NAG FL Interface
f11mmf (direct_​real_​gen_​diag)

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1 Purpose

f11mmf computes the reciprocal pivot growth factor of an LU factorization of a real sparse matrix in compressed column (Harwell–Boeing) format.

2 Specification

Fortran Interface
Subroutine f11mmf ( n, icolzp, a, iprm, il, lval, iu, uval, rpg, ifail)
Integer, Intent (In) :: n, icolzp(*), iprm(7*n), il(*), iu(*)
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: a(*), lval(*), uval(*)
Real (Kind=nag_wp), Intent (Out) :: rpg
C Header Interface
#include <nag.h>
void  f11mmf_ (const Integer *n, const Integer icolzp[], const double a[], const Integer iprm[], const Integer il[], const double lval[], const Integer iu[], const double uval[], double *rpg, Integer *ifail)
The routine may be called by the names f11mmf or nagf_sparse_direct_real_gen_diag.

3 Description

f11mmf computes the reciprocal pivot growth factor maxj(Aj/Uj) from the columns Aj and Uj of an LU factorization of the matrix A, Pr A Pc = LU where Pr is a row permutation matrix, Pc is a column permutation matrix, L is unit lower triangular and U is upper triangular as computed by f11mef.

4 References

None.

5 Arguments

1: n Integer Input
On entry: n, the order of the matrix A.
Constraint: n0.
2: icolzp(*) Integer array Input
Note: the dimension of the array icolzp must be at least n+1.
On entry: the new column index array of sparse matrix A. See Section 2.1.3 in the F11 Chapter Introduction.
3: a(*) Real (Kind=nag_wp) array Input
Note: the dimension of the array a must be at least icolzp(n+1)-1, the number of nonzeros of the sparse matrix A.
On entry: the array of nonzero values in the sparse matrix A.
4: iprm(7×n) Integer array Input
On entry: the column permutation which defines Pc, the row permutation which defines Pr, plus associated data structures as computed by f11mef.
5: il(*) Integer array Input
Note: the dimension of the array il must be at least as large as the dimension of the array of the same name in f11mef.
On entry: records the sparsity pattern of matrix L as computed by f11mef.
6: lval(*) Real (Kind=nag_wp) array Input
Note: the dimension of the array lval must be at least as large as the dimension of the array of the same name in f11mef.
On entry: records the nonzero values of matrix L and some nonzero values of matrix U as computed by f11mef.
7: iu(*) Integer array Input
Note: the dimension of the array iu must be at least as large as the dimension of the array of the same name in f11mef.
On entry: records the sparsity pattern of matrix U as computed by f11mef.
8: uval(*) Real (Kind=nag_wp) array Input
Note: the dimension of the array uval must be at least as large as the dimension of the array of the same name in f11mef.
On entry: records some nonzero values of matrix U as computed by f11mef.
9: rpg Real (Kind=nag_wp) Output
On exit: the reciprocal pivot growth factor maxj(Aj/Uj). If the reciprocal pivot growth factor is much less than 1, the stability of the LU factorization may be poor.
10: ifail Integer Input/Output
On entry: ifail must be set to 0, −1 or 1 to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of 0 causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of −1 means that an error message is printed while a value of 1 means that it is not.
If halting is not appropriate, the value −1 or 1 is recommended. If message printing is undesirable, then the value 1 is recommended. Otherwise, the value 0 is recommended. When the value -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry ifail=0 or −1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
ifail=1
On entry, n=value.
Constraint: n0.
ifail=2
Incorrect column permutations in array iprm.
ifail=-99
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
ifail=-399
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
ifail=-999
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
f11mmf is not threaded in any implementation.

9 Further Comments

If the reciprocal pivot growth factor, rpg, is much less than 1, then the factorization of the matrix A could be poor. This means that using the factorization to obtain solutions to a linear system, forward error bounds and estimates of the condition number could be unreliable. Consider increasing the thresh argument in the call to f11mef.

10 Example

To compute the reciprocal pivot growth for the factorization of the matrix A, where
A=( 2.00 1.00 0 0 0 0 0 1.00 -1.00 0 4.00 0 1.00 0 1.00 0 0 0 1.00 2.00 0 -2.00 0 0 3.00 ) .  
In this case, it should be equal to 1.0.

10.1 Program Text

Program Text (f11mmfe.f90)

10.2 Program Data

Program Data (f11mmfe.d)

10.3 Program Results

Program Results (f11mmfe.r)