(alpha float32, x, y Vector, a Symmetric) {
blas32.Ssyr2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
}
// Spr2 performs a rank-2 update
// A += alpha * x * y^T + alpha * y * x^T,
// where A is an n×n symmetric matrix in packed format, x and y are vectors,
// and alpha is a scalar.
func Spr2(alpha float32, x, y Vector, a SymmetricPacked) {
blas32.Sspr2(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.
func Gemm(tA, tB blas.Transpose, alpha float32, a, b General, beta float32, 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
}
blas32.Sgemm(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 is a scalar.
func Symm(s blas.Side, alpha float32, a Symmetric, b General, beta float32, c General) {
var m, n int
if s == blas.Left {
m, n = a.N, b.Cols
} else {
m, n = b.Rows, a.N
}
blas32.Ssymm(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 or blas.ConjTrans,
// 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 float32, a General, beta float32, c Symmetric) {
var n, k int
if t == blas.NoTrans {
n, k = a.Rows, a.Cols
} else {
n, k = a.Cols, a.Rows
}
blas32.Ssyrk(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 or blas.ConjTrans,
// where C is an n×n symmetric matrix, A and B are n×k matrices if t == NoTrans
// and k×n matrices otherwise, and alpha and beta are scalars.
func Syr2k(t blas.Transpose, alpha float32, a, b General, beta float32, c Symmetric) {
var n, k int
if t == blas.NoTrans {
n, k = a.Rows, a.Cols
} else {
n, k = a.Cols, a.Rows
}
blas32.Ssyr2k(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 or 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 or 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 float32, a Triangular, b General) {
blas32.Strmm(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 or 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 or 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, X contains the values of B, and the result is
// stored in-place into X.
//
// No check is made that A is invertible.
func Trsm(s blas.Side, tA blas.Transpose, alpha float32, a Triangular, b General) {
blas32.Strsm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
}