Computes a matrix-matrix product with general matrices but updates only the upper or lower triangular part of the result matrix.

Syntax

call sgemmt (uplo, transa, transb, n, k, alpha, a, lda, b, ldb, beta, c, ldc)

call dgemmt (uplo, transa, transb, n, k, alpha, a, lda, b, ldb, beta, c, ldc)

call cgemmt (uplo, transa, transb, n, k, alpha, a, lda, b, ldb, beta, c, ldc)

call zgemmt (uplo, transa, transb, n, k, alpha, a, lda, b, ldb, beta, c, ldc)

call gemmt (a, b, c[, uplo] [, transa] [, transb] [, alpha] [, beta])

Include Files

• mkl.fi, blas.f90

Description

The ?gemmt routines compute a scalar-matrix-matrix product with general matrices and add the result to the upper or lower part of a scalar-matrix product. These routines are similar to the ?gemm routines, but they only access and update a triangular part of the square result matrix (see Application Notes below).

The operation is defined as

C := alpha*op(A)*op(B) + beta*C,

where:

op(X) is one of op(X) = X, or op(X) = XT, or op(X) = XH,

alpha and beta are scalars,

A, B and C are matrices:

op(A) is an n-by-k matrix,

op(B) is a k-by-n matrix,

C is an n-by-n upper or lower triangular matrix.

Input Parameters

uplo

CHARACTER*1. Specifies whether the upper or lower triangular part of the array c is used. If uplo = 'U' or 'u', then the upper triangular part of the array c is used. If uplo = 'L' or 'l', then the lower triangular part of the array c is used.

transa

CHARACTER*1. Specifies the form of op(A) used in the matrix multiplication:

if transa = 'N' or 'n', then op(A) = A;

if transa = 'T' or 't', then op(A) = AT;

if transa = 'C' or 'c', then op(A) = AH.

transb

CHARACTER*1. Specifies the form of op(B) used in the matrix multiplication:

if transb = 'N' or 'n', then op(B) = B;

if transb = 'T' or 't', then op(B) = BT;

if transb = 'C' or 'c', then op(B) = BH.

n

INTEGER. Specifies the order of the matrix C. The value of n must be at least zero.

k

INTEGER. Specifies the number of columns of the matrix op(A) and the number of rows of the matrix op(B). The value of k must be at least zero.

alpha

REAL for sgemmt

DOUBLE PRECISION for dgemmt

COMPLEX for cgemmt

DOUBLE COMPLEX for zgemmt

Specifies the scalar alpha.

a

REAL for sgemmt

DOUBLE PRECISION for dgemmt

COMPLEX for cgemmt

DOUBLE COMPLEX for zgemmt

Array, size lda by ka, where ka is k when transa = 'N' or 'n', and is n otherwise. Before entry with transa = 'N' or 'n', the leading n-by-k part of the array a must contain the matrix A, otherwise the leading k-by-n part of the array a must contain the matrix A.

lda

INTEGER.

Specifies the leading dimension of a as declared in the calling (sub)program.

When transa = 'N' or 'n', then lda must be at least max(1, n), otherwise lda must be at least max(1, k).

b

REAL for sgemmt

DOUBLE PRECISION for dgemmt

COMPLEX for cgemmt

DOUBLE COMPLEX for zgemmt

Array, size ldb by kb, where kb is n when transb = 'N' or 'n', and is k otherwise. Before entry with transb = 'N' or 'n', the leading k-by-n part of the array b must contain the matrix B, otherwise the leading n-by-k part of the array b must contain the matrix B.

ldb

INTEGER. Specifies the leading dimension of b as declared in the calling (sub)program.

When transb = 'N' or 'n', then ldb must be at least max(1, k), otherwise ldb must be at least max(1, n).

beta

REAL for sgemmt

DOUBLE PRECISION for dgemmt

COMPLEX for cgemmt

DOUBLE COMPLEX for zgemmt

Specifies the scalar beta. When beta is equal to zero, then c need not be set on input.

c

REAL for sgemmt

DOUBLE PRECISION for dgemmt

COMPLEX for cgemmt

DOUBLE COMPLEX for zgemmt

Array, size ldc by n.

Before entry with uplo = 'U' or 'u', the leading n-by-n upper triangular part of the array c must contain the upper triangular part of the matrix C and the strictly lower triangular part of c is not referenced.

Before entry with uplo = 'L' or 'l', the leading n-by-n lower triangular part of the array c must contain the lower triangular part of the matrix C and the strictly upper triangular part of c is not referenced.

When beta is equal to zero, c need not be set on input.

ldc

INTEGER. Specifies the leading dimension of c as declared in the calling (sub)program. The value of ldc must be at least max(1, n).

Output Parameters

 c When uplo = 'U' or 'u', the upper triangular part of the array c is overwritten by the upper triangular part of the updated matrix. When uplo = 'L' or 'l', the lower triangular part of the array c is overwritten by the lower triangular part of the updated matrix.

Fortran 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see Fortran 95 Interface Conventions.

Specific details for the routine gemmt interface are the following:

a

Holds the matrix A of size (ma,ka) where

ka = k if transa='N',

ka = n otherwise,

ma = n if transa='N',

ma = k otherwise.

b

Holds the matrix B of size (mb,kb) where

kb = n if transb = 'N',

kb = k otherwise,

mb = k if transb = 'N',

mb = n otherwise.

c

Holds the matrix C of size (n,n).

uplo

Must be 'U' or 'L'.

The default value is 'U'.

transa

Must be 'N', 'C', or 'T'.

The default value is 'N'.

transb

Must be 'N', 'C', or 'T'.

The default value is 'N'.

alpha

The default value is 1.

beta

The default value is 0.

Application Notes

These routines only access and update the upper or lower triangular part of the result matrix. This can be useful when the result is known to be symmetric; for example, when computing a product of the form C := alpha*B*S*BT + beta*C , where S and C are symmetric matrices and B is a general matrix. In this case, first compute A := B*S (which can be done using the corresponding ?symm routine), then compute C := alpha*A*BT + beta*C using the ?gemmt routine.