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HPL_dtrsv(3)		     HPL Library Functions		  HPL_dtrsv(3)

NAME
       HPL_dtrsv - x :=	A^{-1} x.

SYNOPSIS
       #include	"hpl.h"

       void  HPL_dtrsv(	 const enum HPL_ORDER ORDER, const enum	HPL_UPLO UPLO,
       const enum HPL_TRANS TRANS, const enum  HPL_DIAG	 DIAG,	const  int  N,
       const double * A, const int LDA,	double * X, const int INCX );

DESCRIPTION
       HPL_dtrsv solves	one of the systems of equations

	   A * x = b,	or   A^T * x = b,

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

ARGUMENTS
       ORDER   (local input)	       const enum HPL_ORDER
	       On  entry,  ORDER  specifies the	storage	format of the operands
	       as follows:
		  ORDER	= HplRowMajor,
		  ORDER	= HplColumnMajor.

       UPLO    (local input)	       const enum HPL_UPLO
	       On  entry,   UPLO   specifies  whether  the  upper   or	 lower
	       triangular   part   of the array	 A  is to be referenced.  When
	       UPLO==HplUpper, only  the upper triangular part of A is	to  be
	       referenced, otherwise only the lower triangular part of A is to
	       be referenced.

       TRANS   (local input)	       const enum HPL_TRANS
	       On  entry,   TRANS  specifies  the equations  to	 be  solved as
	       follows:
		  TRANS==HplNoTrans	A   * x	= b,
		  TRANS==HplTrans	A^T * x	= b.

       DIAG    (local input)	       const enum HPL_DIAG
	       On entry,  DIAG	specifies  whether  A  is unit	triangular  or
	       not.  When  DIAG==HplUnit,  A is	assumed	to be unit triangular,
	       and otherwise, A	is not assumed to be unit triangular.

       N       (local input)	       const int
	       On entry, N specifies the order of the matrix A.	N must	be  at
	       least zero.

       A       (local input)	       const double *
	       On  entry,   A  points  to an array of size equal to or greater
	       than LDA	* n. Before entry with	UPLO==HplUpper,	 the leading n
	       by n upper triangular  part of the array	A must contain the up-
	       per triangular  matrix and  the	 strictly   lower   triangular
	       part  of	 A is not referenced.  When  UPLO==HplLower  on	entry,
	       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==HplUnit,	 the diagonal elements	of   A
	       not referenced  either,	but are	assumed	to be unity.

       LDA     (local input)	       const int
	       On  entry,   LDA	 specifies  the	 leading  dimension  of	 A  as
	       declared	 in  the  calling  (sub) program.  LDA	must   be   at
	       least MAX(1,n).

       X       (local input/output)    double *
	       On entry,  X  is	an incremented array of	dimension  at  least (
	       1  +  (	n  - 1 ) * abs(	INCX ) )  that	contains the vector x.
	       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    (local input)	       const int
	       On entry, INCX specifies	the increment for the elements	of  X.
	       INCX must not be	zero.

EXAMPLE
       #include	"hpl.h"

       int main(int argc, char *argv[])
       {
	  double a[2*2], x[2];
	  a[0] = 4.0; a[1] = 1.0; a[2] = 2.0; a[3] = 5.0;
	  x[0] = 2.0; x[1] = 1.0;
	  HPL_dtrsv( HplColumnMajor, HplLower, HplNoTrans,
		     HplNoUnit,	a, 2, x, 1 );
	  printf("x=[%f,%f]\n",	x[0], x[1]);
	  exit(0); return(0);
       }

SEE ALSO
       HPL_dger	(3), HPL_dgemv (3).

HPL 2.3			       December	2, 2018			  HPL_dtrsv(3)

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