| [a,lda,n,kpvt,rcond,z]=chico(a,lda,n,kpvt,rcond,z); |
function [a,lda,n,kpvt,rcond,z]=chico(a,lda,n,kpvt,rcond,z);
%***BEGIN PROLOGUE CHICO
%***PURPOSE Factor a complex Hermitian matrix by elimination with sym-
% metric pivoting and estimate the condition of the matrix.
%***LIBRARY SLATEC (LINPACK)
%***CATEGORY D2D1A
%***TYPE COMPLEX (SSICO-S, DSICO-D, CHICO-C, CSICO-C)
%***KEYWORDS CONDITION NUMBER, HERMITIAN, LINEAR ALGEBRA, LINPACK,
% MATRIX FACTORIZATION
%***AUTHOR Moler, C. B., (U. of New Mexico)
%***DESCRIPTION
%
% CHICO factors a complex Hermitian matrix by elimination with
% symmetric pivoting and estimates the condition of the matrix.
%
% If RCOND is not needed, CHIFA is slightly faster.
% To solve A*X = B , follow CHICO by CHISL.
% To compute INVERSE(A)*C , follow CHICO by CHISL.
% To compute INVERSE(A) , follow CHICO by CHIDI.
% To compute DETERMINANT(A) , follow CHICO by CHIDI.
% To compute INERTIA(A), follow CHICO by CHIDI.
%
% On Entry
%
% A COMPLEX(LDA, N)
% the Hermitian matrix to be factored.
% Only the diagonal and upper triangle are used.
%
% LDA INTEGER
% the leading dimension of the array A .
%
% N INTEGER
% the order of the matrix A .
%
% Output
%
% A a block diagonal matrix and the multipliers which
% were used to obtain it.
% The factorization can be written A = U*D*CTRANS(U)
% where U is a product of permutation and unit
% upper triangular matrices , CTRANS(U) is the
% conjugate transpose of U , and D is block diagonal
% with 1 by 1 and 2 by 2 blocks.
%
% KVPT INTEGER(N)
% an integer vector of pivot indices.
%
% RCOND REAL
% an estimate of the reciprocal condition of A .
% For the system A*X = B , relative perturbations
% in A and B of size EPSILON may cause
% relative perturbations in X of size EPSILON/RCOND .
% If RCOND is so small that the logical expression
% 1.0 + RCOND .EQ. 1.0
% is truemlv, then A may be singular to working
% precision. In particular, RCOND is zero if
% exact singularity is detected or the estimate
% underflows.
%
% Z COMPLEX(N)
% a work vector whose contents are usually unimportant.
% If A is close to a singular matrix, then Z is
% an approximate null vector in the sense that
% NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
%
%***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
% Stewart, LINPACK Users' Guide, SIAM, 1979.
%***ROUTINES CALLED CAXPY, CDOTC, CHIFA, CSSCAL, SCASUM
%***REVISION HISTORY (YYMMDD)
% 780814 DATE WRITTEN
% 890531 Changed all specific intrinsics to generic. (WRB)
% 890831 Modified array declarations. (WRB)
% 891107 Modified routine equivalence list. (WRB)
% 891107 REVISION DATE from Version 3.2
% 891214 Prologue converted to Version 4.0 format. (BAB)
% 900326 Removed duplicate information from DESCRIPTION section.
% (WRB)
% 920501 Reformatted the REFERENCES section. (WRB)
%***end PROLOGUE CHICO
persistent ak akm1 anorm bk bkm1 denom ek i info j jm1 k kp kps ks s t ynorm zdum zdum2 ;
kpvt_shape=size(kpvt);kpvt=reshape(kpvt,1,[]);
a_shape=size(a);a=reshape([a(:).',zeros(1,ceil(numel(a)./prod([lda])).*prod([lda])-numel(a))],lda,[]);
z_shape=size(z);z=reshape(z,1,[]);
%
if isempty(ak), ak=0; end;
if isempty(akm1), akm1=0; end;
if isempty(bk), bk=0; end;
if isempty(bkm1), bkm1=0; end;
if isempty(denom), denom=0; end;
if isempty(ek), ek=0; end;
if isempty(t), t=0; end;
if isempty(anorm), anorm=0; end;
if isempty(s), s=0; end;
if isempty(ynorm), ynorm=0; end;
if isempty(i), i=0; end;
if isempty(info), info=0; end;
if isempty(j), j=0; end;
if isempty(jm1), jm1=0; end;
if isempty(k), k=0; end;
if isempty(kp), kp=0; end;
if isempty(kps), kps=0; end;
if isempty(ks), ks=0; end;
if isempty(zdum), zdum=0; end;
if isempty(zdum2), zdum2=0; end;
% csign1= @(zdum,zdum2) cabs1(zdum)*(zdum2/cabs1(zdum2));complex :: csign1;
% cabs1= @(zdum) abs(real(zdum)) + abs(aimag(zdum));real :: cabs1;
cabs1= @(zdum) abs(real(zdum)) + abs(imag(zdum));
csign1= @(zdum,zdum2) cabs1(zdum).*(zdum2./cabs1(zdum2));
%
% FIND NORM OF A USING ONLY UPPER HALF
%
%***FIRST EXECUTABLE STATEMENT CHICO
for j = 1 : n;
z(j) = complex(scasum(j,a(sub2ind(size(a),1,j):end),1),0.0e0);
jm1 = fix(j - 1);
if( jm1>=1 )
for i = 1 : jm1;
cabs1= @(zdum) abs(real(zdum)) + abs(imag(zdum));
z(i) = complex(real(z(i))+cabs1(a(i,j)),0.0e0);
end; i = fix(jm1+1);
end;
end; j = fix(n+1);
anorm = 0.0e0;
for j = 1 : n;
anorm = max(anorm,real(z(j)));
end; j = fix(n+1);
%
% FACTOR
%
[a,lda,n,kpvt,info]=chifa(a,lda,n,kpvt,info);
%
% RCOND = 1/(NORM(A)*(ESTIMATE OF NORM(INVERSE(A)))) .
% ESTIMATE = NORM(Z)/NORM(Y) WHERE A*Z = Y AND A*Y = E .
% THE COMPONENTS OF E ARE CHOSEN TO CAUSE MAXIMUM LOCAL
% GROWTH IN THE ELEMENTS OF W WHERE U*D*W = E .
% THE VECTORS ARE FREQUENTLY RESCALED TO AVOID OVERFLOW.
%
% SOLVE U*D*W = E
%
ek =complex(1.0e0,0.0e0);
for j = 1 : n;
z(j) =complex(0.0e0,0.0e0);
end; j = fix(n+1);
k = fix(n);
while( k~=0 );
ks = 1;
if( kpvt(k)<0 )
ks = 2;
end;
kp = fix(abs(kpvt(k)));
kps = fix(k + 1 - ks);
if( kp~=kps )
t = z(kps);
z(kps) = z(kp);
z(kp) = t;
end;
csign1= @(zdum,zdum2) cabs1(zdum).*(zdum2./cabs1(zdum2));
cabs1= @(zdum) abs(real(zdum)) + abs(imag(zdum));
if( cabs1(z(k))~=0.0e0 )
ek = csign1(ek,z(k));
end;
z(k) = z(k) + ek;
[dumvar1,dumvar2,a(sub2ind(size(a),1,k):end),dumvar4,dumvar5]=caxpy(k-ks,z(k),a(sub2ind(size(a),1,k):end),1,z(sub2ind(size(z),max(1,1)):end),1); dumvar2i=find((z(k))~=(dumvar2));dumvar5i=find((z(sub2ind(size(z),max(1,1)):end))~=(dumvar5)); z(k-1+dumvar2i)=dumvar2(dumvar2i); z(1-1+dumvar5i)=dumvar5(dumvar5i);
if( ks~=1 )
csign1= @(zdum,zdum2) cabs1(zdum).*(zdum2./cabs1(zdum2));
cabs1= @(zdum) abs(real(zdum)) + abs(imag(zdum));
if( cabs1(z(k-1))~=0.0e0 )
ek = csign1(ek,z(k-1));
end;
z(k-1) = z(k-1) + ek;
[dumvar1,dumvar2,a(sub2ind(size(a),1,k-1):end),dumvar4,dumvar5]=caxpy(k-ks,z(k-1),a(sub2ind(size(a),1,k-1):end),1,z(sub2ind(size(z),max(1,1)):end),1); dumvar2i=find((z(k-1))~=(dumvar2));dumvar5i=find((z(sub2ind(size(z),max(1,1)):end))~=(dumvar5)); z(k-1-1+dumvar2i)=dumvar2(dumvar2i); z(1-1+dumvar5i)=dumvar5(dumvar5i);
end;
if( ks==2 )
ak = a(k,k)./conj(a(k-1,k));
akm1 = a(k-1,k-1)./a(k-1,k);
bk = z(k)./conj(a(k-1,k));
bkm1 = z(k-1)./a(k-1,k);
denom = ak.*akm1 - 1.0e0;
z(k) =(akm1.*bk-bkm1)./denom;
z(k-1) =(ak.*bkm1-bk)./denom;
else;
cabs1= @(zdum) abs(real(zdum)) + abs(imag(zdum));
if( cabs1(z(k))>cabs1(a(k,k)) )
cabs1= @(zdum) abs(real(zdum)) + abs(imag(zdum));
s = cabs1(a(k,k))./cabs1(z(k));
[n,s,z]=csscal(n,s,z,1);
ek = complex(s,0.0e0).*ek;
end;
cabs1= @(zdum) abs(real(zdum)) + abs(imag(zdum));
if( cabs1(a(k,k))~=0.0e0 )
z(k) = z(k)./a(k,k);
end;
cabs1= @(zdum) abs(real(zdum)) + abs(imag(zdum));
if( cabs1(a(k,k))==0.0e0 )
z(k) =complex(1.0e0,0.0e0);
end;
end;
k = fix(k - ks);
end;
s = 1.0e0./scasum(n,z,1);
[n,s,z]=csscal(n,s,z,1);
%
% SOLVE CTRANS(U)*Y = W
%
k = 1;
while( k<=n );
ks = 1;
if( kpvt(k)<0 )
ks = 2;
end;
if( k~=1 )
z(k) = z(k) + cdotc(k-1,a(sub2ind(size(a),1,k):end),1,z(sub2ind(size(z),max(1,1)):end),1);
if( ks==2 )
z(k+1) = z(k+1) + cdotc(k-1,a(sub2ind(size(a),1,k+1):end),1,z(sub2ind(size(z),max(1,1)):end),1);
end;
kp = fix(abs(kpvt(k)));
if( kp~=k )
t = z(k);
z(k) = z(kp);
z(kp) = t;
end;
end;
k = fix(k + ks);
end;
s = 1.0e0./scasum(n,z,1);
[n,s,z]=csscal(n,s,z,1);
%
ynorm = 1.0e0;
%
% SOLVE U*D*V = Y
%
k = fix(n);
while( k~=0 );
ks = 1;
if( kpvt(k)<0 )
ks = 2;
end;
if( k~=ks )
kp = fix(abs(kpvt(k)));
kps = fix(k + 1 - ks);
if( kp~=kps )
t = z(kps);
z(kps) = z(kp);
z(kp) = t;
end;
[dumvar1,dumvar2,a(sub2ind(size(a),1,k):end),dumvar4,dumvar5]=caxpy(k-ks,z(k),a(sub2ind(size(a),1,k):end),1,z(sub2ind(size(z),max(1,1)):end),1); dumvar2i=find((z(k))~=(dumvar2));dumvar5i=find((z(sub2ind(size(z),max(1,1)):end))~=(dumvar5)); z(k-1+dumvar2i)=dumvar2(dumvar2i); z(1-1+dumvar5i)=dumvar5(dumvar5i);
if( ks==2 )
[dumvar1,dumvar2,a(sub2ind(size(a),1,k-1):end),dumvar4,dumvar5]=caxpy(k-ks,z(k-1),a(sub2ind(size(a),1,k-1):end),1,z(sub2ind(size(z),max(1,1)):end),1); dumvar2i=find((z(k-1))~=(dumvar2));dumvar5i=find((z(sub2ind(size(z),max(1,1)):end))~=(dumvar5)); z(k-1-1+dumvar2i)=dumvar2(dumvar2i); z(1-1+dumvar5i)=dumvar5(dumvar5i);
end;
end;
if( ks==2 )
ak = a(k,k)./conj(a(k-1,k));
akm1 = a(k-1,k-1)./a(k-1,k);
bk = z(k)./conj(a(k-1,k));
bkm1 = z(k-1)./a(k-1,k);
denom = ak.*akm1 - 1.0e0;
z(k) =(akm1.*bk-bkm1)./denom;
z(k-1) =(ak.*bkm1-bk)./denom;
else;
cabs1= @(zdum) abs(real(zdum)) + abs(imag(zdum));
if( cabs1(z(k))>cabs1(a(k,k)) )
cabs1= @(zdum) abs(real(zdum)) + abs(imag(zdum));
s = cabs1(a(k,k))./cabs1(z(k));
[n,s,z]=csscal(n,s,z,1);
ynorm = s.*ynorm;
end;
cabs1= @(zdum) abs(real(zdum)) + abs(imag(zdum));
if( cabs1(a(k,k))~=0.0e0 )
z(k) = z(k)./a(k,k);
end;
cabs1= @(zdum) abs(real(zdum)) + abs(imag(zdum));
if( cabs1(a(k,k))==0.0e0 )
z(k) =complex(1.0e0,0.0e0);
end;
end;
k = fix(k - ks);
end;
s = 1.0e0./scasum(n,z,1);
[n,s,z]=csscal(n,s,z,1);
ynorm = s.*ynorm;
%
% SOLVE CTRANS(U)*Z = V
%
k = 1;
while( k<=n );
ks = 1;
if( kpvt(k)<0 )
ks = 2;
end;
if( k~=1 )
z(k) = z(k) + cdotc(k-1,a(sub2ind(size(a),1,k):end),1,z(sub2ind(size(z),max(1,1)):end),1);
if( ks==2 )
z(k+1) = z(k+1) + cdotc(k-1,a(sub2ind(size(a),1,k+1):end),1,z(sub2ind(size(z),max(1,1)):end),1);
end;
kp = fix(abs(kpvt(k)));
if( kp~=k )
t = z(k);
z(k) = z(kp);
z(kp) = t;
end;
end;
k = fix(k + ks);
end;
% MAKE ZNORM = 1.0
s = 1.0e0./scasum(n,z,1);
[n,s,z]=csscal(n,s,z,1);
ynorm = s.*ynorm;
%
if( anorm~=0.0e0 )
rcond = ynorm./anorm;
end;
if( anorm==0.0e0 )
rcond = 0.0e0;
end;
kpvt_shape=zeros(kpvt_shape);kpvt_shape(:)=kpvt(1:numel(kpvt_shape));kpvt=kpvt_shape;
a_shape=zeros(a_shape);a_shape(:)=a(1:numel(a_shape));a=a_shape;
z_shape=zeros(z_shape);z_shape(:)=z(1:numel(z_shape));z=z_shape;
end %subroutine chico
%DECK CHIDI
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