NAG Library Function Document

nag_dtrsv (f16pjc)

 Contents

    1  Purpose
    7  Accuracy

1
Purpose

nag_dtrsv (f16pjc) solves a system of equations given as a real triangular matrix.

2
Specification

#include <nag.h>
#include <nagf16.h>
void  nag_dtrsv (Nag_OrderType order, Nag_UploType uplo, Nag_TransType trans, Nag_DiagType diag, Integer n, double alpha, const double a[], Integer pda, double x[], Integer incx, NagError *fail)

3
Description

nag_dtrsv (f16pjc) performs one of the matrix-vector operations
xαA-1x   or  xα A-Tx,  
where A is an n by n real triangular matrix, x is an n-element real vector and α is a real scalar. A-T  denotes A-T  or equivalently A-T .

4
References

Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001) Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard University of Tennessee, Knoxville, Tennessee http://www.netlib.org/blas/blast-forum/blas-report.pdf

5
Arguments

1:     order Nag_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 3.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     uplo Nag_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.
3:     trans Nag_TransTypeInput
On entry: specifies the operation to be performed.
trans=Nag_NoTrans
xαA-1x.
trans=Nag_Trans or Nag_ConjTrans
xαA-Tx.
Constraint: trans=Nag_NoTrans, Nag_Trans or Nag_ConjTrans.
4:     diag Nag_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.
5:     n IntegerInput
On entry: n, the order of the matrix A.
Constraint: n0.
6:     alpha doubleInput
On entry: the scalar α.
7:     a[dim] const doubleInput
Note: the dimension, dim, of the array a must be at least max1,pda×n.
On entry: the n by n triangular matrix A.
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, the upper triangular part of A must be stored and the elements of the array below the diagonal are not referenced.
If uplo=Nag_Lower, the lower triangular part of A must be stored and the elements of the array above the diagonal are not referenced.
If diag=Nag_UnitDiag, the diagonal elements of A are assumed to be 1, and are not referenced.
8:     pda IntegerInput
On entry: the stride separating row or column elements (depending on the value of order) of the matrix A in the array a.
Constraint: pdamax1,n.
9:     x[dim] doubleInput/Output
Note: the dimension, dim, of the array x must be at least max1,1+n-1incx.
On entry: the right-hand side vector b.
On exit: the solution vector x.
10:   incx IntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
11:   fail NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6
Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, incx=value.
Constraint: incx0.
On entry, n=value.
Constraint: n0.
NE_INT_2
On entry, pda=value, n=value.
Constraint: pdamax1,n.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7
Accuracy

The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001)).

8
Parallelism and Performance

nag_dtrsv (f16pjc) is not threaded in any implementation.

9
Further Comments

No test for singularity or near-singularity of A is included in nag_dtrsv (f16pjc). Such tests must be performed before calling this function.

10
Example

This example solves the real triangular system of linear equations Ax=y , where A  is the 4 by 4 triangular matrix given by
A = 4.30 -3.96 -4.87 0.40 0.31 -8.02 -0.27 0.07 -5.95 0.12  
and where
y = -12.90,16.75,-17.55,-11.04T .  
The vector y  is stored in array x and nag_dtrsv (f16pjc) returns the solution in x.

10.1
Program Text

Program Text (f16pjce.c)

10.2
Program Data

Program Data (f16pjce.d)

10.3
Program Results

Program Results (f16pjce.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017