SUBROUTINE CHERK ( UPLO, TRANS, N, K, ALPHA, A, LDA, $ BETA, C, LDC ) * .. Scalar Arguments .. CHARACTER*1 UPLO, TRANS INTEGER N, K, LDA, LDC REAL ALPHA, BETA * .. Array Arguments .. COMPLEX A( LDA, * ), C( LDC, * ) * .. * * Purpose * ======= * * CHERK performs one of the hermitian rank k operations * * C := alpha*A*conjg( A' ) + beta*C, * * or * * C := alpha*conjg( A' )*A + beta*C, * * where alpha and beta are real scalars, C is an n by n hermitian * 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 - CHARACTER*1. * 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 - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' C := alpha*A*conjg( A' ) + beta*C. * * TRANS = 'C' or 'c' C := alpha*conjg( A' )*A + beta*C. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix C. N must be * at least zero. * Unchanged on exit. * * K - INTEGER. * On entry with TRANS = 'N' or 'n', K specifies the number * of columns of the matrix A, and on entry with * TRANS = 'C' or 'c', K specifies the number of rows of the * matrix A. K must be at least zero. * Unchanged on exit. * * ALPHA - REAL . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - COMPLEX array of DIMENSION ( 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. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first 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 ). * Unchanged on exit. * * BETA - REAL . * On entry, BETA specifies the scalar beta. * Unchanged on exit. * * C - COMPLEX array of DIMENSION ( 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 hermitian 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. * 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 hermitian 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. * Note that the imaginary parts of the diagonal elements need * not be set, they are assumed to be zero, and on exit they * are set to zero. * * LDC - INTEGER. * 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. * * * Level 3 Blas routine. * * -- Written on 8-February-1989. * Jack Dongarra, Argonne National Laboratory. * Iain Duff, AERE Harwell. * Jeremy Du Croz, Numerical Algorithms Group Ltd. * Sven Hammarling, Numerical Algorithms Group Ltd. * * -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1. * Ed Anderson, Cray Research Inc. * * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CMPLX, CONJG, MAX, REAL * .. Local Scalars .. LOGICAL UPPER INTEGER I, INFO, J, L, NROWA REAL RTEMP COMPLEX TEMP * .. Parameters .. REAL ONE , ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Executable Statements .. * * Test the input parameters. * IF( LSAME( TRANS, 'N' ) )THEN NROWA = N ELSE NROWA = K END IF UPPER = LSAME( UPLO, 'U' ) * 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 * * Quick return if possible. * IF( ( N.EQ.0 ).OR. $ ( ( ( ALPHA.EQ.ZERO ).OR.( K.EQ.0 ) ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * And when alpha.eq.zero. * 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 * * Start the operations. * IF( LSAME( TRANS, 'N' ) )THEN * * Form C := alpha*A*conjg( A' ) + beta*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 ) ) ELSE C( J, J ) = 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 ELSE C( J, J ) = REAL( C( J, J ) ) 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 * * Form C := alpha*conjg( A' )*A + beta*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 * RETURN * * End of CHERK . * END