matmul

Date:: 10-12-2011

NAME

MATMUL - Performs matrix multiplication of numeric or logical matrices

SYNOPSIS

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

IMPLEMENTATION

Cray Linux Environment (CLE)

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 following matrices:

| 1 2 3 |
| 2 3 4 |

and

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

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

MATMUL(A,B) yields the matrix-matrix product AB, as follows:

| 11 20 |
| 16 29 |

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

MATMUL(A,Y) yields the matrix-vector product AY with the value [14,20].