NAG FL Interface
f08kgf (dormbr)
1
Purpose
f08kgf multiplies an arbitrary real
by
matrix
by one of the real orthogonal matrices
or
which were determined by
f08kef when reducing a real matrix to bidiagonal form.
2
Specification
Fortran Interface
Subroutine f08kgf ( |
vect, side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info) |
Integer, Intent (In) |
:: |
m, n, k, lda, ldc, lwork |
Integer, Intent (Out) |
:: |
info |
Real (Kind=nag_wp), Intent (In) |
:: |
tau(*) |
Real (Kind=nag_wp), Intent (Inout) |
:: |
a(lda,*), c(ldc,*) |
Real (Kind=nag_wp), Intent (Out) |
:: |
work(max(1,lwork)) |
Character (1), Intent (In) |
:: |
vect, side, trans |
|
C Header Interface
#include <nag.h>
void |
f08kgf_ (const char *vect, const char *side, const char *trans, const Integer *m, const Integer *n, const Integer *k, double a[], const Integer *lda, const double tau[], double c[], const Integer *ldc, double work[], const Integer *lwork, Integer *info, const Charlen length_vect, const Charlen length_side, const Charlen length_trans) |
|
C++ Header Interface
#include <nag.h> extern "C" {
void |
f08kgf_ (const char *vect, const char *side, const char *trans, const Integer &m, const Integer &n, const Integer &k, double a[], const Integer &lda, const double tau[], double c[], const Integer &ldc, double work[], const Integer &lwork, Integer &info, const Charlen length_vect, const Charlen length_side, const Charlen length_trans) |
}
|
The routine may be called by the names f08kgf, nagf_lapackeig_dormbr or its LAPACK name dormbr.
3
Description
f08kgf is intended to be used after a call to
f08kef, which reduces a real rectangular matrix
to bidiagonal form
by an orthogonal transformation:
.
f08kef represents the matrices
and
as products of elementary reflectors.
This routine may be used to form one of the matrix products
overwriting the result on
(which may be any real rectangular matrix).
4
References
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
5
Arguments
Note: in the descriptions below, denotes the order of or : if , and if , .
-
1:
– Character(1)
Input
-
On entry: indicates whether
or
or
or
is to be applied to
.
- or is applied to .
- or is applied to .
Constraint:
or .
-
2:
– Character(1)
Input
-
On entry: indicates how
or
or
or
is to be applied to
.
- or or or is applied to from the left.
- or or or is applied to from the right.
Constraint:
or .
-
3:
– Character(1)
Input
-
On entry: indicates whether
or
or
or
is to be applied to
.
- or is applied to .
- or is applied to .
Constraint:
or .
-
4:
– Integer
Input
-
On entry: , the number of rows of the matrix .
Constraint:
.
-
5:
– Integer
Input
-
On entry: , the number of columns of the matrix .
Constraint:
.
-
6:
– Integer
Input
-
On entry: if
, the number of columns in the original matrix
.
If , the number of rows in the original matrix .
Constraint:
.
-
7:
– Real (Kind=nag_wp) array
Input
-
Note: the second dimension of the array
a
must be at least
if
and at least
if
.
On entry: details of the vectors which define the elementary reflectors, as returned by
f08kef.
-
8:
– Integer
Input
-
On entry: the first dimension of the array
a as declared in the (sub)program from which
f08kgf is called.
Constraints:
- if , ;
- if , .
-
9:
– Real (Kind=nag_wp) array
Input
-
Note: the dimension of the array
tau
must be at least
.
On entry: further details of the elementary reflectors, as returned by
f08kef in its argument
tauq if
, or in its argument
taup if
.
-
10:
– Real (Kind=nag_wp) array
Input/Output
-
Note: the second dimension of the array
c
must be at least
.
On entry: the matrix .
On exit:
c is overwritten by
or
or
or
or
or
or
or
as specified by
vect,
side and
trans.
-
11:
– Integer
Input
-
On entry: the first dimension of the array
c as declared in the (sub)program from which
f08kgf is called.
Constraint:
.
-
12:
– Real (Kind=nag_wp) array
Workspace
-
On exit: if
,
contains the minimum value of
lwork required for optimal performance.
-
13:
– Integer
Input
-
On entry: the dimension of the array
work as declared in the (sub)program from which
f08kgf is called.
If
, a workspace query is assumed; the routine only calculates the optimal size of the
work array, returns this value as the first entry of the
work array, and no error message related to
lwork is issued.
Suggested value:
for optimal performance, if and at least if , where is the optimal block size.
Constraints:
- if , or ;
- if , or .
-
14:
– Integer
Output
On exit:
unless the routine detects an error (see
Section 6).
6
Error Indicators and Warnings
If , argument had an illegal value. An explanatory message is output, and execution of the program is terminated.
7
Accuracy
The computed result differs from the exact result by a matrix
such that
where
is the
machine precision.
8
Parallelism and Performance
f08kgf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
f08kgf 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
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
The total number of floating-point operations is approximately
- if and , ;
- if and , ;
- if and , ;
- if and , ,
where
is the value of the argument
k.
The complex analogue of this routine is
f08kuf.
10
Example
For this routine two examples are presented. Both illustrate how the reduction to bidiagonal form of a matrix may be preceded by a or factorization of .
In the first example,
, and
The routine first performs a
factorization of
as
and then reduces the factor
to bidiagonal form
:
. Finally it forms
and calls
f08kgf to form
.
In the second example,
, and
The routine first performs an
factorization of
as
and then reduces the factor
to bidiagonal form
:
. Finally it forms
and calls
f08kgf to form
.
10.1
Program Text
10.2
Program Data
10.3
Program Results