NAG FL Interface
f04abf (withdraw_​real_​posdef_​solve_​ref)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{a}\left(\mathbf{lda},*\right)$ – Real (Kind=nag_wp) array Input/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: $\mathbf{lda}$ – Integer Input

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: $\mathbf{b}\left(\mathbf{ldb},*\right)$ – Real (Kind=nag_wp) array Input

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: $\mathbf{ldb}$ – Integer Input

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: $\mathbf{n}$ – Integer Input

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

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

6: $\mathbf{m}$ – Integer Input

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

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

7: $\mathbf{c}\left(\mathbf{ldc},\mathbf{m}\right)$ – Real (Kind=nag_wp) array Output

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: $\mathbf{ldc}$ – Integer Input

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: $\mathbf{wkspce}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) array Workspace

10: $\mathbf{bb}\left(\mathbf{ldbb},\mathbf{m}\right)$ – Real (Kind=nag_wp) array Output

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: $\mathbf{ldbb}$ – Integer Input

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: $\mathbf{ifail}$ – 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

$\mathbf{ifail}=1$

Matrix $A$ is not positive definite.

$\mathbf{ifail}=2$

Matrix $A$ is too ill-conditioned; iterative refinement fails to improve the solution.

$\mathbf{ifail}=3$

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

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

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

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

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 0$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

$\mathbf{ifail}=-99$

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