## Documentation ¶

### Overview ¶

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

### 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.