Package org.ejml.dense.row.decompose.qr

Class QrHelperFunctions_CDRM

  • public class QrHelperFunctions_CDRM
extends java.lang.Object

    Contains different functions that are useful for computing the QR decomposition of a matrix.

    Two different families of functions are provided for help in computing reflectors. Internally both of these functions switch between normalization by division or multiplication. Multiplication is most often significantly faster than division (2 or 3 times) but produces less accurate results on very small numbers. It checks to see if round off error is significant and decides which one it should do.

    Tests were done using the stability benchmark in jmatbench and there doesn't seem to be any advantage to always dividing by the max instead of checking and deciding. The most noticeable difference between the two methods is with very small numbers.

    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      static float computeRowMax​(org.ejml.data.CMatrixRMaj A, int row, int col0, int col1)
      Finds the magnitude of the largest element in the row
      static float computeTauGammaAndDivide​(int start, int stop, float[] x, float max, org.ejml.data.Complex_F32 tau)
      Performs the following operations:
      static void divideElements​(int j, int numRows, float[] u, int startU, float realA, float imagA)
      Performs the following operation:
      u[(startU+j):(startU+numRows)] /= A
      were u and A are a complex
      static float extractColumnAndMax​(org.ejml.data.CMatrixRMaj A, int row0, int row1, int col, float[] u, int offsetU)
      Extracts the column of A and copies it into u while computing the magnitude of the largest element and returning it.
      static void extractHouseholderColumn​(org.ejml.data.CMatrixRMaj A, int row0, int row1, int col, float[] u, int offsetU)
      Extracts a house holder vector from the column of A and stores it in u
      static void extractHouseholderRow​(org.ejml.data.CMatrixRMaj A, int row, int col0, int col1, float[] u, int offsetU)
      Extracts a house holder vector from the rows of A and stores it in u
      static float findMax​(float[] u, int startU, int length)
      Returns the maximum magnitude of the complex numbers
      static void rank1UpdateMultL​(org.ejml.data.CMatrixRMaj A, float[] u, int offsetU, float gammaR, int colA0, int w0, int w1)
      Performs a rank-1 update operation on the submatrix specified by w with the multiply on the left.

      A = A(I - γ*u*uH)
      static void rank1UpdateMultR​(org.ejml.data.CMatrixRMaj A, float[] u, int offsetU, float gamma, int colA0, int w0, int w1, float[] _temp)
      Performs a rank-1 update operation on the submatrix specified by w with the multiply on the right.

      A = (I - γ*u*uH)*A

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    • Constructor Detail

      • QrHelperFunctions_CDRM

        public QrHelperFunctions_CDRM()

    • Method Detail

      • findMax

        public static float findMax​(float[] u,
                            int startU,
                            int length)
        Returns the maximum magnitude of the complex numbers
        Parameters:
        u - Array of complex numbers
        startU - first index to consider in u
        length - Number of complex numebrs to consider
        Returns:
        magnitude

      • divideElements

        public static void divideElements​(int j,
                                  int numRows,
                                  float[] u,
                                  int startU,
                                  float realA,
                                  float imagA)
        Performs the following operation:
        u[(startU+j):(startU+numRows)] /= A
        were u and A are a complex

      • computeTauGammaAndDivide

        public static float computeTauGammaAndDivide​(int start,
                                             int stop,
                                             float[] x,
                                             float max,
                                             org.ejml.data.Complex_F32 tau)
        Performs the following operations: 
         x = x / max
 tau = x0*|x|/|xo|   adjust sign to avoid cancellation
 u = x; u0 = x0 + tau; u = u/u0  (x is not divided by x0)
 gamma = 2/|u|^2
        Note that u is not explicitly computed here.
        Parameters:
        start - Element in 'u' that it starts at.
        stop - Element in 'u' that it stops at.
        x - Array
        max - Max value in 'u' that is used to normalize it.
        tau - Storage for tau
        Returns:
        Returns gamma

      • rank1UpdateMultR

        public static void rank1UpdateMultR​(org.ejml.data.CMatrixRMaj A,
                                    float[] u,
                                    int offsetU,
                                    float gamma,
                                    int colA0,
                                    int w0,
                                    int w1,
                                    float[] _temp)

        Performs a rank-1 update operation on the submatrix specified by w with the multiply on the right.

        A = (I - γ*u*uH)*A

        Parameters:
        A - matrix
        u - vector
        offsetU - offset added to w0 when indexing u. Multiplied by 2 since complex.
        gamma - real component of gamma
        colA0 - first column in A sub-matrix.
        w0 - first index in sub-array in u and row sub-matrix in A
        w1 - last index + 1 in sub-array in u and row sub-matrix in A
        _temp - temporary storage. Same size as u.

      • rank1UpdateMultL

        public static void rank1UpdateMultL​(org.ejml.data.CMatrixRMaj A,
                                    float[] u,
                                    int offsetU,
                                    float gammaR,
                                    int colA0,
                                    int w0,
                                    int w1)

        Performs a rank-1 update operation on the submatrix specified by w with the multiply on the left.

        A = A(I - γ*u*uH)

        The order that matrix multiplies are performed has been carefully selected to minimize the number of operations.

        Before this can become a truly generic operation the submatrix specification needs to be made more generic.

      • extractHouseholderColumn

        public static void extractHouseholderColumn​(org.ejml.data.CMatrixRMaj A,
                                            int row0,
                                            int row1,
                                            int col,
                                            float[] u,
                                            int offsetU)
        Extracts a house holder vector from the column of A and stores it in u
        Parameters:
        A - Complex matrix with householder vectors stored in the lower left triangle
        row0 - first row in A (implicitly assumed to be r + i0)
        row1 - last row + 1 in A
        col - Column in A
        u - Output array storage
        offsetU - first index in U

      • extractHouseholderRow

        public static void extractHouseholderRow​(org.ejml.data.CMatrixRMaj A,
                                         int row,
                                         int col0,
                                         int col1,
                                         float[] u,
                                         int offsetU)
        Extracts a house holder vector from the rows of A and stores it in u
        Parameters:
        A - Complex matrix with householder vectors stored in the upper right triangle
        row - Row in A
        col0 - first row in A (implicitly assumed to be r + i0)
        col1 - last row +1 in A
        u - Output array storage
        offsetU - first index in U

      • extractColumnAndMax

        public static float extractColumnAndMax​(org.ejml.data.CMatrixRMaj A,
                                        int row0,
                                        int row1,
                                        int col,
                                        float[] u,
                                        int offsetU)
        Extracts the column of A and copies it into u while computing the magnitude of the largest element and returning it. 
         u[ (offsetU+row0+i)*2    ] = A.getReal(row0+i,col)
 u[ (offsetU+row0+i)*2 + 1] = A.getImag(row0+i,col)
        Parameters:
        A - Complex matrix
        row0 - First row in A to be copied
        row1 - Last row in A + 1 to be copied
        col - Column in A
        u - Output array storage
        offsetU - first index in U
        Returns:
        magnitude of largest element

      • computeRowMax

        public static float computeRowMax​(org.ejml.data.CMatrixRMaj A,
                                  int row,
                                  int col0,
                                  int col1)
        Finds the magnitude of the largest element in the row
        Parameters:
        A - Complex matrix
        row - Row in A
        col0 - First column in A to be copied
        col1 - Last column in A + 1 to be copied
        Returns:
        magnitude of largest element