f07csc computes the solution to a complex system of linear equations
or
or
, where
is an
tridiagonal matrix and
and
are
matrices, using the
factorization returned by
f07crc.
f07csc should be preceded by a call to
f07crc, which uses Gaussian elimination with partial pivoting and row interchanges to factorize the matrix
as
where
is a permutation matrix,
is unit lower triangular with at most one nonzero subdiagonal element in each column, and
is an upper triangular band matrix, with two superdiagonals.
f07csc then utilizes the factorization to solve the required equations.
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
https://www.netlib.org/lapack/lug
-
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:
– Nag_TransType
Input
-
On entry: specifies the equations to be solved as follows:
- Solve for .
- Solve for .
- Solve for .
Constraint:
, or .
-
3:
– Integer
Input
-
On entry: , the order of the matrix .
Constraint:
.
-
4:
– Integer
Input
-
On entry: , the number of right-hand sides, i.e., the number of columns of the matrix .
Constraint:
.
-
5:
– const Complex
Input
-
Note: the dimension,
dim, of the array
dl
must be at least
.
On entry: must contain the multipliers that define the matrix of the factorization of .
-
6:
– const Complex
Input
-
Note: the dimension,
dim, of the array
d
must be at least
.
On entry: must contain the diagonal elements of the upper triangular matrix from the factorization of .
-
7:
– const Complex
Input
-
Note: the dimension,
dim, of the array
du
must be at least
.
On entry: must contain the elements of the first superdiagonal of .
-
8:
– const Complex
Input
-
Note: the dimension,
dim, of the array
du2
must be at least
.
On entry: must contain the elements of the second superdiagonal of .
-
9:
– const Integer
Input
-
Note: the dimension,
dim, of the array
ipiv
must be at least
.
On entry: must contain the pivot indices that define the permutation matrix . At the th step, row of the matrix was interchanged with row , and must always be either or , indicating that a row interchange was not performed.
-
10:
– 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 matrix of right-hand sides .
On exit: the solution matrix .
-
11:
– Integer
Input
-
On entry: the stride separating row or column elements (depending on the value of
order) in the array
b.
Constraints:
- if ,
;
- if , .
-
12:
– NagError *
Input/Output
-
The NAG error argument (see
Section 7 in the Introduction to the NAG Library CL Interface).
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.
Following the use of this function
f07cuc can be used to estimate the condition number of
and
f07cvc can be used to obtain approximate error bounds.
Background information to multithreading can be found in the
Multithreading documentation.
The real analogue of this function is
f07cec.
This example solves the equations
where
is the tridiagonal matrix
and