nag_dormrz (f08bkc) (PDF version)
f08 Chapter Contents
f08 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_dormrz (f08bkc)

+ Contents

    1  Purpose
    7  Accuracy
    9  Example

1  Purpose

nag_dormrz (f08bkc) multiplies a general real m by n matrix C by the real orthogonal matrix Z from an RZ factorization computed by nag_dtzrzf (f08bhc).

2  Specification

#include <nag.h>
#include <nagf08.h>
void  nag_dormrz (Nag_OrderType order, Nag_SideType side, Nag_TransType trans, Integer m, Integer n, Integer k, Integer l, const double a[], Integer pda, const double tau[], double c[], Integer pdc, NagError *fail)

3  Description

nag_dormrz (f08bkc) is intended to be used following a call to nag_dtzrzf (f08bhc), which performs an RZ factorization of a real upper trapezoidal matrix A and represents the orthogonal matrix Z as a product of elementary reflectors.
This function may be used to form one of the matrix products
ZC ,   ZTC ,   CZ ,   CZT ,
overwriting the result on C, which may be any real rectangular m by n matrix.

4  References

Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J J, Du Croz J J, Greenbaum A, Hammarling S, McKenney A and Sorensen D (1999) LAPACK Users' Guide (3rd Edition) SIAM, Philadelphia http://www.netlib.org/lapack/lug

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 3.2.1.3 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: indicates how Z or ZT is to be applied to C.
side=Nag_LeftSide
Z or ZT is applied to C from the left.
side=Nag_RightSide
Z or ZT is applied to C from the right.
Constraint: side=Nag_LeftSide or Nag_RightSide.
3:     transNag_TransTypeInput
On entry: indicates whether Z or ZT is to be applied to C.
trans=Nag_NoTrans
Z is applied to C.
trans=Nag_Trans
ZT is applied to C.
Constraint: trans=Nag_NoTrans or Nag_Trans.
4:     mIntegerInput
On entry: m, the number of rows of the matrix C.
Constraint: m0.
5:     nIntegerInput
On entry: n, the number of columns of the matrix C.
Constraint: n0.
6:     kIntegerInput
On entry: k, the number of elementary reflectors whose product defines the matrix Z.
Constraints:
  • if side=Nag_LeftSide, m k 0 ;
  • if side=Nag_RightSide, n k 0 .
7:     lIntegerInput
On entry: l, the number of columns of the matrix A containing the meaningful part of the Householder reflectors.
Constraints:
  • if side=Nag_LeftSide, m l 0 ;
  • if side=Nag_RightSide, n l 0 .
8:     a[dim]const doubleInput
Note: the dimension, dim, of the array a must be at least
  • max1,pda×m when side=Nag_LeftSide and order=Nag_ColMajor;
  • max1,k×pda when side=Nag_LeftSide and order=Nag_RowMajor;
  • max1,pda×n when side=Nag_RightSide and order=Nag_ColMajor;
  • max1,k×pda when side=Nag_RightSide and order=Nag_RowMajor.
The i,jth element of the matrix A is stored in
  • a[j-1×pda+i-1] when order=Nag_ColMajor;
  • a[i-1×pda+j-1] when order=Nag_RowMajor.
On entry: the ith row of a must contain the vector which defines the elementary reflector Hi, for i=1,2,,k, as returned by nag_dtzrzf (f08bhc).
9:     pdaIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array a.
Constraints:
  • if order=Nag_ColMajor, pdamax1,k;
  • if order=Nag_RowMajor,
    • if side=Nag_LeftSide, pdamax1,m;
    • if side=Nag_RightSide, pdamax1,n.
10:   tau[dim]const doubleInput
Note: the dimension, dim, of the array tau must be at least max1,k.
On entry: tau[i-1] must contain the scalar factor of the elementary reflector Hi, as returned by nag_dtzrzf (f08bhc).
11:   c[dim]doubleInput/Output
Note: the dimension, dim, of the array c must be at least
  • max1,pdc×n when order=Nag_ColMajor;
  • max1,m×pdc when order=Nag_RowMajor.
The i,jth element of the matrix C is stored in
  • c[j-1×pdc+i-1] when order=Nag_ColMajor;
  • c[i-1×pdc+j-1] when order=Nag_RowMajor.
On entry: the m by n matrix C.
On exit: c is overwritten by ZC or ZTC or CZ or ZTC as specified by side and trans.
12:   pdcIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array c.
Constraints:
  • if order=Nag_ColMajor, pdcmax1,m;
  • if order=Nag_RowMajor, pdcmax1,n.
13:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_ENUM_INT_3
On entry, side=value, m=value, n=value and k=value.
Constraint: if side=Nag_LeftSide, m k 0 ;
if side=Nag_RightSide, n k 0 .
On entry, side=value, m=value, n=value and l=value.
Constraint: if side=Nag_LeftSide, m l 0 ;
if side=Nag_RightSide, n l 0 .
On entry, side=value, pda=value, m=value and n=value.
Constraint: if side=Nag_LeftSide, pdamax1,m;
if side=Nag_RightSide, pdamax1,n.
NE_INT
On entry, m=value.
Constraint: m0.
On entry, n=value.
Constraint: n0.
On entry, pda=value.
Constraint: pda>0.
On entry, pdc=value.
Constraint: pdc>0.
NE_INT_2
On entry, pda=value and k=value.
Constraint: pdamax1,k.
On entry, pdc=value and m=value.
Constraint: pdcmax1,m.
On entry, pdc=value and n=value.
Constraint: pdcmax1,n.
NE_INTERNAL_ERROR
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 computed result differs from the exact result by a matrix E such that
E2 = Oε C2
where ε is the machine precision.

8  Further Comments

The total number of floating point operations is approximately 4nlk if side=Nag_LeftSide and 4mlk if side=Nag_RightSide.
The complex analogue of this function is nag_zunmrz (f08bxc).

9  Example

See Section 9 in nag_dtzrzf (f08bhc).

nag_dormrz (f08bkc) (PDF version)
f08 Chapter Contents
f08 Chapter Introduction
NAG C Library Manual

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