NAG Library Routine Document

f04mcf (real_posdef_vband_solve)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

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

Constraint: $\mathbf{n}\ge 1$.

2:     $\mathbf{al}\left(\mathbf{lal}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the elements within the envelope of the lower triangular matrix $L$, taken in row by row order, as returned by f01mcf. The unit diagonal elements of $L$ must be stored explicitly.

3:     $\mathbf{lal}$ – IntegerInput

On entry: the dimension of the array al as declared in the (sub)program from which f04mcf is called.

Constraint: $\mathbf{lal}\ge \mathbf{nrow}\left(1\right)+\mathbf{nrow}\left(2\right)+\dots +\mathbf{nrow}\left(n\right)$.

4:     $\mathbf{d}\left(*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the dimension of the array d must be at least $1$ if $\mathbf{iselct}\ge 4$, and at least $\mathbf{n}$ otherwise.

On entry: the diagonal elements of the diagonal matrix $D$. d is not referenced if $\mathbf{iselct}\ge 4$.

5:     $\mathbf{nrow}\left(\mathbf{n}\right)$ – Integer arrayInput

On entry: $\mathbf{nrow}\left(i\right)$ must contain the width of row $i$ of $L$, i.e., the number of elements between the first (leftmost) nonzero element and the element on the diagonal, inclusive.

Constraint: $1\le \mathbf{nrow}\left(i\right)\le i$.

6:     $\mathbf{ir}$ – IntegerInput

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

Constraint: $\mathbf{ir}\ge 1$.

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

On entry: the $n$ by $r$ right-hand side matrix $B$. See also Section 9.

8:     $\mathbf{ldb}$ – IntegerInput

On entry: the first dimension of the array b as declared in the (sub)program from which f04mcf is called.

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

9:     $\mathbf{iselct}$ – IntegerInput

On entry: must specify the type of system to be solved, as follows:

$\mathbf{iselct}=1$

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

$\mathbf{iselct}=2$

Solve $LDX=B$.

$\mathbf{iselct}=3$

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

$\mathbf{iselct}=4$

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

$\mathbf{iselct}=5$

Solve $LX=B$.

$\mathbf{iselct}=6$

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

Constraint: $\mathbf{iselct}=1$, $2$, $3$, $4$, $5$ or $6$.

10:   $\mathbf{x}\left(\mathbf{ldx},\mathbf{ir}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: the $n$ by $r$ solution matrix $X$. See also Section 9.

11:   $\mathbf{ldx}$ – IntegerInput

On entry: the first dimension of the array x as declared in the (sub)program from which f04mcf is called.

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

12:   $\mathbf{ifail}$ – 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, $I=〈\mathit{\text{value}}〉$ and $\mathbf{nrow}\left(I\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nrow}\left(I\right)\ge 1$ and $\mathbf{nrow}\left(I\right)\le I$.

On entry, $\mathbf{lal}=〈\mathit{\text{value}}〉$ and $\mathbf{nrow}\left(1\right)+\dots +\mathbf{nrow}\left(\mathbf{n}\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lal}\ge \mathbf{nrow}\left(1\right)+\dots +\mathbf{nrow}\left(\mathbf{n}\right)$.

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

$\mathbf{ifail}=2$

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

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

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

$\mathbf{ifail}=3$

On entry, $\mathbf{iselct}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{iselct}\ge 1$ and $\mathbf{iselct}\le 6$.

$\mathbf{ifail}=4$

On entry, $I=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{d}\left(I\right)\ne 0.0$.

$\mathbf{ifail}=5$

At least one diagonal entry of al is not unit.

$\mathbf{ifail}=-99$

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 (f04mcfe.f90)

10.2

Program Data

Program Data (f04mcfe.d)

10.3

Program Results

Program Results (f04mcfe.r)