CXML

## blas3

A library of linear algebra routines

#### Description

```  Basic Linear Algebra Subroutines Level 3 (BLAS 3) are a part of the Compaq
Extended Math Library (CXML). The BLAS Level 3 subprograms perform
operations of a higher granularity than the BLAS Level 2 subprograms. These
include matrix-matrix operations:

•    Matrix-matrix products

•    Rank-k updates of a symmetric matrix

•    Multiplying a matrix by a triangular matrix

•    Solving triangular systems of equations with multiple right hand sides

The functionality of the public domain BLAS3 has been enhanced by the
inclusion of the following routines:

•    Matrix subtraction

•    Matrix transpose

Where appropriate, the operations are performed on matrices that are:

•    General

•    Symmetric

•    Triangular

The following routines are included in BLAS 3. The Subprogram Name is the
name of the manual page containing documentation on the subprogram.

Routine Name   Operation

sgema

Calculates, in single-precision  arithmetic, the
sum of two real general matrices or their
transposes.

dgema

Calculates, in double-precision  arithmetic, the
sum of two real general matrices or their
transposes.

cgema

Calculates, in single-precision  arithmetic, the
sum of two complex general matrices, their
transposes, their conjugates, or their conjugate
transposes.

zgema

Calculates, in double-precision  arithmetic,  the
sum of two complex general matrices, their
transposes, their conjugates, or their conjugate
transposes.

sgemm

Calculates, in single-precision  arithmetic, a
matrix-matrix product and addition for real
general matrices or their transposes.

dgemm

Calculates, in double-precision  arithmetic, a
matrix-matrix product and addition for real
general matrices or their transposes.

cgemm

Calculates, in single-precision  arithmetic, a
matrix-matrix product and addition for complex
general matrices, their transposes, their
conjugates, or their conjugate transposes.

zgemm

Calculates, in double-precision  arithmetic, a
matrix-matrix product and addition for complex
general matrices, their transposes, their
conjugates, or their conjugate transposes.

sgems

Calculates, in single-precision  arithmetic, the
difference of two real general matrices or their
transposes.

dgems

Calculates, in double-precision  arithmetic, the
difference of two real general matrices or their
transposes.

cgems

Calculates, in single-precision  arithmetic, the
difference of two complex general matrices, their
transposes, their conjugates, or their conjugate
transposes.

zgems

Calculates, in double-precision  arithmetic, the
difference of two complex general matrices, their
transposes, their conjugates, or their conjugate
transposes.

sgemt

Copies a single-precision, real general matrix or
its transpose.

dgemt

Copies a double-precision, real general matrix or
its transpose.

cgemt

Copies a single-precision, complex general matrix,
its transpose, its conjugate, or its conjugate
transpose.

zgemt

Copies a double-precision, complex general matrix,
its transpose, its conjugate, or its conjugate
transpose.

ssymm

Calculates, in single-precision  arithmetic, a
matrix-matrix product and addition where a matrix
multiplier is a real symmetric matrix.

dsymm

Calculates, in double-precision  arithmetic, a
matrix-matrix product and addition where a matrix
multiplier is a real symmetric matrix.

csymm

Calculates, in single-precision  arithmetic, a
matrix-matrix product and addition where a matrix
multiplier is a complex symmetric matrix.

zsymm

Calculates, in double-precision  arithmetic, a
matrix-matrix product and addition where a matrix
multiplier is a complex symmetric matrix.

chemm

Calculates, in single-precision  arithmetic, a
matrix-matrix product and addition where a matrix
multiplier is a complex Hermitian matrix.

zhemm

Calculates, in double-precision  arithmetic, a
matrix-matrix product and addition where a matrix
multiplier is a complex Hermitian matrix.

ssyrk

Calculates, in single-precision  arithmetic, the
rank-k update of a real symmetric matrix.

dsyrk

Calculates, in double-precision  arithmetic, the
rank-k update of a real symmetric matrix.

csyrk

Calculates, in single-precision  arithmetic, the
rank-k update of a complex symmetric matrix.

zsyrk

Calculates, in double-precision  arithmetic, the
rank-k update of a complex symmetric matrix.

cherk

Calculates, in single-precision  arithmetic, the
rank-k update of a complex Hermitian matrix.

zherk

Calculates, in double-precision  arithmetic, the
rank-k update of a complex Hermitian matrix.

ssyr2k

Calculates, in single-precision  arithmetic, the
rank-2k update of a real symmetric matrix.

dsyr2k

Calculates, in double-precision  arithmetic, the
rank-2k update of a real symmetric matrix.

csyr2k

Calculates, in single-precision  arithmetic, the
rank-2k update of a complex symmetric matrix.

zsyr2k

Calculates, in double-precision  arithmetic, the
rank-2k update of a complex symmetric matrix.

cher2k

Calculates, in single-precision  arithmetic, the
rank-2k update of a complex Hermitian matrix.

zher2k

Calculates, in double-precision  arithmetic, the
rank-2k update of a complex Hermitian matrix.

strmm

Calculates, in single-precision  arithmetic, a
matrix-matrix product for a real triangular matrix
or its transpose.

dtrmm

Calculates, in double-precision  arithmetic, a
matrix-matrix product for a real triangular matrix
or its transpose.

ctrmm

Calculates, in single-precision  arithmetic, a
matrix-matrix product for a complex triangular
matrix, its transpose, or its conjugate transpose.

ztrmm

Calculates, in double-precision  arithmetic, a
matrix-matrix product for a complex triangular
matrix, its transpose, or its conjugate transpose.

strsm

Solves, in single-precision  arithmetic, a
triangular system of equations where the
coefficient matrix is a real triangular matrix.

dtrsm

Solves, in double-precision  arithmetic, a
triangular system of equations where the
coefficient matrix is a real triangular matrix.

ctrsm

Solves, in single-precision  arithmetic, a
triangular system of equations where the
coefficient matrix is a complex triangular matrix.

ztrsm

Solves, in double-precision  arithmetic, a
triangular system of equations where the
coefficient matrix is a complex triangular matrix.
```