PROCEDURE sparse(b: glnarray; n: integer; VAR x: glnarray; VAR rsq: real);
{*
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## Version control history
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## $Id$
## $Log$
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*}
(* Programs using routine SPARSE must define the type
TYPE
glnarray = ARRAY [1..n] OF real;
in the main routine. They must also provide two routines,
PROCEDURE asub(x: glnarray; VAR y: glnarray; n: integer);
and
PROCEDURE atsub(x: glnarray; VAR z: glnarray; n: integer);
which calculate A*x and (A transpose)*x *)
LABEL 1,99;
CONST
eps=1.0e-6;
VAR
j,iter,irst: integer;
rp,gg,gam,eps2,dgg,bsq,anum,aden: real;
g,h,xi,xj: glnarray;
BEGIN
eps2 := n*sqr(eps);
irst := 0;
1: irst := irst+1;
asub(x,xi,n);
rp := 0.0;
bsq := 0.0;
FOR j := 1 TO n DO BEGIN
bsq := bsq+sqr(b[j]);
xi[j] := xi[j]-b[j];
rp := rp+sqr(xi[j])
END;
atsub(xi,g,n);
FOR j := 1 TO n DO BEGIN
g[j] := -g[j];
h[j] := g[j]
END;
FOR iter := 1 TO 10*n DO BEGIN
asub(h,xi,n);
anum := 0.0;
aden := 0.0;
FOR j := 1 TO n DO BEGIN
anum := anum+g[j]*h[j];
aden := aden+sqr(xi[j])
END;
IF (aden = 0.0) THEN BEGIN
writeln('pause in routine SPARSE');
writeln('very singular matrix'); readln
END;
anum := anum/aden;
FOR j := 1 TO n DO BEGIN
xi[j] := x[j];
x[j] := x[j]+anum*h[j]
END;
asub(x,xj,n);
rsq := 0.0;
FOR j := 1 TO n DO BEGIN
xj[j] := xj[j]-b[j];
rsq := rsq+sqr(xj[j])
END;
IF ((rsq = rp) OR (rsq <= bsq*eps2)) THEN GOTO 99;
IF (rsq > rp) THEN BEGIN
FOR j := 1 TO n DO BEGIN
x[j] := xi[j]
END;
IF (irst >= 3) THEN GOTO 99;
GOTO 1
END;
rp := rsq;
atsub(xj,xi,n);
gg := 0.0;
dgg := 0.0;
FOR j := 1 TO n DO BEGIN
gg := gg+sqr(g[j]);
dgg := dgg+(xi[j]+g[j])*xi[j]
END;
IF (gg = 0.0) THEN GOTO 99;
gam := dgg/gg;
FOR j := 1 TO n DO BEGIN
g[j] := -xi[j];
h[j] := g[j]+gam*h[j]
END
END;
writeln('pause in routine SPARSE');
writeln('too many iterations'); readln;
99: END;