matmul(3I)

NAME
     MATMUL - Performs matrix multiplication of numeric or logical matrices

SYNOPSIS
     MATMUL ([MATRIX_A=]matrix_a, [MATRIX_B=]matrix_b)

IMPLEMENTATION
     UNICOS, UNICOS/mk, IRIX systems

     CF90, MIPSpro 7 Fortran 90

STANDARDS
     Fortran

DESCRIPTION
     The MATMUL intrinsic function performs matrix multiplication
     operations on numeric or logical matrices.  It accepts the following
     arguments:

     matrix_a  Must be of numeric type (integer, real, or complex) or of
               logical type.  It must be array valued and of rank one or
               two.

     matrix_b  Must be of numeric type if matrix_a is of numeric type and
               of logical type if matrix_a is of logical type.  It must be
               array valued and of rank one or two.  If matrix_a has rank
               one, matrix_b must have rank two.  If matrix_b has rank one,
               matrix_a must have rank two.  The size of the first (or
               only) dimension of matrix_b must equal the size of the last
               (or only) dimension of matrix_a.

     MATMUL is a transformational function.  The name of this intrinsic
     cannot be passed as an argument.

RETURN VALUES
     The result type, type parameter, and shape are as follows.  If the
     arguments are of numeric type, the type and kind type parameter of the
     result are determined by the types of the arguments.  If the arguments
     are of type logical, the result is of type logical with the kind type
     parameter of the arguments.  The shape of the result depends on the
     shapes of the arguments, as follows:

     * If matrix_a has shape (n, m) and matrix_b has shape (m, k), the
       result has shape (n, k).

     * If matrix_a has shape (m) and matrix_b has shape (m, k), the result
       has shape (k).

     * If matrix_a has shape (n, m) and matrix_b has shape (m), the result
       has shape (n).

     Element (i, j) of the result has the value
     SUM(MATRIX_A(i,:)*MATRIX_B(:,j)) if the arguments are of numeric type
     and has the value ANY(MATRIX_A(i,:).AND.MATRIX_B(:,j)) if the
     arguments are of logical type.

     Element (j) of the result has the value SUM(MATRIX_A(:)*MATRIX_B(:,j))
     if the arguments are of numeric type and has the value
     ANY(MATRIX_A(:).AND.MATRIX_B(:,j)) if the arguments are of logical
     type.

     Element (i) of the result has the value SUM(MATRIX_A(i,:)*MATRIX_B(:))
     if the arguments are of numeric type and has the value
     ANY(MATRIX_A(i,:).AND.MATRIX_B(:)) if the arguments are of logical
     type.

EXAMPLES
     Let A and B be the matrices

     | 1 2 3 |
     | 2 3 4 |

     and

     | 1 2 |
     | 2 3 |
     | 2 4 |

     Let X and Y be the vectors [1, 2] and [1, 2, 3].

     The result of MATMUL(A, B) is the matrix-matrix product AB with the
     value

     | 11 20 |
     | 16 29 |

     The result of MATMUL(X, A) is the vector-matrix product XA with the
     value [5, 8, 11].

     The result of MATMUL(A, Y) is the matrix-vector product AY with the
     value [14, 20].

SEE ALSO
     Intrinsic Procedures Reference Manual for the printed version of this
     man page.