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 addition

  •    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.