NAG CL Interface
f16plc (dtpsv)

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1 Purpose

f16plc solves a system of equations given as a real triangular matrix stored in packed form.

2 Specification

#include <nag.h>
void  f16plc (Nag_OrderType order, Nag_UploType uplo, Nag_TransType trans, Nag_DiagType diag, Integer n, double alpha, const double ap[], double x[], Integer incx, NagError *fail)
The function may be called by the names: f16plc, nag_blast_dtpsv or nag_dtpsv.

3 Description

f16plc performs one of the matrix-vector operations
xαA-1x   or   xαA-Tx ,  
where A is an n×n real triangular matrix, stored in packed form, x is an n-element real vector and α is a real scalar. A-T denotes A-T or equivalently A-T.
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

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
xαA-1x.
trans=Nag_Trans or Nag_ConjTrans
xαA-Tx.
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 double Input
On entry: the scalar α.
7: ap[dim] const double Input
Note: the dimension, dim, of the array ap must be at least max(1, n × (n+1) / 2 ) .
On entry: the n×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] double Input/Output
Note: the dimension, dim, of the array x must be at least max(1,1+(n-1)|incx|).
On entry: the right-hand side vector b.
On exit: the solution vector x.
9: incx Integer Input
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
10: 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_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.
f16plc is not threaded in any implementation.

9 Further Comments

None.

10 Example

Solves real triangular system of linear equations, Ax=y, where A is a 4×4 real triangular matrix, stored in packed storage format, and is given by
A = ( 4.30 -3.96 -4.87 0.40 0.31 -8.02 -0.27 0.07 -5.95 0.12 )  
and
y = (-12.90,16.75,-17.55,-11.04) T .  
The vector y is stored in x and f16plc.

10.1 Program Text

Program Text (f16plce.c)

10.2 Program Data

Program Data (f16plce.d)

10.3 Program Results

Program Results (f16plce.r)