cblas128

package
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 Go to latest Published: Oct 18, 2016 License: Apache-2.0 Imports: 2 Imported by: 0

Documentation

Overview

Package cblas128 provides a simple interface to the complex128 BLAS API.

Index

Constants

This section is empty.

Variables

This section is empty.

Functions

func Asum 

func Asum(n int, x Vector) float64

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 Axpy 

func Axpy(n int, alpha complex128, x, y Vector)

Axpy adds alpha times x to y 

y[i] += alpha * x[i] for all i

func Copy 

func Copy(n int, x, y Vector)

Copy copies the elements of x into the elements of y. 

y[i] = x[i] for all i

func Dotc 

func Dotc(n int, x, y Vector) complex128

Dotu computes the dot product of the two vectors with complex conjugation 

x^H * y

func Dotu 

func Dotu(n int, x, y Vector) complex128

Dotu computes the dot product of the two vectors without complex conjugation 

x^T * y

func Dscal 

func Dscal(n int, alpha float64, x Vector)

Dscal scales x by alpha. 

x[i] *= alpha

Dscal will panic if the vector increment is negative

func Gbmv 

func Gbmv(tA blas.Transpose, alpha complex128, a Band, x Vector, beta complex128, y Vector)

Gbmv computes 

y = alpha * A * x + beta * y if tA == blas.NoTrans
y = alpha * A^T * x + beta * y if tA = blas.Trans
y = alpha * A^H * x + beta * y if tA = blas.ConjTrans

where a is an m×n band matrix kL subdiagonals and kU super-diagonals, and m and n refer to the size of the full dense matrix it represents. x and y are vectors, and alpha and beta are scalars.

func Gemm 

func Gemm(tA, tB blas.Transpose, alpha complex128, a, b General, beta complex128, c General)

Gemm computes 

C = beta * C + alpha * A * B.

tA and tB specify whether A or B are transposed or conjugated. A, B, and C are m×n dense matrices.

func Gemv 

func Gemv(tA blas.Transpose, alpha complex128, a General, x Vector, beta complex128, y Vector)

Gemv computes 

y = alpha * a * x + beta * y if tA = blas.NoTrans
y = alpha * A^T * x + beta * y if tA = blas.Trans
y = alpha * A^H * x + beta * y if tA = blas.ConjTrans

where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.

func Gerc 

func Gerc(alpha complex128, x, y Vector, a General)

Gerc performs the rank-one operation 

A += alpha * x * y^H

where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.

func Geru 

func Geru(alpha complex128, x, y Vector, a General)

Geru performs the rank-one operation 

A += alpha * x * y^T

where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.

func Hbmv 

func Hbmv(alpha complex128, a HermitianBand, x Vector, beta complex128, y Vector)

Hbmv performs 

y = alpha * A * x + beta * y

where A is an n×n Hermitian banded matrix, x and y are vectors, and alpha and beta are scalars.

func Hemm 

func Hemm(s blas.Side, alpha complex128, a Hermitian, b General, beta complex128, c General)

Hemm performs 

B = alpha * A * B if tA == blas.NoTrans and side == blas.Left
B = alpha * A^H * B if tA == blas.ConjTrans and side == blas.Left
B = alpha * B * A if tA == blas.NoTrans and side == blas.Right
B = alpha * B * A^H if tA == blas.ConjTrans and side == blas.Right

where A is an n×n Hermitia matrix, and B is an m×n matrix.

func Hemv 

func Hemv(alpha complex128, a Hermitian, x Vector, beta complex128, y Vector)

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 Her 

func Her(alpha float64, x Vector, a Hermitian)

Ger performs the rank-one operation 

A += alpha * x * y^H

where A is an m×n Hermitian matrix, x and y are vectors, and alpha is a scalar.

func Her2 

func Her2(alpha complex128, x, y Vector, a Hermitian)

Her2 performs the symmetric rank-two update 

A += alpha * x * y^H + alpha * y * x^H

where A is a symmetric n×n matrix, x and y are vectors, and alpha is a scalar.

func Her2k 

func Her2k(t blas.Transpose, alpha complex128, a, b General, beta float64, c Hermitian)

Her2k performs the symmetric rank 2k operation 

C = alpha * A * B^H + alpha * B * A^H + beta * C

where C is an n×n Hermitian matrix. A and B are n×k matrices if tA == NoTrans and k×n otherwise. alpha and beta are scalars.

func Herk 

func Herk(t blas.Transpose, alpha float64, a General, beta float64, c Hermitian)

Herk performs the symmetric rank-k operation 

C = alpha * A * A^H + beta*C

C is an n×n Hermitian matrix. A is an n×k matrix if tA == blas.NoTrans, and a k×n matrix otherwise. alpha and beta are scalars.

func Hpmv 

func Hpmv(alpha complex128, a HermitianPacked, x Vector, beta complex128, y Vector)

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 Hpr 

func Hpr(alpha float64, x Vector, a HermitianPacked)

Hpr computes the rank-one operation 

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 Hpr2 

func Hpr2(alpha complex128, x, y Vector, a HermitianPacked)

Hpr2 performs the symmetric rank-2 update 

a += alpha * x * y^H + alpha * y * x^H

where a is an n×n symmetric matirx in packed format and x and y are vectors.

func Iamax 

func Iamax(n int, x Vector) int

Iamax returns the index of the largest element of x. 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 Implementation 

func Implementation() blas.Complex128

Implementation returns the current BLAS complex128 implementation.

Implementation allows direct calls to the current the BLAS complex128 implementation giving finer control of parameters.

func Nrm2 

func Nrm2(n int, x Vector) float64

Nrm2 computes the Euclidean norm of a vector, 

sqrt(\sum_i x[i] * x[i]).

Nrm2 will panic if the vector increment is negative.

func Scal 

func Scal(n int, alpha complex128, x Vector)

Scal scales x by alpha. 

x[i] *= alpha

Scal will panic if the vector increment is negative

func Swap 

func Swap(n int, x, y Vector)

Swap exchanges the elements of two vectors. 

x[i], y[i] = y[i], x[i] for all i

func Symm 

func Symm(s blas.Side, alpha complex128, a Symmetric, b General, beta complex128, c General)

Symm performs one of 

C = alpha * A * B + beta * C if side == blas.Left
C = alpha * B * A + beta * C if side == blas.Right

where A is an n×n symmetric matrix, B and C are m×n matrices, and alpha is a scalar.

func Syr2k 

func Syr2k(t blas.Transpose, alpha complex128, a, b General, beta complex128, c Symmetric)

Syr2k performs the symmetric rank 2k operation 

C = alpha * A * B^T + alpha * B * A^T + beta * C

where C is an n×n symmetric matrix. A and B are n×k matrices if tA == NoTrans and k×n otherwise. alpha and beta are scalars.

func Syrk 

func Syrk(t blas.Transpose, alpha complex128, a General, beta complex128, c Symmetric)

Syrk performs the symmetric rank-k operation 

C = alpha * A * A^T + beta*C

C is an n×n symmetric matrix. A is an n×k matrix if tA == blas.NoTrans, and a k×n matrix otherwise. alpha and beta are scalars.

func Tbmv 

func Tbmv(tA blas.Transpose, a TriangularBand, x Vector)

Tbmv computes 

x = A * x if tA == blas.NoTrans
x = A^T * x if tA == blas.Trans
x = A^H * x if tA == blas.ConjTrans

where A is an n×n triangular banded matrix with k diagonals, and x is a vector.

func Tbsv 

func Tbsv(tA blas.Transpose, a TriangularBand, x Vector)

Tbsv solves 

A * x = b if tA == blas.NoTrans
A^T * x = b if tA == blas.Trans
A^H * x = b if tA == blas.ConjTrans

where A is an n×n triangular banded matrix with k diagonals 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 Tpmv 

func Tpmv(tA blas.Transpose, a TriangularPacked, x Vector)

Tpmv computes 

x = A * x if tA == blas.NoTrans
x = A^T * x if tA == blas.Trans
x = A^H * x if tA == blas.ConjTrans

where A is an n×n unit triangular matrix in packed format, and x is a vector.

func Tpsv 

func Tpsv(tA blas.Transpose, a TriangularPacked, x Vector)

Tpsv solves 

A * x = b if tA == blas.NoTrans
A^T * x = b if tA == blas.Trans
A^H * x = b if tA == 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 Trmm 

func Trmm(s blas.Side, tA blas.Transpose, alpha complex128, a Triangular, b General)

Trmm performs 

B = alpha * A * B if tA == blas.NoTrans and side == blas.Left
B = alpha * A^T * B if tA == blas.Trans and side == blas.Left
B = alpha * A^H * B if tA == blas.ConjTrans and side == blas.Left
B = alpha * B * A if tA == blas.NoTrans and side == blas.Right
B = alpha * B * A^T if tA == blas.Trans and side == blas.Right
B = alpha * B * A^H if tA == blas.ConjTrans and side == blas.Right

where A is an n×n triangular matrix, and B is an m×n matrix.

func Trmv 

func Trmv(tA blas.Transpose, a Triangular, x Vector)

Trmv computes 

x = A * x if tA == blas.NoTrans
x = A^T * x if tA == blas.Trans
x = A^H * x if tA == blas.ConjTrans

A is an n×n Triangular matrix and x is a vector.

func Trsm 

func Trsm(s blas.Side, tA blas.Transpose, alpha complex128, a Triangular, b General)

Trsm solves 

A * X = alpha * B if tA == blas.NoTrans and side == blas.Left
A^T * X = alpha * B if tA == blas.Trans and side == blas.Left
A^H * X = alpha * B if tA == blas.ConjTrans and side == blas.Left
X * A = alpha * B if tA == blas.NoTrans and side == blas.Right
X * A^T = alpha * B if tA == blas.Trans and side == blas.Right
X * A^H = alpha * B if tA ==  blas.ConjTrans and side == blas.Right

where A is an n×n triangular matrix, x is an m×n matrix, 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 Trsv 

func Trsv(tA blas.Transpose, a Triangular, x Vector)

Trsv solves 

A * x = b if tA == blas.NoTrans
A^T * x = b if tA == blas.Trans
A^H * x = b if tA == blas.ConjTrans

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 Use 

func Use(b blas.Complex128)

Use sets the BLAS complex128 implementation to be used by subsequent BLAS calls. The default implementation is cgo.Implementation.

Types

type Band 

type Band struct {
	Rows, Cols int
	KL, KU     int
	Stride     int
	Data       []complex128
}

Band represents a band matrix using the band storage scheme.

type General 

type General struct {
	Rows, Cols int
	Stride     int
	Data       []complex128
}

General represents a matrix using the conventional storage scheme.

type Hermitian 

type Hermitian Symmetric

Hermitian represents an Hermitian matrix using the conventional storage scheme.

type HermitianBand 

type HermitianBand SymmetricBand

HermitianBand represents an Hermitian matrix using the band storage scheme.

type HermitianPacked 

type HermitianPacked SymmetricPacked

HermitianPacked represents an Hermitian matrix using the packed storage scheme.

type Symmetric 

type Symmetric struct {
	N      int
	Stride int
	Data   []complex128
	Uplo   blas.Uplo
}

Symmetric represents a symmetric matrix using the conventional storage scheme.

type SymmetricBand 

type SymmetricBand struct {
	N, K   int
	Stride int
	Data   []complex128
	Uplo   blas.Uplo
}

SymmetricBand represents a symmetric matrix using the band storage scheme.

type SymmetricPacked 

type SymmetricPacked struct {
	N    int
	Data []complex128
	Uplo blas.Uplo
}

SymmetricPacked represents a symmetric matrix using the packed storage scheme.

type Triangular 

type Triangular struct {
	N      int
	Stride int
	Data   []complex128
	Uplo   blas.Uplo
	Diag   blas.Diag
}

Triangular represents a triangular matrix using the conventional storage scheme.

type TriangularBand 

type TriangularBand struct {
	N, K   int
	Stride int
	Data   []complex128
	Uplo   blas.Uplo
	Diag   blas.Diag
}

TriangularBand represents a triangular matrix using the band storage scheme.

type TriangularPacked 

type TriangularPacked struct {
	N    int
	Data []complex128
	Uplo blas.Uplo
	Diag blas.Diag
}

TriangularPacked represents a triangular matrix using the packed storage scheme.

type Vector 

type Vector struct {
	Inc  int
	Data []complex128
}

Vector represents a vector with an associated element increment.

Source Files

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