nag_ztrsv (f16sjc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_ztrsv (f16sjc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_ztrsv (f16sjc) solves a system of equations given as a complex triangular matrix.

2  Specification

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

3  Description

nag_ztrsv (f16sjc) performs one of the matrix-vector operations
xα A-1x,  xα A-Tx  or  x A-Hx,
where A is an n by n complex triangular matrix, x is an n-element complex vector and α is a complex scalar. A-T denotes A-T or equivalently A-T ; A-H denotes AH-1 or equivalently A-1H.

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:     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.
3:     transNag_TransTypeInput
On entry: specifies the operation to be performed.
trans=Nag_NoTrans
xA-1x.
trans=Nag_Trans
xA-Tx.
trans=Nag_ConjTrans
xA-Hx.
Constraint: trans=Nag_NoTrans, Nag_Trans or Nag_ConjTrans.
4:     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.
5:     nIntegerInput
On entry: n, the order of the matrix A.
Constraint: n0.
6:     alphaComplexInput
On entry: the scalar α.
7:     a[dim]const ComplexInput
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:     pdaIntegerInput
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]ComplexInput/Output
Note: the dimension, dim, of the array x must be at least max1,1+n-1incx.
On entry: the vector x.
On exit: the solution vector x.
10:   incxIntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
11:   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_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.

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_ztrsv (f16sjc). Such tests must be performed before calling this function.

9  Example

Solves complex triangular system of linear equations, Ax=y, where A is a complex triangular 4 by 4 matrix given by
A = 4.78+4.56i 2.00-0.30i -4.11+1.25i 2.89-1.34i 2.36-4.25i 4.15+0.80i -1.89+1.15i 0.04-3.69i -0.02+0.46i 0.33-0.26i ,
and
y = -14.78-32.36i 2.98-02.14i -20.96+17.06i 9.54+09.91i .

9.1  Program Text

Program Text (f16sjce.c)

9.2  Program Data

Program Data (f16sjce.d)

9.3  Program Results

Program Results (f16sjce.r)


nag_ztrsv (f16sjc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

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