NAG FL Interface
f04aef (withdraw_​real_​square_​solve_​ref)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

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

Note: the second dimension of the array a must be at least $\max (1,\mathbf{n})$.

On entry: the $n\times n$ matrix $A$.

2: $\mathbf{lda}$ – Integer Input

On entry: the first dimension of the array a as declared in the (sub)program from which f04aef is called.

Constraint: $\mathbf{lda}\ge \max (1,\mathbf{n})$.

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

Note: the second dimension of the array b must be at least $\max (1,\mathbf{m})$.

On entry: the $n\times m$ 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 f04aef is called.

Constraint: $\mathbf{ldb}\ge \max (1,\mathbf{n})$.

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: $\mathbf{c}(\mathbf{ldc},*)$ – Real (Kind=nag_wp) array Output

Note: the second dimension of the array c must be at least $\max (1,\mathbf{m})$.

On exit: the $n\times m$ 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 f04aef is called.

Constraint: $\mathbf{ldc}\ge \max (1,\mathbf{n})$.

9: $\mathbf{wkspce}\left(\max (1,\mathbf{n})\right)$ – Real (Kind=nag_wp) array Workspace

10: $\mathbf{aa}(\mathbf{ldaa},*)$ – Real (Kind=nag_wp) array Output

Note: the second dimension of the array aa must be at least $\max (1,\mathbf{n})$.

On exit: the triangular factors $L$ and $U$, except that the unit diagonal elements of $U$ are not stored.

11: $\mathbf{ldaa}$ – Integer Input

On entry: the first dimension of the array aa as declared in the (sub)program from which f04aef is called.

Constraint: $\mathbf{ldaa}\ge \max (1,\mathbf{n})$.

12: $\mathbf{bb}(\mathbf{ldbb},*)$ – Real (Kind=nag_wp) array Output

Note: the second dimension of the array bb must be at least $\max (1,\mathbf{m})$.

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

13: $\mathbf{ldbb}$ – Integer Input

On entry: the first dimension of the array bb as declared in the (sub)program from which f04aef is called.

Constraint: $\mathbf{ldbb}\ge \max (1,\mathbf{n})$.

14: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $\mathrm{-1}$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $\mathrm{-1}$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $\mathrm{-1}$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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 approximately singular.

$\mathbf{ifail}=2$

The matrix $A$ is too ill-conditioned.

$\mathbf{ifail}=3$

On entry, $\mathbf{ldaa}=⟨\mathit{\text{value}}⟩$ and $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ldaa}\ge \max (1,\mathbf{n})$.

On entry, $\mathbf{lda}=⟨\mathit{\text{value}}⟩$ and $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{lda}\ge \max (1,\mathbf{n})$.

On entry, $\mathbf{ldb}=⟨\mathit{\text{value}}⟩$ and $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ldb}\ge \max (1,\mathbf{n})$.

On entry, $\mathbf{ldbb}=⟨\mathit{\text{value}}⟩$ and $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ldbb}\ge \max (1,\mathbf{n})$.

On entry, $\mathbf{ldc}=⟨\mathit{\text{value}}⟩$ and $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ldc}\ge \max (1,\mathbf{n})$.

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