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# Technical Reference: Base Operating System and Extensions , Volume 2

## SSYRK, DSYRK, CSYRK, or ZSYRK Subroutine

### Purpose

Perform symmetric rank k operations.

### Library

BLAS Library (libblas.a)

### FORTRAN Syntax

SUBROUTINE SSYRK(UPLO, TRANS, N, K, ALPHA,
A, LDA, BETA, C, LDC)
CHARACTER*1 UPLO, TRANS
INTEGER N, K, LDA, LDC
REAL ALPHA, BETA
REAL A(LDA,*), C(LDC,*)

```SUBROUTINE DSYRK(UPLO, TRANS, N, K, ALPHA,
A, LDA, BETA, C, LDC)
CHARACTER*1 UPLO,TRANS
INTEGER N,K,LDA,LDC
DOUBLE PRECISION ALPHA,BETA
DOUBLE PRECISION A(LDA,*), C(LDC,*)
```

```SUBROUTINE CSYRK(UPLO, TRANS, N, K, ALPHA,
A, LDA, BETA, C, LDC)
CHARACTER*1 UPLO,TRANS
INTEGER N,K,LDA,LDC
COMPLEX ALPHA,BETA
COMPLEX A(LDA,*), C(LDC,*)
```

```SUBROUTINE ZSYRK(UPLO, TRANS, N, K, ALPHA,
A, LDA, BETA, C, LDC)
CHARACTER*1 UPLO,TRANS
INTEGER N,K,LDA,LDC
COMPLEX*16 ALPHA,BETA
COMPLEX*16 A(LDA,*), C(LDC,*)
```

### Description

The SSYRK, DSYRK, CSYRK or ZSYRK subroutine performs one of the symmetric rank k operations:

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, and A is an N by K matrix in the first case and a K by N matrix in the second case.

### Parameters

 UPLO On entry, UPLO specifies whether the upper or lower triangular part of the array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced. Unchanged on exit. TRANS On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha * A * A' + beta * C TRANS = 'T' or 't' C := alpha * A' * A + beta * C TRANS = 'C' or 'c' C := alpha * A' * A + beta * C Unchanged on exit. N On entry, N specifies the order of the matrix C; N must be at least 0; unchanged on exit. K On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrix A, and on entry with TRANS = 'T' or 't' or 'C' or 'c', K specifies the number of rows of the matrix A; K must be at least 0; unchanged on exit. ALPHA On entry, ALPHA specifies the scalar alpha; unchanged on exit. A An array of dimension ( LDA, KA ), where KA is K when TRANS = 'N' or 'n', and is N otherwise; on 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; unchanged on exit. LDA On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = 'N' or 'n', LDA must be at least max( 1, N ); otherwise LDA must be at least max( 1, K ); unchanged on exit. BETA On entry, BETA specifies the scalar beta; unchanged on exit. C An array of dimension ( LDC, N ); on 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; on exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix; on 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; on exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. LDC On entry, LDC specifies the first dimension of C as declared in the calling (sub) program; LDC must be at least max( 1, N ); unchanged on exit.

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