*DECK CHER2K SUBROUTINE CHER2K (UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, $ C, LDC) C***BEGIN PROLOGUE CHER2K C***PURPOSE Perform Hermitian rank 2k update of a complex. C***LIBRARY SLATEC (BLAS) C***CATEGORY D1B6 C***TYPE COMPLEX (SHER2-S, DHER2-D, CHER2-C, CHER2K-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 CHER2K performs one of the hermitian rank 2k operations C C C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C, C C or C C C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C, C C where alpha and beta are scalars with beta real, C is an n by n C hermitian matrix and A and B are n by k matrices in the first case C and k by n matrices 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( B' ) + C conjg( alpha )*B*conjg( A' ) + C beta*C. C C TRANS = 'C' or 'c' C := alpha*conjg( A' )*B + C conjg( alpha )*conjg( B' )*A + C 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 matrices A and B, and on entry with C TRANS = 'C' or 'c', K specifies the number of rows of the C matrices A and B. K must be at least zero. C Unchanged on exit. C C ALPHA - COMPLEX . 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 B - COMPLEX array of DIMENSION ( LDB, kb ), where kb 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 B must contain the matrix B, otherwise C the leading k by n part of the array B must contain the C 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. When TRANS = 'N' or 'n' C then LDB must be at least max( 1, n ), otherwise LDB 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 CHER2K C .. Scalar Arguments .. CHARACTER*1 UPLO, TRANS INTEGER N, K, LDA, LDB, LDC REAL BETA COMPLEX ALPHA C .. Array Arguments .. COMPLEX A( LDA, * ), B( LDB, * ), C( LDC, * ) C .. External Functions .. LOGICAL LSAME EXTERNAL LSAME C .. External Subroutines .. EXTERNAL XERBLA C .. Intrinsic Functions .. INTRINSIC CONJG, MAX, REAL C .. Local Scalars .. LOGICAL UPPER INTEGER I, INFO, J, L, NROWA COMPLEX TEMP1, TEMP2 C .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) C***FIRST EXECUTABLE STATEMENT CHER2K 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( LDB.LT.MAX( 1, NROWA ) )THEN INFO = 9 ELSE IF( LDC.LT.MAX( 1, N ) )THEN INFO = 12 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CHER2K', 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.REAL( 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.REAL( 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( B' ) + conjg( alpha )*B*conjg( A' ) + C C. C IF( UPPER )THEN DO 130, J = 1, N IF( BETA.EQ.REAL( 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.ZERO ).OR. $ ( B( J, L ).NE.ZERO ) )THEN TEMP1 = ALPHA*CONJG( B( J, L ) ) TEMP2 = CONJG( ALPHA*A( J, L ) ) DO 110, I = 1, J - 1 C( I, J ) = C( I, J ) + A( I, L )*TEMP1 + $ B( I, L )*TEMP2 110 CONTINUE C( J, J ) = REAL( C( J, J ) ) + $ REAL( A( J, L )*TEMP1 + $ B( J, L )*TEMP2 ) END IF 120 CONTINUE 130 CONTINUE ELSE DO 180, J = 1, N IF( BETA.EQ.REAL( ZERO ) )THEN DO 140, I = J, N C( I, J ) = ZERO 140 CONTINUE ELSE IF( BETA.NE.ONE )THEN DO 150, I = J + 1, N C( I, J ) = BETA*C( I, J ) 150 CONTINUE C( J, J ) = BETA*REAL( C( J, J ) ) END IF DO 170, L = 1, K IF( ( A( J, L ).NE.ZERO ).OR. $ ( B( J, L ).NE.ZERO ) )THEN TEMP1 = ALPHA*CONJG( B( J, L ) ) TEMP2 = CONJG( ALPHA*A( J, L ) ) DO 160, I = J + 1, N C( I, J ) = C( I, J ) + A( I, L )*TEMP1 + $ B( I, L )*TEMP2 160 CONTINUE C( J, J ) = REAL( C( J, J ) ) + $ REAL( A( J, L )*TEMP1 + $ B( J, L )*TEMP2 ) END IF 170 CONTINUE 180 CONTINUE END IF ELSE C C Form C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + C C. C IF( UPPER )THEN DO 210, J = 1, N DO 200, I = 1, J TEMP1 = ZERO TEMP2 = ZERO DO 190, L = 1, K TEMP1 = TEMP1 + CONJG( A( L, I ) )*B( L, J ) TEMP2 = TEMP2 + CONJG( B( L, I ) )*A( L, J ) 190 CONTINUE IF( I.EQ.J )THEN IF( BETA.EQ.REAL( ZERO ) )THEN C( J, J ) = REAL( ALPHA *TEMP1 + $ CONJG( ALPHA )*TEMP2 ) ELSE C( J, J ) = BETA*REAL( C( J, J ) ) + $ REAL( ALPHA *TEMP1 + $ CONJG( ALPHA )*TEMP2 ) END IF ELSE IF( BETA.EQ.REAL( ZERO ) )THEN C( I, J ) = ALPHA*TEMP1 + CONJG( ALPHA )*TEMP2 ELSE C( I, J ) = BETA *C( I, J ) + $ ALPHA*TEMP1 + CONJG( ALPHA )*TEMP2 END IF END IF 200 CONTINUE 210 CONTINUE ELSE DO 240, J = 1, N DO 230, I = J, N TEMP1 = ZERO TEMP2 = ZERO DO 220, L = 1, K TEMP1 = TEMP1 + CONJG( A( L, I ) )*B( L, J ) TEMP2 = TEMP2 + CONJG( B( L, I ) )*A( L, J ) 220 CONTINUE IF( I.EQ.J )THEN IF( BETA.EQ.REAL( ZERO ) )THEN C( J, J ) = REAL( ALPHA *TEMP1 + $ CONJG( ALPHA )*TEMP2 ) ELSE C( J, J ) = BETA*REAL( C( J, J ) ) + $ REAL( ALPHA *TEMP1 + $ CONJG( ALPHA )*TEMP2 ) END IF ELSE IF( BETA.EQ.REAL( ZERO ) )THEN C( I, J ) = ALPHA*TEMP1 + CONJG( ALPHA )*TEMP2 ELSE C( I, J ) = BETA *C( I, J ) + $ ALPHA*TEMP1 + CONJG( ALPHA )*TEMP2 END IF END IF 230 CONTINUE 240 CONTINUE END IF END IF C RETURN C C End of CHER2K. C END