Pseudoinverse

Compute Moore-Penrose pseudoinverse of matrix

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

Description

The Pseudoinverse block computes the Moore-Penrose pseudoinverse of input matrix A.

The equivalent MATLAB^® code is given by:

[U,S,V] = svd(A,0)

Ports

Input

A — Input

vector | matrix

Specify the input as a vector or a matrix.

Data Types: single | double
Complex Number Support: Yes

Output

X — Pseudoinverse output

vector | matrix

Pseudoinverse output, returned as a vector or a matrix. If the pseudoinverse calculation fails to converge, the output on this port is an undefined matrix of the correct size.

Data Types: single | double
Complex Number Support: Yes

E — Error status

0 | 1

The possible values of error status you can receive on this port are:

• 0 — The pseudoinverse calculation converges.

• 1 — The pseudoinverse calculation does not converge.

If the pseudoinverse calculation fails to converge, the output at port X is an undefined matrix of the correct size.

Data Types: Boolean

Parameters

Show error status port (E) — Show error status port

off (default) | on

Select to enable the E output port, which reports a failure to converge. For more details, see the description for the E output port.

Simulate using — Type of simulation to run

Interpreted execution (default) | Code generation

Specify the type of simulation to run. You can set this parameter to:

• Interpreted execution –– Simulate model using the MATLAB interpreter. This option shortens startup time. For this block, the simulation speed in this mode is faster than in Code generation.

• Code generation –– Simulate model using generated C code. The first time you run a simulation, Simulink^® generates C code for the block. The C code is reused for subsequent simulations, as long as the model does not change. This option requires additional startup time but the simulation speed increases with subsequent simulations.

Block Characteristics

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

More About

Pseudoinverse

The pseudoinverse of input matrix A is the matrix $$A^{†}$$ such that

$$A^{†}=V{S}^{†}{U}^{\ast }$$

where U and V are orthogonal matrices, and S is a diagonal matrix.

The pseudoinverse has the following properties:

• $$A{A}^{†}={(A{A}^{†})}^{\ast }$$

• $$A^{†}A={(A^{†}A)}^{\ast }$$

• $$A{A}^{†}A=A$$

• $$A^{†}A{A}^{†}=A^{†}$$

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