NAG Library Routine Document

F07BTF (ZGBEQU)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     M – INTEGERInput

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

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

2:     N – INTEGERInput

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

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

3:     KL – INTEGERInput

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

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

4:     KU – INTEGERInput

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

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

5:     AB(LDAB,$*$) – COMPLEX (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 8 in F07BNF (ZGBSV) for further details.

6:     LDAB – INTEGERInput

On entry: the first dimension of the array AB as declared in the (sub)program from which F07BTF (ZGBEQU) is called.

Constraint: $\mathbf{LDAB}\ge \mathbf{KL}+\mathbf{KU}+1$.

7:     R(M) – 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:     C(N) – 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:     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:   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:   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:   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.

$\mathbf{INFO}>0\text{ and }\mathbf{INFO}\le \mathbf{M}$

If $\mathbf{INFO}=i$, the $i$th row of $A$ is exactly zero.

$\mathbf{INFO}>\mathbf{M}$

If $\mathbf{INFO}=i$, the $\left(i-\mathbf{M}\right)$th column of $A$ is exactly zero.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f07btfe.f90)

9.2  Program Data

Program Data (f07btfe.d)

9.3  Program Results

Program Results (f07btfe.r)