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SUBROUTINE MINFIT(NM,M,N,A,W,IP,B,IERR,RV1)
C
INTEGER I,J,K,L,M,N,II,IP,I1,KK,K1,LL,L1,M1,NM,ITS,IERR
REAL A(NM,N),W(N),B(NM,IP),RV1(N)
REAL C,F,G,H,S,X,Y,Z,TST1,TST2,SCALE,PYTHAG
C
C THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE MINFIT,
C NUM. MATH. 14, 403-420(1970) BY GOLUB AND REINSCH.
C HANDBOOK FOR AUTO. COMP., VOL II-LINEAR ALGEBRA, 134-151(1971).
C
C THIS SUBROUTINE DETERMINES, TOWARDS THE SOLUTION OF THE LINEAR
C T
C SYSTEM AX=B, THE SINGULAR VALUE DECOMPOSITION A=USV OF A REAL
C T
C M BY N RECTANGULAR MATRIX, FORMING U B RATHER THAN U. HOUSEHOLDER
C BIDIAGONALIZATION AND A VARIANT OF THE QR ALGORITHM ARE USED.
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. NOTE THAT NM MUST BE AT LEAST
C AS LARGE AS THE MAXIMUM OF M AND N.
C
C M IS THE NUMBER OF ROWS OF A AND B.
C
C N IS THE NUMBER OF COLUMNS OF A AND THE ORDER OF V.
C
C A CONTAINS THE RECTANGULAR COEFFICIENT MATRIX OF THE SYSTEM.
C
C IP IS THE NUMBER OF COLUMNS OF B. IP CAN BE ZERO.
C
C B CONTAINS THE CONSTANT COLUMN MATRIX OF THE SYSTEM
C IF IP IS NOT ZERO. OTHERWISE B IS NOT REFERENCED.
C
C ON OUTPUT
C
C A HAS BEEN OVERWRITTEN BY THE MATRIX V (ORTHOGONAL) OF THE
C DECOMPOSITION IN ITS FIRST N ROWS AND COLUMNS. IF AN
C ERROR EXIT IS MADE, THE COLUMNS OF V CORRESPONDING TO
C INDICES OF CORRECT SINGULAR VALUES SHOULD BE CORRECT.
C
C W CONTAINS THE N (NON-NEGATIVE) SINGULAR VALUES OF A (THE
C DIAGONAL ELEMENTS OF S). THEY ARE UNORDERED. IF AN
C ERROR EXIT IS MADE, THE SINGULAR VALUES SHOULD BE CORRECT
C FOR INDICES IERR+1,IERR+2,...,N.
C
C T
C B HAS BEEN OVERWRITTEN BY U B. IF AN ERROR EXIT IS MADE,
C T
C THE ROWS OF U B CORRESPONDING TO INDICES OF CORRECT
C SINGULAR VALUES SHOULD BE CORRECT.
C
C IERR IS SET TO
C ZERO FOR NORMAL RETURN,
C K IF THE K-TH SINGULAR VALUE HAS NOT BEEN
C DETERMINED AFTER 30 ITERATIONS.
C
C RV1 IS A TEMPORARY STORAGE ARRAY.
C
C CALLS PYTHAG FOR SQRT(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
C ------------------------------------------------------------------
C