*DECK CHERK SUBROUTINE CHERK (UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC) C***BEGIN PROLOGUE CHERK C***PURPOSE Perform Hermitian rank k update of a complex Hermitian C matrix. C***LIBRARY SLATEC (BLAS) C***CATEGORY D1B6 C***TYPE COMPLEX (SHERK-S, DHERK-D, CHERK-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 CHERK performs one of the hermitian rank k operations C C C := alpha*A*conjg( A' ) + beta*C, C C or C C C := alpha*conjg( A' )*A + beta*C, C C where alpha and beta are real scalars, C is an n by n hermitian C matrix and A is an n by k matrix in the first case and a k by n C matrix 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*conjg( A' ) + beta*C. C C TRANS = 'C' or 'c' C := alpha*conjg( 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 = 'C' or 'c', K specifies the number of rows of the C 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 - COMPLEX 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 - COMPLEX 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 hermitian 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 hermitian 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 Note that the imaginary parts of the diagonal elements need C not be set, they are assumed to be zero, and on exit they C are set to zero. 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 CHERK C .. Scalar Arguments .. CHARACTER*1 UPLO, TRANS INTEGER N, K, LDA, LDC REAL ALPHA, BETA C .. Array Arguments .. COMPLEX A( LDA, * ), C( LDC, * ) C .. External Functions .. LOGICAL LSAME EXTERNAL LSAME C .. External Subroutines .. EXTERNAL XERBLA C .. Intrinsic Functions .. INTRINSIC CMPLX, CONJG, MAX, REAL C .. Local Scalars .. LOGICAL UPPER INTEGER I, INFO, J, L, NROWA REAL RTEMP COMPLEX TEMP C .. Parameters .. REAL ONE , ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) C***FIRST EXECUTABLE STATEMENT CHERK C C Test the input parameters. C IF( LSAME( TRANS, 'N' ) )THEN NROWA = N ELSE NROWA = K END IF UPPER = LSAME( UPLO, 'U' ) C INFO = 0 IF( ( .NOT.UPPER ).AND. $ ( .NOT.LSAME( UPLO , 'L' ) ) )THEN INFO = 1 ELSE IF( ( .NOT.LSAME( TRANS, 'N' ) ).AND. $ ( .NOT.LSAME( TRANS, 'C' ) ) )THEN INFO = 2 ELSE IF( N .LT.0 )THEN INFO = 3 ELSE IF( K .LT.0 )THEN INFO = 4 ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN INFO = 7 ELSE IF( LDC.LT.MAX( 1, N ) )THEN INFO = 10 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CHERK ', INFO ) RETURN END IF C C Quick return if possible. C IF( ( N.EQ.0 ).OR. $ ( ( ( ALPHA.EQ.ZERO ).OR.( K.EQ.0 ) ).AND.( BETA.EQ.ONE ) ) ) $ RETURN C C And when alpha.eq.zero. C IF( ALPHA.EQ.ZERO )THEN IF( UPPER )THEN IF( BETA.EQ.ZERO )THEN DO 20, J = 1, N DO 10, I = 1, J C( I, J ) = ZERO 10 CONTINUE 20 CONTINUE ELSE DO 40, J = 1, N DO 30, I = 1, J - 1 C( I, J ) = BETA*C( I, J ) 30 CONTINUE C( J, J ) = BETA*REAL( C( J, J ) ) 40 CONTINUE END IF ELSE IF( BETA.EQ.ZERO )THEN DO 60, J = 1, N DO 50, I = J, N C( I, J ) = ZERO 50 CONTINUE 60 CONTINUE ELSE DO 80, J = 1, N C( J, J ) = BETA*REAL( C( J, J ) ) DO 70, I = J + 1, N C( I, J ) = BETA*C( I, J ) 70 CONTINUE 80 CONTINUE END IF END IF RETURN END IF C C Start the operations. C IF( LSAME( TRANS, 'N' ) )THEN C C Form C := alpha*A*conjg( A' ) + beta*C. C IF( UPPER )THEN DO 130, J = 1, N IF( BETA.EQ.ZERO )THEN DO 90, I = 1, J C( I, J ) = ZERO 90 CONTINUE ELSE IF( BETA.NE.ONE )THEN DO 100, I = 1, J - 1 C( I, J ) = BETA*C( I, J ) 100 CONTINUE C( J, J ) = BETA*REAL( C( J, J ) ) END IF DO 120, L = 1, K IF( A( J, L ).NE.CMPLX( ZERO ) )THEN TEMP = ALPHA*CONJG( A( J, L ) ) DO 110, I = 1, J - 1 C( I, J ) = C( I, J ) + TEMP*A( I, L ) 110 CONTINUE C( J, J ) = REAL( C( J, J ) ) + $ REAL( TEMP*A( I, L ) ) END IF 120 CONTINUE 130 CONTINUE ELSE DO 180, J = 1, N IF( BETA.EQ.ZERO )THEN DO 140, I = J, N C( I, J ) = ZERO 140 CONTINUE ELSE IF( BETA.NE.ONE )THEN C( J, J ) = BETA*REAL( C( J, J ) ) DO 150, I = J + 1, N C( I, J ) = BETA*C( I, J ) 150 CONTINUE END IF DO 170, L = 1, K IF( A( J, L ).NE.CMPLX( ZERO ) )THEN TEMP = ALPHA*CONJG( A( J, L ) ) C( J, J ) = REAL( C( J, J ) ) + $ REAL( TEMP*A( J, L ) ) DO 160, I = J + 1, N C( I, J ) = C( I, J ) + TEMP*A( I, L ) 160 CONTINUE END IF 170 CONTINUE 180 CONTINUE END IF ELSE C C Form C := alpha*conjg( A' )*A + beta*C. C IF( UPPER )THEN DO 220, J = 1, N DO 200, I = 1, J - 1 TEMP = ZERO DO 190, L = 1, K TEMP = TEMP + CONJG( A( L, I ) )*A( L, J ) 190 CONTINUE IF( BETA.EQ.ZERO )THEN C( I, J ) = ALPHA*TEMP ELSE C( I, J ) = ALPHA*TEMP + BETA*C( I, J ) END IF 200 CONTINUE RTEMP = ZERO DO 210, L = 1, K RTEMP = RTEMP + CONJG( A( L, J ) )*A( L, J ) 210 CONTINUE IF( BETA.EQ.ZERO )THEN C( J, J ) = ALPHA*RTEMP ELSE C( J, J ) = ALPHA*RTEMP + BETA*REAL( C( J, J ) ) END IF 220 CONTINUE ELSE DO 260, J = 1, N RTEMP = ZERO DO 230, L = 1, K RTEMP = RTEMP + CONJG( A( L, J ) )*A( L, J ) 230 CONTINUE IF( BETA.EQ.ZERO )THEN C( J, J ) = ALPHA*RTEMP ELSE C( J, J ) = ALPHA*RTEMP + BETA*REAL( C( J, J ) ) END IF DO 250, I = J + 1, N TEMP = ZERO DO 240, L = 1, K TEMP = TEMP + CONJG( A( L, I ) )*A( L, J ) 240 CONTINUE IF( BETA.EQ.ZERO )THEN C( I, J ) = ALPHA*TEMP ELSE C( I, J ) = ALPHA*TEMP + BETA*C( I, J ) END IF 250 CONTINUE 260 CONTINUE END IF END IF C RETURN C C End of CHERK . C END