nag_sparse_herm_precon_ichol_solve (f11jpc) (PDF version)
f11 Chapter Contents
f11 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_sparse_herm_precon_ichol_solve (f11jpc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_sparse_herm_precon_ichol_solve (f11jpc) solves a system of complex linear equations involving the incomplete Cholesky preconditioning matrix generated by nag_sparse_herm_chol_fac (f11jnc).

2  Specification

#include <nag.h>
#include <nagf11.h>
void  nag_sparse_herm_precon_ichol_solve (Integer n, const Complex a[], Integer la, const Integer irow[], const Integer icol[], const Integer ipiv[], const Integer istr[], Nag_SparseSym_CheckData check, const Complex y[], Complex x[], NagError *fail)

3  Description

nag_sparse_herm_precon_ichol_solve (f11jpc) solves a system of linear equations
Mx=y
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 nag_sparse_herm_chol_fac (f11jnc).
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 nag_sparse_herm_precon_ichol_solve (f11jpc) through the matrix
C=L+D-1-I
which is a lower triangular n by n complex sparse matrix, stored in SCS format, as returned by nag_sparse_herm_chol_fac (f11jnc). The permutation matrix P is returned from nag_sparse_herm_chol_fac (f11jnc) via the array ipiv.
nag_sparse_herm_precon_ichol_solve (f11jpc) may also be used in combination with nag_sparse_herm_chol_fac (f11jnc) to solve a sparse complex Hermitian positive definite system of linear equations directly (see nag_sparse_herm_chol_fac (f11jnc)). This is illustrated in Section 9.

4  References

None.

5  Arguments

1:     nIntegerInput
On entry: n, the order of the matrix M. This must be the same value as was supplied in the preceding call to nag_sparse_herm_chol_fac (f11jnc).
Constraint: n1.
2:     a[la]const ComplexInput
On entry: the values returned in the array a by a previous call to nag_sparse_herm_chol_fac (f11jnc).
3:     laIntegerInput
On entry: the dimension of the arrays a, irow and icol. This must be the same value supplied in the preceding call to nag_sparse_herm_chol_fac (f11jnc).
4:     irow[la]const IntegerInput
5:     icol[la]const IntegerInput
6:     ipiv[n]const IntegerInput
7:     istr[n+1]const IntegerInput
On entry: the values returned in arrays irow, icol, ipiv and istr by a previous call to nag_sparse_herm_chol_fac (f11jnc).
8:     checkNag_SparseSym_CheckDataInput
On entry: specifies whether or not the input data should be checked.
check=Nag_SparseSym_Check
Checks are carried out on the values of n, irow, icol, ipiv and istr.
check=Nag_SparseSym_NoCheck
None of these checks are carried out.
Constraint: check=Nag_SparseSym_Check or Nag_SparseSym_NoCheck.
9:     y[n]const ComplexInput
On entry: the right-hand side vector y.
10:   x[n]ComplexOutput
On exit: the solution vector x.
11:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, n=value.
Constraint: n1.
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.
NE_INVALID_ROWCOL_PIVOT
Check that a, irow, icol, ipiv and istr have not been corrupted between calls to nag_sparse_herm_chol_fac (f11jnc) and nag_sparse_herm_precon_ichol_solve (f11jpc).
NE_INVALID_SCS
Check that a, irow, icol, ipiv and istr have not been corrupted between calls to nag_sparse_herm_chol_fac (f11jnc) and nag_sparse_herm_precon_ichol_solve (f11jpc).
NE_INVALID_SCS_PRECOND
Check that a, irow, icol, ipiv and istr have not been corrupted between calls to nag_sparse_herm_chol_fac (f11jnc) and nag_sparse_herm_precon_ichol_solve (f11jpc).
NE_NOT_STRICTLY_INCREASING
Check that a, irow, icol, ipiv and istr have not been corrupted between calls to nag_sparse_herm_chol_fac (f11jnc) and nag_sparse_herm_precon_ichol_solve (f11jpc).

7  Accuracy

The computed solution x is the exact solution of a perturbed system of equations M+δMx=y, where
δMcnεPLDLHPT,
cn is a modest linear function of n, and ε is the machine precision.

8  Further Comments

8.1  Timing

The time taken for a call to nag_sparse_herm_precon_ichol_solve (f11jpc) is proportional to the value of nnzc returned from nag_sparse_herm_chol_fac (f11jnc).

9  Example

This example reads in a complex sparse Hermitian positive definite matrix A and a vector y. It then calls nag_sparse_herm_chol_fac (f11jnc), with lfill=-1 and dtol=0.0, to compute the complete Cholesky decomposition of A:
A=PLDLHPT.
Finally it calls nag_sparse_herm_precon_ichol_solve (f11jpc) to solve the system
PLDLHPTx=y.

9.1  Program Text

Program Text (f11jpce.c)

9.2  Program Data

Program Data (f11jpce.d)

9.3  Program Results

Program Results (f11jpce.r)


nag_sparse_herm_precon_ichol_solve (f11jpc) (PDF version)
f11 Chapter Contents
f11 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012