NAG Library Routine Document

F04MCF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     N – INTEGERInput

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

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

2:     AL(LAL) – 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:     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:     D($*$) – 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:     NROW(N) – 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:     IR – INTEGERInput

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

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

7:     B(LDB,IR) – REAL (KIND=nag_wp) arrayInput

On entry: the $n$ by $r$ right-hand side matrix $B$. See also Section 8.

8:     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:     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:   X(LDX,IR) – REAL (KIND=nag_wp) arrayOutput

On exit: the $n$ by $r$ solution matrix $X$. See also Section 8.

11:   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:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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,	$\mathbf{N}<1$,
or	for some $i$, $\mathbf{NROW}\left(i\right)<1$ or $\mathbf{NROW}\left(i\right)>i$,
or	$\mathbf{LAL}<\mathbf{NROW}\left(1\right)+\mathbf{NROW}\left(2\right)+\cdots +\mathbf{NROW}\left(\mathbf{N}\right)$.

$\mathbf{IFAIL}=2$

On entry,	$\mathbf{IR}<1$,
or	$\mathbf{LDB}<\mathbf{N}$,
or	$\mathbf{LDX}<\mathbf{N}$.

$\mathbf{IFAIL}=3$

On entry,	$\mathbf{ISELCT}<1$,
or	$\mathbf{ISELCT}>6$.

$\mathbf{IFAIL}=4$

The diagonal matrix $D$ is singular, i.e., at least one of the elements of D is zero. This can only occur if $\mathbf{ISELCT}\le 3$.

$\mathbf{IFAIL}=5$

At least one of the diagonal elements of $L$ is not equal to unity.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f04mcfe.f90)

9.2  Program Data

Program Data (f04mcfe.d)

9.3  Program Results

Program Results (f04mcfe.r)