ztrmv(3) [debian man page]

ZTRMV(3)							   BLAS routine 							  ZTRMV(3)

NAME

       ZTRMV - perform one of the matrix-vector operations   x := A*x, or x := A'*x, or x := conjg( A' )*x,

SYNOPSIS

       SUBROUTINE ZTRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )

	   INTEGER	INCX, LDA, N

	   CHARACTER*1	DIAG, TRANS, UPLO

	   COMPLEX*16	A( LDA, * ), X( * )

PURPOSE

       ZTRMV  performs one of the matrix-vector operations

       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*16	 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 refer-
	      enced.  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*16	 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 Cen-
	      tral Office.  Richard Hanson, Sandia National Labs.

BLAS routine							  16 October 1992							  ZTRMV(3)

ZTRSV(l)							   BLAS routine 							  ZTRSV(l)

NAME

       ZTRSV - solve one of the systems of equations   A*x = b, or A'*x = b, or conjg( A' )*x = b,

SYNOPSIS

       SUBROUTINE ZTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )

	   INTEGER	INCX, LDA, N

	   CHARACTER*1	DIAG, TRANS, UPLO

	   COMPLEX*16	A( LDA, * ), X( * )

PURPOSE

       ZTRSV  solves one of the systems of equations

       where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix.

       No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.

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 equations to be solved as follows:

	      TRANS = 'N' or 'n'   A*x = b.

	      TRANS = 'T' or 't'   A'*x = b.

	      TRANS = 'C' or 'c'   conjg( A' )*x = b.

	      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*16	 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 refer-
	      enced.  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*16	 array of dimension at least
	      ( 1 + ( n - 1 )*abs( INCX ) ).  Before entry, the incremented array X must contain the n element right-hand side vector b. On  exit,
	      X is overwritten with the solution 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 Cen-
	      tral Office.  Richard Hanson, Sandia National Labs.

BLAS routine							  16 October 1992							  ZTRSV(l)