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89 lines
2.1 KiB
C++
89 lines
2.1 KiB
C++
//$$ cholesky.cpp cholesky decomposition
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// Copyright (C) 1991,2,3,4: R B Davies
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#define WANT_MATH
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//#define WANT_STREAM
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#include "include.h"
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#include "newmat.h"
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#ifdef use_namespace
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namespace NEWMAT {
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#endif
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#ifdef DO_REPORT
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#define REPORT { static ExeCounter ExeCount(__LINE__,14); ++ExeCount; }
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#else
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#define REPORT {}
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#endif
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/********* Cholesky decomposition of a positive definite matrix *************/
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// Suppose S is symmetrix and positive definite. Then there exists a unique
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// lower triangular matrix L such that L L.t() = S;
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inline Real square(Real x) { return x*x; }
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ReturnMatrix Cholesky(const SymmetricMatrix& S)
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{
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REPORT
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Tracer trace("Cholesky");
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int nr = S.Nrows();
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LowerTriangularMatrix T(nr);
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Real* s = S.Store(); Real* t = T.Store(); Real* ti = t;
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for (int i=0; i<nr; i++)
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{
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Real* tj = t; Real sum; int k;
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for (int j=0; j<i; j++)
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{
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Real* tk = ti; sum = 0.0; k = j;
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while (k--) { sum += *tj++ * *tk++; }
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*tk = (*s++ - sum) / *tj++;
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}
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sum = 0.0; k = i;
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while (k--) { sum += square(*ti++); }
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Real d = *s++ - sum;
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if (d<=0.0) Throw(NPDException(S));
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*ti++ = sqrt(d);
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}
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T.Release(); return T.ForReturn();
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}
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ReturnMatrix Cholesky(const SymmetricBandMatrix& S)
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{
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REPORT
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Tracer trace("Band-Cholesky");
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int nr = S.Nrows(); int m = S.lower;
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LowerBandMatrix T(nr,m);
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Real* s = S.Store(); Real* t = T.Store(); Real* ti = t;
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for (int i=0; i<nr; i++)
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{
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Real* tj = t; Real sum; int l;
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if (i<m) { REPORT l = m-i; s += l; ti += l; l = i; }
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else { REPORT t += (m+1); l = m; }
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for (int j=0; j<l; j++)
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{
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Real* tk = ti; sum = 0.0; int k = j; tj += (m-j);
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while (k--) { sum += *tj++ * *tk++; }
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*tk = (*s++ - sum) / *tj++;
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}
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sum = 0.0;
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while (l--) { sum += square(*ti++); }
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Real d = *s++ - sum;
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if (d<=0.0) Throw(NPDException(S));
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*ti++ = sqrt(d);
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}
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T.Release(); return T.ForReturn();
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}
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#ifdef use_namespace
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}
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#endif
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