nag_ztrsm (f16zjc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_ztrsm (f16zjc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_ztrsm (f16zjc) solves a system of equations given as a complex triangular matrix with multiple right-hand sides.

2  Specification

#include <nag.h>
#include <nagf16.h>
void  nag_ztrsm (Nag_OrderType order, Nag_SideType side, Nag_UploType uplo, Nag_TransType trans, Nag_DiagType diag, Integer m, Integer n, Complex alpha, const Complex a[], Integer pda, Complex b[], Integer pdb, NagError *fail)

3  Description

nag_ztrsm (f16zjc) performs one of the matrix-matrix operations
BαA-1B, BαA-TB, BαA-HB, BαBA-1, BαBA-T  or BαBA-H,
where A is a complex triangular matrix, B is an m by n complex matrix, 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

Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001) Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard University of Tennessee, Knoxville, Tennessee

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 in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     sideNag_SideTypeInput
On entry: specifies whether B is operated on from the left or the right.
B is pre-multiplied from the left.
B is post-multiplied from the right.
Constraint: side=Nag_LeftSide or Nag_RightSide.
3:     uploNag_UploTypeInput
On entry: specifies whether A is upper or lower triangular.
A is upper triangular.
A is lower triangular.
Constraint: uplo=Nag_Upper or Nag_Lower.
4:     transNag_TransTypeInput
On entry: specifies the operation to be performed.
trans=Nag_Trans and side=Nag_LeftSide
trans=Nag_NoTrans and side=Nag_LeftSide
trans=Nag_ConjTrans and side=Nag_LeftSide
trans=Nag_Trans and side=Nag_RightSide
trans=Nag_NoTrans and side=Nag_RightSide
trans=Nag_ConjTrans and side=Nag_RightSide
  • side=Nag_LeftSide or Nag_RightSide;
  • trans=Nag_NoTrans or Nag_Trans.
5:     diagNag_DiagTypeInput
On entry: specifies whether A has nonunit or unit diagonal elements.
The diagonal elements are stored explicitly.
The diagonal elements are assumed to be 1 and are not referenced.
Constraint: diag=Nag_NonUnitDiag or Nag_UnitDiag.
6:     mIntegerInput
On entry: m, the number of rows of the matrix B; the order of A if side=Nag_LeftSide.
Constraint: m0.
7:     nIntegerInput
On entry: n, the number of columns of the matrix B; the order of A if side=Nag_RightSide.
Constraint: n0.
8:     alphaComplexInput
On entry: the scalar α.
9:     a[dim]const ComplexInput
Note: the dimension, dim, of the array a must be at least
  • max1,pda×m when side=Nag_LeftSide;
  • max1,pda×n when side=Nag_RightSide.
On entry: the triangular matrix A; A is m by m if side=Nag_LeftSide, or n by n if side=Nag_RightSide.
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.
If diag=Nag_UnitDiag, the diagonal elements of A are assumed to be 1, and are not referenced.
10:   pdaIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) of the matrix A in the array a.
  • if side=Nag_LeftSide, pdamax1,m;
  • if side=Nag_RightSide, pdamax1,n.
11:   b[dim]ComplexInput/Output
Note: the dimension, dim, of the array b must be at least
  • max1,pdb×n when order=Nag_ColMajor;
  • max1,m×pdb when order=Nag_RowMajor.
If order=Nag_ColMajor, Bij is stored in b[j-1×pdb+i-1].
If order=Nag_RowMajor, Bij is stored in b[i-1×pdb+j-1].
On entry: the m by n matrix B.
If alpha=0, b need not be set.
On exit: the updated matrix B.
12:   pdbIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array b.
  • if order=Nag_ColMajor, pdbmax1,m;
  • if order=Nag_RowMajor, pdbmax1,n.
13:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

Dynamic memory allocation failed.
On entry, argument value had an illegal value.
On entry, side=value, pda=value, m=value.
Constraint: if side=Nag_LeftSide, pdamax1,m.
On entry, side=value, pda=value, n=value.
Constraint: if side=Nag_RightSide, pdamax1,n.
On entry, m=value.
Constraint: m0.
On entry, n=value.
Constraint: n0.
On entry, pda=value; n=value.
Constraint: pdamax1,n.
On entry, pdb=value; m=value.
Constraint: pdbmax1,m.
On entry, pdb=value, m=value.
Constraint: pdbmax1,m.
On entry, pdb=value and n=value.
Constraint: pdbmax1,n.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

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

nag_ztrsm (f16zjc) is not threaded by NAG in any implementation.
nag_ztrsm (f16zjc) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the Users' Note for your implementation for any additional implementation-specific information.

9  Further Comments

No test for singularity or near-singularity of A is included in nag_ztrsm (f16zjc). Such tests must be performed before calling this function.

10  Example

Premultiply complex 4 by 2 matrix B by inverse of lower triangular 4 by 4 matrix A, BA-1B (or solve AX=B and return result in B), where
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
B = -14.78-32.36i -18.02+28.46i 2.98-02.14i 14.22+15.42i -20.96+17.06i 5.62+35.89i 9.54+09.91i -16.46-01.73i .

10.1  Program Text

Program Text (f16zjce.c)

10.2  Program Data

Program Data (f16zjce.d)

10.3  Program Results

Program Results (f16zjce.r)

nag_ztrsm (f16zjc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014