NAG CL Interface
f08zpc (zggglm)
1
Purpose
f08zpc solves a complex general Gauss–Markov linear (least squares) model problem.
2
Specification
void |
f08zpc (Nag_OrderType order,
Integer m,
Integer n,
Integer p,
Complex a[],
Integer pda,
Complex b[],
Integer pdb,
Complex d[],
Complex x[],
Complex y[],
NagError *fail) |
|
The function may be called by the names: f08zpc, nag_lapackeig_zggglm or nag_zggglm.
3
Description
f08zpc solves the complex general Gauss–Markov linear model (GLM) problem
where
is an
by
matrix,
is an
by
matrix and
is an
element vector. It is assumed that
,
and
, where
. Under these assumptions, the problem has a unique solution
and a minimal
-norm solution
, which is obtained using a generalized
factorization of the matrices
and
.
In particular, if the matrix
is square and nonsingular, then the GLM problem is equivalent to the weighted linear least squares problem
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
Anderson E, Bai Z and Dongarra J (1992) Generalized QR factorization and its applications Linear Algebra Appl. (Volume 162–164) 243–271
5
Arguments
-
1:
– 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
. 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:
or .
-
2:
– Integer
Input
-
On entry: , the number of rows of the matrices and .
Constraint:
.
-
3:
– Integer
Input
-
On entry: , the number of columns of the matrix .
Constraint:
.
-
4:
– Integer
Input
-
On entry: , the number of columns of the matrix .
Constraint:
.
-
5:
– Complex
Input/Output
-
Note: the dimension,
dim, of the array
a
must be at least
- when
;
- when
.
The
th element of the matrix
is stored in
- when ;
- when .
On entry: the by matrix .
On exit:
a is overwritten.
-
6:
– Integer
Input
-
On entry: the stride separating row or column elements (depending on the value of
order) in the array
a.
Constraints:
- if ,
;
- if , .
-
7:
– Complex
Input/Output
-
Note: the dimension,
dim, of the array
b
must be at least
- when
;
- when
.
The
th element of the matrix
is stored in
- when ;
- when .
On entry: the by matrix .
On exit:
b is overwritten.
-
8:
– Integer
Input
-
On entry: the stride separating row or column elements (depending on the value of
order) in the array
b.
Constraints:
- if ,
;
- if , .
-
9:
– Complex
Input/Output
-
On entry: the left-hand side vector of the GLM equation.
On exit:
d is overwritten.
-
10:
– Complex
Output
-
On exit: the solution vector of the GLM problem.
-
11:
– Complex
Output
-
On exit: the solution vector of the GLM problem.
-
12:
– 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 had an illegal value.
- NE_INT
-
On entry, .
Constraint: .
On entry, .
Constraint: .
On entry, .
Constraint: .
- NE_INT_2
-
On entry, and .
Constraint: .
On entry, and .
Constraint: .
On entry, and .
Constraint: .
On entry, and .
Constraint: .
On entry, and .
Constraint: .
- NE_INT_3
-
On entry, , and .
Constraint: .
- 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.
See
Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
- 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.
- NE_SINGULAR
-
The bottom by part of the upper trapezoidal factor associated with in the generalized factorization of the pair is singular, so that ; the least squares solutions could not be computed.
The upper triangular factor associated with in the generalized factorization of the pair is singular, so that ; the least squares solution could not be computed.
7
Accuracy
For an error analysis, see
Anderson et al. (1992). See also Section 4.6 of
Anderson et al. (1999).
8
Parallelism and Performance
f08zpc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
f08zpc 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 function. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
When , the total number of real floating-point operations is approximately ; when , the total number of real floating-point operations is approximately .
10
Example
This example solves the weighted least squares problem
where
and
10.1
Program Text
10.2
Program Data
10.3
Program Results