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SUBROUTINE TQL2(NM,N,D,E,Z,IERR)
C
INTEGER I,J,K,L,M,N,II,L1,L2,NM,MML,IERR
DOUBLE PRECISION D(N),E(N),Z(NM,N)
DOUBLE PRECISION C,C2,C3,DL1,EL1,F,G,H,P,R,S,S2,TST1,TST2,PYTHAG
C
C THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE TQL2,
C NUM. MATH. 11, 293-306(1968) BY BOWDLER, MARTIN, REINSCH, AND
C WILKINSON.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 227-240(1971).
C
C THIS SUBROUTINE FINDS THE EIGENVALUES AND EIGENVECTORS
C OF A SYMMETRIC TRIDIAGONAL MATRIX BY THE QL METHOD.
C THE EIGENVECTORS OF A FULL SYMMETRIC MATRIX CAN ALSO
C BE FOUND IF TRED2 HAS BEEN USED TO REDUCE THIS
C FULL MATRIX TO TRIDIAGONAL FORM.
C
C ON INPUT
C
C NM MUST BE SET TO THE ROW DIMENSION OF TWO-DIMENSIONAL
C ARRAY PARAMETERS AS DECLARED IN THE CALLING PROGRAM
C DIMENSION STATEMENT.
C
C N IS THE ORDER OF THE MATRIX.
C
C D CONTAINS THE DIAGONAL ELEMENTS OF THE INPUT MATRIX.
C
C E CONTAINS THE SUBDIAGONAL ELEMENTS OF THE INPUT MATRIX
C IN ITS LAST N-1 POSITIONS. E(1) IS ARBITRARY.
C
C Z CONTAINS THE TRANSFORMATION MATRIX PRODUCED IN THE
C REDUCTION BY TRED2, IF PERFORMED. IF THE EIGENVECTORS
C OF THE TRIDIAGONAL MATRIX ARE DESIRED, Z MUST CONTAIN
C THE IDENTITY MATRIX.
C
C ON OUTPUT
C
C D CONTAINS THE EIGENVALUES IN ASCENDING ORDER. IF AN
C ERROR EXIT IS MADE, THE EIGENVALUES ARE CORRECT BUT
C UNORDERED FOR INDICES 1,2,...,IERR-1.
C
C E HAS BEEN DESTROYED.
C
C Z CONTAINS ORTHONORMAL EIGENVECTORS OF THE SYMMETRIC
C TRIDIAGONAL (OR FULL) MATRIX. IF AN ERROR EXIT IS MADE,
C Z CONTAINS THE EIGENVECTORS ASSOCIATED WITH THE STORED
C EIGENVALUES.
C
C IERR IS SET TO
C ZERO FOR NORMAL RETURN,
C J IF THE J-TH EIGENVALUE HAS NOT BEEN
C DETERMINED AFTER 30 ITERATIONS.
C
C CALLS PYTHAG FOR DSQRT(A*A + B*B) .
C
C QUESTIONS AND COMMENTS SHOULD BE DIRECTED TO BURTON S. GARBOW,
C MATHEMATICS AND COMPUTER SCIENCE DIV, ARGONNE NATIONAL LABORATORY
C
C THIS VERSION DATED AUGUST 1983.
C
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C