Previous: qzhes Up: ../eispas.html Next: qzval
SUBROUTINE QZIT(NM,N,A,B,EPS1,MATZ,Z,IERR)
C
INTEGER I,J,K,L,N,EN,K1,K2,LD,LL,L1,NA,NM,ISH,ITN,ITS,KM1,LM1,
X ENM2,IERR,LOR1,ENORN
REAL A(NM,N),B(NM,N),Z(NM,N)
REAL R,S,T,A1,A2,A3,EP,SH,U1,U2,U3,V1,V2,V3,ANI,A11,
X A12,A21,A22,A33,A34,A43,A44,BNI,B11,B12,B22,B33,B34,
X B44,EPSA,EPSB,EPS1,ANORM,BNORM,EPSLON
LOGICAL MATZ,NOTLAS
C
C THIS SUBROUTINE IS THE SECOND STEP OF THE QZ ALGORITHM
C FOR SOLVING GENERALIZED MATRIX EIGENVALUE PROBLEMS,
C SIAM J. NUMER. ANAL. 10, 241-256(1973) BY MOLER AND STEWART,
C AS MODIFIED IN TECHNICAL NOTE NASA TN D-7305(1973) BY WARD.
C
C THIS SUBROUTINE ACCEPTS A PAIR OF REAL MATRICES, ONE OF THEM
C IN UPPER HESSENBERG FORM AND THE OTHER IN UPPER TRIANGULAR FORM.
C IT REDUCES THE HESSENBERG MATRIX TO QUASI-TRIANGULAR FORM USING
C ORTHOGONAL TRANSFORMATIONS WHILE MAINTAINING THE TRIANGULAR FORM
C OF THE OTHER MATRIX. IT IS USUALLY PRECEDED BY QZHES AND
C FOLLOWED BY QZVAL AND, POSSIBLY, QZVEC.
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 MATRICES.
C
C A CONTAINS A REAL UPPER HESSENBERG MATRIX.
C
C B CONTAINS A REAL UPPER TRIANGULAR MATRIX.
C
C EPS1 IS A TOLERANCE USED TO DETERMINE NEGLIGIBLE ELEMENTS.
C EPS1 = 0.0 (OR NEGATIVE) MAY BE INPUT, IN WHICH CASE AN
C ELEMENT WILL BE NEGLECTED ONLY IF IT IS LESS THAN ROUNDOFF
C ERROR TIMES THE NORM OF ITS MATRIX. IF THE INPUT EPS1 IS
C POSITIVE, THEN AN ELEMENT WILL BE CONSIDERED NEGLIGIBLE
C IF IT IS LESS THAN EPS1 TIMES THE NORM OF ITS MATRIX. A
C POSITIVE VALUE OF EPS1 MAY RESULT IN FASTER EXECUTION,
C BUT LESS ACCURATE RESULTS.
C
C MATZ SHOULD BE SET TO .TRUE. IF THE RIGHT HAND TRANSFORMATIONS
C ARE TO BE ACCUMULATED FOR LATER USE IN COMPUTING
C EIGENVECTORS, AND TO .FALSE. OTHERWISE.
C
C Z CONTAINS, IF MATZ HAS BEEN SET TO .TRUE., THE
C TRANSFORMATION MATRIX PRODUCED IN THE REDUCTION
C BY QZHES, IF PERFORMED, OR ELSE THE IDENTITY MATRIX.
C IF MATZ HAS BEEN SET TO .FALSE., Z IS NOT REFERENCED.
C
C ON OUTPUT
C
C A HAS BEEN REDUCED TO QUASI-TRIANGULAR FORM. THE ELEMENTS
C BELOW THE FIRST SUBDIAGONAL ARE STILL ZERO AND NO TWO
C CONSECUTIVE SUBDIAGONAL ELEMENTS ARE NONZERO.
C
C B IS STILL IN UPPER TRIANGULAR FORM, ALTHOUGH ITS ELEMENTS
C HAVE BEEN ALTERED. THE LOCATION B(N,1) IS USED TO STORE
C EPS1 TIMES THE NORM OF B FOR LATER USE BY QZVAL AND QZVEC.
C
C Z CONTAINS THE PRODUCT OF THE RIGHT HAND TRANSFORMATIONS
C (FOR BOTH STEPS) IF MATZ HAS BEEN SET TO .TRUE..
C
C IERR IS SET TO
C ZERO FOR NORMAL RETURN,
C J IF THE LIMIT OF 30*N ITERATIONS IS EXHAUSTED
C WHILE THE J-TH EIGENVALUE IS BEING SOUGHT.
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
C ------------------------------------------------------------------
C