NAG Library Routine Document

f07bff (dgbequ)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{m}$ – IntegerInput

On entry: $m$, the number of rows of the matrix $A$.

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

2:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of columns of the matrix $A$.

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

3:     $\mathbf{kl}$ – IntegerInput

On entry: $k_l$, the number of subdiagonals of the matrix $A$.

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

4:     $\mathbf{ku}$ – IntegerInput

On entry: $k_u$, the number of superdiagonals of the matrix $A$.

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

5:     $\mathbf{ab}\left(\mathbf{ldab},*\right)$ – Real (Kind=nag_wp) arrayInput

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

On entry: the $m$ by $n$ band matrix $A$ whose scaling factors are to be computed.

The matrix is stored in rows $1$ to $k_l+k_u+1$, more precisely, the element $A_{ij}$ must be stored in

$$\mathbf{ab}\left(k_u+1+i-j,j\right)\text{\hspace{1em} for }\max \left(1,j-k_u\right)\le i\le \min \left(m,j+k_l\right)\text{.}$$

See Section 9 in f07baf (dgbsv) for further details.

6:     $\mathbf{ldab}$ – IntegerInput

On entry: the first dimension of the array ab as declared in the (sub)program from which f07bff (dgbequ) is called.

Constraint: $\mathbf{ldab}\ge \mathbf{kl}+\mathbf{ku}+1$.

7:     $\mathbf{r}\left(\mathbf{m}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: if $\mathbf{info}=\mathbf{0}$ or $\mathbf{info}>\mathbf{m}$, r contains the row scale factors, the diagonal elements of $D_R$. The elements of r will be positive.

8:     $\mathbf{c}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: if $\mathbf{info}=\mathbf{0}$, c contains the column scale factors, the diagonal elements of $D_C$. The elements of c will be positive.

9:     $\mathbf{rowcnd}$ – Real (Kind=nag_wp)Output

On exit: if $\mathbf{info}=\mathbf{0}$ or $\mathbf{info}>\mathbf{m}$, rowcnd contains the ratio of the smallest value of $\mathbf{r}\left(i\right)$ to the largest value of $\mathbf{r}\left(i\right)$. If $\mathbf{rowcnd}\ge 0.1$ and amax is neither too large nor too small, it is not worth scaling by $D_R$.

10:   $\mathbf{colcnd}$ – Real (Kind=nag_wp)Output

On exit: if $\mathbf{info}=\mathbf{0}$, colcnd contains the ratio of the smallest value of $\mathbf{c}\left(i\right)$ to the largest value of $\mathbf{c}\left(i\right)$.

If $\mathbf{colcnd}\ge 0.1$, it is not worth scaling by $D_C$.

11:   $\mathbf{amax}$ – 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.

12:   $\mathbf{info}$ – IntegerOutput

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

6

Error Indicators and Warnings

$\mathbf{info}<0$

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

$\mathbf{info}>0\hspace{0.17em}\text{and}\hspace{0.17em}\mathbf{info}\le \mathbf{m}$

Row $〈\mathit{\text{value}}〉$ of $A$ is exactly zero.

$\mathbf{info}>\mathbf{m}$

Column $〈\mathit{\text{value}}〉$ of $A$ is exactly zero.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f07bffe.f90)

10.2

Program Data

Program Data (f07bffe.d)

10.3

Program Results

Program Results (f07bffe.r)