Centre Blaise Pascal » HPL sur GPU

.TH HPL_dtrsv 3 "September 10, 2008" "HPL 2.0" "HPL Library Functions"

.SH NAME

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

.SH SYNOPSIS

\fB\&#include "hpl.h"\fR

\fB\&void\fR

\fB\&HPL_dtrsv(\fR

\fB\&const enum HPL_ORDER\fR

\fI\&ORDER\fR,

\fB\&const enum HPL_UPLO\fR

\fI\&UPLO\fR,

\fB\&const enum HPL_TRANS\fR

\fI\&TRANS\fR,

\fB\&const enum HPL_DIAG\fR

\fI\&DIAG\fR,

\fB\&const int\fR

\fI\&N\fR,

\fB\&const double *\fR

\fI\&A\fR,

\fB\&const int\fR

\fI\&LDA\fR,

\fB\&double *\fR

\fI\&X\fR,

\fB\&const int\fR

\fI\&INCX\fR

\fB\&);\fR

.SH DESCRIPTION

\fB\&HPL_dtrsv\fR

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.

.SH ARGUMENTS

.TP 8

ORDER   (local input)           const enum HPL_ORDER

On entry, ORDER  specifies the storage format of the operands

as follows:                                                  

   ORDER = HplRowMajor,                                      

   ORDER = HplColumnMajor.                                   

.TP 8

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. 

.TP 8

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.

.TP 8

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.

.TP 8

N       (local input)           const int

On entry, N specifies the order of the matrix A. N must be at

least zero.

.TP 8

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

upper 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.

.TP 8

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).

.TP 8

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.

.TP 8

INCX    (local input)           const int

On entry, INCX specifies the increment for the elements of X.

INCX must not be zero.

.SH EXAMPLE

\fI\&#include "hpl.h"\fR

int main(int argc, char *argv[])

.br

{

.br

   double a[2*2], x[2];

.br

   a[0] = 4.0; a[1] = 1.0; a[2] = 2.0; a[3] = 5.0;

.br

   x[0] = 2.0; x[1] = 1.0;

.br

   HPL_dtrsv( HplColumnMajor, HplLower, HplNoTrans,

.br

              HplNoUnit, a, 2, x, 1 );

.br

   printf("x=[%f,%f]\en", x[0], x[1]);

.br

   exit(0); return(0);

.br

}

.SH SEE ALSO

.BR HPL_dger \ (3),

.BR HPL_dgemv \ (3).