NAG FL Interface
f04lhf (real_​blkdiag_​fac_​solve)

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1 Purpose

f04lhf calculates the approximate solution of a set of real linear equations with multiple right-hand sides, AX=B or ATX=B, where A is an almost block-diagonal matrix which has been factorized by f01lhf.

2 Specification

Fortran Interface
Subroutine f04lhf ( trans, n, nbloks, blkstr, a, lena, pivot, b, ldb, ir, ifail)
Integer, Intent (In) :: n, nbloks, blkstr(3,nbloks), lena, pivot(n), ldb, ir
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: a(lena)
Real (Kind=nag_wp), Intent (Inout) :: b(ldb,ir)
Character (1), Intent (In) :: trans
C Header Interface
#include <nag.h>
void  f04lhf_ (const char *trans, const Integer *n, const Integer *nbloks, const Integer blkstr[], const double a[], const Integer *lena, const Integer pivot[], double b[], const Integer *ldb, const Integer *ir, Integer *ifail, const Charlen length_trans)
The routine may be called by the names f04lhf or nagf_linsys_real_blkdiag_fac_solve.

3 Description

f04lhf solves a set of real linear equations AX=B or ATX=B, where A is almost block-diagonal. A must first be factorized by f01lhf. f04lhf then computes X by forward and backward substitution over the blocks.

4 References

Diaz J C, Fairweather G and Keast P (1983) Fortran packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination ACM Trans. Math. Software 9 358–375

5 Arguments

1: trans Character(1) Input
On entry: specifies the equations to be solved.
Solve AX=B.
Solve ATX=B.
Constraint: trans='N' or 'T'.
2: n Integer Input
On entry: n, the order of the matrix A.
Constraint: n>0.
3: nbloks Integer Input
On entry: the total number of blocks of the matrix A, as supplied to f04lhf.
Constraint: 0<nbloksn.
4: blkstr(3,nbloks) Integer array Input
On entry: information which describes the block structure of A, as supplied to f04lhf.
5: a(lena) Real (Kind=nag_wp) array Input
On entry: the elements in the factorization of A, as returned by f04lhf.
6: lena Integer Input
On entry: the dimension of the array a as declared in the (sub)program from which f04lhf is called.
Constraint: lenak=1nbloks blkstr(1,k) × blkstr(2,k) .
7: pivot(n) Integer array Input
On entry: details of the interchanges in the factorization, as returned by f04lhf.
8: b(ldb,ir) Real (Kind=nag_wp) array Input/Output
On entry: the n×r right-hand side matrix B.
On exit: b is overwritten by the n×r solution matrix X.
9: ldb Integer Input
On entry: the first dimension of the array b as declared in the (sub)program from which f04lhf is called.
Constraint: ldbn.
10: ir Integer Input
On entry: r, the number of right-hand sides.
Constraint: ir>0.
11: 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:
On entry, ir=value.
Constraint: ir1.
On entry, K=value, blkstr(2,K)=value, blkstr(3,K)=value and blkstr(1,K)=value.
Constraint: blkstr(2,K)-blkstr(3,K)blkstr(1,K).
On entry, K=value, blkstr(2,K)=value and blkstr(1,K)=value.
Constraint: blkstr(2,K)blkstr(1,K).
On entry, K=value, blkstr(3,K)=value, blkstr(3,K-1)=value and blkstr(2,K)=value.
Constraint: blkstr(3,K)+blkstr(3,K-1)blkstr(2,K).
On entry, K=value and blkstr(1,K)=value.
Constraint: blkstr(1,K)1.
On entry, K=value and blkstr(2,K)=value.
Constraint: blkstr(2,K)1.
On entry, K=value and blkstr(3,K)=value.
Constraint: blkstr(3,K)0.
On entry, ldb=value and n=value.
Constraint: ldbn.
On entry, lena is too small. lena=value. Minimum possible dimension: value.
On entry, n=value.
Constraint: n1.
On entry, n=value and nbloks=value.
Constraint: nnbloks.
On entry, nbloks=value.
Constraint: nbloks1.
On entry, the following equality does not hold: blkstr(2,1)+sum(blkstr(2,k)-blkstr(3,k-1):k=2,nbloks)=n.
On entry, the following equality does not hold: sum( blkstr(1,k) : k=1 ,nbloks) = n .
On entry, the following inequality was not satisfied for: J=value. sum( blkstr(2,k) - blkstr(3,k) : k=1 ,J) sum( blkstr(1,k) : k=1 ,J) blkstr(2,1) + sum( blkstr(2,k) - blkstr(3,k-1) : k=2 ,J) .
On entry, trans'N' or 'T': trans=value.
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.
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.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

The accuracy of the computed solution depends on the conditioning of the original matrix A.

8 Parallelism and Performance

f04lhf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments


10 Example

This example solves the set of linear equations Ax=b where
A=( -1.00 -0.98 -0.79 -0.15 -1.00 -0.25 -0.87 0.35 0.78 0.31 -0.85 0.89 -0.69 -0.98 -0.76 -0.82 0.12 -0.01 0.75 0.32 -1.00 -0.53 -0.83 -0.98 -0.58 0.04 0.87 0.38 -1.00 -0.21 -0.93 -0.84 0.37 -0.94 -0.96 -1.00 -0.99 -0.91 -0.28 0.90 0.78 -0.93 -0.76 0.48 -0.87 -0.14 -1.00 -0.59 -0.99 0.21 -0.73 -0.48 -0.93 -0.91 0.10 -0.89 -0.68 -0.09 -0.58 -0.21 0.85 -0.39 0.79 -0.71 0.39 -0.99 -0.12 -0.75 0.17 -1.37 1.29 -1.59 1.10 -1.63 -1.01 -0.27 0.08 0.61 0.54 -0.41 0.16 -0.46 -0.67 0.56 -0.99 0.16 -0.16 0.98 -0.24 -0.41 0.40 -0.93 0.70 0.43 0.71 -0.97 -0.60 -0.30 0.18 -0.47 -0.98 -0.73 0.07 0.04 -0.25 -0.92 -0.52 -0.46 -0.58 0.89 -0.94 -0.54 -1.00 -0.36 )  
b=( -2.92 -1.17 -1.30 -1.17 -2.10 -4.51 -1.71 -4.59 -4.19 -0.93 -3.31 0.52 -0.12 -0.05 -0.98 -2.07 -2.73 -1.95 )  
The exact solution is

10.1 Program Text

Program Text (f04lhfe.f90)

10.2 Program Data

Program Data (f04lhfe.d)

10.3 Program Results

Program Results (f04lhfe.r)