*DECK CTRMV SUBROUTINE CTRMV (UPLO, TRANS, DIAG, N, A, LDA, X, INCX) C***BEGIN PROLOGUE CTRMV C***PURPOSE Multiply a complex vector by a complex triangular matrix. C***LIBRARY SLATEC (BLAS) C***CATEGORY D1B4 C***TYPE COMPLEX (STRMV-S, DTRMV-D, CTRMV-C) C***KEYWORDS LEVEL 2 BLAS, LINEAR ALGEBRA C***AUTHOR Dongarra, J. J., (ANL) C Du Croz, J., (NAG) C Hammarling, S., (NAG) C Hanson, R. J., (SNLA) C***DESCRIPTION C C CTRMV performs one of the matrix-vector operations C C x := A*x, or x := A'*x, or x := conjg( A')*x, C C where x is an n element vector and A is an n by n unit, or non-unit, C upper or lower triangular matrix. C C Parameters C ========== C C UPLO - CHARACTER*1. C On entry, UPLO specifies whether the matrix is an upper or C lower triangular matrix as follows: C C UPLO = 'U' or 'u' A is an upper triangular matrix. C C UPLO = 'L' or 'l' A is a lower triangular matrix. 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' x := A*x. C C TRANS = 'T' or 't' x := A'*x. C C TRANS = 'C' or 'c' x := conjg( A' )*x. C C Unchanged on exit. C C DIAG - CHARACTER*1. C On entry, DIAG specifies whether or not A is unit C triangular as follows: C C DIAG = 'U' or 'u' A is assumed to be unit triangular. C C DIAG = 'N' or 'n' A is not assumed to be unit C triangular. C C Unchanged on exit. C C N - INTEGER. C On entry, N specifies the order of the matrix A. C N must be at least zero. C Unchanged on exit. C C A - COMPLEX array of DIMENSION ( LDA, n ). C Before entry with UPLO = 'U' or 'u', the leading n by n C upper triangular part of the array A must contain the upper C triangular matrix and the strictly lower triangular part of C A is not referenced. C Before entry with UPLO = 'L' or 'l', the leading n by n C lower triangular part of the array A must contain the lower C triangular matrix and the strictly upper triangular part of C A is not referenced. C Note that when DIAG = 'U' or 'u', the diagonal elements of C A are not referenced either, but are assumed to be unity. 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. LDA must be at least C max( 1, n ). C Unchanged on exit. C C X - COMPLEX array of dimension at least C ( 1 + ( n - 1 )*abs( INCX ) ). C Before entry, the incremented array X must contain the n C element vector x. On exit, X is overwritten with the C transformed vector x. C C INCX - INTEGER. C On entry, INCX specifies the increment for the elements of C X. INCX must not be zero. C Unchanged on exit. C C***REFERENCES Dongarra, J. J., Du Croz, J., Hammarling, S., and C Hanson, R. J. An extended set of Fortran basic linear C algebra subprograms. ACM TOMS, Vol. 14, No. 1, C pp. 1-17, March 1988. C***ROUTINES CALLED LSAME, XERBLA C***REVISION HISTORY (YYMMDD) C 861022 DATE WRITTEN C 910605 Modified to meet SLATEC prologue standards. Only comment C lines were modified. (BKS) C***END PROLOGUE CTRMV C .. Scalar Arguments .. INTEGER INCX, LDA, N CHARACTER*1 DIAG, TRANS, UPLO C .. Array Arguments .. COMPLEX A( LDA, * ), X( * ) C .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) C .. Local Scalars .. COMPLEX TEMP INTEGER I, INFO, IX, J, JX, KX LOGICAL NOCONJ, NOUNIT C .. External Functions .. LOGICAL LSAME EXTERNAL LSAME C .. External Subroutines .. EXTERNAL XERBLA C .. Intrinsic Functions .. INTRINSIC CONJG, MAX C***FIRST EXECUTABLE STATEMENT CTRMV C C Test the input parameters. C INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. \$ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. \$ .NOT.LSAME( TRANS, 'T' ).AND. \$ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. \$ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CTRMV ', INFO ) RETURN END IF C C Quick return if possible. C IF( N.EQ.0 ) \$ RETURN C NOCONJ = LSAME( TRANS, 'T' ) NOUNIT = LSAME( DIAG , 'N' ) C C Set up the start point in X if the increment is not unity. This C will be ( N - 1 )*INCX too small for descending loops. C IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF C C Start the operations. In this version the elements of A are C accessed sequentially with one pass through A. C IF( LSAME( TRANS, 'N' ) )THEN C C Form x := A*x. C IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = X( J ) DO 10, I = 1, J - 1 X( I ) = X( I ) + TEMP*A( I, J ) 10 CONTINUE IF( NOUNIT ) \$ X( J ) = X( J )*A( J, J ) END IF 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 30, I = 1, J - 1 X( IX ) = X( IX ) + TEMP*A( I, J ) IX = IX + INCX 30 CONTINUE IF( NOUNIT ) \$ X( JX ) = X( JX )*A( J, J ) END IF JX = JX + INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN TEMP = X( J ) DO 50, I = N, J + 1, -1 X( I ) = X( I ) + TEMP*A( I, J ) 50 CONTINUE IF( NOUNIT ) \$ X( J ) = X( J )*A( J, J ) END IF 60 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 80, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 70, I = N, J + 1, -1 X( IX ) = X( IX ) + TEMP*A( I, J ) IX = IX - INCX 70 CONTINUE IF( NOUNIT ) \$ X( JX ) = X( JX )*A( J, J ) END IF JX = JX - INCX 80 CONTINUE END IF END IF ELSE C C Form x := A'*x or x := conjg( A' )*x. C IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 110, J = N, 1, -1 TEMP = X( J ) IF( NOCONJ )THEN IF( NOUNIT ) \$ TEMP = TEMP*A( J, J ) DO 90, I = J - 1, 1, -1 TEMP = TEMP + A( I, J )*X( I ) 90 CONTINUE ELSE IF( NOUNIT ) \$ TEMP = TEMP*CONJG( A( J, J ) ) DO 100, I = J - 1, 1, -1 TEMP = TEMP + CONJG( A( I, J ) )*X( I ) 100 CONTINUE END IF X( J ) = TEMP 110 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 140, J = N, 1, -1 TEMP = X( JX ) IX = JX IF( NOCONJ )THEN IF( NOUNIT ) \$ TEMP = TEMP*A( J, J ) DO 120, I = J - 1, 1, -1 IX = IX - INCX TEMP = TEMP + A( I, J )*X( IX ) 120 CONTINUE ELSE IF( NOUNIT ) \$ TEMP = TEMP*CONJG( A( J, J ) ) DO 130, I = J - 1, 1, -1 IX = IX - INCX TEMP = TEMP + CONJG( A( I, J ) )*X( IX ) 130 CONTINUE END IF X( JX ) = TEMP JX = JX - INCX 140 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 170, J = 1, N TEMP = X( J ) IF( NOCONJ )THEN IF( NOUNIT ) \$ TEMP = TEMP*A( J, J ) DO 150, I = J + 1, N TEMP = TEMP + A( I, J )*X( I ) 150 CONTINUE ELSE IF( NOUNIT ) \$ TEMP = TEMP*CONJG( A( J, J ) ) DO 160, I = J + 1, N TEMP = TEMP + CONJG( A( I, J ) )*X( I ) 160 CONTINUE END IF X( J ) = TEMP 170 CONTINUE ELSE JX = KX DO 200, J = 1, N TEMP = X( JX ) IX = JX IF( NOCONJ )THEN IF( NOUNIT ) \$ TEMP = TEMP*A( J, J ) DO 180, I = J + 1, N IX = IX + INCX TEMP = TEMP + A( I, J )*X( IX ) 180 CONTINUE ELSE IF( NOUNIT ) \$ TEMP = TEMP*CONJG( A( J, J ) ) DO 190, I = J + 1, N IX = IX + INCX TEMP = TEMP + CONJG( A( I, J ) )*X( IX ) 190 CONTINUE END IF X( JX ) = TEMP JX = JX + INCX 200 CONTINUE END IF END IF END IF C RETURN C C End of CTRMV . C END