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Visible to Intel only — GUID: GUID-6ECAD09E-3EF5-4B4D-8C3F-5AAFC83C6C8D
?syrk
Performs a symmetric rank-k update.
Syntax
call ssyrk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
call dsyrk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
call csyrk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
call zsyrk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
call syrk(a, c [,uplo] [, trans] [,alpha][,beta])
Include Files
- mkl.fi, blas.f90
Description
The ?syrk routines perform a rank-k matrix-matrix operation for a symmetric matrix C using a general matrix A . The operation is defined as:
C := alpha*A*A' + beta*C,
or
C := alpha*A'*A + beta*C,
where:
alpha and beta are scalars,
C is an n-by-n symmetric matrix,
A is an n-by-k matrix in the first case and a k-by-n matrix in the second case.
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 low triangular part of the array c is used.
- trans
-
CHARACTER*1. Specifies the operation:
if trans= 'N' or 'n', then C := alpha*A*A' + beta*C;
if trans= 'T' or 't', then C := alpha*A'*A + beta*C;
if trans= 'C' or 'c', then C := alpha*A'*A + beta*C.
- n
-
INTEGER. Specifies the order of the matrix C. The value of n must be at least zero.
- k
-
INTEGER. On entry with trans= 'N' or 'n', k specifies the number of columns of the matrix a, and on entry with trans= 'T', 't', 'C', or 'c' , k specifies the number of rows of the matrix a.
The value of k must be at least zero.
- alpha
-
REAL for ssyrk
DOUBLE PRECISION for dsyrk
COMPLEX for csyrk
DOUBLE COMPLEX for zsyrk
Specifies the scalar alpha.
- a
-
REAL for ssyrk
DOUBLE PRECISION for dsyrk
COMPLEX for csyrk
DOUBLE COMPLEX for zsyrk
Array, size (lda, ka), where ka is k when trans= 'N' or 'n', and is n otherwise. Before entry with trans= '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.
Array, size (lda, ka), where ka is k when trans= 'N' or 'n', and is n otherwise. Before entry with trans= '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 trans= 'N' or 'n', then lda must be at least max(1, n), otherwise lda must be at least max(1, k).
- beta
-
REAL for ssyrk
DOUBLE PRECISION for dsyrk
COMPLEX for csyrk
DOUBLE COMPLEX for zsyrk
Specifies the scalar beta.
- c
-
REAL for ssyrk
DOUBLE PRECISION for dsyrk
COMPLEX for csyrk
DOUBLE COMPLEX for zsyrk
Array, size (ldc, 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 symmetric matrix 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 symmetric matrix and the strictly upper triangular part of c is not referenced.
- 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
-
With uplo = 'U' or 'u', the upper triangular part of the array c is overwritten by the upper triangular part of the updated matrix.
With uplo = 'L' or 'l', the lower triangular part of the array c is overwritten by the lower triangular part of the 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 syrk 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.
- c
-
Holds the matrix C of size (n,n).
- uplo
-
Must be 'U' or 'L'. The default value is 'U'.
- trans
-
Must be 'N', 'C', or 'T'.
The default value is 'N'.
- alpha
-
The default value is 1.
- beta
-
The default value is 0.