* ************************************************************************ * * File of the EXTENDED-COMPLEX Level-2 BLAS. * =================================================== * * SUBROUTINE ECGEMV( TRANS, M, N, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE ECGBMV( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE ECHEMV( UPLO, N, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE ECHBMV( UPLO, N, K, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE ECHPMV( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY ) * * SUBROUTINE ECTRMV( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * * SUBROUTINE ECTBMV( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * * SUBROUTINE ECTPMV( UPLO, TRANS, DIAG, N, AP, X, INCX ) * * SUBROUTINE ECTRSV( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * * SUBROUTINE ECTBSV( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * * SUBROUTINE ECTPSV( UPLO, TRANS, DIAG, N, AP, X, INCX ) * * SUBROUTINE ECGERU( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * * SUBROUTINE ECGERC( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * * SUBROUTINE ECHER ( UPLO, N, ALPHA, X, INCX, A, LDA ) * * SUBROUTINE ECHPR ( UPLO, N, ALPHA, X, INCX, AP ) * * SUBROUTINE ECHER2( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * * SUBROUTINE ECHPR2( UPLO, N, ALPHA, X, INCX, Y, INCY, AP ) * * See: * * Dongarra J. J., Du Croz J. J., Hammarling S. and Hanson R. J.. * A proposal for an extended set of Fortran Basic Linear Algebra * Subprograms. * * Technical Memorandum No.41 (revision 1), Mathematics and * Computer Science Division, Argonne National Laboratory, 9700 * South Cass Avenue, Argonne, Illinois 60439, US. * * Or * * NAG Technical Report TR3/86, Numerical Algorithms Group Ltd., * NAG Central Office, 256 Banbury Road, Oxford OX2 7DE, UK, and * Numerical Algorithms Group Inc., 1101 31st Street, Suite 100, * Downers Grove, Illinois 60515-1263, USA. * ************************************************************************ * SUBROUTINE ECGEMV( TRANS, M, N, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. COMPLEX ALPHA, BETA INTEGER INCX, INCY, LDA, M, N CHARACTER*1 TRANS * .. Array Arguments .. COMPLEX*16 Y( * ) COMPLEX A( LDA, * ), X( * ) * .. * * Purpose * ======= * * ECGEMV performs one of the matrix-vector operations * * y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or * * y := alpha*conjg( A' )*x + beta*y, * * where alpha and beta are scalars, x and y are vectors and A is an * m by n matrix. Additional precision arithmetic is used in the * computation. * * Parameters * ========== * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' y := alpha*A*x + beta*y. * * TRANS = 'T' or 't' y := alpha*A'*x + beta*y. * * TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y. * * Unchanged on exit. * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - COMPLEX array of DIMENSION ( LDA, n ). * Before entry, the leading m by n part of the array A must * contain the matrix of coefficients. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, m ). * Unchanged on exit. * * X - COMPLEX array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. * Before entry, the incremented array X must contain the * vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - COMPLEX . * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - COMPLEX*16 array of DIMENSION at least * ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. * Before entry with BETA non-zero, the incremented array Y * must contain the vector y. On exit, Y is overwritten by the * updated vector y. At least double precision arithmetic is * used in the computation of y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 20-July-1986. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY, LENX, LENY LOGICAL NOCONJ * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCMPLX, CONJG, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) ) THEN INFO = 1 ELSE IF ( M.LT.0 ) THEN INFO = 2 ELSE IF ( N.LT.0 ) THEN INFO = 3 ELSE IF ( LDA.LT.MAX(1,M) ) THEN INFO = 6 ELSE IF ( INCX.EQ.0 ) THEN INFO = 8 ELSE IF ( INCY.EQ.0 ) THEN INFO = 11 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ECGEMV', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR. $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) * * Set LENX and LENY, the lengths of the vectors x and y. * IF( LSAME( TRANS, 'N' ) )THEN LENX = N LENY = M ELSE LENX = M LENY = N END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * * First form y := beta*y and set up the start points in X and Y if * the increments are not both unity. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN IF( BETA.NE.ONE )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, LENY Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, LENY Y( I ) = BETA*Y( I ) 20 CONTINUE END IF END IF ELSE IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( LENX - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( LENY - 1 )*INCY END IF IF( BETA.NE.ONE )THEN IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, LENY Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, LENY Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN IF( LSAME( TRANS, 'N' ) )THEN * * Form y := alpha*A*x + y. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = DCMPLX( ALPHA )*X( J ) DO 50, I = 1, M Y( I ) = Y( I ) + TEMP*A( I, J ) 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = DCMPLX( ALPHA )*X( JX ) IY = KY DO 70, I = 1, M Y( IY ) = Y( IY ) + TEMP*A( I, J ) IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF ELSE * * Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 110, J = 1, N TEMP = ZERO IF( NOCONJ )THEN DO 90, I = 1, M TEMP = TEMP + A( I, J )*DCMPLX( X( I ) ) 90 CONTINUE ELSE DO 100, I = 1, M TEMP = TEMP + CONJG( A( I, J ) )*DCMPLX( X( I ) ) 100 CONTINUE END IF Y( J ) = Y( J ) + ALPHA*TEMP 110 CONTINUE ELSE JY = KY DO 140, J = 1, N TEMP = ZERO IX = KX IF( NOCONJ )THEN DO 120, I = 1, M TEMP = TEMP + A( I, J )*DCMPLX( X( IX ) ) IX = IX + INCX 120 CONTINUE ELSE DO 130, I = 1, M TEMP = TEMP + CONJG( A( I, J ) )*DCMPLX( X( IX ) ) IX = IX + INCX 130 CONTINUE END IF Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 140 CONTINUE END IF END IF * RETURN * * End of ECGEMV. * END