Class LUDecompositionQuick

java.lang.Object
cern.colt.matrix.linalg.LUDecompositionQuick
All Implemented Interfaces:
Serializable

public class LUDecompositionQuick extends Object implements Serializable
A low level version of LUDecomposition, avoiding unnecessary memory allocation and copying. The input to decompose methods is overriden with the result (LU). The input to solve methods is overriden with the result (X). In addition to LUDecomposition, this class also includes a faster variant of the decomposition, specialized for tridiagonal (and hence also diagonal) matrices, as well as a solver tuned for vectors. Its disadvantage is that it is a bit more difficult to use than LUDecomposition. Thus, you may want to disregard this class and come back later, if a need for speed arises.

An instance of this class remembers the result of its last decomposition. Usage pattern is as follows: Create an instance of this class, call a decompose method, then retrieve the decompositions, determinant, and/or solve as many equation problems as needed. Once another matrix needs to be LU-decomposed, you need not create a new instance of this class. Start again by calling a decompose method, then retrieve the decomposition and/or solve your equations, and so on. In case a LU matrix is already available, call method setLU instead of decompose and proceed with solving et al.

If a matrix shall not be overriden, use matrix.copy() and hand the the copy to methods.

For an m x n matrix A with m >= n, the LU decomposition is an m x n unit lower triangular matrix L, an n x n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U; If m invalid input: '<' n, then L is m x m and U is m x n.

The LU decomposition with pivoting always exists, even if the matrix is singular, so the decompose methods will never fail. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations. Attempting to solve such a system will throw an exception if isNonsingular() returns false.

See Also:
  • Field Details

    • serialVersionUID

      static final long serialVersionUID
      See Also:
    • LU

      protected DoubleMatrix2D LU
      Array for internal storage of decomposition.
    • pivsign

      protected int pivsign
      pivot sign.
    • piv

      protected int[] piv
      Internal storage of pivot vector.
    • isNonSingular

      protected boolean isNonSingular
    • algebra

      protected Algebra algebra
    • workDouble

      protected transient double[] workDouble
    • work1

      protected transient int[] work1
    • work2

      protected transient int[] work2
  • Constructor Details

    • LUDecompositionQuick

      public LUDecompositionQuick()
      Constructs and returns a new LU Decomposition object with default tolerance 1.0E-9 for singularity detection.
    • LUDecompositionQuick

      public LUDecompositionQuick(double tolerance)
      Constructs and returns a new LU Decomposition object which uses the given tolerance for singularity detection;
  • Method Details

    • decompose

      public void decompose(DoubleMatrix2D A)
      Decomposes matrix A into L and U (in-place). Upon return A is overridden with the result LU, such that L*U = A. Uses a "left-looking", dot-product, Crout/Doolittle algorithm.
      Parameters:
      A - any matrix.
    • decompose

      public void decompose(DoubleMatrix2D A, int semiBandwidth)
      Decomposes the banded and square matrix A into L and U (in-place). Upon return A is overridden with the result LU, such that L*U = A. Currently supports diagonal and tridiagonal matrices, all other cases fall through to decompose(DoubleMatrix2D).
      Parameters:
      A - any matrix.
      semiBandwidth - == 1 --> A is diagonal, == 2 --> A is tridiagonal.
    • det

      public double det()
      Returns the determinant, det(A).
      Throws:
      IllegalArgumentException - if A.rows() != A.columns() (Matrix must be square).
    • getDoublePivot

      protected double[] getDoublePivot()
      Returns pivot permutation vector as a one-dimensional double array
      Returns:
      (double) piv
    • getL

      public DoubleMatrix2D getL()
      Returns the lower triangular factor, L.
      Returns:
      L
    • getLU

      public DoubleMatrix2D getLU()
      Returns a copy of the combined lower and upper triangular factor, LU.
      Returns:
      LU
    • getPivot

      public int[] getPivot()
      Returns the pivot permutation vector (not a copy of it).
      Returns:
      piv
    • getU

      public DoubleMatrix2D getU()
      Returns the upper triangular factor, U.
      Returns:
      U
    • isNonsingular

      public boolean isNonsingular()
      Returns whether the matrix is nonsingular (has an inverse).
      Returns:
      true if U, and hence A, is nonsingular; false otherwise.
    • isNonsingular

      protected boolean isNonsingular(DoubleMatrix2D matrix)
      Returns whether the matrix is nonsingular.
      Returns:
      true if matrix is nonsingular; false otherwise.
    • lowerTriangular

      protected DoubleMatrix2D lowerTriangular(DoubleMatrix2D A)
      Modifies the matrix to be a lower triangular matrix.

      Examples:

      3 x 5 matrix:
      9, 9, 9, 9, 9
      9, 9, 9, 9, 9
      9, 9, 9, 9, 9
      triang.Upper
      ==>
      3 x 5 matrix:
      9, 9, 9, 9, 9
      0, 9, 9, 9, 9
      0, 0, 9, 9, 9
      5 x 3 matrix:
      9, 9, 9
      9, 9, 9
      9, 9, 9
      9, 9, 9
      9, 9, 9
      triang.Upper
      ==>
      5 x 3 matrix:
      9, 9, 9
      0, 9, 9
      0, 0, 9
      0, 0, 0
      0, 0, 0
      3 x 5 matrix:
      9, 9, 9, 9, 9
      9, 9, 9, 9, 9
      9, 9, 9, 9, 9
      triang.Lower
      ==>
      3 x 5 matrix:
      1, 0, 0, 0, 0
      9, 1, 0, 0, 0
      9, 9, 1, 0, 0
      5 x 3 matrix:
      9, 9, 9
      9, 9, 9
      9, 9, 9
      9, 9, 9
      9, 9, 9
      triang.Lower
      ==>
      5 x 3 matrix:
      1, 0, 0
      9, 1, 0
      9, 9, 1
      9, 9, 9
      9, 9, 9
      Returns:
      A (for convenience only).
      See Also:
      • invalid reference
        #triangulateUpper(DoubleMatrix2D)
    • m

      protected int m()
    • n

      protected int n()
    • setLU

      public void setLU(DoubleMatrix2D LU)
      Sets the combined lower and upper triangular factor, LU. The parameter is not checked; make sure it is indeed a proper LU decomposition.
    • solve

      public void solve(DoubleMatrix1D B)
      Solves the system of equations A*X = B (in-place). Upon return B is overridden with the result X, such that L*U*X = B(piv).
      Parameters:
      B - A vector with B.size() == A.rows().
      Throws:
      IllegalArgumentException - if B.size() != A.rows().
      IllegalArgumentException - if A is singular, that is, if !isNonsingular().
      IllegalArgumentException - if A.rows() invalid input: '<' A.columns().
    • solve

      public void solve(DoubleMatrix2D B)
      Solves the system of equations A*X = B (in-place). Upon return B is overridden with the result X, such that L*U*X = B(piv,:).
      Parameters:
      B - A matrix with as many rows as A and any number of columns.
      Throws:
      IllegalArgumentException - if B.rows() != A.rows().
      IllegalArgumentException - if A is singular, that is, if !isNonsingular().
      IllegalArgumentException - if A.rows() invalid input: '<' A.columns().
    • solveOld

      private void solveOld(DoubleMatrix2D B)
      Solves A*X = B.
      Parameters:
      B - A matrix with as many rows as A and any number of columns.
      Throws:
      IllegalArgumentException - if B.rows() != A.rows().
      IllegalArgumentException - if A is singular, that is, if !this.isNonsingular().
      IllegalArgumentException - if A.rows() invalid input: '<' A.columns().
    • toString

      public String toString()
      Returns a String with (propertyName, propertyValue) pairs. Useful for debugging or to quickly get the rough picture. For example,
      rank          : 3
      trace         : 0
      
      Overrides:
      toString in class Object
    • upperTriangular

      protected DoubleMatrix2D upperTriangular(DoubleMatrix2D A)
      Modifies the matrix to be an upper triangular matrix.
      Returns:
      A (for convenience only).
      See Also:
      • invalid reference
        #triangulateLower(DoubleMatrix2D)
    • xgetDoublePivot

      private double[] xgetDoublePivot()
      Returns pivot permutation vector as a one-dimensional double array
      Returns:
      (double) piv