cblas128

package
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 Go to latest Published: Mar 17, 2021 License: BSD-3-Clause 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(x Vector) float64

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 Axpy 

func Axpy(alpha complex128, x, y Vector)

Axpy computes 

y = alpha * x + y,

where x and y are vectors, and alpha is a scalar. Axpy will panic if the lengths of x and y do not match.

func Copy 

func Copy(x, y Vector)

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

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

Copy will panic if the lengths of x and y do not match.

func Dotc 

func Dotc(x, y Vector) complex128

Dotc computes the dot product of the two vectors with complex conjugation: 

xᴴ * y.

Dotc will panic if the lengths of x and y do not match.

func Dotu 

func Dotu(x, y Vector) complex128

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

xᵀ * y.

Dotu will panic if the lengths of x and y do not match.

func Dscal 

func Dscal(alpha float64, x Vector)

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 Gbmv 

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

Gbmv computes 

y = alpha * A * x + beta * y   if t == blas.NoTrans,
y = alpha * Aᵀ * x + beta * y  if t == blas.Trans,
y = alpha * Aᴴ * 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 Gemm 

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

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 Gemv 

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

Gemv computes 

y = alpha * A * x + beta * y   if t == blas.NoTrans,
y = alpha * Aᵀ * x + beta * y  if t == blas.Trans,
y = alpha * Aᴴ * 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 Gerc 

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

Gerc performs a rank-1 update 

A += alpha * x * yᴴ,

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 a rank-1 update 

A += alpha * x * yᵀ,

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 band 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 

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 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)

Her performs a rank-1 update 

A += alpha * x * yᵀ,

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 a rank-2 update 

A += alpha * x * yᴴ + conj(alpha) * y * xᴴ,

where A is an n×n Hermitian 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 Hermitian rank-2k update 

C = alpha * A * Bᴴ + conj(alpha) * B * Aᴴ + beta * C  if t == blas.NoTrans,
C = alpha * Aᴴ * B + conj(alpha) * Bᴴ * 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 Herk 

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

Herk performs the Hermitian rank-k update 

C = alpha * A * Aᴴ + beta*C  if t == blas.NoTrans,
C = alpha * Aᴴ * 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 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 performs a rank-1 update 

A += alpha * x * xᴴ,

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 a rank-2 update 

A += alpha * x * yᴴ + conj(alpha) * y * xᴴ,

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

func Iamax 

func Iamax(x Vector) int

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 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(x Vector) float64

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 Scal 

func Scal(alpha complex128, x Vector)

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 Swap 

func Swap(x, y Vector)

Swap exchanges the elements of two vectors: 

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

Swap will panic if the lengths of x and y do not match.

func Symm 

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

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 Syr2k 

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

Syr2k performs a symmetric rank-2k update 

C = alpha * A * Bᵀ + alpha * B * Aᵀ + beta * C  if t == blas.NoTrans,
C = alpha * Aᵀ * B + alpha * Bᵀ * 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 Syrk 

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

Syrk performs a symmetric rank-k update 

C = alpha * A * Aᵀ + beta * C  if t == blas.NoTrans,
C = alpha * Aᵀ * 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 Tbmv 

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

Tbmv computes 

x = A * x   if t == blas.NoTrans,
x = Aᵀ * x  if t == blas.Trans,
x = Aᴴ * x  if t == blas.ConjTrans,

where A is an n×n triangular band matrix, and x is a vector.

func Tbsv 

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

Tbsv solves 

A * x = b   if t == blas.NoTrans,
Aᵀ * x = b  if t == blas.Trans,
Aᴴ * 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 Tpmv 

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

Tpmv computes 

x = A * x   if t == blas.NoTrans,
x = Aᵀ * x  if t == blas.Trans,
x = Aᴴ * x  if t == blas.ConjTrans,

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

func Tpsv 

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

Tpsv solves 

A * x = b   if t == blas.NoTrans,
Aᵀ * x = b  if t == blas.Trans,
Aᴴ * 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 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 s == blas.Left,
B = alpha * Aᵀ * B  if tA == blas.Trans and s == blas.Left,
B = alpha * Aᴴ * B  if tA == blas.ConjTrans and s == blas.Left,
B = alpha * B * A   if tA == blas.NoTrans and s == blas.Right,
B = alpha * B * Aᵀ  if tA == blas.Trans and s == blas.Right,
B = alpha * B * Aᴴ  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 Trmv 

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

Trmv computes 

x = A * x   if t == blas.NoTrans,
x = Aᵀ * x  if t == blas.Trans,
x = Aᴴ * x  if t == blas.ConjTrans,

where 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 s == blas.Left,
Aᵀ * X = alpha * B  if tA == blas.Trans and s == blas.Left,
Aᴴ * X = alpha * B  if tA == blas.ConjTrans and s == blas.Left,
X * A = alpha * B   if tA == blas.NoTrans and s == blas.Right,
X * Aᵀ = alpha * B  if tA == blas.Trans and s == blas.Right,
X * Aᴴ = 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 Trsv 

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

Trsv solves 

A * x = b   if t == blas.NoTrans,
Aᵀ * x = b  if t == blas.Trans,
Aᴴ * 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 Use 

func Use(b blas.Complex128)

Use sets the BLAS complex128 implementation to be used by subsequent BLAS calls. The default implementation is gonum.org/v1/gonum/blas/gonum.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.

func (Band) From 

func (t Band) From(a BandCols)

From fills the receiver with elements from a. The receiver must have the same dimensions and bandwidth as a and have adequate backing data storage.

type BandCols 

type BandCols Band

BandCols represents a matrix using the band column-major storage scheme.

func (BandCols) From 

func (t BandCols) From(a Band)

From fills the receiver with elements from a. The receiver must have the same dimensions and bandwidth as a and have adequate backing data storage.

type General 

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

General represents a matrix using the conventional storage scheme.

func (General) From 

func (t General) From(a GeneralCols)

From fills the receiver with elements from a. The receiver must have the same dimensions as a and have adequate backing data storage.

type GeneralCols 

type GeneralCols General

GeneralCols represents a matrix using the conventional column-major storage scheme.

func (GeneralCols) From 

func (t GeneralCols) From(a General)

From fills the receiver with elements from a. The receiver must have the same dimensions as a and have adequate backing data storage.

type Hermitian 

type Hermitian Symmetric

Hermitian represents an Hermitian matrix using the conventional storage scheme.

func (Hermitian) From 

func (t Hermitian) From(a HermitianCols)

From fills the receiver with elements from a. The receiver must have the same dimensions and uplo as a and have adequate backing data storage.

type HermitianBand 

type HermitianBand SymmetricBand

HermitianBand represents an Hermitian matrix using the band storage scheme.

func (HermitianBand) From 

func (t HermitianBand) From(a HermitianBandCols)

From fills the receiver with elements from a. The receiver must have the same dimensions, bandwidth and uplo as a and have adequate backing data storage.

type HermitianBandCols 

type HermitianBandCols HermitianBand

HermitianBandCols represents an Hermitian matrix using the band column-major storage scheme.

func (HermitianBandCols) From 

func (t HermitianBandCols) From(a HermitianBand)

From fills the receiver with elements from a. The receiver must have the same dimensions, bandwidth and uplo as a and have adequate backing data storage.

type HermitianCols 

type HermitianCols Hermitian

HermitianCols represents a matrix using the conventional column-major storage scheme.

func (HermitianCols) From 

func (t HermitianCols) From(a Hermitian)

From fills the receiver with elements from a. The receiver must have the same dimensions and uplo as a and have adequate backing data storage.

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.

func (Symmetric) From 

func (t Symmetric) From(a SymmetricCols)

From fills the receiver with elements from a. The receiver must have the same dimensions and uplo as a and have adequate backing data storage.

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.

func (SymmetricBand) From 

func (t SymmetricBand) From(a SymmetricBandCols)

From fills the receiver with elements from a. The receiver must have the same dimensions, bandwidth and uplo as a and have adequate backing data storage.

type SymmetricBandCols 

type SymmetricBandCols SymmetricBand

SymmetricBandCols represents a symmetric matrix using the band column-major storage scheme.

func (SymmetricBandCols) From 

func (t SymmetricBandCols) From(a SymmetricBand)

From fills the receiver with elements from a. The receiver must have the same dimensions, bandwidth and uplo as a and have adequate backing data storage.

type SymmetricCols 

type SymmetricCols Symmetric

SymmetricCols represents a matrix using the conventional column-major storage scheme.

func (SymmetricCols) From 

func (t SymmetricCols) From(a Symmetric)

From fills the receiver with elements from a. The receiver must have the same dimensions and uplo as a and have adequate backing data storage.

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.

func (Triangular) From 

func (t Triangular) From(a TriangularCols)

From fills the receiver with elements from a. The receiver must have the same dimensions, uplo and diag as a and have adequate backing data storage.

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.

func (TriangularBand) From 

func (t TriangularBand) From(a TriangularBandCols)

From fills the receiver with elements from a. The receiver must have the same dimensions, bandwidth and uplo as a and have adequate backing data storage.

type TriangularBandCols 

type TriangularBandCols TriangularBand

TriangularBandCols represents a triangular matrix using the band column-major storage scheme.

func (TriangularBandCols) From 

func (t TriangularBandCols) From(a TriangularBand)

From fills the receiver with elements from a. The receiver must have the same dimensions, bandwidth and uplo as a and have adequate backing data storage.

type TriangularCols 

type TriangularCols Triangular

TriangularCols represents a matrix using the conventional column-major storage scheme.

func (TriangularCols) From 

func (t TriangularCols) From(a Triangular)

From fills the receiver with elements from a. The receiver must have the same dimensions, uplo and diag as a and have adequate backing data storage.

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 {
	N    int
	Inc  int
	Data []complex128
}

Vector represents a vector with an associated element increment.

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