nag_ztpsv (f16slc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_ztpsv (f16slc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_ztpsv (f16slc) solves a system of equations given as a complex triangular matrix stored in packed form.

2  Specification

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

3  Description

nag_ztpsv (f16slc) performs one of the matrix-vector operations
xαA-1x ,   xαA-Tx   or   xαA-Hx ,
where A is an n by n complex triangular matrix, stored in packed form, 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.
No test for singularity or near-singularity of A is included in this function. Such tests must be performed before calling this function.

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
xαA-1x.
trans=Nag_Trans
xαA-Tx.
trans=Nag_ConjTrans
xαA-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:     ap[dim]const ComplexInput
Note: the dimension, dim, of the array ap must be at least max1, n × n+1 / 2 .
On entry: the n by n triangular matrix A, packed by rows or columns.
The storage of elements Aij depends on the order and uplo arguments as follows:
  • if order=Nag_ColMajor and uplo=Nag_Upper,
              Aij is stored in ap[j-1×j/2+i-1], for ij;
  • if order=Nag_ColMajor and uplo=Nag_Lower,
              Aij is stored in ap[2n-j×j-1/2+i-1], for ij;
  • if order=Nag_RowMajor and uplo=Nag_Upper,
              Aij is stored in ap[2n-i×i-1/2+j-1], for ij;
  • if order=Nag_RowMajor and uplo=Nag_Lower,
              Aij is stored in ap[i-1×i/2+j-1], for ij.
If diag=Nag_UnitDiag, the diagonal elements of AP are assumed to be 1, and are not referenced; the same storage scheme is used whether diag=Nag_NonUnitDiag or diag=Nag_UnitDiag.
8:     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.
9:     incxIntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
10:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

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.

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

None.

9  Example

Solves complex triangular system of linear equations, Ax=y, where A is a complex triangular 4 by 4 matrix, stored in packed storage format, 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 (f16slce.c)

9.2  Program Data

Program Data (f16slce.d)

9.3  Program Results

Program Results (f16slce.r)


nag_ztpsv (f16slc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

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