The routine may be called by the names f11dbf or nagf_sparse_real_gen_precon_ilu_solve.
f11dbf solves a system of linear equations
according to the value of the argument trans, where the matrix , corresponds to an incomplete decomposition of a sparse matrix stored in coordinate storage (CS) format (see Section 2.1.1 in the F11 Chapter Introduction), as generated by f11daf.
In the above decomposition is a lower triangular sparse matrix with unit diagonal elements, is a diagonal matrix, is an upper triangular sparse matrix with unit diagonal elements and, and are permutation matrices. , and are supplied to f11dbf through the matrix
which is an n by n sparse matrix, stored in CS format, as returned by f11daf. The permutation matrices and are returned from f11daf via the arrays ipivp and ipivq.
It is envisaged that a common use of f11dbf will be to carry out the preconditioning step required in the application of f11bef to sparse linear systems. f11dbf is used for this purpose by the Black Box routine f11dcf.
f11dbf may also be used in combination with f11daf to solve a sparse system of linear equations directly (see Section 9.5 in f11daf).
1: – Character(1)Input
On entry: specifies whether or not the matrix is transposed.
2: – IntegerInput
On entry: , the order of the matrix . This must be the same value as was supplied in the preceding call to f11daf.
3: – Real (Kind=nag_wp) arrayInput
On entry: the values returned in the array a by a previous call to f11daf.
4: – IntegerInput
On entry: the dimension of the arrays a, irow and icol as declared in the (sub)program from which f11dbf is called. This must be the same value returned by the preceding call to f11daf.
On entry: ifail must be set to , or to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of means that an error message is printed while a value of means that it is not.
If halting is not appropriate, the value or is recommended. If message printing is undesirable, then the value is recommended. Otherwise, the value is recommended. When the value or is used it is essential to test the value of ifail on exit.
On exit: unless the routine detects an error or a warning has been flagged (see Section 6).
6Error Indicators and Warnings
If on entry or , explanatory error messages are output on the current error message unit (as defined by x04aaf).
It is expected that a common use of f11dbf will be to carry out the preconditioning step required in the application of f11bef to sparse linear systems. In this situation f11dbf is likely to be called many times with the same matrix . In the interests of both reliability and efficiency, you are recommended to set for the first of such calls, and for all subsequent calls set .
This example reads in a sparse nonsymmetric matrix and a vector . It then calls f11daf, with and , to compute the complete