dtpsv man page on Scientific

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DTPSV(1)			 BLAS routine			      DTPSV(1)

NAME
       DTPSV - solves one of the systems of equations	A*x = b, or A'*x = b,

SYNOPSIS
       SUBROUTINE DTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)

	   INTEGER				     INCX,N

	   CHARACTER				     DIAG,TRANS,UPLO

	   DOUBLE				     PRECISION AP(*),X(*)

PURPOSE
       DTPSV  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, supplied in packed form.

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

ARGUMENTS
       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'   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.

       AP     - DOUBLE PRECISION array of DIMENSION at least
	      ( ( n*( n + 1 ) )/2 ).  Before entry with	 UPLO =	 'U'  or  'u',
	      the  array  AP  must  contain the upper triangular matrix packed
	      sequentially, column by column, so that AP( 1 ) contains a( 1, 1
	      ),  AP(  2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respec‐
	      tively, and so on.  Before entry with UPLO =  'L'	 or  'l',  the
	      array AP must contain the lower triangular matrix packed sequen‐
	      tially, column by column, so that AP( 1 ) contains a(  1,	 1  ),
	      AP(  2  )	 and  AP(  3 ) contain a( 2, 1 ) and a( 3, 1 ) respec‐
	      tively, and so on.  Note that when  DIAG = 'U' or 'u', the diag‐
	      onal  elements  of  A  are not referenced, but are assumed to be
	      unity.  Unchanged on exit.

       X      - DOUBLE PRECISION 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.

FURTHER DETAILS
       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.

BLAS routine			 November 2008			      DTPSV(1)
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