ctrmvf.f

SUBROUTINECTRMVF ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )
* .. Scalar Arguments ..
INTEGER INCX, LDA, N
CHARACTER*1 DIAG, TRANS, UPLO
* .. Array Arguments ..
COMPLEX A( LDA, * ), X( * )
* ..
*
* Purpose
* =======
*
* CTRMV performs one of the matrix-vector operations
*
* x := A*x, or x := A'*x, or x := conjg( A' )*x,
*
* where x is an n element vector and A is an n by n unit, or non-unit,
* upper or lower triangular matrix.
*
* Parameters
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the matrix is an upper or
* lower triangular matrix as follows:
*
* UPLO = 'U' or 'u' A is an upper triangular matrix.
*
* UPLO = 'L' or 'l' A is a lower triangular matrix.
*
* Unchanged on exit.
*
* TRANS - CHARACTER*1.
* On entry, TRANS specifies the operation to be performed as
* follows:
*
* TRANS = 'N' or 'n' x := A*x.
*
* TRANS = 'T' or 't' x := A'*x.
*
* TRANS = 'C' or 'c' x := conjg( A' )*x.
*
* Unchanged on exit.
*
* DIAG - CHARACTER*1.
* On entry, DIAG specifies whether or not A is unit
* triangular as follows:
*
* DIAG = 'U' or 'u' A is assumed to be unit triangular.
*
* DIAG = 'N' or 'n' A is not assumed to be unit
* triangular.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* 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 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 matrix and the strictly upper triangular part of
* A is not referenced.
* Note that when DIAG = 'U' or 'u', the diagonal elements of
* A are not referenced either, but are assumed to be unity.
* 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. On exit, X is overwritten with the
* tranformed vector x.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX 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 ZERO
PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
* .. Local Scalars ..
COMPLEX TEMP
INTEGER I, INFO, IX, J, JX, KX
LOGICAL NOCONJ, NOUNIT
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* .. External Subroutines ..
EXTERNAL XERBLA
* .. Intrinsic Functions ..
INTRINSIC CONJG, MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
 INFO =0
IF ( .NOT.LSAME( UPLO , 'U' ).AND.
 $ .NOT.LSAME( UPLO , 'L' ) )THEN
 INFO =1
ELSEIF( .NOT.LSAME( TRANS, 'N' ).AND.
 $ .NOT.LSAME( TRANS, 'T' ).AND.
 $ .NOT.LSAME( TRANS, 'R' ).AND.
 $ .NOT.LSAME( TRANS, 'C' ) )THEN
 INFO =2
ELSEIF( .NOT.LSAME( DIAG , 'U' ).AND.
 $ .NOT.LSAME( DIAG , 'N' ) )THEN
 INFO =3
ELSEIF( N.LT.0 )THEN
 INFO =4
ELSEIF( LDA.LT.MAX( 1, N ) )THEN
 INFO =6
ELSEIF( INCX.EQ.0 )THEN
 INFO =8
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'CTRMV ', INFO )
RETURN
END IF
*
* Quick return if possible.
*
IF( N.EQ.0 )
 $ RETURN
*
 NOCONJ = LSAME( TRANS, 'N' ) .OR. LSAME( TRANS, 'T' )
 NOUNIT = LSAME( DIAG , 'N' )
*
* Set up the start point in X if the increment is not unity. This
* will be ( N - 1 )*INCX too small for descending loops.
*
IF( INCX.LE.0 )THEN
 KX =1- ( N -1 )*INCX
ELSEIF( INCX.NE.1 )THEN
 KX =1
END IF
*
* Start the operations. In this version the elements of A are
* accessed sequentially with one pass through A.
*
IF( LSAME( TRANS, 'N' ) .OR. LSAME( TRANS, 'R' ))THEN
*
* Form x := A*x.
*
IF( LSAME( UPLO, 'U' ) )THEN
IF( INCX.EQ.1 )THEN
DO20, J =1, N
IF( X( J ).NE.ZERO )THEN
 TEMP = X( J )
DO10, I =1, J -1
IF (NOCONJ) THEN
 X( I ) = X( I ) + TEMP*A( I, J )
ELSE
 X( I ) = X( I ) + TEMP*CONJG(A( I, J ))
ENDIF
10CONTINUE
IF (NOCONJ) THEN
IF( NOUNIT )
 $ X( J ) = X( J )*A( J, J )
ELSE
IF( NOUNIT )
 $ X( J ) = X( J )*CONJG(A( J, J ))
ENDIF
END IF
20CONTINUE
ELSE
 JX = KX
DO40, J =1, N
IF( X( JX ).NE.ZERO )THEN
 TEMP = X( JX )
 IX = KX
DO30, I =1, J -1
IF (NOCONJ) THEN
 X( IX ) = X( IX ) + TEMP*A( I, J )
ELSE
 X( IX ) = X( IX ) + TEMP*CONJG(A( I, J ))
ENDIF
 IX = IX + INCX
30CONTINUE
IF (NOCONJ) THEN
IF( NOUNIT )
 $ X( JX ) = X( JX )*A( J, J )
ELSE
IF( NOUNIT )
 $ X( JX ) = X( JX )*CONJG(A( J, J ))
ENDIF
END IF
 JX = JX + INCX
40CONTINUE
END IF
ELSE
IF( INCX.EQ.1 )THEN
DO60, J = N, 1, -1
IF( X( J ).NE.ZERO )THEN
 TEMP = X( J )
DO50, I = N, J +1, -1
IF (NOCONJ) THEN
 X( I ) = X( I ) + TEMP*A( I, J )
ELSE
 X( I ) = X( I ) + TEMP*CONJG(A( I, J ))
ENDIF
50CONTINUE
IF (NOCONJ) THEN
IF( NOUNIT )
 $ X( J ) = X( J )*A( J, J )
ELSE
IF( NOUNIT )
 $ X( J ) = X( J )*CONJG(A( J, J ))
ENDIF
END IF
60CONTINUE
ELSE
 KX = KX + ( N -1 )*INCX
 JX = KX
DO80, J = N, 1, -1
IF( X( JX ).NE.ZERO )THEN
 TEMP = X( JX )
 IX = KX
DO70, I = N, J +1, -1
IF (NOCONJ) THEN
 X( IX ) = X( IX ) + TEMP*A( I, J )
ELSE
 X( IX ) = X( IX ) + TEMP*CONJG(A( I, J ))
ENDIF
 IX = IX - INCX
70CONTINUE
IF (NOCONJ) THEN
IF( NOUNIT )
 $ X( JX ) = X( JX )*A( J, J )
ELSE
IF( NOUNIT )
 $ X( JX ) = X( JX )*CONJG(A( J, J ))
ENDIF
END IF
 JX = JX - INCX
80CONTINUE
END IF
END IF
ELSE
*
* Form x := A'*x or x := conjg( A' )*x.
*
IF( LSAME( UPLO, 'U' ) )THEN
IF( INCX.EQ.1 )THEN
DO110, J = N, 1, -1
 TEMP = X( J )
IF( NOCONJ )THEN
IF( NOUNIT )
 $ TEMP = TEMP*A( J, J )
DO90, I = J -1, 1, -1
 TEMP = TEMP + A( I, J )*X( I )
90CONTINUE
ELSE
IF( NOUNIT )
 $ TEMP = TEMP*CONJG( A( J, J ) )
DO100, I = J -1, 1, -1
 TEMP = TEMP +CONJG( A( I, J ) )*X( I )
100CONTINUE
END IF
 X( J ) = TEMP
110CONTINUE
ELSE
 JX = KX + ( N -1 )*INCX
DO140, J = N, 1, -1
 TEMP = X( JX )
 IX = JX
IF( NOCONJ )THEN
IF( NOUNIT )
 $ TEMP = TEMP*A( J, J )
DO120, I = J -1, 1, -1
 IX = IX - INCX
 TEMP = TEMP + A( I, J )*X( IX )
120CONTINUE
ELSE
IF( NOUNIT )
 $ TEMP = TEMP*CONJG( A( J, J ) )
DO130, I = J -1, 1, -1
 IX = IX - INCX
 TEMP = TEMP +CONJG( A( I, J ) )*X( IX )
130CONTINUE
END IF
 X( JX ) = TEMP
 JX = JX - INCX
140CONTINUE
END IF
ELSE
IF( INCX.EQ.1 )THEN
DO170, J =1, N
 TEMP = X( J )
IF( NOCONJ )THEN
IF( NOUNIT )
 $ TEMP = TEMP*A( J, J )
DO150, I = J +1, N
 TEMP = TEMP + A( I, J )*X( I )
150CONTINUE
ELSE
IF( NOUNIT )
 $ TEMP = TEMP*CONJG( A( J, J ) )
DO160, I = J +1, N
 TEMP = TEMP +CONJG( A( I, J ) )*X( I )
160CONTINUE
END IF
 X( J ) = TEMP
170CONTINUE
ELSE
 JX = KX
DO200, J =1, N
 TEMP = X( JX )
 IX = JX
IF( NOCONJ )THEN
IF( NOUNIT )
 $ TEMP = TEMP*A( J, J )
DO180, I = J +1, N
 IX = IX + INCX
 TEMP = TEMP + A( I, J )*X( IX )
180CONTINUE
ELSE
IF( NOUNIT )
 $ TEMP = TEMP*CONJG( A( J, J ) )
DO190, I = J +1, N
 IX = IX + INCX
 TEMP = TEMP +CONJG( A( I, J ) )*X( IX )
190CONTINUE
END IF
 X( JX ) = TEMP
 JX = JX + INCX
200CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of CTRMV .
*
END