NAG Library Routine Document

F07FFF (DPOEQU)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     N – INTEGERInput

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

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

2:     A(LDA,$*$) – REAL (KIND=nag_wp) arrayInput

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

On entry: the matrix $A$ whose scaling factors are to be computed. Only the diagonal elements of the array A are referenced.

3:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F07FFF (DPOEQU) is called.

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

4:     S(N) – REAL (KIND=nag_wp) arrayOutput

On exit: if $\mathbf{INFO}=\mathbf{0}$, S contains the diagonal elements of the scaling matrix $S$.

5:     SCOND – REAL (KIND=nag_wp)Output

On exit: if $\mathbf{INFO}=\mathbf{0}$, SCOND contains the ratio of the smallest value of S to the largest value of S. If $\mathbf{SCOND}\ge 0.1$ and AMAX is neither too large nor too small, it is not worth scaling by $S$.

6:     AMAX – REAL (KIND=nag_wp)Output

On exit: $\max \left|a_{ij}\right|$. If AMAX is very close to overflow or underflow, the matrix $A$ should be scaled.

7:     INFO – INTEGEROutput

On exit: $\mathbf{INFO}=0$ unless the routine detects an error (see Section 6).

6  Error Indicators and Warnings

$\mathbf{INFO}<0$

If $\mathbf{INFO}=-i$, the $i$th argument had an illegal value. An explanatory message is output, and execution of the program is terminated.

$\mathbf{INFO}>0$

If $\mathbf{INFO}=i$, the $i$th diagonal element of $A$ is not positive (and hence $A$ cannot be positive definite).

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f07fffe.f90)

9.2  Program Data

Program Data (f07fffe.d)

9.3  Program Results

Program Results (f07fffe.r)