NAG Library Routine Document

F04ABF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     A(LDA,$*$) – REAL (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array A must be at least $\max \left(1,\mathbf{N}\right)$.

On entry: the upper triangle of the $n$ by $n$ positive definite symmetric matrix $A$. The elements of the array below the diagonal need not be set.

On exit: the elements of the array below the diagonal are overwritten; the upper triangle of $A$ is unchanged.

2:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F04ABF is called.

Constraint: $\mathbf{LDA}\ge \max \left(1,\mathbf{N}\right)$.

3:     B(LDB,$*$) – REAL (KIND=nag_wp) arrayInput

Note: the second dimension of the array B must be at least $\max \left(1,\mathbf{M}\right)$.

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

4:     LDB – INTEGERInput

On entry: the first dimension of the array B as declared in the (sub)program from which F04ABF is called.

Constraint: $\mathbf{LDB}\ge \max \left(1,\mathbf{N}\right)$.

5:     N – INTEGERInput

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

Constraint: $\mathbf{N}\ge 0$.

6:     M – INTEGERInput

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

Constraint: $\mathbf{M}\ge 0$.

7:     C(LDC,$\mathbf{M}$) – REAL (KIND=nag_wp) arrayOutput

Note: the second dimension of the array C must be at least $\max \left(1,\mathbf{M}\right)$.

On exit: the $n$ by $m$ solution matrix $X$.

8:     LDC – INTEGERInput

On entry: the first dimension of the array C as declared in the (sub)program from which F04ABF is called.

Constraint: $\mathbf{LDC}\ge \max \left(1,\mathbf{N}\right)$.

9:     WKSPCE(N) – REAL (KIND=nag_wp) arrayWorkspace

10:   BB(LDBB,$\mathbf{M}$) – REAL (KIND=nag_wp) arrayOutput

Note: the second dimension of the array BB must be at least $\max \left(1,\mathbf{M}\right)$.

On exit: the final $n$ by $m$ residual matrix $R=B-AX$.

11:   LDBB – INTEGERInput

On entry: the first dimension of the array BB as declared in the (sub)program from which F04ABF is called.

Constraint: $\mathbf{LDBB}\ge \max \left(1,\mathbf{N}\right)$.

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

$\mathbf{IFAIL}=1$

The matrix $A$ is not positive definite, possibly due to rounding errors.

$\mathbf{IFAIL}=2$

Iterative refinement fails to improve the solution, i.e., the matrix $A$ is too ill-conditioned.

$\mathbf{IFAIL}=3$

On entry,	$\mathbf{N}<0$,
or	$\mathbf{M}<0$,
or	$\mathbf{LDA}<\max \left(1,\mathbf{N}\right)$,
or	$\mathbf{LDB}<\max \left(1,\mathbf{N}\right)$,
or	$\mathbf{LDC}<\max \left(1,\mathbf{N}\right)$,
or	$\mathbf{LDBB}<\max \left(1,\mathbf{N}\right)$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f04abfe.f90)

9.2  Program Data

Program Data (f04abfe.d)

9.3  Program Results

Program Results (f04abfe.r)