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Reference Guide for OpenMatrix Language Functions
The Reference Guide contains documentation for all functions supported in the OpenMatrix language.
Linear Algebra Commands
pinv
Compute the matrix pseudo-inverse.

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Reference Guides
Explore the Extended Definitions, OML Guides, Block Library, API Guide and Glossary.
- Extended Definitions for Advanced Users
  In-depth information on key topics in the User's Guide.
- Scripting Guide for OpenMatrix Language
  OpenMatrix is a mathematical scripting language.
- Reference Guide for OpenMatrix Language Functions
  The Reference Guide contains documentation for all functions supported in the OpenMatrix language.
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  - Linear Algebra Commands
    - balance
      Returns a matrix with rows and columns of roughly equal magnitude.
    - bicgstab
      Solve a system of linear equations with the biconjugate gradient stabilized method.
    - chol
      Cholesky decomposition.
    - cond
      Compute the condition number of a matrix.
    - conv
      Convolution of two vectors.
    - conv2
      Compute 2D convolution.
    - cross
      Vector cross product.
    - ctranspose
      Matrix transpose.
    - det
      Compute the matrix determinant.
    - dot
      Vector dot product.
    - eig
      Eigen decomposition.
    - eigs
      Partial Eigen decomposition of a matrix.
    - full
      Creates a fully populated matrix from sparse.
    - gradient
      Compute the gradient of a real function or sampled data.
    - gmres
      Solve a system of linear equations with the generalized minimum residual method.
    - hankel
      Computes the Hankel matrix.
    - inv
      Compute the inverse matrix.
    - isbanded
      Determines if the input is a banded matrix.
    - isdiag
      Determines if the input is a diagonal matrix.
    - ishermitian
      Hermitian matrix test.
    - issparse
      Determines if an input is a matrix with sparse storage.
    - issquare
      Determines if x is a square matrix.
    - issymmetric
      Symmetric matrix test.
    - istril
      Determines if the input is a lower triangular matrix.
    - istriu
      Determines if the input is a upper triangular matrix.
    - kron
      Kronecker matrix product.
    - kronprod
      Kronecker matrix product object.
    - ldl
      LDL decomposition.
    - linsolve
      Solve a linear system of equations.
    - lu
      LU decomposition.
    - nnz
      Finds the number of non-zero values in a matrix.
    - norm
      Compute matrix and vector norms.
    - null
      Compute an orthonormal basis for the nullspace of a matrix.
    - orth
      Compute an orthonormal basis for the column space of a matrix.
    - pcg
      Solve a system of linear equations with the preconditioned conjugate gradient method.
    - pinv
      Compute the matrix pseudo-inverse.
    - qr
      QR decomposition.
    - rank
      Compute the rank of matrix A.
    - rcond
      Compute the 1-norm estimate of the reciprocal condition number.
    - schur
      Schur decomposition.
    - sparse
      Sparse matrix creation.
    - speye
      Sparse identity matrix creation.
    - spones
      Set non-zero matrix elements to 1.
    - svd
      Singular value decomposition.
    - toeplitz
      Computes the Toeplitz matrix.
    - trace
      Compute the trace of a matrix, the sum of the diagonal elements.
    - transpose
      Matrix transpose.
    - tril
      Returns a lower triangular matrix.
    - triu
      Returns a upper triangular matrix.
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  - Python to OML Bridge Commands
- Block Reference Guide
  Describes all of the blocks in the installed Twin Activate library.
- Function Guide for Twin Activate
  Provides information about developing and simulating models through the Twin Activate Application Program Interface.
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- Keyboard Shortcuts
  This page lists default shortcuts.
- Glossary
  Key terms associated with the software.
Frequently Asked Questions
You've got questions? We've got answers!

pinv

Compute the matrix pseudo-inverse.

Syntax

R = pinv(A)

R = pinv(A, tol)

Inputs

A: The matrix to pseudo-invert.; Dimension: matrix
tol: Singular values less than this value are zeroed in the inversion.; The default tolerance is max(size(A)) * eps.; Type: double; Dimension: scalar

Outputs

R: The pseudo-inverse.

Example

R = pinv([1, 2; 3, 5; 4, 8])

R = [Matrix] 2 x 3
-0.29412   2.00000  -1.17647
 0.17647  -1.00000   0.70588