NAG FL Interface
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: $\mathbf{n}$ – Integer Input

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

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

3: $\mathbf{nbloks}$ – Integer Input

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 array Input

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) array Input

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

6: $\mathbf{lena}$ – Integer Input

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 array Input

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) array Input/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: $\mathbf{ldb}$ – Integer Input

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: $\mathbf{ir}$ – Integer Input

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

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

11: $\mathbf{ifail}$ – Integer Input/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 4 in the Introduction to the NAG Library FL Interface 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 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

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.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results