LinAlg Documentation

Reference for the Linear Algebra module.

Data Analysis
    Simple analysis
    Eigensystems
    Finding equations solution
Data Manipulation
    Simple matrix manipulations
    Optimization
    Data comprimation
    Discrete Fourier transformation
Vectors and Matrices

Data Analysis

Simple analysis

• Stochastic
  • Calculate mean values
    • Alone
    • With variances
  • Calculate variances
    • Alone
    • With mean values
  • Calculate covariances
    • version 1
    • version 2
  • Calculate correlation coefficient
    • version 1
    • version 2
• Matrix-oriented
  • Calculate matrix determinants
  • Calculate matrix rank
    • Normal calculation
    • Using eigenvalues
    • Using singular values
  • Calculate generalized inverse matrix
    • version 1
    • version 2
  • Calculate sum of matrix diagonal

Eigensystems

• Calculating eigenvectors and eigenvalues of symmetric matrices
  • Alone
  • Alone, using Jacobi rotation
    • version 1
    • version 2
  • Together with matrix rank
  • Together with matrix determinant
• Calculating eigenvalues of non-symmetric matrices
  • Alone
• Sorting eigenvectors and eigenvalues
• Calculating the relative errors of eigenvalues

Finding equations solution

• Singular value decomposition
  • Calculating singular values
    • Alone
    • Together with matrix rank
    • Together with generalized inverse matrix
      • version 1
      • version 2
  • Sorting singular values
• Line search
• Cubic line search

Data Manipulation

Simple matrix manipulation

• Matrix transposition
• Creating matrix with input vector as diagonal

Optimization

• For one dimension
  • Minimization with line search
  • Minimization with cubic line search
  • Minimization with linmin
  • Minimization with linmin using derivative information

Discrete Fourier transformation

• Fast Fourier transformation

Vectors and Matrices

The LinAlg module uses the class Array<double> to represent both vectors and matrices. For convenience, in particular for using overloaded operators, specialized sub-classes

• Vector
• Matrix

are provided.