NAG CL Interface
f16tgc (ztr_​load)

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1 Purpose

f16tgc initializes a complex triangular matrix.

2 Specification

#include <nag.h>
void  f16tgc (Nag_OrderType order, Nag_UploType uplo, Integer n, Complex alpha, Complex diag, Complex a[], Integer pda, NagError *fail)
The function may be called by the names: f16tgc, nag_blast_ztr_load or nag_ztr_load.

3 Description

f16tgc forms the complex n×n triangular matrix A given by
aij={ d if i=j α if ij .  

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 the upper or lower triangular part of A is stored.
uplo=Nag_Upper
The upper triangular part of A is stored.
uplo=Nag_Lower
The lower triangular part of A is stored.
Constraint: uplo=Nag_Upper or Nag_Lower.
3: n Integer Input
On entry: n, the order of the matrix A.
Constraint: n0.
4: alpha Complex Input
On entry: the value, α, to be assigned to the off-diagonal elements of A.
5: diag Complex Input
On entry: the value, d, to be assigned to the diagonal elements of A.
6: a[dim] Complex Output
Note: the dimension, dim, of the array a must be at least max(1,pda×n).
On exit: the n×n triangular matrix A with diagonal elements set to diag and strictly upper or lower elements set to alpha.
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.
7: 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).
8: 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, 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

f16tgc is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example initializes a 4×4 lower triangular matrix A, setting diagonal elements to 9.0+0.0i and strictly lower elements to 0.5-0.3i .

10.1 Program Text

Program Text (f16tgce.c)

10.2 Program Data

Program Data (f16tgce.d)

10.3 Program Results

Program Results (f16tgce.r)