blas

package
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 Go to latest Published: Sep 17, 2024 License: LGPL-3.0, LGPL-3.0 Imports: 7 Imported by: 0

Documentation

Overview

Interface to the double-precision real and complex BLAS library.

This package is implementation of CVXOPT Python blas interface in GO.

Double and complex matrices and vectors are stored in column major matrices using the conventional BLAS storage schemes, with the matrix buffers interpreted as one-dimensional arrays.

For each matrix argument X, an additional integer argument offsetX specifies the start of the array, i.e., the pointer of X[offsetX:] is passed to the BLAS function. The other arguments (dimensions and options) have the same meaning as in the BLAS definition. Default values of the dimension arguments are derived from the matrix sizes.

Index

Constants

This section is empty.

Variables

This section is empty.

Functions

func Asum 

func Asum(X matrix.Matrix, opts ...linalg.Option) (v matrix.Scalar)

Returns ||Re x||_1 + ||Im x||_1.

ARGUMENTS 

X       float or complex matrix

OPTIONS 

n       integer.  If n<0, the default value of n is used.
        The default value is equal to n = 1+(len(x)-offset-1)/inc or 0 if
        len(x) > offset+1
inc     positive integer
offset  nonnegative integer

func AsumComplex 

func AsumComplex(X *matrix.ComplexMatrix, opts ...linalg.Option) (v float64, err error)

See function Asum.

func AsumFloat 

func AsumFloat(X *matrix.FloatMatrix, opts ...linalg.Option) (v float64)

See function Asum.

func Axpy 

func Axpy(X, Y matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error)

Constant times a vector plus a vector (Y := alpha*X+Y).

ARGUMENTS 

X         float or complex matrix
Y         float or complex matrix.  Must have the same type as X.
alpha     number (float or complex singleton matrix).  Complex alpha is only
          allowed if x is complex.

OPTIONS 

n         integer.  If n<0, the default value of n is used.
          The default value is equal to 1+(len(x)-offsetx-1)/incx
          or 0 if  len(x) >= offsetx+1
incx      nonzero integer
incy      nonzero integer
offsetx   nonnegative integer
offsety   nonnegative integer;

func AxpyFloat 

func AxpyFloat(X, Y *matrix.FloatMatrix, alpha float64, opts ...linalg.Option) (err error)

See function Axpy.

func Copy 

func Copy(X, Y matrix.Matrix, opts ...linalg.Option) (err error)

Copies a vector X to a vector Y (Y := X).

ARGUMENTS 

X         float or complex matrix
Y         float or complex matrix.  Must have the same type as X.

OPTIONS 

n         integer.  If n<0, the default value of n is used.
          The default value is given by 1+(len(x)-offsetx-1)/incx or 0
          if len(x) > offsetx+1
incx      nonzero integer
incy      nonzero integer
offsetx   nonnegative integer
offsety   nonnegative integer;

func CopyFloat 

func CopyFloat(X, Y *matrix.FloatMatrix, opts ...linalg.Option) (err error)

See function Copy.

func Dot 

func Dot(X, Y matrix.Matrix, opts ...linalg.Option) (v matrix.Scalar)

Returns Y = X^H*Y for real or complex X, Y.

ARGUMENTS 

X         float or complex matrix
Y         float or complex matrix.  Must have the same type as X.

OPTIONS 

n         integer.  If n<0, the default value of n is used.
          The default value is equal to nx = 1+(len(x)-offsetx-1)/incx or 0 if
          len(x) > offsetx+1.  If the default value is used, it must be equal to
          ny = 1+(len(y)-offsetx-1)/|incy| or 0 if len(y) > offsety+1
incx      nonzero integer [default=1]
incy      nonzero integer [default=1]
offsetx   nonnegative integer [default=0]
offsety   nonnegative integer [default=0]

func DotFloat 

func DotFloat(X, Y *matrix.FloatMatrix, opts ...linalg.Option) (v float64)

See functin Dot.

func DotcComplex 

func DotcComplex(X, Y *matrix.ComplexMatrix, opts ...linalg.Option) (v complex128, err error)

See function Dotc.

func Dotu 

func Dotu(X, Y matrix.Matrix, opts ...linalg.Option) (v matrix.Scalar)

Returns Y = X^T*Y for real or complex X, Y.

ARGUMENTS 

X         float or complex matrix
Y         float or complex matrix.  Must have the same type as X.

OPTIONS 

n         integer.  If n<0, the default value of n is used.
          The default value is equal to nx = 1+(len(x)-offsetx-1)/incx or 0 if
          len(x) > offsetx+1.  If the default value is used, it must be equal to
          ny = 1+(len(y)-offsetx-1)/|incy| or 0 if len(y) > offsety+1
incx      nonzero integer, [default=1]
incy      nonzero integer, [default=1]
offsetx   nonnegative integer, [default=0]
offsety   nonnegative integer, [default=0]

func DotuComplex 

func DotuComplex(X, Y *matrix.ComplexMatrix, opts ...linalg.Option) (v complex128, err error)

See function Dot.

func Gbmv 

func Gbmv(A, X, Y matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error)

Matrix-vector product with a general banded matrix. (L2)

Computes 

Y := alpha*A*X + beta*Y,   if trans = PNoTrans
Y := alpha*A^T*X + beta*Y, if trans = PTrans
Y := beta*y,               if n=0, m>0, and trans = PNoTrans
Y := beta*y,               if n>0, m=0, and trans = PTrans

The matrix A is m by n with upper bandwidth ku and lower bandwidth kl. Returns immediately if n=0 and trans is 'Trans', or if m=0 and trans is 'N'.

ARGUMENTS 

X         float n*1 matrix.
Y         float m*1 matrix
A         float m*n matrix.
alpha     number (float).
beta      number (float).

OPTIONS 

trans     NoTrans or Trans
m         nonnegative integer, default A.Rows()
kl        nonnegative integer
n         nonnegative integer.  If negative, the default value is used.
ku        nonnegative integer.  If negative, the default value is used.
ldA       positive integer.  ldA >= kl+ku+1. If zero, the default value is used.
incx      nonzero integer, default =1
incy      nonzero integer, default =1
offsetA   nonnegative integer, default =0
offsetx   nonnegative integer, default =0
offsety   nonnegative integer, default =0

func GbmvFloat 

func GbmvFloat(A, X, Y *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error)

See function Gbmv.

func Gemm 

func Gemm(A, B, C matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error)

General matrix-matrix product. (L3)

PURPOSE Computes 

C := alpha*A*B + beta*C     if transA = PNoTrans   and transB = PNoTrans.
C := alpha*A^T*B + beta*C   if transA = PTrans     and transB = PNoTrans.
C := alpha*A^H*B + beta*C   if transA = PConjTrans and transB = PNoTrans.
C := alpha*A*B^T + beta*C   if transA = PNoTrans   and transB = PTrans.
C := alpha*A^T*B^T + beta*C if transA = PTrans     and transB = PTrans.
C := alpha*A^H*B^T + beta*C if transA = PConjTrans and transB = PTrans.
C := alpha*A*B^H + beta*C   if transA = PNoTrans   and transB = PConjTrans.
C := alpha*A^T*B^H + beta*C if transA = PTrans     and transB = PConjTrans.
C := alpha*A^H*B^H + beta*C if transA = PConjTrans and transB = PConjTrans.

The number of rows of the matrix product is m. The number of columns is n. The inner dimension is k. If k=0, this reduces to C := beta*C.

ARGUMENTS 

A         float or complex matrix, m*k
B         float or complex matrix, k*n
C         float or complex matrix, m*n
alpha     number (float or complex singleton matrix)
beta      number (float or complex singleton matrix)

OPTIONS 

transA    PNoTrans, PTrans or PConjTrans
transB    PNoTrans, PTrans or PConjTrans
m         integer.  If negative, the default value is used. The default value is
          m = A.Rows of if transA != PNoTrans m = A.Cols.
n         integer.  If negative, the default value is used. The default value is
          n = (transB == PNoTrans) ? B.Cols : B.Rows.
k         integer.  If negative, the default value is used. The default value is
          k=A.Cols or if transA != PNoTrans) k = A.Rows, transA=PNoTrans.
          If the default value is used it should also be equal to
          (transB == PNoTrans) ? B.Rows : B.Cols.
ldA       nonnegative integer.  ldA >= max(1,m) of if transA != NoTrans max(1,k).
          If zero, the default value is used.
ldB       nonnegative integer.  ldB >= max(1,k) or if transB != NoTrans max(1,n).
          If zero, the default value is used.
ldC       nonnegative integer.  ldC >= max(1,m).
          If zero, the default value is used.
offsetA   nonnegative integer
offsetB   nonnegative integer
offsetC   nonnegative integer;

func GemmFloat 

func GemmFloat(A, B, C *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error)

See function Gemm.

func Gemv 

func Gemv(A, X, Y matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error)

General matrix-vector product. (L2)

Computes: 

Y := alpha*A*X + beta*Y,   if trans is NoTrans
Y := alpha*A^T*X + beta*Y, if trans is Trans
Y := beta*Y,               if n=0, m>0 and trans is NoTrans
Y := beta*Y,               if n>0, m=0 and trans is Trans

The matrix A is m by n. Returns immediately if n=0 and trans is PTrans, or if m=0 and trans is PNoTrans.

ARGUMENTS 

A         float or complex m*n matrix
X         float or complex n*1 matrix.
Y         float or complex m*1 matrix.
alpha     number (float or complex singleton matrix)
beta      number (float or complex singleton matrix)

OPTIONS 

trans     PNoTrans, PTrans, PConjTrans
m         integer.  If negative, the default value is used.
n         integer.  If negative, the default value is used.
ldA       nonnegative integer.  ldA >= max(1,m). If zero, the default value is used.
incx      nonzero integer
incy      nonzero integer
offsetA   nonnegative integer
offsetx   nonnegative integer
offsety   nonnegative integer

func GemvFloat 

func GemvFloat(A, X, Y *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error)

See function Gemv.

func Ger 

func Ger(X, Y, A matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error)

General rank-1 update. (L2)

Ger(X, Y, A, alpha=1.0, m=A.Rows, n=A.Cols, incx=1, incy=1, ldA=max(1,A.Rows), offsetx=0, offsety=0, offsetA=0)

COMPUTES 

A := A + alpha*X*Y^H with A m*n, real or complex.

ARGUMENTS 

X         float or complex matrix.
Y         float or complex matrix. Must have the same type as X.
A         float or complex matrix. Must have the same type as X.
alpha     number (float or complex singleton matrix).

OPTIONS 

m         integer.  If negative, the default value is used.
n         integer.  If negative, the default value is used.
incx      nonzero integer
incy      nonzero integer
ldA       nonnegative integer.  ldA >= max(1,m).
          If zero, the default value is used.
offsetx   nonnegative integer
offsety   nonnegative integer
offsetA   nonnegative integer;

func GerFloat 

func GerFloat(X, Y, A *matrix.FloatMatrix, alpha float64, opts ...linalg.Option) (err error)

See function Ger.

func Geru 

func Geru(X, Y, A matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error)

General rank-1 update. (L2)

Geru(X, Y, A, alpha=1.0, m=A.Rows, n=A.Cols, incx=1, incy=1, ldA=max(1,A.Rows), offsetx=0, offsety=0, offsetA=0)

COMPUTES 

A := A + alpha*X*Y^T with A m*n, real or complex.

ARGUMENTS 

X         float or complex matrix.
Y         float or complex matrix. Must have the same type as X.
A         float or complex matrix. Must have the same type as X.
alpha     number (float or complex singleton matrix).

OPTIONS 

m         integer.  If negative, the default value is used.
n         integer.  If negative, the default value is used.
incx      nonzero integer
incy      nonzero integer
ldA       nonnegative integer.  ldA >= max(1,m).
          If zero, the default value is used.
offsetx   nonnegative integer
offsety   nonnegative integer
offsetA   nonnegative integer;

func Hbmv 

func Hbmv(A, X, Y matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error)

Matrix-vector product with a real symmetric or complex hermitian band matrix.

Computes with A real symmetric and banded of order n and with bandwidth k. 

Y := alpha*A*X + beta*Y

ARGUMENTS 

A         float or complex n*n matrix
X         float or complex n*1 matrix
Y         float or complex n*1 matrix
alpha     number (float or complex singleton matrix)
beta      number (float or complex singleton matrix)

OPTIONS 

uplo      PLower or PUpper
n         integer.  If negative, the default value is used.
k         integer.  If negative, the default value is used.
          The default value is k = max(0,A.Rows()-1).
ldA       nonnegative integer.  ldA >= k+1.
          If zero, the default vaule is used.
incx      nonzero integer
incy      nonzero integer
offsetA   nonnegative integer
offsetx   nonnegative integer
offsety   nonnegative integer

func Hemm 

func Hemm(A, B, C matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error)

func Hemv 

func Hemv(A, X, Y matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error)

Matrix-vector product with a real symmetric or complex Hermitian matrix. (L2)

Hemv(A, X, Y, alpha=1.0, beta=0.0, uplo=PLower, n=A.Rows, ldA=max(1,A.Rows), incx=1, incy=1, offsetA=0, offsetx=0, offsety=0)

Computes 

Y := alpha*A*X + beta*Y  with A real symmetric of order n.

ARGUMENTS 

A         float or complex n*n matrix
X         float or complex n*1 matrix
Y         float or complex n*1 matrix
alpha     number (float or complex singleton matrix)
beta      number (float or complex singleton matrix)

OPTIONS 

uplo      PLower or PUpper
n         integer.  If negative, the default value is used.
          If the default value is used, we require that  A.Rows()=A.Cols().
ldA       nonnegative integer.  ldA >= max(1,n). If zero, the default value is used.
incx      nonzero integer
incy      nonzero integer
offsetA   nonnegative integer
offsetx   nonnegative integer
offsety   nonnegative integer

func Her 

func Her(X, A matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error)

Symmetric rank-1 update. (L2)

Her(X, A, alpha, uplo=PLowoer, n=A.Rows, incx=1, ldA=max(1,A.Rows), offsetx=0, offsetA=0)

COMPUTES 

A := A + alpha*X*X^H

A real symmetric or complex hermitian matrix of order n.

ARGUMENTS 

X         float or complex matrix.
A         float or complex matrix.
alpha     number (float or complex singleton matrix)

OPTIONS: 

uplo      PLower or PUpper
n         integer.  If negative, the default value is used.
incx      nonzero integer
ldA       nonnegative integer.  ldA >= max(1,n).
          If zero, the default value is used.
offsetx   nonnegative integer
offsetA   nonnegative integer;

func Her2 

func Her2(X, Y, A matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error)

Symmetric rank-2 update. her2(x, y, A, uplo='L', alpha=1.0, n=A.size[0], incx=1, incy=1, 

ldA=max(1,A.size[0]), offsetx=0, offsety=0, offsetA=0)

PURPOSE Computes A := A + alpha*(x*y^T + y*x^T) with A real symmetric or complex hermitian matix of order n.

ARGUMENTS x float or complex matrix y float or complex matrix A float or complex matrix alpha float or complex singleton value

OPTIONS: uplo 'L' or 'U' n integer. If negative, the default value is used. incx nonzero integer incy nonzero integer ldA nonnegative integer. ldA >= max(1,n). 

If zero the default value is used.

offsetx nonnegative integer offsety nonnegative integer offsetA nonnegative integer;

func Her2k 

func Her2k(A, B, C matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error)

Rank-2k update of symmetric matrix. (L3)

Her2k(A, B, C, alpha, beta, uplo=PLower, trans=PNoTrans, n=-1, k=-1, ldA=max(1,A.Rows), ldB=max(1,B.Rows), ldC=max(1,C.Rows), offsetA=0, offsetB=0, offsetC=0)

PURPOSE 

C := alpha*(A*B^T + B*A^T) + beta*C, if trans is PNoTrans
C := alpha*(A^T*B + B^T*A) + beta*C, if trans is PTrans

C is symmetric (real or complex) of order n. The inner dimension of the matrix product is k. If k=0 this is interpreted as C := beta*C.

ARGUMENTS 

A         float or complex matrix
B         float or complex matrix.  Must have the same type as A.
C         float or complex matrix.  Must have the same type as A.
alpha     number (float or complex).  Complex alpha is only
          allowed if A is complex.
beta      number (float or complex).  Complex beta is only
          allowed if A is complex.

OPTIONS 

uplo      PLower or PUpper
trans     PNoTrans, PTrans or PConjTrans (PConjTrans is only allowed when in the real
          case and means the same as PTrans)
n         integer.  If negative, the default value is used.
          The default value is n = A.Rows or trans != PNoTrans n = A.Cols
          If the default value is used, it should be equal to B.Rows or
          if trans != PNoTrans then B.Cols.
k         integer.  If negative, the default value is used.
          The default value is  k = A.Cols or if trans != PNoTrans then k = A.Rows
          If the default value is used, it should be equal to B.Cols or if
          trans != PNoTrans then equal to B.Rows.
ldA       nonnegative integer.  ldA >= max(1,n) or if trans != PNoTrans ldA >= max(1,k).
          If zero, the default value is used.
ldB       nonnegative integer.
          ldB >= max(1,n) or if trans != PNoTrans then ldB >= max(1,k).
          If zero, the default value is used.
ldC       nonnegative integer.  ldC >= max(1,n).
          If zero, the default value is used.
offsetA   nonnegative integer
offsetB   nonnegative integer
offsetC   nonnegative integer

func Herk 

func Herk(A, C matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error)

Rank-k update of symmetric matrix. (L3)

Herk(A, C, alpha, beta, uplo=PLower, trans=PNoTrans, n=-1, k=-1, ldA=max(1,A.Rows), ldC=max(1,C.Rows), offsetA=0, offsetB=0)

Computes 

C := alpha*A*A^T + beta*C, if trans is PNoTrans
C := alpha*A^T*A + beta*C, if trans is PTrans

C is symmetric (real or complex) of order n. The inner dimension of the matrix product is k. If k=0 this is interpreted as C := beta*C.

ARGUMENTS 

A         float or complex matrix.
C         float or complex matrix.  Must have the same type as A.
alpha     number (float or complex singleton matrix).  Complex alpha is only
          allowed if A is complex.
beta      number (float or complex singleton matrix).  Complex beta is only
          allowed if A is complex.

OPTIONS 

uplo      PLower or PUpper
trans     PNoTrans or PTrans
n         integer.  If negative, the default value is used.
          The default value is n = A.Rows or if trans == PNoTrans n = A.Cols.
k         integer.  If negative, the default value is used.
          The default value is k =  A.Cols, or if trans == PNoTrans k = A.Rows.
ldA       nonnegative integer.
          ldA >= max(1,n) or if trans != PNoTrans ldA >= max(1,k).
          If zero, the default value is used.
ldC       nonnegative integer.  ldC >= max(1,n).
          If zero, the default value is used.
offsetA   nonnegative integer
offsetC   nonnegative integer;

func Nrm2 

func Nrm2(X matrix.Matrix, opts ...linalg.Option) (v matrix.Scalar)

Returns the Euclidean norm of a vector (returns ||x||_2).

ARGUMENTS 

X         float or complex matrix

OPTIONS 

n         integer.  If n<0, the default value of n is used.
          The default value is equal to 1+(len(x)-offsetx-1)/incx or 0
          if len(x) > offsetx+1
inc       positive integer
offset    nonnegative integer

func Nrm2Complex 

func Nrm2Complex(X *matrix.ComplexMatrix, opts ...linalg.Option) (v float64, err error)

See function Nrm2.

func Nrm2Float 

func Nrm2Float(X *matrix.FloatMatrix, opts ...linalg.Option) (v float64)

See function Nrm2.

func PanicOnError 

func PanicOnError(flag bool)

func Sbmv 

func Sbmv(A, X, Y matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error)

Matrix-vector product with a real symmetric band matrix. (L2)

Sbmv(A, X, Y, alpha=1.0, beta=0.0, uplo=PLower, n=A.Cols, k=-1, ldA=A.Rows, incx=1, incy=1, offsetA=0, offsetx=0, offsety=0)

Computes with A real symmetric and banded of order n and with bandwidth k. 

Y := alpha*A*X + beta*Y

ARGUMENTS 

A         float or complex n*n matrix
X         float or complex n*1 matrix
Y         float or complex n*1 matrix
alpha     number (float or complex singleton matrix)
beta      number (float or complex singleton matrix)

OPTIONS 

  uplo      PLower or PUpper
  n         integer.  If negative, the default value is used.
  k         integer.  If negative, the default value is used. The default value is
		     k = max(0,A.Rows()-1).
  ldA       nonnegative integer.  ldA >= k+1. If zero, the default vaule is used.
  incx      nonzero integer
  incy      nonzero integer
  offsetA   nonnegative integer
  offsetx   nonnegative integer
  offsety   nonnegative integer

func SbmvFloat 

func SbmvFloat(A, X, Y *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error)

See function Sbmv.

func Scal 

func Scal(X matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error)

Scales a vector by a constant (X := alpha*X).

ARGUMENTS 

X         float or complex matrix
alpha     number (float or complex singleton matrix).  Complex alpha is only
          allowed if X is complex.

OPTIONS 

n         integer.  If n<0, the default value of n is used.
          The default value is equal to 1+(len(x)-offset-1)/inc or 0
          if len(x) > offset+1.
inc       positive integer, default = 1
offset    nonnegative integer, default = 0

func ScalFloat 

func ScalFloat(X *matrix.FloatMatrix, alpha float64, opts ...linalg.Option) (err error)

See function Scal.

func Swap 

func Swap(X, Y matrix.Matrix, opts ...linalg.Option) (err error)

Interchanges two vectors (X <-> Y).

ARGUMENTS 

X         float or complex matrix
Y         float or complex matrix.  Must have the same type as X.

OPTIONS 

n         integer.  If n<0, the default value of n is used.
          The default value is equal to 1+(len(x)-offsetx-1)/abs(incx) or
          0 if len(x) > offsetx+1. Also if the default value is used,
          it must be equal to 1+(len(y)-offsetx-1)/abs(incy) or 0 if
          len(y) > offsety + 1.
incx      nonzero integer
incy      nonzero integer
offsetx   nonnegative integer
offsety   nonnegative integer;

func SwapFloat 

func SwapFloat(X, Y *matrix.FloatMatrix, opts ...linalg.Option) (err error)

See function Swap.

func Symm 

func Symm(A, B, C matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error)
 Matrix-matrix product where one matrix is symmetric. (L3)

 Computes
  C := alpha*A*B + beta*C, if side is PLeft
  C := alpha*B*A + beta*C, if side is PRight

 C is m by n and A is real symmetric.

 ARGUMENTS
  A         float or complex matrix
  B         float or complex matrix.
  C         float m*n matrix.
  alpha     number (float).
  beta      number (float).

 OPTIONS
  side      PLeft or PRight'
  uplo      PLower or PUpper
  m         integer.  If negative, the default value is used.
            If the default value is used and side = PLeft, then m
            must be equal to A.Rows and A.Cols.
  n         integer.  If negative, the default value is used.
            If the default value is used and side = PRight, then
            must be equal to A.Rows and A.Cols.
  ldA       nonnegative integer.
            ldA >= max(1, m) or if side == PRight ldA >= max(1, n).
		    If zero, the default value is used.
  ldB       nonnegative integer.
            ldB >= max(1,n) or if side == PRight ldB >= max(1, m).
            If zero, the default value is used.
  ldC       nonnegative integer.  ldC >= max(1,m). If zero, the default value is used.
  offsetA   nonnegative integer
  offsetB   nonnegative integer
  offsetC   nonnegative integer

func SymmFloat 

func SymmFloat(A, B, C *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error)

See function Symm.

func Symv 

func Symv(A, X, Y matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error)

Matrix-vector product with a real symmetric matrix. (L2)

Computes with A real symmetric of order n. 

Y := alpha*A*X + beta*Y

ARGUMENTS 

A         float or complex n*n matrix
X         float or complex n*1 matrix
Y         float or complex n*1 matrix
alpha     number (float or complex singleton matrix)
beta      number (float or complex singleton matrix)

OPTIONS 

uplo      PLower or PUpper
n         integer.  If negative, the default value is used.
          If the default value is used, we require that A.Rows()=A.Cols().
ldA       nonnegative integer.  ldA >= max(1,n). If zero, the default value is used.
incx      nonzero integer
incy      nonzero integer
offsetA   nonnegative integer
offsetx   nonnegative integer
offsety   nonnegative integer

func SymvFloat 

func SymvFloat(A, X, Y *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error)

See function Symv.

func Syr 

func Syr(X, A matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error)

Symmetric rank-1 update. (L2)

syr(X, A, alpha=1.0, uplo=PLower, n=A.Rows, incx=1, ldA=max(1,A.Rows), offsetx=0, offsetA=0)

COMPUTES 

A := A + alpha*X*X^T

A real symmetric matrix of order n.

ARGUMENTS 

X         float or complex matrix.
A         float or complex matrix.
alpha     real number

OPTIONS: 

uplo      PLower or PUpper
n         integer.  If negative, the default value is used.
incx      nonzero integer
ldA       nonnegative integer.  ldA >= max(1,n).
          If zero, the default value is used.
offsetx   nonnegative integer
offsetA   nonnegative integer;

func Syr2 

func Syr2(X, Y, A matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error)

Symmetric rank-2 update. syr2(x, y, A, uplo='L', alpha=1.0, n=A.size[0], incx=1, incy=1, 

ldA=max(1,A.size[0]), offsetx=0, offsety=0, offsetA=0)

PURPOSE Computes A := A + alpha*(x*y^T + y*x^T) with A real symmetric matrix of order n. ARGUMENTS x float matrix y float matrix A float matrix alpha real number (int or float)

OPTIONS uplo 'L' or 'U' n integer. If negative, the default value is used. incx nonzero integer incy nonzero integer ldA nonnegative integer. ldA >= max(1,n). 

If zero the default value is used.

offsetx nonnegative integer offsety nonnegative integer offsetA nonnegative integer;

func Syr2Float 

func Syr2Float(X, Y, A *matrix.FloatMatrix, alpha float64, opts ...linalg.Option) (err error)

See function Syr2.

func Syr2k 

func Syr2k(A, B, C matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error)

Rank-2k update of symmetric matrix. (L3)

syr2k(A, B, C, alpha, beta, uplo=PLower, trans=PNoTrnas, n=-1, k=-1, ldA=max(1,A.Rows), ldB=max(1,B.Rows), ldC=max(1,C.Rows), offsetA=0, offsetB=0, offsetC=0)

PURPOSE 

C := alpha*(A*B^T + B*A^T) + beta*C, if trans is NoTrans
C := alpha*(A^T*B + B^T*A) + beta*C, if trans is Trans

C is symmetric (real or complex) of order n. The inner dimension of the matrix product is k. If k=0 this is interpreted as C := beta*C.

ARGUMENTS 

A         float or complex matrix
B         float or complex matrix.  Must have the same type as A.
C         float or complex matrix.  Must have the same type as A.
alpha     number (int, float or complex).  Complex alpha is only
          allowed if A is complex.
beta      number (int, float or complex).  Complex beta is only
          allowed if A is complex.

OPTIONS 

uplo      PLower or PUpper
trans     PNoTrans, PTrans or PConjTrans (PConjTrans is only allowed when in the real
          case and means the same as PTrans)
n         integer.  If negative, the default value is used.
          The default value is n = A.Rows or trans != PNoTrans n = A.Cols
          If the default value is used, it should be equal to B.Rows or
          if trans != PNoTrans then B.Cols.
k         integer.  If negative, the default value is used.
          The default value is  k = A.Cols or if trans != PNoTrans then k = A.Rows
          If the default value is used, it should be equal to B.Cols or if
          trans != PNoTrans then equal to B.Rows.
ldA       nonnegative integer.  ldA >= max(1,n) or if trans != PNoTrans ldA >= max(1,k).
          If zero, the default value is used.
ldB       nonnegative integer.
          ldB >= max(1,n) or if trans != PNoTrans then ldB >= max(1,k).
          If zero, the default value is used.
ldC       nonnegative integer.  ldC >= max(1,n).
          If zero, the default value is used.
offsetA   nonnegative integer
offsetB   nonnegative integer
offsetC   nonnegative integer

func Syr2kFloat 

func Syr2kFloat(A, B, C *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error)

See function Syrk2.

func SyrFloat 

func SyrFloat(X, A *matrix.FloatMatrix, alpha float64, opts ...linalg.Option) (err error)

See function Syr.

func Syrk 

func Syrk(A, C matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error)

Rank-k update of symmetric matrix. (L3)

Syrk(A, C, alpha=1.0, beta=0.0, uplo=PLower, trans=PNoTrans, n=-1, k=-1, ldA=max(1,A.Rows), ldC=max(1,C.Rows), offsetA=0, offsetB=0)

PURPOSE 

C := alpha*A*A^T + beta*C, if trans is PNoTrans
C := alpha*A^T*A + beta*C, if trans is PTrans
C := alpha*A^H*A + beta*C, if trans is PConjTrans

C is symmetric (real or complex) of order n. The inner dimension of the matrix product is k. If k=0 this is interpreted as C := beta*C.

ARGUMENTS 

A         float or complex n*k matrix
C         float or complex n*n matrix.  Must have the same type as A.
alpha     number (float or complex singleton matrix).  Complex alpha is only
          allowed if A is complex.
beta      number (float or complex singleton matrix).  Complex beta is only
          allowed if A is complex.

OPTIONS 

uplo      PLower or PUpper
trans     PNoTrans, PTrans or PConjTrans
n         integer.  If negative, the default value is used.
          The default value is  n = A.Rows of if trans != PNoTrans) n = A.Cols.
k         integer.  If negative, the default value is used.
          The default value is k = A.Cols or if trans != PNoTrans k = A.Rows.
ldA       nonnegative integer. ldA >= max(1, n) or if trans != PNoTrans max(1, k).
          If zero, the default value [max(1, A.Rows)] is used.
ldC       nonnegative integer.  ldC >= max(1,n).  If zero, the default value is used.
offsetA   nonnegative integer
offsetC   nonnegative integer;

func SyrkFloat 

func SyrkFloat(A, C *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error)

See function Syrk.

func Tbmv 

func Tbmv(A, X matrix.Matrix, opts ...linalg.Option) (err error)

Matrix-vector product with a triangular band matrix. (L2)

Tbmv(A, x, uplo=PLower, trans=PNoTrans, diag=PNonUnit, n=A.Cols, k=max(0,A.Rows-1), ldA=A.size[0], incx=1, offsetA=0, offsetx=0)

COMPUTES 

X := A*X,   if trans is PNoTrans
X := A^T*X, if trans is PTrans
X := A^H*X, if trans is PConjTrans

A is banded triangular of order n and with bandwith k.

ARGUMENTS 

A         float or complex matrix
X         float or complex  matrix.  Must have the same type as A.

OPTIONS 

uplo      PLower or PUpper
trans     PNoTrans or PTrans
diag      PNonUnit or PUnit
n         nonnegative integer.  If negative, the default value is used.
k         nonnegative integer.  If negative, the default value is used.
ldA       nonnegative integer.  lda >= 1+k.
          If zero the default value is used.
incx      nonzero integer
offsetA   nonnegative integer
offsetx   nonnegative integer

func TbmvFloat 

func TbmvFloat(A, X *matrix.FloatMatrix, opts ...linalg.Option) (err error)

See function Tbmv.

func Tbsv 

func Tbsv(A, X matrix.Matrix, opts ...linalg.Option) (err error)
Solution of a triangular and banded set of equations.

Tbsv(A, X, uplo=PLower, trans=PNoTrans, diag=PNonDiag, n=A.Cols,
k=max(0,A.Rows-1), ldA=A.size[0], incx=1, offsetA=0, offsetx=0)

PURPOSE 

 X := A^{-1}*X, if trans is PNoTrans
 X := A^{-T}*X, if trans is PTrans
 X := A^{-H}*X, if trans is PConjTrans

A is banded triangular of order n and with bandwidth k.

ARGUMENTS
 A         float or complex m*k matrix.
 X         float or complex k*1 matrix. Must have the same type as A.

OPTIONS
 uplo      PLower   or PUpper
 trans     PNoTrans, PTrans or PConjTrans
 diag      PNoNUnit or PUnit
 n         nonnegative integer.  If negative, the default value is used.
 k         nonnegative integer.  If negative, the default value is used.
 ldA       nonnegative integer.  ldA >= 1+k.
           If zero the default value is used.
 incx      nonzero integer
 offsetA   nonnegative integer
 offsetx   nonnegative integer;

func TbsvFloat 

func TbsvFloat(A, X *matrix.FloatMatrix, opts ...linalg.Option) (err error)

See function Tbsv.

func Trmm 

func Trmm(A, B matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error)

Matrix-matrix product where one matrix is triangular. (L3)

Trmm(A, B, alpha, side=PLeft, uplo=PLower, transA=PNoTrans, diag=PNonUnit, m=-1, n=-1, ldA=max(1,A.Rows), ldB=max(1,B.Rows), offsetA=0, offsetB=0)

Computes 

B := alpha*A*B   if transA is PNoTrans   and side = PLeft
B := alpha*B*A   if transA is PNoTrans   and side = PRight
B := alpha*A^T*B if transA is PTrans     and side = PLeft
B := alpha*B*A^T if transA is PTrans     and side = PRight
B := alpha*A^H*B if transA is PConjTrans and side = PLeft
B := alpha*B*A^H if transA is PConjTrans and side = PRight

B is m by n and A is triangular.

ARGUMENTS 

A         float or complex matrix
B         float or complex matrix.  Must have the same type as A.
alpha     number (float or complex).  Complex alpha is only
          allowed if A is complex.

OPTIONS 

side      PLeft or PRight
uplo      PLower or PUpper
transA    PNoTrans or PTrans
diag      PNonUnit or PUnit
m         integer.  If negative, the default value is used.
          The default value is m = A.Rows or if side == PRight m = B.Rows
          If the default value is used and side is PLeft, m must be equal to A.Cols.
n         integer.  If negative, the default value is used.
          The default value is n = B.Cols or if side )= PRight n = A.Rows.
          If the default value is used and side is PRight, n must be equal to A.Cols.
ldA       nonnegative integer.
          ldA >= max(1,m) of if  side == PRight lda >= max(1,n).
          If zero, the default value is used.
ldB       nonnegative integer.  ldB >= max(1,m).
          If zero, the default value is used.
offsetA   nonnegative integer
offsetB   nonnegative integer

func TrmmFloat 

func TrmmFloat(A, B *matrix.FloatMatrix, alpha float64, opts ...linalg.Option) (err error)

See function Trmm.

func Trmv 

func Trmv(A, X matrix.Matrix, opts ...linalg.Option) (err error)

Matrix-vector product with a triangular matrix. (L2)

Trmv(A, x, uplo=PLower, trans=PNoTrans, diag=PNonUnit, n=A.Rows, ldA=max(1,A.Rows), incx=1, offsetA=0, offsetx=0)

COMPUTES 

X := A*X,   if trans is PNoTrans
X := A^T*X, if trans is PTrans
X := A^H*X, if trans is PConjTrans

A is triangular of order n.

ARGUMENTS 

A         float or complex matrix
X         float or complex  matrix.  Must have the same type as A.

OPTIONS 

uplo      PLower or PUpper
trans     PNoTrans or PTrans
diag      PNonUnit or PUnit
n         integer.  If negative, the default value is used.
          If the default value is used, we require that A.Rows = A.Cols.
ldA       nonnegative integer.  ldA >= max(1,n).
          If zero the default value is used.
incx      nonzero integer, default=1
offsetA   nonnegative integer, default=0
offsetx   nonnegative integer, default=0

func TrmvFloat 

func TrmvFloat(A, X *matrix.FloatMatrix, opts ...linalg.Option) (err error)

See function Trmv.

func Trsm 

func Trsm(A, B matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error)

Solution of a triangular system of equations with multiple righthand sides. (L3)

Trsm(A, B, alpha, side=PLeft, uplo=PLower, transA=PNoTrans, diag=PNonUnit, m=-1, n=-1, ldA=max(1,A.Rows), ldB=max(1,B.Rows), offsetA=0, offsetB=0)

Computes 

B := alpha*A^{-1}*B if transA is PNoTrans   and side = PLeft
B := alpha*B*A^{-1} if transA is PNoTrans   and side = PRight
B := alpha*A^{-T}*B if transA is PTrans     and side = PLeft
B := alpha*B*A^{-T} if transA is PTrans     and side = PRight
B := alpha*A^{-H}*B if transA is PConjTrans and side = PLeft
B := alpha*B*A^{-H} if transA is PConjTrans and side = PRight

B is m by n and A is triangular. The code does not verify whether A is nonsingular.

ARGUMENTS 

A         float or complex matrix.
B         float or complex matrix.  Must have the same type as A.
alpha     number (float or complex).  Complex alpha is only
          allowed if A is complex.

OPTIONS 

side      PLeft or PRight
uplo      PLower or PUpper
transA    PNoTrans or PTrans
diag      PNonUnit or PUnit
m         integer.  If negative, the default value is used.
          The default value is m = A.Rows or if side == PRight m = B.Rows
          If the default value is used and side is PLeft, m must be equal to A.Cols.
n         integer.  If negative, the default value is used.
          The default value is n = B.Cols or if side )= PRight n = A.Rows.
          If the default value is used and side is PRight, n must be equal to A.Cols.
ldA       nonnegative integer.
          ldA >= max(1,m) of if  side == PRight lda >= max(1,n).
          If zero, the default value is used.
ldB       nonnegative integer.  ldB >= max(1,m).
          If zero, the default value is used.
offsetA   nonnegative integer
offsetB   nonnegative integer

func TrsmFloat 

func TrsmFloat(A, B *matrix.FloatMatrix, alpha float64, opts ...linalg.Option) (err error)

See function Trsm.

func Trsv 

func Trsv(A, X matrix.Matrix, opts ...linalg.Option) (err error)

Solution of a triangular set of equations with one righthand side. (L2)

Trsv(A, x, uplo=PLower, trans=PNoTrans, diag=PNonUnit, n=A.Cols, ldA=max(1,A.Rows), incx=1, offsetA=0, offsetx=0)

PURPOSE 

X := A^{-1}*X, if trans is PNoTrans
X := A^{-T}*X, if trans is PTrans
X := A^{-H}*X, if trans is PConjTrans

A is triangular of order n. The code does not verify whether A is nonsingular.

ARGUMENTS 

A         float or complex m*n matrix.
X         float or complex n*1 matrix. Must have the same type as A.

OPTIONS 

uplo      PLower   or PUpper
trans     PNoTrans or PTrans
diag      PNoNUnit or PUnit
n         integer.  If negative, the default value is used.
          If the default value is used, we require that A.rows = A.cols.
ldA       nonnegative integer.  ldA >= max(1,n). If zero, the default value is used.
incx      nonzero integer
offsetA   nonnegative integer
offsetx   nonnegative integer

func TrsvFloat 

func TrsvFloat(A, X *matrix.FloatMatrix, opts ...linalg.Option) (err error)

See function Trsv.

Types

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