IRIX Base Documentation 2001 May/SGI IRIX Base Documentation 2001 May.iso/usr/share/catman/p_man/cat3/complib/TSTURM.z/TSTURM

Text File | 1998-10-30 | 6.6 KB | 133 lines

____TTTTSSSSTTTTUUUURRRRMMMM((((3333FFFF))))                                                        ____TTTTSSSSTTTTUUUURRRRMMMM((((3333FFFF))))



NNNNAAAAMMMMEEEE
     TSTURM, STSTURM  -  EISPACK routine.  This subroutine finds those
     eigenvalues of a TRIDIAGONAL SYMMETRIC matrix which lie in a specified
     interval and their associated eigenvectors, using bisection and inverse
     iteration.


SSSSYYYYNNNNOOOOPPPPSSSSYYYYSSSS
          ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee  ttttssssttttuuuurrrrmmmm((((nnnnmmmm,,,,nnnn,,,,eeeeppppssss1111,,,,dddd,,,,eeee,,,,eeee2222,,,,llllbbbb,,,,uuuubbbb,,,,mmmmmmmm,,,,mmmm,,,,wwww,,,,zzzz,,,,iiiieeeerrrrrrrr,,,,rrrrvvvv1111,,,,rrrrvvvv2222,,,,
          1             rv3,rv4,rv5,rv6)
          iiiinnnntttteeeeggggeeeerrrr          nnnnmmmm,,,, nnnn,,,, mmmmmmmm,,,, mmmm,,,, iiiieeeerrrrrrrr
          ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn eeeeppppssss1111,,,, llllbbbb,,,, uuuubbbb
          ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn dddd((((nnnn)))),,,, eeee((((nnnn)))),,,, eeee2222((((nnnn)))),,,, wwww((((mmmmmmmm)))),,,, zzzz((((nnnnmmmm,,,, mmmmmmmm))))
          ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn rrrrvvvv1111((((nnnn)))),,,, rrrrvvvv2222((((nnnn)))),,,, rrrrvvvv3333((((nnnn)))),,,, rrrrvvvv4444((((nnnn)))),,,, rrrrvvvv5555((((nnnn)))),,,, rrrrvvvv6666((((nnnn))))

          ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ssssttttssssttttuuuurrrrmmmm((((nnnnmmmm,,,,nnnn,,,,eeeeppppssss1111,,,,dddd,,,,eeee,,,,eeee2222,,,,llllbbbb,,,,uuuubbbb,,,,mmmmmmmm,,,,mmmm,,,,wwww,,,,zzzz,,,,iiiieeeerrrrrrrr,,,,rrrrvvvv1111,,,,rrrrvvvv2222,,,,
          1             rv3,rv4,rv5,rv6)
          iiiinnnntttteeeeggggeeeerrrr          nnnnmmmm,,,, nnnn,,,, mmmmmmmm,,,, mmmm,,,, iiiieeeerrrrrrrr
          rrrreeeeaaaallll             eeeeppppssss1111,,,, llllbbbb,,,, uuuubbbb
          rrrreeeeaaaallll             dddd((((nnnn)))),,,, eeee((((nnnn)))),,,, eeee2222((((nnnn)))),,,, wwww((((mmmmmmmm)))),,,, zzzz((((nnnnmmmm,,,, mmmmmmmm))))
          rrrreeeeaaaallll             rrrrvvvv1111((((nnnn)))),,,, rrrrvvvv2222((((nnnn)))),,,, rrrrvvvv3333((((nnnn)))),,,, rrrrvvvv4444((((nnnn)))),,,, rrrrvvvv5555((((nnnn)))),,,, rrrrvvvv6666((((nnnn))))



DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
     On Input

     NNNNMMMM must be set to the row dimension of two-dimensional array parameters
     as declared in the calling program dimension statement.

     NNNN is the order of the matrix.

     EEEEPPPPSSSS1111 is an absolute error tolerance for the computed eigenvalues.  It
     should be chosen commensurate with relative perturbations in the matrix
     elements of the order of the relative machine precision.  If the input
     EPS1 is non-positive, it is reset for each submatrix to a default value,
     namely, minus the product of the relative machine precision and the 1-
     norm of the submatrix.

     DDDD contains the diagonal elements of the input matrix.

     EEEE contains the subdiagonal elements of the input matrix in its last N-1
     positions.  E(1) is arbitrary.

     EEEE2222 contains the squares of the corresponding elements of E. E2(1) is
     arbitrary.

     LLLLBBBB and UB define the interval to be searched for eigenvalues. If LB is
     not less than UB, no eigenvalues will be found.

     MMMMMMMM should be set to an upper bound for the number of eigenvalues in the
     interval.  WARNING. If more than MM eigenvalues are determined to lie in



                                                                        PPPPaaaaggggeeee 1111






____TTTTSSSSTTTTUUUURRRRMMMM((((3333FFFF))))                                                        ____TTTTSSSSTTTTUUUURRRRMMMM((((3333FFFF))))



     the interval, an error return is made with no values or vectors found.
     On Output

     EEEEPPPPSSSS1111 is unaltered unless it has been reset to its (last) default value.

     DDDD and E are unaltered. ELEMENTS of E2, corresponding to elements of E
     regarded as negligible, have been replaced by zero causing the matrix to
     split into a direct sum of submatrices.  E2(1) is also set to zero.

     MMMM is the number of eigenvalues determined to lie in (LB,UB).

     WWWW contains the M eigenvalues in ascending order if the matrix does not
     split.  If the matrix splits, the eigenvalues are in ascending order for
     each submatrix.  If a vector error exit is made, W contains those values
     already found.

     ZZZZ contains the associated set of orthonormal eigenvectors. If an error
     exit is made, Z contains those vectors already found.

     IIIIEEEERRRRRRRR is set to Zero       for normal return, 3*N+1      if M exceeds MM.
     4*N+R      if the eigenvector corresponding to the R-th
        eigenvalue fails to converge in 5 iterations.

     RRRRVVVV1111 , RV2, RV3, RV4, RV5, and RV6 are temporary storage arrays. The ALGOL
     procedure STURMCNT contained in TRISTURM appears in TSTURM in-line.
     Questions and comments should be directed to B. S. Garbow, APPLIED
     MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY




























                                                                        PPPPaaaaggggeeee 2222