Module imagingbook.common
Package imagingbook.common.math.eigen.eispack

Class QZIT

java.lang.Object
imagingbook.common.math.eigen.eispack.QZIT
public abstract class QZIT extends Object

  • Method Summary

    Modifier and Type
    Method
    Description
    static int
    qzit(double[][] a, double[][] b, double eps1, boolean matz, double[][] z)
    This subroutine is the second step of the qz algorithm for solving generalized matrix eigenvalue problems, Siam J.

    Methods inherited from class java.lang.Object

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

  • Method Details

    • qzit

      public static int qzit(double[][] a, double[][] b, double eps1, boolean matz, double[][] z)

      This subroutine is the second step of the qz algorithm for solving generalized matrix eigenvalue problems, Siam J. Numer. anal. 10, 241-256(1973) by Moler and Stewart, as modified in technical note NASA TN D-7305(1973) by Ward. This description has been adapted from the original version (dated August 1983).

      This subroutine accepts a pair of real matrices, one of them in upper Hessenberg form and the other in upper triangular form. It reduces the Hessenberg matrix to quasi-triangular form using orthogonal transformations while maintaining the triangular form of the other matrix. It is usually preceded by qzhes and followed by qzval and, possibly, qzvec.

      On output:

      • a has been reduced to quasi-triangular form. The elements below the first subdiagonal are still zero and no two consecutive subdiagonal elements are nonzero.
      • b is still in upper triangular form, although its elements have been altered. The location b(n,1) is used to store eps1 times the norm of b for later use by qzval and qzvec.
      • z contains the product of the right hand transformations (for both steps) if matz has been set to true.
      Parameters:
      a - contains a real upper hessenberg matrix.
      b - contains a real upper triangular matrix.
      eps1 - is a tolerance used to determine negligible elements. eps1 = 0.0 (or negative) may be input, in which case an element will be neglected only if it is less than roundoff error times the norm of its matrix. If the input eps1 is positive, then an element will be considered negligible if it is less than eps1 times the norm of its matrix. A positive value of eps1 may result in faster execution, but less accurate results.
      matz - should be set to true if the right hand transformations are to be accumulated for later use in computing eigenvectors, and to false otherwise.
      z - contains, if matz has been set to true, the transformation matrix produced in the reduction by qzhes, if performed, or else the identity matrix. If matz has been set to false, z is not referenced.
      Returns:
      -1 for normal return, j if the limit of 30*n iterations is exhausted while the j-th eigenvalue is being is being sought.