nag_ztrmm (f16zfc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_ztrmm (f16zfc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_ztrmm (f16zfc) performs matrix-matrix multiplication for a complex triangular matrix.

2  Specification

#include <nag.h>
#include <nagf16.h>
void  nag_ztrmm (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_ztrmm (f16zfc) performs one of the matrix-matrix operations
where B is an m by n complex matrix, A is a complex triangular matrix, and α is a complex scalar.

4  References

The BLAS Technical Forum Standard (2001)

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 whether the operation involves A, AT or AH.
It involves A.
It involves AT.
It involves AH.
Constraint: trans=Nag_NoTrans, Nag_Trans or Nag_ConjTrans.
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, pda max1,m ;
  • if side=Nag_RightSide, pda max1,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, m=value, pda=value.
Constraint: if side=Nag_LeftSide, pda max1,m .
On entry, side=value, n=value, pda=value.
Constraint: if side=Nag_RightSide, pda max1,n .
On entry, m=value.
Constraint: m0.
On entry, n=value.
Constraint: n0.
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 The BLAS Technical Forum Standard (2001)).

8  Further Comments


9  Example

Premultiply complex 4 by 2 matrix B by lower triangular 4 by 4 matrix A, BAB, 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 = -5.0-2.0i 1.0+5.0i -3.0-1.0i -2.0-2.0i 2.0+1.0i 3.0+4.0i 4.0+3.0i 4.0-3.0i .

9.1  Program Text

Program Text (f16zfce.c)

9.2  Program Data

Program Data (f16zfce.d)

9.3  Program Results

Program Results (f16zfce.r)

nag_ztrmm (f16zfc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

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