NAG CL Interface
f16sjc (ztrsv)

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1 Purpose

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

2 Specification

#include <nag.h>
void  f16sjc (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)
The function may be called by the names: f16sjc, nag_blast_ztrsv or nag_ztrsv.

3 Description

f16sjc performs one of the matrix-vector operations
xα A-1x,  xα A-Tx  or  x A-Hx,  
where A is an n×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-1)H.

4 References

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

5 Arguments

1: order Nag_OrderType Input
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 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2: uplo Nag_UploType Input
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_TransType Input
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: diag Nag_DiagType Input
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 Integer Input
On entry: n, the order of the matrix A.
Constraint: n0.
6: alpha Complex Input
On entry: the scalar α.
7: a[dim] const Complex Input
Note: the dimension, dim, of the array a must be at least max(1,pda×n).
On entry: the n×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 Integer Input
On entry: the stride separating row or column elements (depending on the value of order) of the matrix A in the array a.
Constraint: pdamax(1,n).
9: x[dim] Complex Input/Output
Note: the dimension, dim, of the array x must be at least max(1,1+(n-1)|incx|).
On entry: the vector x.
On exit: the solution vector x.
10: incx Integer Input
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 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface 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: pdamax(1,n).
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface 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

Background information to multithreading can be found in the Multithreading documentation.
f16sjc is not threaded in any implementation.

9 Further Comments

No test for singularity or near-singularity of A is included in f16sjc. Such tests must be performed before calling this function.

10 Example

Solves complex triangular system of linear equations, Ax=y, where A is a complex triangular 4×4 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 ) .  

10.1 Program Text

Program Text (f16sjce.c)

10.2 Program Data

Program Data (f16sjce.d)

10.3 Program Results

Program Results (f16sjce.r)