NAG Library Routine Document

f04lhf (real_blkdiag_fac_solve)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{trans}$ – Character(1)Input

On entry: specifies the equations to be solved.

$\mathbf{trans}=\text{'N'}$

Solve $AX=B$.

$\mathbf{trans}=\text{'T'}$

Solve $A^{\mathrm{T}}X=B$.

Constraint: $\mathbf{trans}=\text{'N'}$ or $\text{'T'}$.

2:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the order of the matrix $A$.

Constraint: $\mathbf{n}>0$.

3:     $\mathbf{nbloks}$ – IntegerInput

On entry: the total number of blocks of the matrix $A$, as supplied to f04lhf.

Constraint: $0<\mathbf{nbloks}\le \mathbf{n}$.

4:     $\mathbf{blkstr}\left(3,\mathbf{nbloks}\right)$ – Integer arrayInput

On entry: information which describes the block structure of $A$, as supplied to f04lhf.

5:     $\mathbf{a}\left(\mathbf{lena}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the elements in the factorization of $A$, as returned by f04lhf.

6:     $\mathbf{lena}$ – IntegerInput

On entry: the dimension of the array a as declared in the (sub)program from which f04lhf is called.

Constraint: $\mathbf{lena}\ge {\displaystyle \sum _{k=1}^{\mathbf{nbloks}}}\mathbf{blkstr}\left(1,k\right)\times \mathbf{blkstr}\left(2,k\right)$.

7:     $\mathbf{pivot}\left(\mathbf{n}\right)$ – Integer arrayInput

On entry: details of the interchanges in the factorization, as returned by f04lhf.

8:     $\mathbf{b}\left(\mathbf{ldb},\mathbf{ir}\right)$ – Real (Kind=nag_wp) arrayInput/Output

On entry: the $n$ by $r$ right-hand side matrix $B$.

On exit: b is overwritten by the $n$ by $r$ solution matrix $X$.

9:     $\mathbf{ldb}$ – IntegerInput

On entry: the first dimension of the array b as declared in the (sub)program from which f04lhf is called.

Constraint: $\mathbf{ldb}\ge \mathbf{n}$.

10:   $\mathbf{ir}$ – IntegerInput

On entry: $r$, the number of right-hand sides.

Constraint: $\mathbf{ir}>0$.

11:   $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{ir}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ir}\ge 1$.

On entry, $K=〈\mathit{\text{value}}〉$, $\mathbf{blkstr}\left(2,K\right)=〈\mathit{\text{value}}〉$, $\mathbf{blkstr}\left(3,K\right)=〈\mathit{\text{value}}〉$ and $\mathbf{blkstr}\left(1,K\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{blkstr}\left(2,K\right)-\mathbf{blkstr}\left(3,K\right)\le \mathbf{blkstr}\left(1,K\right)$.

On entry, $K=〈\mathit{\text{value}}〉$, $\mathbf{blkstr}\left(2,K\right)=〈\mathit{\text{value}}〉$ and $\mathbf{blkstr}\left(1,K\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{blkstr}\left(2,K\right)\ge \mathbf{blkstr}\left(1,K\right)$.

On entry, $K=〈\mathit{\text{value}}〉$, $\mathbf{blkstr}\left(3,K\right)=〈\mathit{\text{value}}〉$, $\mathbf{blkstr}\left(3,K-1\right)=〈\mathit{\text{value}}〉$ and $\mathbf{blkstr}\left(2,K\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{blkstr}\left(3,K\right)+\mathbf{blkstr}\left(3,K-1\right)\ge \mathbf{blkstr}\left(2,K\right)$.

On entry, $K=〈\mathit{\text{value}}〉$ and $\mathbf{blkstr}\left(1,K\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{blkstr}\left(1,K\right)\ge 1$.

On entry, $K=〈\mathit{\text{value}}〉$ and $\mathbf{blkstr}\left(2,K\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{blkstr}\left(2,K\right)\ge 1$.

On entry, $K=〈\mathit{\text{value}}〉$ and $\mathbf{blkstr}\left(3,K\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{blkstr}\left(3,K\right)\ge 0$.

On entry, $\mathbf{ldb}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldb}\ge \mathbf{n}$.

On entry, lena is too small. $\mathbf{lena}=〈\mathit{\text{value}}〉$. Minimum possible dimension: $〈\mathit{\text{value}}〉$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$ and $\mathbf{nbloks}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge \mathbf{nbloks}$.

On entry, $\mathbf{nbloks}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nbloks}\ge 1$.

On entry, the following equality does not hold: $\mathbf{blkstr}\left(2,1\right)+\mathrm{sum}\left(\mathbf{blkstr}\left(2,k\right)-\mathbf{blkstr}\left(3,k-1\right):k=2,\mathbf{nbloks}\right)=\mathbf{n}$.

On entry, the following equality does not hold: $\mathrm{sum}\left(\mathbf{blkstr}\left(1,k\right):k=1,\mathbf{nbloks}\right)=\mathbf{n}$.

On entry, the following inequality was not satisfied for: $J=〈\mathit{\text{value}}〉$. $\mathrm{sum}\left(\mathbf{blkstr}\left(2,k\right)-\mathbf{blkstr}\left(3,k\right):k=1,J\right)\le$ $\mathrm{sum}\left(\mathbf{blkstr}\left(1,k\right):k=1,J\right)\le$ $\mathbf{blkstr}\left(2,1\right)+\mathrm{sum}\left(\mathbf{blkstr}\left(2,k\right)-\mathbf{blkstr}\left(3,k-1\right):k=2,J\right)$.

On entry, $\mathbf{trans}\ne \text{'N'}$ or $\text{'T'}$: $\mathbf{trans}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f04lhfe.f90)

10.2

Program Data

Program Data (f04lhfe.d)

10.3

Program Results

Program Results (f04lhfe.r)