Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
?symm
Computes a matrix-matrix product where one input matrix is symmetric.
Syntax
call ssymm(side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
call dsymm(side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
call csymm(side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
call zsymm(side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)call symm(a, b, c [, side] [, uplo] [, alpha] [, beta])Include Files
mkl.fi, mkl_blas.f90
Description
The ?symm routines compute a scalar-matrix-matrix product with one symmetric matrix and add the result to a scalar-matrix product . The operation is defined as C:=alpha * A * B+ beta * C ,
or C:=alpha * B * A+ beta * C ,
where:
alpha and beta are scalars,
A is a symmetric matrix,
B and C are m -by- n matrices.
Input Parameters
- Layout
-
Specifies whether two-dimensional array storage is row-major ( CblasRowMajor ) or column-major ( CblasColMajor ).
side
CHARACTER*1 . Specifies whether the symmetric matrix A appears on the left or right in the operation:
if side = 'L' or 'l' , then C := alpha*A*B + beta*C ;
if side = 'R' or 'r' , then C := alpha*B*A + beta*C .
uplo
CHARACTER*1 . Specifies whether the upper or lower triangular part of the symmetric matrix A is used:
if uplo = 'U' or ‘u’ uplo = CblasUpper , then the upper triangular part is used;
if uplo = 'L' or ‘l’ , then the lower triangular part is used.
m
INTEGER . Specifies the number of rows of the matrix C .
The value of m must be at least zero.
n
INTEGER . Specifies the number of columns of the matrix C .
The value of n must be at least zero.
- alpha
-
REAL for ssymm DOUBLE PRECISION for dsymm COMPLEX for csymm DOUBLE COMPLEX for zsymm Specifies the scalar alpha .
- a
-
REAL for ssymm DOUBLE PRECISION for dsymm COMPLEX for csymm DOUBLE COMPLEX for zsymm
Array, size (lda, ka)lda* ka , where ka is m when side = 'L' or 'l' and is n otherwise.
Before entry with side = 'L' or 'l' , the m -by- m part of the array a must contain the symmetric matrix, such that when uplo = 'U' or ‘u’ uplo = CblasUpper , the leading m -by- m upper triangular part of the array a must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of a is not referenced, and when uplo = 'L' or 'l' , the leading m -by- m lower triangular part of the array a must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of a is not referenced.
Before entry with side = 'R' or 'r' , the n -by- n part of the array a must contain the symmetric matrix, such that when uplo = 'U' or ‘u’ uplo = CblasUpper e array a must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of a is not referenced, and when uplo = 'L' or 'l' , the leading n -by- n lower triangular part of the array a must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of a is not referenced.
lda
INTEGER . Specifies the leading dimension of a as declared in the calling (sub)program. When side = 'L' or 'l' then lda must be at least max(1, m) , otherwise lda must be at least max(1, n) .
- b
-
REAL for ssymm DOUBLE PRECISION for dsymm COMPLEX for csymm DOUBLE COMPLEX for zsymm Array, size ldb by n .
The leading m -by- n part of the array b must contain the matrix B .
For Layout = CblasRowMajor : array, size ldb * m . The leading n -by- m 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. ldb must be at least max(1, m)
- beta
-
REAL for ssymm DOUBLE PRECISION for dsymm COMPLEX for csymm DOUBLE COMPLEX for zsymm Specifies the scalar beta . When beta is set to zero, then c need not be set on input.
- c
-
REAL for ssymm DOUBLE PRECISION for dsymm COMPLEX for csymm DOUBLE COMPLEX for zsymm Array, size (c, n) . Before entry, the leading m -by- n part of the array c must contain the matrix C , except when beta is zero, in which case c need not be set on entry. For Layout = CblasColMajor : array, size ldc*n . Before entry, the leading m -by- n part of the array c must contain the matrix C , except when beta is zero, in which case c need not be set on entry. For Layout = CblasRowMajor : array, size ldc*m . Before entry, the leading n -by- m part of the array c must contain the matrix C , except when beta is zero, in which case c need not be set on entry.
ldc
INTEGER . Specifies the leading dimension of c as declared in the calling (sub)program. ldc must be at least max(1, m)
Output Parameters
- c
-
Overwritten by the m -by- n updated matrix.
BLAS 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 BLAS 95 Interface Conventions .
Specific details for the routine symm interface are the following:
- a
-
Holds the matrix A of size ( k , k ) where k = m if side = 'L' , k = n otherwise.
- b
-
Holds the matrix B of size ( m , n ).
- c
-
Holds the matrix C of size ( m , n ).
- side
-
Must be ‘L’ or ‘R’ . The default value is ‘L’ .
- uplo
-
Must be ‘U’ or ‘L’ . The default value is ‘U’ .
- alpha
-
The default value is 1.
- beta
-
The default value is 0.