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SUBROUTINE INVIT(NM,N,A,WR,WI,SELECT,MM,M,Z,IERR,RM1,RV1,RV2)
C
INTEGER I,J,K,L,M,N,S,II,IP,MM,MP,NM,NS,N1,UK,IP1,ITS,KM1,IERR
DOUBLE PRECISION A(NM,N),WR(N),WI(N),Z(NM,MM),RM1(N,N),
X RV1(N),RV2(N)
DOUBLE PRECISION T,W,X,Y,EPS3,NORM,NORMV,EPSLON,GROWTO,ILAMBD,
X PYTHAG,RLAMBD,UKROOT
LOGICAL SELECT(N)
C
C THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE INVIT
C BY PETERS AND WILKINSON.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 418-439(1971).
C
C THIS SUBROUTINE FINDS THOSE EIGENVECTORS OF A REAL UPPER
C HESSENBERG MATRIX CORRESPONDING TO SPECIFIED EIGENVALUES,
C USING INVERSE ITERATION.
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 A CONTAINS THE HESSENBERG MATRIX.
C
C WR AND WI CONTAIN THE REAL AND IMAGINARY PARTS, RESPECTIVELY,
C OF THE EIGENVALUES OF THE MATRIX. THE EIGENVALUES MUST BE
C STORED IN A MANNER IDENTICAL TO THAT OF SUBROUTINE HQR,
C WHICH RECOGNIZES POSSIBLE SPLITTING OF THE MATRIX.
C
C SELECT SPECIFIES THE EIGENVECTORS TO BE FOUND. THE
C EIGENVECTOR CORRESPONDING TO THE J-TH EIGENVALUE IS
C SPECIFIED BY SETTING SELECT(J) TO .TRUE..
C
C MM SHOULD BE SET TO AN UPPER BOUND FOR THE NUMBER OF
C COLUMNS REQUIRED TO STORE THE EIGENVECTORS TO BE FOUND.
C NOTE THAT TWO COLUMNS ARE REQUIRED TO STORE THE
C EIGENVECTOR CORRESPONDING TO A COMPLEX EIGENVALUE.
C
C ON OUTPUT
C
C A AND WI ARE UNALTERED.
C
C WR MAY HAVE BEEN ALTERED SINCE CLOSE EIGENVALUES ARE PERTURBED
C SLIGHTLY IN SEARCHING FOR INDEPENDENT EIGENVECTORS.
C
C SELECT MAY HAVE BEEN ALTERED. IF THE ELEMENTS CORRESPONDING
C TO A PAIR OF CONJUGATE COMPLEX EIGENVALUES WERE EACH
C INITIALLY SET TO .TRUE., THE PROGRAM RESETS THE SECOND OF
C THE TWO ELEMENTS TO .FALSE..
C
C M IS THE NUMBER OF COLUMNS ACTUALLY USED TO STORE
C THE EIGENVECTORS.
C
C Z CONTAINS THE REAL AND IMAGINARY PARTS OF THE EIGENVECTORS.
C IF THE NEXT SELECTED EIGENVALUE IS REAL, THE NEXT COLUMN
C OF Z CONTAINS ITS EIGENVECTOR. IF THE EIGENVALUE IS
C COMPLEX, THE NEXT TWO COLUMNS OF Z CONTAIN THE REAL AND
C IMAGINARY PARTS OF ITS EIGENVECTOR. THE EIGENVECTORS ARE
C NORMALIZED SO THAT THE COMPONENT OF LARGEST MAGNITUDE IS 1.
C ANY VECTOR WHICH FAILS THE ACCEPTANCE TEST IS SET TO ZERO.
C
C IERR IS SET TO
C ZERO FOR NORMAL RETURN,
C -(2*N+1) IF MORE THAN MM COLUMNS OF Z ARE NECESSARY
C TO STORE THE EIGENVECTORS CORRESPONDING TO
C THE SPECIFIED EIGENVALUES.
C -K IF THE ITERATION CORRESPONDING TO THE K-TH
C VALUE FAILS,
C -(N+K) IF BOTH ERROR SITUATIONS OCCUR.
C
C RM1, RV1, AND RV2 ARE TEMPORARY STORAGE ARRAYS. NOTE THAT RM1
C IS SQUARE OF DIMENSION N BY N AND, AUGMENTED BY TWO COLUMNS
C OF Z, IS THE TRANSPOSE OF THE CORRESPONDING ALGOL B ARRAY.
C
C THE ALGOL PROCEDURE GUESSVEC APPEARS IN INVIT IN LINE.
C
C CALLS CDIV FOR COMPLEX DIVISION.
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