SLATEC Routines --- SSYRK ---


    Note: this is a BLAS routine and is not in libslatec.a

*DECK SSYRK
      SUBROUTINE SSYRK (UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
C***BEGIN PROLOGUE  SSYRK
C***PURPOSE  Perform symmetric rank k update of a real symmetric matrix.
C***LIBRARY   SLATEC (BLAS)
C***CATEGORY  D1B6
C***TYPE      SINGLE PRECISION (SSYRK-S, DSYRK-D, CSYRK-C)
C***KEYWORDS  LEVEL 3 BLAS, LINEAR ALGEBRA
C***AUTHOR  Dongarra, J., (ANL)
C           Duff, I., (AERE)
C           Du Croz, J., (NAG)
C           Hammarling, S. (NAG)
C***DESCRIPTION
C
C  SSYRK  performs one of the symmetric rank k operations
C
C     C := alpha*A*A' + beta*C,
C
C  or
C
C     C := alpha*A'*A + beta*C,
C
C  where  alpha and beta  are scalars, C is an  n by n  symmetric matrix
C  and  A  is an  n by k  matrix in the first case and a  k by n  matrix
C  in the second case.
C
C  Parameters
C  ==========
C
C  UPLO   - CHARACTER*1.
C           On  entry,   UPLO  specifies  whether  the  upper  or  lower
C           triangular  part  of the  array  C  is to be  referenced  as
C           follows:
C
C              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
C                                  is to be referenced.
C
C              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
C                                  is to be referenced.
C
C           Unchanged on exit.
C
C  TRANS  - CHARACTER*1.
C           On entry,  TRANS  specifies the operation to be performed as
C           follows:
C
C              TRANS = 'N' or 'n'   C := alpha*A*A' + beta*C.
C
C              TRANS = 'T' or 't'   C := alpha*A'*A + beta*C.
C
C              TRANS = 'C' or 'c'   C := alpha*A'*A + beta*C.
C
C           Unchanged on exit.
C
C  N      - INTEGER.
C           On entry,  N specifies the order of the matrix C.  N must be
C           at least zero.
C           Unchanged on exit.
C
C  K      - INTEGER.
C           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
C           of  columns   of  the   matrix   A,   and  on   entry   with
C           TRANS = 'T' or 't' or 'C' or 'c',  K  specifies  the  number
C           of rows of the matrix  A.  K must be at least zero.
C           Unchanged on exit.
C
C  ALPHA  - REAL            .
C           On entry, ALPHA specifies the scalar alpha.
C           Unchanged on exit.
C
C  A      - REAL             array of DIMENSION ( LDA, ka ), where ka is
C           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
C           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
C           part of the array  A  must contain the matrix  A,  otherwise
C           the leading  k by n  part of the array  A  must contain  the
C           matrix A.
C           Unchanged on exit.
C
C  LDA    - INTEGER.
C           On entry, LDA specifies the first dimension of A as declared
C           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
C           then  LDA must be at least  max( 1, n ), otherwise  LDA must
C           be at least  max( 1, k ).
C           Unchanged on exit.
C
C  BETA   - REAL            .
C           On entry, BETA specifies the scalar beta.
C           Unchanged on exit.
C
C  C      - REAL             array of DIMENSION ( LDC, n ).
C           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
C           upper triangular part of the array C must contain the upper
C           triangular part  of the  symmetric matrix  and the strictly
C           lower triangular part of C is not referenced.  On exit, the
C           upper triangular part of the array  C is overwritten by the
C           upper triangular part of the updated matrix.
C           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
C           lower triangular part of the array C must contain the lower
C           triangular part  of the  symmetric matrix  and the strictly
C           upper triangular part of C is not referenced.  On exit, the
C           lower triangular part of the array  C is overwritten by the
C           lower triangular part of the updated matrix.
C
C  LDC    - INTEGER.
C           On entry, LDC specifies the first dimension of C as declared
C           in  the  calling  (sub)  program.   LDC  must  be  at  least
C           max( 1, n ).
C           Unchanged on exit.
C
C***REFERENCES  Dongarra, J., Du Croz, J., Duff, I., and Hammarling, S.
C                 A set of level 3 basic linear algebra subprograms.
C                 ACM TOMS, Vol. 16, No. 1, pp. 1-17, March 1990.
C***ROUTINES CALLED  LSAME, XERBLA
C***REVISION HISTORY  (YYMMDD)
C   890208  DATE WRITTEN
C   910605  Modified to meet SLATEC prologue standards.  Only comment
C           lines were modified.  (BKS)
C***END PROLOGUE  SSYRK