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# slicot_mb04md

### Syntax

 [MAXRED_OUT, A_OUT, SCALE, INFO] = slicot_mb04md(MAXRED_IN, A_IN)

### Input argument

MAXRED_IN

The maximum allowed reduction in the 1-norm of A (in an iteration) if zero rows or columns are encountered. If MAXRED greater than 0.0, MAXRED must be larger than one (to enable the norm reduction). If MAXRED less or equal than 0.0, then the value 10.0 for MAXRED is used.

A_IN

The leading N-by-N part of this array must contain the input matrix A.

### Output argument

MAXRED_OUT

If the 1-norm of the given matrix A is non-zero, the ratio between the 1-norm of the given matrix and the 1-norm of the balanced matrix. Usually, this ratio will be larger than one, but it can sometimes be one, or even less than one (for instance, for some companion matrices).

A_OUT

The leading N-by-N part of this array contains the balanced matrix.

SCALE

The scaling factors applied to A. If D(j) is the scaling factor applied to row and column j, then SCALE(j) = D(j), for j = 1,...,N.

INFO

= 0: successful exit.

### Description

To reduce the 1-norm of a general real matrix A by balancing. This involves diagonal similarity transformations applied iteratively to A to make the rows and columns as close in norm as possible.

MB04MD

### Bibliography

http://slicot.org/objects/software/shared/doc/MB04MD.html

### Example

``````MAXRED_IN  = 0.0;
A_IN = [1.0   0.0   0.0   0.0;
300.0 400.0 500.0 600.0;
1.0   2.0   0.0   0.0;
1.0   1.0   1.0   1.0];
[MAXRED_OUT, A_OUT, SCALE, INFO] = slicot_mb04md(MAXRED_IN, A_IN)
```
```

### History

Version Description
1.0.0 initial version

### Author

SLICOT Documentation