Reciprocal Condition

Compute reciprocal condition of square matrix in 1-norm

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Libraries:
DSP System Toolbox / Math Functions / Matrices and Linear Algebra / Matrix Operations

Description

The Reciprocal Condition block computes the reciprocal of the condition number for a square input matrix A.

Here is the equivalent MATLAB^® code.

y = rcond(A)					

or

$$y=\frac{1}{\kappa }=\frac{1}{{\Vert A^{-1}\Vert }_1{\Vert A^{}\Vert }_1},$$

where κ is the condition number (κ ≥ 1), and y is the scalar output (0 ≤ y < 1).

The matrix 1-norm, $${\Vert A\Vert }_1$$, is the maximum column-sum in the M-by-M matrix A.

$${\Vert A\Vert }_1=\stackrel{\max }{{\displaystyle 1\le j\le M}}{\displaystyle \sum _{i=1}^M\left|a_{ij}\right|}$$

For a 3-by-3 matrix:

Ports

Input

Input — Input matrix

square matrix

Specify the input matrix as a square matrix.

Data Types: single | double

Output

Output — Reciprocal condition output

scalar

Reciprocal of the condition number for a square input matrix A, returned as a scalar.

If input is well conditioned, the output is near 1.0. If input is badly conditioned, the output is near 0.0.

Data Types: single | double

Block Characteristics

Data Types	double | single
Direct Feedthrough	no
Multidimensional Signals	no
Variable-Size Signals	no
Zero-Crossing Detection	no

References

[1] Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

Generated code relies on the memcpy or memset function (string.h) under certain conditions.

Version History

Introduced before R2006a