| SUBROUTINE CHEMVF ( UPLO, N, ALPHA, A, LDA, X, INCX, |
| $ BETA, Y, INCY ) |
| * .. Scalar Arguments .. |
| COMPLEX ALPHA, BETA |
| INTEGER INCX, INCY, LDA, N |
| CHARACTER*1 UPLO |
| * .. Array Arguments .. |
| COMPLEX A( LDA, * ), X( * ), Y( * ) |
| * .. |
| * |
| * Purpose |
| * ======= |
| * |
| * CHEMV performs the matrix-vector operation |
| * |
| * y := alpha*A*x + beta*y, |
| * |
| * where alpha and beta are scalars, x and y are n element vectors and |
| * A is an n by n hermitian matrix. |
| * |
| * Parameters |
| * ========== |
| * |
| * UPLO - CHARACTER*1. |
| * On entry, UPLO specifies whether the upper or lower |
| * triangular part of the array A is to be referenced as |
| * follows: |
| * |
| * UPLO = 'U' or 'u' Only the upper triangular part of A |
| * is to be referenced. |
| * |
| * UPLO = 'L' or 'l' Only the lower triangular part of A |
| * is to be referenced. |
| * |
| * Unchanged on exit. |
| * |
| * N - INTEGER. |
| * On entry, N specifies the order 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 with UPLO = 'U' or 'u', the leading n by n |
| * upper triangular part of the array A must contain the upper |
| * triangular part of the hermitian matrix and the strictly |
| * lower triangular part of A is not referenced. |
| * Before entry with UPLO = 'L' or 'l', the leading n by n |
| * lower triangular part of the array A must contain the lower |
| * triangular part of the hermitian matrix and the strictly |
| * upper triangular part of A is not referenced. |
| * Note that the imaginary parts of the diagonal elements need |
| * not be set and are assumed to be zero. |
| * 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, n ). |
| * Unchanged on exit. |
| * |
| * X - COMPLEX array of dimension at least |
| * ( 1 + ( n - 1 )*abs( INCX ) ). |
| * Before entry, the incremented array X must contain the n |
| * element 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 array of dimension at least |
| * ( 1 + ( n - 1 )*abs( INCY ) ). |
| * Before entry, the incremented array Y must contain the n |
| * element vector y. On exit, Y is overwritten by the updated |
| * vector 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 22-October-1986. |
| * Jack Dongarra, Argonne National Lab. |
| * Jeremy Du Croz, Nag Central Office. |
| * 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 TEMP1, TEMP2 |
| INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY |
| * .. External Functions .. |
| LOGICAL LSAME |
| EXTERNAL LSAME |
| * .. External Subroutines .. |
| EXTERNAL XERBLA |
| * .. Intrinsic Functions .. |
| INTRINSIC CONJG, MAX, REAL |
| * .. |
| * .. Executable Statements .. |
| * |
| * Test the input parameters. |
| * |
| INFO = 0 |
| IF ( .NOT.LSAME( UPLO, 'U' ).AND. |
| $ .NOT.LSAME( UPLO, 'L' ).AND. |
| $ .NOT.LSAME( UPLO, 'V' ).AND. |
| $ .NOT.LSAME( UPLO, 'M' ))THEN |
| INFO = 1 |
| ELSE IF( N.LT.0 )THEN |
| INFO = 2 |
| ELSE IF( LDA.LT.MAX( 1, N ) )THEN |
| INFO = 5 |
| ELSE IF( INCX.EQ.0 )THEN |
| INFO = 7 |
| ELSE IF( INCY.EQ.0 )THEN |
| INFO = 10 |
| END IF |
| IF( INFO.NE.0 )THEN |
| CALL XERBLA( 'CHEMV ', INFO ) |
| RETURN |
| END IF |
| * |
| * Quick return if possible. |
| * |
| IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) |
| $ RETURN |
| * |
| * Set up the start points in X and Y. |
| * |
| IF( INCX.GT.0 )THEN |
| KX = 1 |
| ELSE |
| KX = 1 - ( N - 1 )*INCX |
| END IF |
| IF( INCY.GT.0 )THEN |
| KY = 1 |
| ELSE |
| KY = 1 - ( N - 1 )*INCY |
| END IF |
| * |
| * Start the operations. In this version the elements of A are |
| * accessed sequentially with one pass through the triangular part |
| * of A. |
| * |
| * First form y := beta*y. |
| * |
| IF( BETA.NE.ONE )THEN |
| IF( INCY.EQ.1 )THEN |
| IF( BETA.EQ.ZERO )THEN |
| DO 10, I = 1, N |
| Y( I ) = ZERO |
| 10 CONTINUE |
| ELSE |
| DO 20, I = 1, N |
| Y( I ) = BETA*Y( I ) |
| 20 CONTINUE |
| END IF |
| ELSE |
| IY = KY |
| IF( BETA.EQ.ZERO )THEN |
| DO 30, I = 1, N |
| Y( IY ) = ZERO |
| IY = IY + INCY |
| 30 CONTINUE |
| ELSE |
| DO 40, I = 1, N |
| Y( IY ) = BETA*Y( IY ) |
| IY = IY + INCY |
| 40 CONTINUE |
| END IF |
| END IF |
| END IF |
| IF( ALPHA.EQ.ZERO ) |
| $ RETURN |
| |
| |
| IF( LSAME( UPLO, 'U' ) )THEN |
| * |
| * Form y when A is stored in upper triangle. |
| * |
| IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN |
| DO 60, J = 1, N |
| TEMP1 = ALPHA*X( J ) |
| TEMP2 = ZERO |
| DO 50, I = 1, J - 1 |
| Y( I ) = Y( I ) + TEMP1*A( I, J ) |
| TEMP2 = TEMP2 + CONJG( A( I, J ) )*X( I ) |
| 50 CONTINUE |
| Y( J ) = Y( J ) + TEMP1*REAL( A( J, J ) ) + ALPHA*TEMP2 |
| 60 CONTINUE |
| ELSE |
| JX = KX |
| JY = KY |
| DO 80, J = 1, N |
| TEMP1 = ALPHA*X( JX ) |
| TEMP2 = ZERO |
| IX = KX |
| IY = KY |
| DO 70, I = 1, J - 1 |
| Y( IY ) = Y( IY ) + TEMP1*A( I, J ) |
| TEMP2 = TEMP2 + CONJG( A( I, J ) )*X( IX ) |
| IX = IX + INCX |
| IY = IY + INCY |
| 70 CONTINUE |
| Y( JY ) = Y( JY ) + TEMP1*REAL( A( J, J ) ) + ALPHA*TEMP2 |
| JX = JX + INCX |
| JY = JY + INCY |
| 80 CONTINUE |
| END IF |
| RETURN |
| ENDIF |
| |
| IF( LSAME( UPLO, 'L' ) )THEN |
| * |
| * Form y when A is stored in lower triangle. |
| * |
| IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN |
| DO 100, J = 1, N |
| TEMP1 = ALPHA*X( J ) |
| TEMP2 = ZERO |
| Y( J ) = Y( J ) + TEMP1*REAL( A( J, J ) ) |
| DO 90, I = J + 1, N |
| Y( I ) = Y( I ) + TEMP1*A( I, J ) |
| TEMP2 = TEMP2 + CONJG( A( I, J ) )*X( I ) |
| 90 CONTINUE |
| Y( J ) = Y( J ) + ALPHA*TEMP2 |
| 100 CONTINUE |
| ELSE |
| JX = KX |
| JY = KY |
| DO 120, J = 1, N |
| TEMP1 = ALPHA*X( JX ) |
| TEMP2 = ZERO |
| Y( JY ) = Y( JY ) + TEMP1*REAL( A( J, J ) ) |
| IX = JX |
| IY = JY |
| DO 110, I = J + 1, N |
| IX = IX + INCX |
| IY = IY + INCY |
| Y( IY ) = Y( IY ) + TEMP1*A( I, J ) |
| TEMP2 = TEMP2 + CONJG( A( I, J ) )*X( IX ) |
| 110 CONTINUE |
| Y( JY ) = Y( JY ) + ALPHA*TEMP2 |
| JX = JX + INCX |
| JY = JY + INCY |
| 120 CONTINUE |
| END IF |
| RETURN |
| END IF |
| |
| IF( LSAME( UPLO, 'V' ) )THEN |
| * |
| * Form y when A is stored in upper triangle. |
| * |
| IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN |
| DO 160, J = 1, N |
| TEMP1 = ALPHA*X( J ) |
| TEMP2 = ZERO |
| DO 150, I = 1, J - 1 |
| Y( I ) = Y( I ) + TEMP1* CONJG(A( I, J )) |
| TEMP2 = TEMP2 + A( I, J )*X( I ) |
| 150 CONTINUE |
| Y( J ) = Y( J ) + TEMP1*REAL( A( J, J ) ) + ALPHA*TEMP2 |
| 160 CONTINUE |
| ELSE |
| JX = KX |
| JY = KY |
| DO 180, J = 1, N |
| TEMP1 = ALPHA*X( JX ) |
| TEMP2 = ZERO |
| IX = KX |
| IY = KY |
| DO 170, I = 1, J - 1 |
| Y( IY ) = Y( IY ) + TEMP1* CONJG(A( I, J )) |
| TEMP2 = TEMP2 + A( I, J )*X( IX ) |
| IX = IX + INCX |
| IY = IY + INCY |
| 170 CONTINUE |
| Y( JY ) = Y( JY ) + TEMP1*REAL( A( J, J ) ) + ALPHA*TEMP2 |
| JX = JX + INCX |
| JY = JY + INCY |
| 180 CONTINUE |
| END IF |
| RETURN |
| ENDIF |
| |
| |
| IF( LSAME( UPLO, 'M' ) )THEN |
| * |
| * Form y when A is stored in lower triangle. |
| * |
| IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN |
| DO 200, J = 1, N |
| TEMP1 = ALPHA*X( J ) |
| TEMP2 = ZERO |
| Y( J ) = Y( J ) + TEMP1*REAL( A( J, J ) ) |
| DO 190, I = J + 1, N |
| Y( I ) = Y( I ) + TEMP1*CONJG(A( I, J )) |
| TEMP2 = TEMP2 + A( I, J )*X( I ) |
| 190 CONTINUE |
| Y( J ) = Y( J ) + ALPHA*TEMP2 |
| 200 CONTINUE |
| ELSE |
| JX = KX |
| JY = KY |
| DO 220, J = 1, N |
| TEMP1 = ALPHA*X( JX ) |
| TEMP2 = ZERO |
| Y( JY ) = Y( JY ) + TEMP1*REAL( A( J, J ) ) |
| IX = JX |
| IY = JY |
| DO 210, I = J + 1, N |
| IX = IX + INCX |
| IY = IY + INCY |
| Y( IY ) = Y( IY ) + TEMP1*CONJG(A( I, J )) |
| TEMP2 = TEMP2 + A( I, J )*X( IX ) |
| 210 CONTINUE |
| Y( JY ) = Y( JY ) + ALPHA*TEMP2 |
| JX = JX + INCX |
| JY = JY + INCY |
| 220 CONTINUE |
| END IF |
| RETURN |
| END IF |
| |
| * |
| * |
| * End of CHEMV . |
| * |
| END |