F11JPF solves a system of complex linear equations involving the incomplete Cholesky preconditioning matrix generated by
F11JNF.
F11JPF solves a system of linear equations
involving the preconditioning matrix
M=PLDLHPT, corresponding to an incomplete Cholesky decomposition of a complex sparse Hermitian matrix stored in symmetric coordinate storage (SCS) format (see
Section 2.1.2 in the F11 Chapter Introduction), as generated by
F11JNF.
In the above decomposition
L is a complex lower triangular sparse matrix with unit diagonal,
D is a real diagonal matrix and
P is a permutation matrix.
L and
D are supplied to F11JPF through the matrix
which is a lower triangular
n by
n complex sparse matrix, stored in SCS format, as returned by
F11JNF. The permutation matrix
P is returned from
F11JNF via the array
IPIV.
F11JPF may also be used in combination with
F11JNF to solve a sparse complex Hermitian positive definite system of linear equations directly (see
F11JNF). This is illustrated in
Section 9.
None.
If on entry
IFAIL=0 or
-1, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
The computed solution
x is the exact solution of a perturbed system of equations
M+δMx=y, where
cn is a modest linear function of
n, and
ε is the
machine precision.
The time taken for a call to F11JPF is proportional to the value of
NNZC returned from
F11JNF.
This example reads in a complex sparse Hermitian positive definite matrix
A and a vector
y. It then calls
F11JNF, with
LFILL=-1 and
DTOL=0.0, to compute the
complete Cholesky decomposition of
A:
Finally it calls F11JPF to solve the system