relibc_openlibm/slatec/ssymm.f

*DECK SSYMM
      SUBROUTINE SSYMM (SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA,
     $   C, LDC)
C***BEGIN PROLOGUE  SSYMM
C***PURPOSE  Multiply a real general matrix by a real symmetric matrix.
C***LIBRARY   SLATEC (BLAS)
C***CATEGORY  D1B6
C***TYPE      SINGLE PRECISION (SSYMM-S, DSYMM-D, CSYMM-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  SSYMM  performs one of the matrix-matrix operations
C
C     C := alpha*A*B + beta*C,
C
C  or
C
C     C := alpha*B*A + beta*C,
C
C  where alpha and beta are scalars,  A is a symmetric matrix and  B and
C  C are  m by n matrices.
C
C  Parameters
C  ==========
C
C  SIDE   - CHARACTER*1.
C           On entry,  SIDE  specifies whether  the  symmetric matrix  A
C           appears on the  left or right  in the  operation as follows:
C
C              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,
C
C              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,
C
C           Unchanged on exit.
C
C  UPLO   - CHARACTER*1.
C           On  entry,   UPLO  specifies  whether  the  upper  or  lower
C           triangular  part  of  the  symmetric  matrix   A  is  to  be
C           referenced as follows:
C
C              UPLO = 'U' or 'u'   Only the upper triangular part of the
C                                  symmetric matrix is to be referenced.
C
C              UPLO = 'L' or 'l'   Only the lower triangular part of the
C                                  symmetric matrix is to be referenced.
C
C           Unchanged on exit.
C
C  M      - INTEGER.
C           On entry,  M  specifies the number of rows of the matrix  C.
C           M  must be at least zero.
C           Unchanged on exit.
C
C  N      - INTEGER.
C           On entry, N specifies the number of columns of the matrix C.
C           N  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           m  when  SIDE = 'L' or 'l'  and is  n otherwise.
C           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of
C           the array  A  must contain the  symmetric matrix,  such that
C           when  UPLO = 'U' or 'u', the leading m by m upper triangular
C           part of the array  A  must contain the upper triangular part
C           of the  symmetric matrix and the  strictly  lower triangular
C           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
C           the leading  m by m  lower triangular part  of the  array  A
C           must  contain  the  lower triangular part  of the  symmetric
C           matrix and the  strictly upper triangular part of  A  is not
C           referenced.
C           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of
C           the array  A  must contain the  symmetric matrix,  such that
C           when  UPLO = 'U' or 'u', the leading n by n upper triangular
C           part of the array  A  must contain the upper triangular part
C           of the  symmetric matrix and the  strictly  lower triangular
C           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
C           the leading  n by n  lower triangular part  of the  array  A
C           must  contain  the  lower triangular part  of the  symmetric
C           matrix and the  strictly upper triangular part of  A  is not
C           referenced.
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  SIDE = 'L' or 'l'  then
C           LDA must be at least  max( 1, m ), otherwise  LDA must be at
C           least  max( 1, n ).
C           Unchanged on exit.
C
C  B      - REAL             array of DIMENSION ( LDB, n ).
C           Before entry, the leading  m by n part of the array  B  must
C           contain the matrix B.
C           Unchanged on exit.
C
C  LDB    - INTEGER.
C           On entry, LDB specifies the first dimension of B as declared
C           in  the  calling  (sub)  program.   LDB  must  be  at  least
C           max( 1, m ).
C           Unchanged on exit.
C
C  BETA   - REAL            .
C           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
C           supplied as zero then C need not be set on input.
C           Unchanged on exit.
C
C  C      - REAL             array of DIMENSION ( LDC, n ).
C           Before entry, the leading  m by n  part of the array  C must
C           contain the matrix  C,  except when  beta  is zero, in which
C           case C need not be set on entry.
C           On exit, the array  C  is overwritten by the  m by n updated
C           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, m ).
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  SSYMM
C     .. Scalar Arguments ..
      CHARACTER*1        SIDE, UPLO
      INTEGER            M, N, LDA, LDB, LDC
      REAL               ALPHA, BETA
C     .. Array Arguments ..
      REAL               A( LDA, * ), B( LDB, * ), C( LDC, * )
C     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
C     .. External Subroutines ..
      EXTERNAL           XERBLA
C     .. Intrinsic Functions ..
      INTRINSIC          MAX
C     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            I, INFO, J, K, NROWA
      REAL               TEMP1, TEMP2
C     .. Parameters ..
      REAL               ONE         , ZERO
      PARAMETER        ( ONE = 1.0E+0, ZERO = 0.0E+0 )
C***FIRST EXECUTABLE STATEMENT  SSYMM
C
C     Set NROWA as the number of rows of A.
C
      IF( LSAME( SIDE, 'L' ) )THEN
         NROWA = M
      ELSE
         NROWA = N
      END IF
      UPPER = LSAME( UPLO, 'U' )
C
C     Test the input parameters.
C
      INFO = 0
      IF(      ( .NOT.LSAME( SIDE, 'L' ) ).AND.
     $         ( .NOT.LSAME( SIDE, 'R' ) )      )THEN
         INFO = 1
      ELSE IF( ( .NOT.UPPER              ).AND.
     $         ( .NOT.LSAME( UPLO, 'L' ) )      )THEN
         INFO = 2
      ELSE IF( M  .LT.0               )THEN
         INFO = 3
      ELSE IF( N  .LT.0               )THEN
         INFO = 4
      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
         INFO = 7
      ELSE IF( LDB.LT.MAX( 1, M     ) )THEN
         INFO = 9
      ELSE IF( LDC.LT.MAX( 1, M     ) )THEN
         INFO = 12
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'SSYMM ', INFO )
         RETURN
      END IF
C
C     Quick return if possible.
C
      IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
     $    ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
C
C     And when  alpha.eq.zero.
C
      IF( ALPHA.EQ.ZERO )THEN
         IF( BETA.EQ.ZERO )THEN
            DO 20, J = 1, N
               DO 10, I = 1, M
                  C( I, J ) = ZERO
   10          CONTINUE
   20       CONTINUE
         ELSE
            DO 40, J = 1, N
               DO 30, I = 1, M
                  C( I, J ) = BETA*C( I, J )
   30          CONTINUE
   40       CONTINUE
         END IF
         RETURN
      END IF
C
C     Start the operations.
C
      IF( LSAME( SIDE, 'L' ) )THEN
C
C        Form  C := alpha*A*B + beta*C.
C
         IF( UPPER )THEN
            DO 70, J = 1, N
               DO 60, I = 1, M
                  TEMP1 = ALPHA*B( I, J )
                  TEMP2 = ZERO
                  DO 50, K = 1, I - 1
                     C( K, J ) = C( K, J ) + TEMP1    *A( K, I )
                     TEMP2     = TEMP2     + B( K, J )*A( K, I )
   50             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = TEMP1*A( I, I ) + ALPHA*TEMP2
                  ELSE
                     C( I, J ) = BETA *C( I, J ) +
     $                           TEMP1*A( I, I ) + ALPHA*TEMP2
                  END IF
   60          CONTINUE
   70       CONTINUE
         ELSE
            DO 100, J = 1, N
               DO 90, I = M, 1, -1
                  TEMP1 = ALPHA*B( I, J )
                  TEMP2 = ZERO
                  DO 80, K = I + 1, M
                     C( K, J ) = C( K, J ) + TEMP1    *A( K, I )
                     TEMP2     = TEMP2     + B( K, J )*A( K, I )
   80             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = TEMP1*A( I, I ) + ALPHA*TEMP2
                  ELSE
                     C( I, J ) = BETA *C( I, J ) +
     $                           TEMP1*A( I, I ) + ALPHA*TEMP2
                  END IF
   90          CONTINUE
  100       CONTINUE
         END IF
      ELSE
C
C        Form  C := alpha*B*A + beta*C.
C
         DO 170, J = 1, N
            TEMP1 = ALPHA*A( J, J )
            IF( BETA.EQ.ZERO )THEN
               DO 110, I = 1, M
                  C( I, J ) = TEMP1*B( I, J )
  110          CONTINUE
            ELSE
               DO 120, I = 1, M
                  C( I, J ) = BETA*C( I, J ) + TEMP1*B( I, J )
  120          CONTINUE
            END IF
            DO 140, K = 1, J - 1
               IF( UPPER )THEN
                  TEMP1 = ALPHA*A( K, J )
               ELSE
                  TEMP1 = ALPHA*A( J, K )
               END IF
               DO 130, I = 1, M
                  C( I, J ) = C( I, J ) + TEMP1*B( I, K )
  130          CONTINUE
  140       CONTINUE
            DO 160, K = J + 1, N
               IF( UPPER )THEN
                  TEMP1 = ALPHA*A( J, K )
               ELSE
                  TEMP1 = ALPHA*A( K, J )
               END IF
               DO 150, I = 1, M
                  C( I, J ) = C( I, J ) + TEMP1*B( I, K )
  150          CONTINUE
  160       CONTINUE
  170    CONTINUE
      END IF
C
      RETURN
C
C     End of SSYMM .
C
      END