nag_zgtsv (f07cnc) computes the solution to a complex system of linear equations
where
is an
by
tridiagonal matrix and
and
are
by
matrices.
Note that the equations
may be solved by interchanging the order of the arguments
du and
dl.
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
- 1:
– Nag_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
. See
Section 3.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.
Constraint:
or .
- 2:
– IntegerInput
-
On entry: , the number of linear equations, i.e., the order of the matrix .
Constraint:
.
- 3:
– IntegerInput
-
On entry: , the number of right-hand sides, i.e., the number of columns of the matrix .
Constraint:
.
- 4:
– ComplexInput/Output
-
Note: the dimension,
dim, of the array
dl
must be at least
.
On entry: must contain the subdiagonal elements of the matrix .
On exit: if no constraints are violated,
dl is overwritten by the (
) elements of the second superdiagonal of the upper triangular matrix
from the
factorization of
, in
.
- 5:
– ComplexInput/Output
-
Note: the dimension,
dim, of the array
d
must be at least
.
On entry: must contain the diagonal elements of the matrix .
On exit: if no constraints are violated,
d is overwritten by the
diagonal elements of the upper triangular matrix
from the
factorization of
.
- 6:
– ComplexInput/Output
-
Note: the dimension,
dim, of the array
du
must be at least
.
On entry: must contain the superdiagonal elements of the matrix .
On exit: if no constraints are violated,
du is overwritten by the
elements of the first superdiagonal of
.
- 7:
– ComplexInput/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 right-hand side matrix .
On exit: if NE_NOERROR, the by solution matrix .
- 8:
– IntegerInput
-
On entry: the stride separating row or column elements (depending on the value of
order) in the array
b.
Constraints:
- if ,
;
- if , .
- 9:
– NagError *Input/Output
-
The NAG error argument (see
Section 3.7 in How to Use the NAG Library and its Documentation).
- NE_ALLOC_FAIL
-
Dynamic memory allocation failed.
See
Section 2.3.1.2 in How to Use the NAG Library and its Documentation 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: .
- 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 2.7.6 in How to Use the NAG Library and its Documentation for further information.
- NE_NO_LICENCE
-
Your licence key may have expired or may not have been installed correctly.
See
Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
- NE_SINGULAR
-
Element of the diagonal is exactly zero,
and the solution has not been computed. The factorization has not been
completed unless .
The computed solution for a single right-hand side,
, satisfies an equation of the form
where
and
is the
machine precision. An approximate error bound for the computed solution is given by
where
, the condition number of
with respect to the solution of the linear equations. See Section 4.4 of
Anderson et al. (1999) for further details.
Alternatives to
nag_zgtsv (f07cnc), which return condition and error estimates are
nag_complex_tridiag_lin_solve (f04ccc) and
nag_zgtsvx (f07cpc).
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.
The real analogue of this function is
nag_dgtsv (f07cac).
This example solves the equations
where
is the tridiagonal matrix
and