Class SingularOps_DDRM

java.lang.Object
org.ejml.dense.row.SingularOps_DDRM

public class SingularOps_DDRM
extends Object
Operations related to singular value decomposition.
  • Constructor Details

    • SingularOps_DDRM

      public SingularOps_DDRM()
  • Method Details

    • singularValues

      public static double[] singularValues​(DMatrixRMaj A)
      Returns an array of all the singular values in A sorted in ascending order
      Parameters:
      A - Matrix. Not modified.
      Returns:
      singular values
    • ratioSmallestOverLargest

      public static double ratioSmallestOverLargest​(double[] sv)
      Computes the ratio of the smallest value to the largest. Does not assume the array is sorted first
      Parameters:
      sv - array
      Returns:
      smallest / largest
    • rank

      public static int rank​(DMatrixRMaj A, double threshold)
      Returns the matrix's rank
      Parameters:
      A - Matrix. Not modified.
      threshold - Tolerance used to determine of a singular value is singular.
      Returns:
      The rank of the decomposed matrix.
    • rank

      public static int rank​(DMatrixRMaj A)
      Returns the matrix's rank. Automatic selection of threshold
      Parameters:
      A - Matrix. Not modified.
      Returns:
      The rank of the decomposed matrix.
    • svd

      public static boolean svd​(DMatrixRMaj A, @Nullable @Nullable DMatrixRMaj U, DGrowArray sv, @Nullable @Nullable DMatrixRMaj Vt)
      Computes the SVD and sorts singular values in descending order. While easier to use this can reduce performance when performed on small matrices numerous times. U*W*VT = A
      Parameters:
      A - (Input) Matrix being decomposed
      U - (Output) Storage for U. If null then it's ignored.
      sv - (Output) sorted list of singular values. Can be null.
      Vt - (Output) Storage for transposed V. Can be null.
    • descendingOrder

      public static void descendingOrder​(DMatrixRMaj U, boolean tranU, DMatrixRMaj W, DMatrixRMaj V, boolean tranV)

      Adjusts the matrices so that the singular values are in descending order.

      In most implementations of SVD the singular values are automatically arranged in in descending order. In EJML this is not the case since it is often not needed and some computations can be saved by not doing that.

      Parameters:
      U - Matrix. Modified.
      tranU - is U transposed or not.
      W - Diagonal matrix with singular values. Modified.
      V - Matrix. Modified.
      tranV - is V transposed or not.
    • descendingOrder

      public static void descendingOrder​(@Nullable @Nullable DMatrixRMaj U, boolean tranU, double[] singularValues, int singularLength, @Nullable @Nullable DMatrixRMaj V, boolean tranV)

      Similar to descendingOrder(DMatrixRMaj, boolean, DMatrixRMaj, DMatrixRMaj, boolean) but takes in an array of singular values instead.

      Parameters:
      U - Matrix. Modified.
      tranU - is U transposed or not.
      singularValues - Array of singular values. Modified.
      singularLength - Number of elements in singularValues array
      V - Matrix. Modified.
      tranV - is V transposed or not.
    • checkSvdMatrixSize

      public static void checkSvdMatrixSize​(@Nullable @Nullable DMatrixRMaj U, boolean tranU, DMatrixRMaj W, @Nullable @Nullable DMatrixRMaj V, boolean tranV)
      Checks to see if all the provided matrices are the expected size for an SVD. If an error is encountered then an exception is thrown. This automatically handles compact and non-compact formats
    • nullSpace

      public static DMatrixRMaj nullSpace​(SingularValueDecomposition_F64<DMatrixRMaj> svd, @Nullable @Nullable DMatrixRMaj nullSpace, double tol)

      Returns the null-space from the singular value decomposition. The null space is a set of non-zero vectors that when multiplied by the original matrix return zero.

      The null space is found by extracting the columns in V that are associated singular values less than or equal to the threshold. In some situations a non-compact SVD is required.

      Parameters:
      svd - A precomputed decomposition. Not modified.
      nullSpace - Storage for null space. Will be reshaped as needed. Modified.
      tol - Threshold for selecting singular values. Try UtilEjml.EPS.
      Returns:
      The null space.
    • nullspaceQR

      public static DMatrixRMaj nullspaceQR​(DMatrixRMaj A, int totalSingular)
      Computes the null space using QR decomposition. This is much faster than using SVD
      Parameters:
      A - (Input) Matrix
      totalSingular - Number of singular values
      Returns:
      Null space
    • nullspaceQRP

      public static DMatrixRMaj nullspaceQRP​(DMatrixRMaj A, int totalSingular)
      Computes the null space using QRP decomposition. This is faster than using SVD but slower than QR. Much more stable than QR though.
      Parameters:
      A - (Input) Matrix
      totalSingular - Number of singular values
      Returns:
      Null space
    • nullspaceSVD

      public static DMatrixRMaj nullspaceSVD​(DMatrixRMaj A, int totalSingular)
      Computes the null space using SVD. Slowest bust most stable way to find the solution
      Parameters:
      A - (Input) Matrix
      totalSingular - Number of singular values
      Returns:
      Null space
    • nullVector

      public static DMatrixRMaj nullVector​(SingularValueDecomposition_F64<DMatrixRMaj> svd, boolean isRight, @Nullable @Nullable DMatrixRMaj nullVector)

      The vector associated will the smallest singular value is returned as the null space of the decomposed system. A right null space is returned if 'isRight' is set to true, and a left null space if false.

      Parameters:
      svd - A precomputed decomposition. Not modified.
      isRight - true for right null space and false for left null space. Right is more commonly used.
      nullVector - Optional storage for a vector for the null space. Modified.
      Returns:
      Vector in V associated with smallest singular value..
    • singularThreshold

      public static double singularThreshold​(SingularValueDecomposition_F64<?> svd)
      Returns a reasonable threshold for singular values.

      tol = max (size (A)) * largest sigma * eps;
      Parameters:
      svd - A precomputed decomposition. Not modified.
      Returns:
      threshold for singular values
    • singularThreshold

      public static double singularThreshold​(SingularValueDecomposition_F64<?> svd, double tolerance)
    • rank

      public static int rank​(SingularValueDecomposition_F64<?> svd)
      Extracts the rank of a matrix using a preexisting decomposition and default threshold.
      Parameters:
      svd - A precomputed decomposition. Not modified.
      Returns:
      The rank of the decomposed matrix.
      See Also:
      singularThreshold(SingularValueDecomposition_F64)
    • rank

      public static int rank​(SingularValueDecomposition_F64<?> svd, double threshold)
      Extracts the rank of a matrix using a preexisting decomposition.
      Parameters:
      svd - A precomputed decomposition. Not modified.
      threshold - Tolerance used to determine of a singular value is singular.
      Returns:
      The rank of the decomposed matrix.
      See Also:
      singularThreshold(SingularValueDecomposition_F64)
    • nullity

      public static int nullity​(SingularValueDecomposition_F64<?> svd)
      Extracts the nullity of a matrix using a preexisting decomposition and default threshold.
      Parameters:
      svd - A precomputed decomposition. Not modified.
      Returns:
      The nullity of the decomposed matrix.
      See Also:
      singularThreshold(SingularValueDecomposition_F64)
    • nullity

      public static int nullity​(SingularValueDecomposition_F64<?> svd, double threshold)
      Extracts the nullity of a matrix using a preexisting decomposition.
      Parameters:
      svd - A precomputed decomposition. Not modified.
      threshold - Tolerance used to determine of a singular value is singular.
      Returns:
      The nullity of the decomposed matrix.
      See Also:
      singularThreshold(SingularValueDecomposition_F64)
    • nullity

      public static int nullity​(DMatrixRMaj A, double threshold)
      Returns the matrix's nullity
      Parameters:
      A - Matrix. Not modified.
      threshold - Tolerance used to determine of a singular value is singular.
      Returns:
      nullity