gonum: gonum.org/v1/gonum/blas/blas64 Index | Files

package blas64

import "gonum.org/v1/gonum/blas/blas64"

Package blas64 provides a simple interface to the float64 BLAS API.

Index

Package Files

blas64.go conv.go conv_symmetric.go doc.go

func Asum Uses

❖
func Asum(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 Uses

❖
func Axpy(alpha float64, x, y Vector)

Axpy adds x scaled by alpha to y: 

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

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

func Copy Uses

❖
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 Dot Uses

❖
func Dot(x, y Vector) float64

Dot computes the dot product of the two vectors: 

\sum_i x[i]*y[i].

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

func Gbmv Uses

❖
func Gbmv(t blas.Transpose, alpha float64, a Band, x Vector, beta float64, y Vector)

Gbmv computes 

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

❖
func Gemm(tA, tB blas.Transpose, alpha float64, a, b General, beta float64, 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.

func Gemv Uses

❖
func Gemv(t blas.Transpose, alpha float64, a General, x Vector, beta float64, y Vector)

Gemv computes 

y = alpha * A * x + beta * y   if t == blas.NoTrans,
y = alpha * Aᵀ * 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 Ger Uses

❖
func Ger(alpha float64, x, y Vector, a General)

Ger 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 Iamax Uses

❖
func Iamax(x Vector) int

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 Implementation Uses

❖
func Implementation() blas.Float64

Implementation returns the current BLAS float64 implementation.

Implementation allows direct calls to the current the BLAS float64 implementation giving finer control of parameters.

func Nrm2 Uses

❖
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 Rot Uses

❖
func Rot(x, y Vector, c, s float64)

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 Rotg Uses

❖
func Rotg(a, b float64) (c, s, r, z float64)

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 Rotm Uses

❖
func Rotm(x, y Vector, p blas.DrotmParams)

Rotm applies the modified Givens rotation to n points represented by the vectors x and y.

func Rotmg Uses

❖
func Rotmg(d1, d2, b1, b2 float64) (p blas.DrotmParams, rd1, rd2, rb1 float64)

Rotmg computes the modified Givens rotation. See http://www.netlib.org/lapack/explore-html/df/deb/drotmg_8f.html for more details.

func Sbmv Uses

❖
func Sbmv(alpha float64, a SymmetricBand, x Vector, beta float64, y Vector)

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 Scal Uses

❖
func Scal(alpha float64, x Vector)

Scal scales the vector x by alpha: 

x[i] *= alpha for all i.

Scal will panic if the vector increment is negative.

func Spmv Uses

❖
func Spmv(alpha float64, a SymmetricPacked, x Vector, beta float64, y Vector)

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 Spr Uses

❖
func Spr(alpha float64, x Vector, a SymmetricPacked)

Spr performs the rank-1 update 

A += alpha * x * xᵀ,

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

func Spr2 Uses

❖
func Spr2(alpha float64, x, y Vector, a SymmetricPacked)

Spr2 performs a rank-2 update 

A += alpha * x * yᵀ + alpha * y * xᵀ,

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

func Swap Uses

❖
func Swap(x, y Vector)

Swap exchanges the elements of the 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 Uses

❖
func Symm(s blas.Side, alpha float64, a Symmetric, b General, beta float64, 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 is a scalar.

func Symv Uses

❖
func Symv(alpha float64, a Symmetric, x Vector, beta float64, y Vector)

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 Syr Uses

❖
func Syr(alpha float64, x Vector, a Symmetric)

Syr performs a rank-1 update 

A += alpha * x * xᵀ,

where A is an n×n symmetric matrix, x is a vector, and alpha is a scalar.

func Syr2 Uses

❖
func Syr2(alpha float64, x, y Vector, a Symmetric)

Syr2 performs a rank-2 update 

A += alpha * x * yᵀ + alpha * y * xᵀ,

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

func Syr2k Uses

❖
func Syr2k(t blas.Transpose, alpha float64, a, b General, beta float64, 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 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 Syrk Uses

❖
func Syrk(t blas.Transpose, alpha float64, a General, beta float64, 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 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 Tbmv Uses

❖
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 or blas.ConjTrans,

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

func Tbsv Uses

❖
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 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 Tpmv Uses

❖
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 or blas.ConjTrans,

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

func Tpsv Uses

❖
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 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 Trmm Uses

❖
func Trmm(s blas.Side, tA blas.Transpose, alpha float64, 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 or 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 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 Trmv Uses

❖
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 or blas.ConjTrans,

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

func Trsm Uses

❖
func Trsm(s blas.Side, tA blas.Transpose, alpha float64, 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 or 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 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 Trsv Uses

❖
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 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 Use Uses

❖
func Use(b blas.Float64)

Use sets the BLAS float64 implementation to be used by subsequent BLAS calls. The default implementation is gonum.org/v1/gonum/blas/gonum.Implementation.

type Band Uses

❖
type Band struct {
    Rows, Cols int
    KL, KU     int
    Data       []float64
    Stride     int
}

Band represents a band matrix using the band storage scheme.

func (Band) From Uses

❖
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 Uses

❖
type BandCols Band

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

func (BandCols) From Uses

❖
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 Uses

❖
type General struct {
    Rows, Cols int
    Data       []float64
    Stride     int
}

General represents a matrix using the conventional storage scheme.

func (General) From Uses

❖
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 Uses

❖
type GeneralCols General

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

func (GeneralCols) From Uses

❖
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 Symmetric Uses

❖
type Symmetric struct {
    Uplo   blas.Uplo
    N      int
    Data   []float64
    Stride int
}

Symmetric represents a symmetric matrix using the conventional storage scheme.

func (Symmetric) From Uses

❖
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 Uses

❖
type SymmetricBand struct {
    Uplo   blas.Uplo
    N, K   int
    Data   []float64
    Stride int
}

SymmetricBand represents a symmetric matrix using the band storage scheme.

func (SymmetricBand) From Uses

❖
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 Uses

❖
type SymmetricBandCols SymmetricBand

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

func (SymmetricBandCols) From Uses

❖
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 Uses

❖
type SymmetricCols Symmetric

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

func (SymmetricCols) From Uses

❖
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 Uses

❖
type SymmetricPacked struct {
    Uplo blas.Uplo
    N    int
    Data []float64
}

SymmetricPacked represents a symmetric matrix using the packed storage scheme.

type Triangular Uses

❖
type Triangular struct {
    Uplo   blas.Uplo
    Diag   blas.Diag
    N      int
    Data   []float64
    Stride int
}

Triangular represents a triangular matrix using the conventional storage scheme.

func (Triangular) From Uses

❖
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 Uses

❖
type TriangularBand struct {
    Uplo   blas.Uplo
    Diag   blas.Diag
    N, K   int
    Data   []float64
    Stride int
}

TriangularBand represents a triangular matrix using the band storage scheme.

func (TriangularBand) From Uses

❖
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 Uses

❖
type TriangularBandCols TriangularBand

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

func (TriangularBandCols) From Uses

❖
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 Uses

❖
type TriangularCols Triangular

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

func (TriangularCols) From Uses

❖
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 Uses

❖
type TriangularPacked struct {
    Uplo blas.Uplo
    Diag blas.Diag
    N    int
    Data []float64
}

TriangularPacked represents a triangular matrix using the packed storage scheme.

type Vector Uses

❖
type Vector struct {
    N    int
    Data []float64
    Inc  int
}

Vector represents a vector with an associated element increment.

Package blas64 imports 2 packages (graph) and is imported by 20 packages. Updated 2021-01-02. Refresh now. Tools for package owners.