blas64

package
Version: v0.9.1 Latest Latest

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Published: Mar 29, 2021 License: BSD-3-Clause

Documentation ¶

Overview ¶

Package blas64 provides a simple interface to the float64 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 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(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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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 ¶

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.

Types ¶

type Band ¶

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 ¶

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
Data       []float64
Stride     int
}

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 Symmetric ¶

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 ¶

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 {
Uplo   blas.Uplo
N, K   int
Data   []float64
Stride int
}

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 {
Uplo blas.Uplo
N    int
Data []float64
}

SymmetricPacked represents a symmetric matrix using the packed storage scheme.

type Triangular ¶

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 ¶

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 {
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 ¶

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 {
Uplo blas.Uplo
Diag blas.Diag
N    int
Data []float64
}

TriangularPacked represents a triangular matrix using the packed storage scheme.

type Vector ¶

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

Vector represents a vector with an associated element increment.