nag_dtrsm (f16yjc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_dtrsm (f16yjc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_dtrsm (f16yjc) solves a system of equations given as a real triangular matrix with multiple right-hand sides.

2  Specification

#include <nag.h>
#include <nagf16.h>
void  nag_dtrsm (Nag_OrderType order, Nag_SideType side, Nag_UploType uplo, Nag_TransType trans, Nag_DiagType diag, Integer m, Integer n, double alpha, const double a[], Integer pda, double b[], Integer pdb, NagError *fail)

3  Description

nag_dtrsm (f16yjc) performs one of the matrix-matrix operations
BαA-1B, BαA-TB, BαBA-1  or BαBA-T,
where A is a real triangular matrix, B is an m by n real matrix, and α is a real scalar. A-T denotes A-T or equivalently A-T.

4  References

The BLAS Technical Forum Standard (2001) http://www.netlib.org/blas/blast-forum

5  Arguments

1:     orderNag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by order=Nag_RowMajor. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     sideNag_SideTypeInput
On entry: specifies whether B is operated on from the left or the right.
side=Nag_LeftSide
B is pre-multiplied from the left.
side=Nag_RightSide
B is post-multiplied from the right.
Constraint: side=Nag_LeftSide or Nag_RightSide.
3:     uploNag_UploTypeInput
On entry: specifies whether A is upper or lower triangular.
uplo=Nag_Upper
A is upper triangular.
uplo=Nag_Lower
A is lower triangular.
Constraint: uplo=Nag_Upper or Nag_Lower.
4:     transNag_TransTypeInput
On entry: specifies the operation to be performed.
trans=Nag_Trans or Nag_ConjTrans and side=Nag_LeftSide
BαA-TB.
trans=Nag_NoTrans and side=Nag_LeftSide
BαA-1B.
trans=Nag_Trans or Nag_ConjTrans and side=Nag_RightSide
BαBA-T.
trans=Nag_NoTrans and side=Nag_RightSide
BαBA-1.
Constraint: trans=Nag_NoTrans, Nag_Trans or Nag_ConjTrans.
5:     diagNag_DiagTypeInput
On entry: specifies whether A has nonunit or unit diagonal elements.
diag=Nag_NonUnitDiag
The diagonal elements are stored explicitly.
diag=Nag_UnitDiag
The diagonal elements are assumed to be 1 and are not referenced.
Constraint: diag=Nag_NonUnitDiag or Nag_UnitDiag.
6:     mIntegerInput
On entry: m, the number of rows of the matrix B; the order of A if side=Nag_LeftSide.
Constraint: m0.
7:     nIntegerInput
On entry: n, the number of columns of the matrix B; the order of A if side=Nag_RightSide.
Constraint: n0.
8:     alphadoubleInput
On entry: the scalar α.
9:     a[dim]const doubleInput
Note: the dimension, dim, of the array a must be at least
  • max1,pda×m when side=Nag_LeftSide;
  • max1,pda×n when side=Nag_RightSide.
On entry: the triangular matrix A; A is m by m if side=Nag_LeftSide, or n by n if side=Nag_RightSide.
If order=Nag_ColMajor, Aij is stored in a[j-1×pda+i-1].
If order=Nag_RowMajor, Aij is stored in a[i-1×pda+j-1].
If uplo=Nag_Upper, A is upper triangular and the elements of the array corresponding to the lower triangular part of A are not referenced.
If uplo=Nag_Lower, A is lower triangular and the elements of the array corresponding to the upper triangular part of A are not referenced.
If diag=Nag_UnitDiag, the diagonal elements of A are assumed to be 1, and are not referenced.
10:   pdaIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) of the matrix A in the array a.
Constraints:
  • if side=Nag_LeftSide, pdamax1,m;
  • if side=Nag_RightSide, pdamax1,n.
11:   b[dim]doubleInput/Output
Note: the dimension, dim, of the array b must be at least
  • max1,pdb×n when order=Nag_ColMajor;
  • max1,m×pdb when order=Nag_RowMajor.
If order=Nag_ColMajor, Bij is stored in b[j-1×pdb+i-1].
If order=Nag_RowMajor, Bij is stored in b[i-1×pdb+j-1].
On entry: the m by n matrix B.
If alpha=0, b need not be set.
On exit: the updated matrix B.
12:   pdbIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array b.
Constraints:
  • if order=Nag_ColMajor, pdbmax1,m;
  • if order=Nag_RowMajor, pdbmax1,n.
13:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_ENUM_INT_2
On entry, side=value, pda=value, m=value.
Constraint: if side=Nag_LeftSide, pdamax1,m.
On entry, side=value, pda=value, n=value.
Constraint: if side=Nag_RightSide, pdamax1,n.
NE_INT
On entry, m=value.
Constraint: m0.
On entry, n=value.
Constraint: n0.
NE_INT_2
On entry, pdb=value, m=value.
Constraint: pdbmax1,m.
On entry, pdb=value and n=value.
Constraint: pdbmax1,n.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

7  Accuracy

The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of The BLAS Technical Forum Standard (2001)).

8  Further Comments

No test for singularity or near-singularity of A is included in nag_dtrsm (f16yjc). Such tests must be performed before calling this function.

9  Example

Premultiply real 4 by 2 matrix B by inverse of lower triangular 4 by 4 matrix A, BA-1B (or solve AX=B and return result in B), where
A = 4.30 -3.96 -4.87 0.40 0.31 -8.02 -0.27 0.07 -5.95 0.12
and
B = -12.90 -21.50 16.75 14.93 -17.55 6.33 -11.04 8.09 .

9.1  Program Text

Program Text (f16yjce.c)

9.2  Program Data

Program Data (f16yjce.d)

9.3  Program Results

Program Results (f16yjce.r)


nag_dtrsm (f16yjc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012