1HPL_dtrsv(3)                 HPL Library Functions                HPL_dtrsv(3)
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4

NAME

6       HPL_dtrsv - x := A^{-1} x.
7

SYNOPSIS

9       #include "hpl.h"
10
11       void  HPL_dtrsv(  const enum HPL_ORDER ORDER, const enum HPL_UPLO UPLO,
12       const enum HPL_TRANS TRANS, const enum  HPL_DIAG  DIAG,  const  int  N,
13       const double * A, const int LDA, double * X, const int INCX );
14

DESCRIPTION

16       HPL_dtrsv solves one of the systems of equations
17
18           A * x = b,   or   A^T * x = b,
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20       where  b  and x are n-element vectors and  A  is an n by n non-unit, or
21       unit, upper or lower triangular matrix.
22
23       No test for  singularity  or  near-singularity  is included   in   this
24       routine. Such tests must be performed before calling this routine.
25

ARGUMENTS

27       ORDER   (local input)           const enum HPL_ORDER
28               On  entry,  ORDER  specifies the storage format of the operands
29               as follows:
30                  ORDER = HplRowMajor,
31                  ORDER = HplColumnMajor.
32
33       UPLO    (local input)           const enum HPL_UPLO
34               On  entry,   UPLO   specifies  whether  the  upper   or   lower
35               triangular   part   of the array  A  is to be referenced.  When
36               UPLO==HplUpper, only  the upper triangular part of A is  to  be
37               referenced, otherwise only the lower triangular part of A is to
38               be referenced.
39
40       TRANS   (local input)           const enum HPL_TRANS
41               On entry,  TRANS  specifies  the equations  to  be   solved  as
42               follows:
43                  TRANS==HplNoTrans     A   * x = b,
44                  TRANS==HplTrans       A^T * x = b.
45
46       DIAG    (local input)           const enum HPL_DIAG
47               On  entry,   DIAG  specifies  whether  A  is unit triangular or
48               not. When DIAG==HplUnit,  A is assumed to be  unit  triangular,
49               and otherwise, A is not assumed to be unit triangular.
50
51       N       (local input)           const int
52               On  entry,  N specifies the order of the matrix A. N must be at
53               least zero.
54
55       A       (local input)           const double *
56               On entry,  A  points  to an array of size equal to  or  greater
57               than LDA * n. Before entry with  UPLO==HplUpper,  the leading n
58               by n upper triangular  part of the array  A  must  contain  the
59               upper  triangular   matrix and the  strictly  lower  triangular
60               part of A is not referenced.  When  UPLO==HplLower   on  entry,
61               the   leading  n by n lower triangular part of the array A must
62               contain the lower triangular matrix  and  the   strictly  upper
63               triangular part of A is not referenced.
64
65               Note   that   when  DIAG==HplUnit,  the diagonal elements of  A
66               not referenced  either,  but are assumed to be unity.
67
68       LDA     (local input)           const int
69               On entry,  LDA  specifies  the  leading  dimension  of   A   as
70               declared   in   the  calling  (sub) program.  LDA  must  be  at
71               least MAX(1,n).
72
73       X       (local input/output)    double *
74               On entry,  X  is an incremented array of dimension  at  least (
75               1  +  (  n  - 1 ) * abs( INCX ) )  that  contains the vector x.
76               Before entry,  the  incremented array  X  must contain   the  n
77               element  right-hand  side vector b. On exit,  X  is overwritten
78               with the solution vector x.
79
80       INCX    (local input)           const int
81               On entry, INCX specifies the increment for the elements  of  X.
82               INCX must not be zero.
83

EXAMPLE

85       #include "hpl.h"
86
87       int main(int argc, char *argv[])
88       {
89          double a[2*2], x[2];
90          a[0] = 4.0; a[1] = 1.0; a[2] = 2.0; a[3] = 5.0;
91          x[0] = 2.0; x[1] = 1.0;
92          HPL_dtrsv( HplColumnMajor, HplLower, HplNoTrans,
93                     HplNoUnit, a, 2, x, 1 );
94          printf("x=[%f,%f]\n", x[0], x[1]);
95          exit(0); return(0);
96       }
97

SEE ALSO

99       HPL_dger (3), HPL_dgemv (3).
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103HPL 2.2                        February 24, 2016                  HPL_dtrsv(3)
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