Centre Blaise Pascal » HPL sur GPU

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

.SH NAME

HPL_dtrsm \- B := A^{-1} * B  or  B := B * A^{-1}.

.SH SYNOPSIS

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

\fB\&void\fR

\fB\&HPL_dtrsm(\fR

\fB\&const enum HPL_ORDER\fR

\fI\&ORDER\fR,

\fB\&const enum HPL_SIDE\fR

\fI\&SIDE\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\&M\fR,

\fB\&const int\fR

\fI\&N\fR,

\fB\&const double\fR

\fI\&ALPHA\fR,

\fB\&const double *\fR

\fI\&A\fR,

\fB\&const int\fR

\fI\&LDA\fR,

\fB\&double *\fR

\fI\&B\fR,

\fB\&const int\fR

\fI\&LDB\fR

\fB\&);\fR

.SH DESCRIPTION

\fB\&HPL_dtrsm\fR

solves one of the matrix equations

   op( A ) * X = alpha * B,   or  X * op( A ) = alpha * B,

where alpha is a scalar, X and B are m by n matrices, A is a unit, or

non-unit, upper or lower triangular matrix and op(A) is one of

   op( A ) = A   or   op( A ) = A^T.

The matrix X is overwritten on B.

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

SIDE    (local input)           const enum HPL_SIDE

On entry, SIDE  specifies  whether  op(A) appears on the left

or right of X as follows:

   SIDE==HplLeft    op( A ) * X = alpha * B,

   SIDE==HplRight   X * op( A ) = alpha * B.

.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, TRANSA  specifies the form of  op(A)  to be used in

the matrix-matrix operation follows:                         

   TRANSA==HplNoTrans    : op( A ) = A,                     

   TRANSA==HplTrans      : op( A ) = A^T,                   

   TRANSA==HplConjTrans  : op( A ) = A^T.                   

.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

M       (local input)           const int

On entry,  M  specifies  the number of rows of the  matrix B.

M must be at least zero.

.TP 8

N       (local input)           const int

On entry, N  specifies the number of columns of the matrix B.

N must be at least zero.

.TP 8

ALPHA   (local input)           const double

On entry, ALPHA specifies the scalar alpha.   When  ALPHA  is

supplied  as  zero then the elements of the matrix B need not

be set on input.

.TP 8

A       (local input)           const double *

On entry,  A  points  to an array of size equal to or greater

than LDA * k,  where  k is m  when  SIDE==HplLeft  and  is  n

otherwise.  Before  entry  with  UPLO==HplUpper,  the leading

k by k 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 k by k 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,m) when SIDE==HplLeft, and MAX(1,n) otherwise.

.TP 8

B       (local input/output)    double *

On entry,  B  points  to an array of size equal to or greater

than LDB * n.  Before entry, the leading  m by n  part of the

array B must contain the matrix  B, except when beta is zero,

in which case B need not be set on entry.  On exit, the array

B is overwritten by the m by n solution matrix.

.TP 8

LDB     (local input)           const int

On entry,  LDB  specifies  the  leading  dimension  of  B  as

declared  in  the  calling  (sub) program.  LDB  must  be  at

least MAX(1,m).

.SH EXAMPLE

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

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

.br

{

.br

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

.br

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

.br

   b[0] = 2.0; b[1] = 1.0; b[2] = 1.0; b[3] = 2.0;

.br

   HPL_dtrsm( HplColumnMajor, HplLeft, HplUpper,

.br

              HplNoTrans, HplNonUnit, 2, 2, 2.0,

.br

              a, 2, b, 2 );

.br

   printf("  [%f,%f]\en", b[0], b[2]);

.br

   printf("b=[%f,%f]\en", b[1], b[3]);

.br

   exit(0); return(0);

.br

}

.SH SEE ALSO

.BR HPL_dgemm \ (3).