734 lines
20 KiB
Text
734 lines
20 KiB
Text
//$$ newmat8.cpp Advanced LU transform, scalar functions
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// Copyright (C) 1991,2,3,4,8: R B Davies
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#define WANT_MATH
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#include "include.h"
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#include "newmat.h"
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#include "newmatrc.h"
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#include "precisio.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__,8); ++ExeCount; }
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#else
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#define REPORT {}
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#endif
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/************************** LU transformation ****************************/
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void CroutMatrix::ludcmp()
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// LU decomposition from Golub & Van Loan, algorithm 3.4.1, (the "outer
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// product" version).
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// This replaces the code derived from Numerical Recipes in C in previous
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// versions of newmat and being row oriented runs much faster with large
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// matrices.
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{
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REPORT
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Tracer trace( "Crout(ludcmp)" ); sing = false;
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Real* akk = store; // runs down diagonal
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Real big = fabs(*akk); int mu = 0; Real* ai = akk; int k;
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for (k = 1; k < nrows; k++)
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{
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ai += nrows; const Real trybig = fabs(*ai);
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if (big < trybig) { big = trybig; mu = k; }
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}
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if (nrows) for (k = 0;;)
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{
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/*
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int mu1;
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{
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Real big = fabs(*akk); mu1 = k; Real* ai = akk; int i;
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for (i = k+1; i < nrows; i++)
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{
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ai += nrows; const Real trybig = fabs(*ai);
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if (big < trybig) { big = trybig; mu1 = i; }
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}
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}
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if (mu1 != mu) cout << k << " " << mu << " " << mu1 << endl;
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*/
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indx[k] = mu;
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if (mu != k) //row swap
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{
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Real* a1 = store + nrows * k; Real* a2 = store + nrows * mu; d = !d;
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int j = nrows;
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while (j--) { const Real temp = *a1; *a1++ = *a2; *a2++ = temp; }
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}
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Real diag = *akk; big = 0; mu = k + 1;
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if (diag != 0)
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{
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ai = akk; int i = nrows - k - 1;
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while (i--)
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{
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ai += nrows; Real* al = ai; Real mult = *al / diag; *al = mult;
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int l = nrows - k - 1; Real* aj = akk;
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// work out the next pivot as part of this loop
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// this saves a column operation
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if (l-- != 0)
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{
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*(++al) -= (mult * *(++aj));
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const Real trybig = fabs(*al);
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if (big < trybig) { big = trybig; mu = nrows - i - 1; }
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while (l--) *(++al) -= (mult * *(++aj));
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}
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}
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}
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else sing = true;
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if (++k == nrows) break; // so next line won't overflow
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akk += nrows + 1;
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}
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}
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void CroutMatrix::lubksb(Real* B, int mini)
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{
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REPORT
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// this has been adapted from Numerical Recipes in C. The code has been
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// substantially streamlined, so I do not think much of the original
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// copyright remains. However there is not much opportunity for
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// variation in the code, so it is still similar to the NR code.
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// I follow the NR code in skipping over initial zeros in the B vector.
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Tracer trace("Crout(lubksb)");
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if (sing) Throw(SingularException(*this));
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int i, j, ii = nrows; // ii initialised : B might be all zeros
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// scan for first non-zero in B
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for (i = 0; i < nrows; i++)
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{
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int ip = indx[i]; Real temp = B[ip]; B[ip] = B[i]; B[i] = temp;
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if (temp != 0.0) { ii = i; break; }
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}
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Real* bi; Real* ai;
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i = ii + 1;
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if (i < nrows)
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{
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bi = B + ii; ai = store + ii + i * nrows;
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for (;;)
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{
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int ip = indx[i]; Real sum = B[ip]; B[ip] = B[i];
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Real* aij = ai; Real* bj = bi; j = i - ii;
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while (j--) sum -= *aij++ * *bj++;
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B[i] = sum;
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if (++i == nrows) break;
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ai += nrows;
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}
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}
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ai = store + nrows * nrows;
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for (i = nrows - 1; i >= mini; i--)
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{
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Real* bj = B+i; ai -= nrows; Real* ajx = ai+i;
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Real sum = *bj; Real diag = *ajx;
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j = nrows - i; while(--j) sum -= *(++ajx) * *(++bj);
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B[i] = sum / diag;
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}
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}
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/****************************** scalar functions ****************************/
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inline Real square(Real x) { return x*x; }
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Real GeneralMatrix::SumSquare() const
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{
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REPORT
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Real sum = 0.0; int i = storage; Real* s = store;
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while (i--) sum += square(*s++);
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((GeneralMatrix&)*this).tDelete(); return sum;
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}
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Real GeneralMatrix::SumAbsoluteValue() const
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{
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REPORT
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Real sum = 0.0; int i = storage; Real* s = store;
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while (i--) sum += fabs(*s++);
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((GeneralMatrix&)*this).tDelete(); return sum;
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}
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Real GeneralMatrix::Sum() const
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{
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REPORT
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Real sum = 0.0; int i = storage; Real* s = store;
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while (i--) sum += *s++;
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((GeneralMatrix&)*this).tDelete(); return sum;
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}
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// maxima and minima
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// There are three sets of routines
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// MaximumAbsoluteValue, MinimumAbsoluteValue, Maximum, Minimum
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// ... these find just the maxima and minima
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// MaximumAbsoluteValue1, MinimumAbsoluteValue1, Maximum1, Minimum1
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// ... these find the maxima and minima and their locations in a
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// one dimensional object
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// MaximumAbsoluteValue2, MinimumAbsoluteValue2, Maximum2, Minimum2
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// ... these find the maxima and minima and their locations in a
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// two dimensional object
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// If the matrix has no values throw an exception
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// If we do not want the location find the maximum or minimum on the
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// array stored by GeneralMatrix
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// This won't work for BandMatrices. We call ClearCorner for
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// MaximumAbsoluteValue but for the others use the AbsoluteMinimumValue2
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// version and discard the location.
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// For one dimensional objects, when we want the location of the
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// maximum or minimum, work with the array stored by GeneralMatrix
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// For two dimensional objects where we want the location of the maximum or
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// minimum proceed as follows:
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// For rectangular matrices use the array stored by GeneralMatrix and
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// deduce the location from the location in the GeneralMatrix
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// For other two dimensional matrices use the Matrix Row routine to find the
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// maximum or minimum for each row.
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static void NullMatrixError(const GeneralMatrix* gm)
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{
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((GeneralMatrix&)*gm).tDelete();
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Throw(ProgramException("Maximum or minimum of null matrix"));
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}
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Real GeneralMatrix::MaximumAbsoluteValue() const
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{
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REPORT
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if (storage == 0) NullMatrixError(this);
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Real maxval = 0.0; int l = storage; Real* s = store;
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while (l--) { Real a = fabs(*s++); if (maxval < a) maxval = a; }
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((GeneralMatrix&)*this).tDelete(); return maxval;
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}
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Real GeneralMatrix::MaximumAbsoluteValue1(int& i) const
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{
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REPORT
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if (storage == 0) NullMatrixError(this);
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Real maxval = 0.0; int l = storage; Real* s = store; int li = storage;
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while (l--)
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{ Real a = fabs(*s++); if (maxval <= a) { maxval = a; li = l; } }
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i = storage - li;
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((GeneralMatrix&)*this).tDelete(); return maxval;
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}
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Real GeneralMatrix::MinimumAbsoluteValue() const
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{
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REPORT
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if (storage == 0) NullMatrixError(this);
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int l = storage - 1; Real* s = store; Real minval = fabs(*s++);
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while (l--) { Real a = fabs(*s++); if (minval > a) minval = a; }
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((GeneralMatrix&)*this).tDelete(); return minval;
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}
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Real GeneralMatrix::MinimumAbsoluteValue1(int& i) const
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{
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REPORT
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if (storage == 0) NullMatrixError(this);
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int l = storage - 1; Real* s = store; Real minval = fabs(*s++); int li = l;
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while (l--)
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{ Real a = fabs(*s++); if (minval >= a) { minval = a; li = l; } }
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i = storage - li;
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((GeneralMatrix&)*this).tDelete(); return minval;
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}
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Real GeneralMatrix::Maximum() const
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{
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REPORT
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if (storage == 0) NullMatrixError(this);
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int l = storage - 1; Real* s = store; Real maxval = *s++;
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while (l--) { Real a = *s++; if (maxval < a) maxval = a; }
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((GeneralMatrix&)*this).tDelete(); return maxval;
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}
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Real GeneralMatrix::Maximum1(int& i) const
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{
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REPORT
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if (storage == 0) NullMatrixError(this);
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int l = storage - 1; Real* s = store; Real maxval = *s++; int li = l;
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while (l--) { Real a = *s++; if (maxval <= a) { maxval = a; li = l; } }
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i = storage - li;
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((GeneralMatrix&)*this).tDelete(); return maxval;
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}
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Real GeneralMatrix::Minimum() const
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{
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REPORT
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if (storage == 0) NullMatrixError(this);
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int l = storage - 1; Real* s = store; Real minval = *s++;
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while (l--) { Real a = *s++; if (minval > a) minval = a; }
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((GeneralMatrix&)*this).tDelete(); return minval;
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}
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Real GeneralMatrix::Minimum1(int& i) const
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{
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REPORT
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if (storage == 0) NullMatrixError(this);
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int l = storage - 1; Real* s = store; Real minval = *s++; int li = l;
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while (l--) { Real a = *s++; if (minval >= a) { minval = a; li = l; } }
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i = storage - li;
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((GeneralMatrix&)*this).tDelete(); return minval;
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}
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Real GeneralMatrix::MaximumAbsoluteValue2(int& i, int& j) const
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{
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REPORT
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if (storage == 0) NullMatrixError(this);
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Real maxval = 0.0; int nr = Nrows();
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MatrixRow mr((GeneralMatrix*)this, LoadOnEntry+DirectPart);
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for (int r = 1; r <= nr; r++)
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{
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int c; maxval = mr.MaximumAbsoluteValue1(maxval, c);
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if (c > 0) { i = r; j = c; }
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mr.Next();
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}
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((GeneralMatrix&)*this).tDelete(); return maxval;
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}
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Real GeneralMatrix::MinimumAbsoluteValue2(int& i, int& j) const
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{
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REPORT
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if (storage == 0) NullMatrixError(this);
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Real minval = FloatingPointPrecision::Maximum(); int nr = Nrows();
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MatrixRow mr((GeneralMatrix*)this, LoadOnEntry+DirectPart);
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for (int r = 1; r <= nr; r++)
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{
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int c; minval = mr.MinimumAbsoluteValue1(minval, c);
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if (c > 0) { i = r; j = c; }
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mr.Next();
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}
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((GeneralMatrix&)*this).tDelete(); return minval;
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}
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Real GeneralMatrix::Maximum2(int& i, int& j) const
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{
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REPORT
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if (storage == 0) NullMatrixError(this);
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Real maxval = -FloatingPointPrecision::Maximum(); int nr = Nrows();
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MatrixRow mr((GeneralMatrix*)this, LoadOnEntry+DirectPart);
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for (int r = 1; r <= nr; r++)
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{
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int c; maxval = mr.Maximum1(maxval, c);
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if (c > 0) { i = r; j = c; }
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mr.Next();
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}
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((GeneralMatrix&)*this).tDelete(); return maxval;
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}
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Real GeneralMatrix::Minimum2(int& i, int& j) const
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{
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REPORT
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if (storage == 0) NullMatrixError(this);
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Real minval = FloatingPointPrecision::Maximum(); int nr = Nrows();
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MatrixRow mr((GeneralMatrix*)this, LoadOnEntry+DirectPart);
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for (int r = 1; r <= nr; r++)
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{
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int c; minval = mr.Minimum1(minval, c);
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if (c > 0) { i = r; j = c; }
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mr.Next();
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}
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((GeneralMatrix&)*this).tDelete(); return minval;
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}
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Real Matrix::MaximumAbsoluteValue2(int& i, int& j) const
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{
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REPORT
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int k; Real m = GeneralMatrix::MaximumAbsoluteValue1(k); k--;
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i = k / Ncols(); j = k - i * Ncols(); i++; j++;
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return m;
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}
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Real Matrix::MinimumAbsoluteValue2(int& i, int& j) const
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{
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REPORT
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int k; Real m = GeneralMatrix::MinimumAbsoluteValue1(k); k--;
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i = k / Ncols(); j = k - i * Ncols(); i++; j++;
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return m;
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}
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Real Matrix::Maximum2(int& i, int& j) const
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{
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REPORT
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int k; Real m = GeneralMatrix::Maximum1(k); k--;
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i = k / Ncols(); j = k - i * Ncols(); i++; j++;
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return m;
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}
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Real Matrix::Minimum2(int& i, int& j) const
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{
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REPORT
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int k; Real m = GeneralMatrix::Minimum1(k); k--;
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i = k / Ncols(); j = k - i * Ncols(); i++; j++;
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return m;
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}
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Real SymmetricMatrix::SumSquare() const
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{
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REPORT
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Real sum1 = 0.0; Real sum2 = 0.0; Real* s = store; int nr = nrows;
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for (int i = 0; i<nr; i++)
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{
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int j = i;
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while (j--) sum2 += square(*s++);
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sum1 += square(*s++);
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}
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((GeneralMatrix&)*this).tDelete(); return sum1 + 2.0 * sum2;
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}
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Real SymmetricMatrix::SumAbsoluteValue() const
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{
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REPORT
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Real sum1 = 0.0; Real sum2 = 0.0; Real* s = store; int nr = nrows;
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for (int i = 0; i<nr; i++)
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{
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int j = i;
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while (j--) sum2 += fabs(*s++);
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sum1 += fabs(*s++);
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}
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((GeneralMatrix&)*this).tDelete(); return sum1 + 2.0 * sum2;
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}
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Real IdentityMatrix::SumAbsoluteValue() const
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{ REPORT return fabs(Trace()); } // no need to do tDelete?
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Real SymmetricMatrix::Sum() const
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{
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REPORT
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Real sum1 = 0.0; Real sum2 = 0.0; Real* s = store; int nr = nrows;
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for (int i = 0; i<nr; i++)
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{
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int j = i;
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while (j--) sum2 += *s++;
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sum1 += *s++;
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}
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((GeneralMatrix&)*this).tDelete(); return sum1 + 2.0 * sum2;
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}
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Real IdentityMatrix::SumSquare() const
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{
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Real sum = *store * *store * nrows;
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((GeneralMatrix&)*this).tDelete(); return sum;
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}
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Real BaseMatrix::SumSquare() const
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{
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REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
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Real s = gm->SumSquare(); return s;
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}
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Real BaseMatrix::NormFrobenius() const
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{ REPORT return sqrt(SumSquare()); }
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Real BaseMatrix::SumAbsoluteValue() const
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{
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REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
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Real s = gm->SumAbsoluteValue(); return s;
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}
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Real BaseMatrix::Sum() const
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{
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REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
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Real s = gm->Sum(); return s;
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}
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Real BaseMatrix::MaximumAbsoluteValue() const
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{
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REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
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Real s = gm->MaximumAbsoluteValue(); return s;
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}
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Real BaseMatrix::MaximumAbsoluteValue1(int& i) const
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{
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REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
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Real s = gm->MaximumAbsoluteValue1(i); return s;
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}
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Real BaseMatrix::MaximumAbsoluteValue2(int& i, int& j) const
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{
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REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
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Real s = gm->MaximumAbsoluteValue2(i, j); return s;
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}
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Real BaseMatrix::MinimumAbsoluteValue() const
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{
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REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
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Real s = gm->MinimumAbsoluteValue(); return s;
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}
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Real BaseMatrix::MinimumAbsoluteValue1(int& i) const
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{
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REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
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Real s = gm->MinimumAbsoluteValue1(i); return s;
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}
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Real BaseMatrix::MinimumAbsoluteValue2(int& i, int& j) const
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{
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REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
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Real s = gm->MinimumAbsoluteValue2(i, j); return s;
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}
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Real BaseMatrix::Maximum() const
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{
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REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
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Real s = gm->Maximum(); return s;
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}
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Real BaseMatrix::Maximum1(int& i) const
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{
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REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
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Real s = gm->Maximum1(i); return s;
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}
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Real BaseMatrix::Maximum2(int& i, int& j) const
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{
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REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
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Real s = gm->Maximum2(i, j); return s;
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}
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Real BaseMatrix::Minimum() const
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{
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REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
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Real s = gm->Minimum(); return s;
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}
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Real BaseMatrix::Minimum1(int& i) const
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{
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REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
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Real s = gm->Minimum1(i); return s;
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}
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|
Real BaseMatrix::Minimum2(int& i, int& j) const
|
|
{
|
|
REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
|
|
Real s = gm->Minimum2(i, j); return s;
|
|
}
|
|
|
|
Real DotProduct(const Matrix& A, const Matrix& B)
|
|
{
|
|
REPORT
|
|
int n = A.storage;
|
|
if (n != B.storage) Throw(IncompatibleDimensionsException(A,B));
|
|
Real sum = 0.0; Real* a = A.store; Real* b = B.store;
|
|
while (n--) sum += *a++ * *b++;
|
|
return sum;
|
|
}
|
|
|
|
Real Matrix::Trace() const
|
|
{
|
|
REPORT
|
|
Tracer trace("Trace");
|
|
int i = nrows; int d = i+1;
|
|
if (i != ncols) Throw(NotSquareException(*this));
|
|
Real sum = 0.0; Real* s = store;
|
|
// while (i--) { sum += *s; s += d; }
|
|
if (i) for (;;) { sum += *s; if (!(--i)) break; s += d; }
|
|
((GeneralMatrix&)*this).tDelete(); return sum;
|
|
}
|
|
|
|
Real DiagonalMatrix::Trace() const
|
|
{
|
|
REPORT
|
|
int i = nrows; Real sum = 0.0; Real* s = store;
|
|
while (i--) sum += *s++;
|
|
((GeneralMatrix&)*this).tDelete(); return sum;
|
|
}
|
|
|
|
Real SymmetricMatrix::Trace() const
|
|
{
|
|
REPORT
|
|
int i = nrows; Real sum = 0.0; Real* s = store; int j = 2;
|
|
// while (i--) { sum += *s; s += j++; }
|
|
if (i) for (;;) { sum += *s; if (!(--i)) break; s += j++; }
|
|
((GeneralMatrix&)*this).tDelete(); return sum;
|
|
}
|
|
|
|
Real LowerTriangularMatrix::Trace() const
|
|
{
|
|
REPORT
|
|
int i = nrows; Real sum = 0.0; Real* s = store; int j = 2;
|
|
// while (i--) { sum += *s; s += j++; }
|
|
if (i) for (;;) { sum += *s; if (!(--i)) break; s += j++; }
|
|
((GeneralMatrix&)*this).tDelete(); return sum;
|
|
}
|
|
|
|
Real UpperTriangularMatrix::Trace() const
|
|
{
|
|
REPORT
|
|
int i = nrows; Real sum = 0.0; Real* s = store;
|
|
while (i) { sum += *s; s += i--; } // won t cause a problem
|
|
((GeneralMatrix&)*this).tDelete(); return sum;
|
|
}
|
|
|
|
Real BandMatrix::Trace() const
|
|
{
|
|
REPORT
|
|
int i = nrows; int w = lower+upper+1;
|
|
Real sum = 0.0; Real* s = store+lower;
|
|
// while (i--) { sum += *s; s += w; }
|
|
if (i) for (;;) { sum += *s; if (!(--i)) break; s += w; }
|
|
((GeneralMatrix&)*this).tDelete(); return sum;
|
|
}
|
|
|
|
Real SymmetricBandMatrix::Trace() const
|
|
{
|
|
REPORT
|
|
int i = nrows; int w = lower+1;
|
|
Real sum = 0.0; Real* s = store+lower;
|
|
// while (i--) { sum += *s; s += w; }
|
|
if (i) for (;;) { sum += *s; if (!(--i)) break; s += w; }
|
|
((GeneralMatrix&)*this).tDelete(); return sum;
|
|
}
|
|
|
|
Real IdentityMatrix::Trace() const
|
|
{
|
|
Real sum = *store * nrows;
|
|
((GeneralMatrix&)*this).tDelete(); return sum;
|
|
}
|
|
|
|
|
|
Real BaseMatrix::Trace() const
|
|
{
|
|
REPORT
|
|
MatrixType Diag = MatrixType::Dg; Diag.SetDataLossOK();
|
|
GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate(Diag);
|
|
Real sum = gm->Trace(); return sum;
|
|
}
|
|
|
|
void LogAndSign::operator*=(Real x)
|
|
{
|
|
if (x > 0.0) { log_value += log(x); }
|
|
else if (x < 0.0) { log_value += log(-x); sign = -sign; }
|
|
else sign = 0;
|
|
}
|
|
|
|
void LogAndSign::PowEq(int k)
|
|
{
|
|
if (sign)
|
|
{
|
|
log_value *= k;
|
|
if ( (k & 1) == 0 ) sign = 1;
|
|
}
|
|
}
|
|
|
|
Real LogAndSign::Value() const
|
|
{
|
|
Tracer et("LogAndSign::Value");
|
|
if (log_value >= FloatingPointPrecision::LnMaximum())
|
|
Throw(OverflowException("Overflow in exponential"));
|
|
return sign * exp(log_value);
|
|
}
|
|
|
|
LogAndSign::LogAndSign(Real f)
|
|
{
|
|
if (f == 0.0) { log_value = 0.0; sign = 0; return; }
|
|
else if (f < 0.0) { sign = -1; f = -f; }
|
|
else sign = 1;
|
|
log_value = log(f);
|
|
}
|
|
|
|
LogAndSign DiagonalMatrix::LogDeterminant() const
|
|
{
|
|
REPORT
|
|
int i = nrows; LogAndSign sum; Real* s = store;
|
|
while (i--) sum *= *s++;
|
|
((GeneralMatrix&)*this).tDelete(); return sum;
|
|
}
|
|
|
|
LogAndSign LowerTriangularMatrix::LogDeterminant() const
|
|
{
|
|
REPORT
|
|
int i = nrows; LogAndSign sum; Real* s = store; int j = 2;
|
|
// while (i--) { sum *= *s; s += j++; }
|
|
if (i) for(;;) { sum *= *s; if (!(--i)) break; s += j++; }
|
|
((GeneralMatrix&)*this).tDelete(); return sum;
|
|
}
|
|
|
|
LogAndSign UpperTriangularMatrix::LogDeterminant() const
|
|
{
|
|
REPORT
|
|
int i = nrows; LogAndSign sum; Real* s = store;
|
|
while (i) { sum *= *s; s += i--; }
|
|
((GeneralMatrix&)*this).tDelete(); return sum;
|
|
}
|
|
|
|
LogAndSign IdentityMatrix::LogDeterminant() const
|
|
{
|
|
REPORT
|
|
int i = nrows; LogAndSign sum;
|
|
if (i > 0) { sum = *store; sum.PowEq(i); }
|
|
((GeneralMatrix&)*this).tDelete(); return sum;
|
|
}
|
|
|
|
LogAndSign BaseMatrix::LogDeterminant() const
|
|
{
|
|
REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
|
|
LogAndSign sum = gm->LogDeterminant(); return sum;
|
|
}
|
|
|
|
LogAndSign GeneralMatrix::LogDeterminant() const
|
|
{
|
|
REPORT
|
|
Tracer tr("LogDeterminant");
|
|
if (nrows != ncols) Throw(NotSquareException(*this));
|
|
CroutMatrix C(*this); return C.LogDeterminant();
|
|
}
|
|
|
|
LogAndSign CroutMatrix::LogDeterminant() const
|
|
{
|
|
REPORT
|
|
if (sing) return 0.0;
|
|
int i = nrows; int dd = i+1; LogAndSign sum; Real* s = store;
|
|
if (i) for(;;)
|
|
{
|
|
sum *= *s;
|
|
if (!(--i)) break;
|
|
s += dd;
|
|
}
|
|
if (!d) sum.ChangeSign(); return sum;
|
|
|
|
}
|
|
|
|
Real BaseMatrix::Determinant() const
|
|
{
|
|
REPORT
|
|
Tracer tr("Determinant");
|
|
REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
|
|
LogAndSign ld = gm->LogDeterminant();
|
|
return ld.Value();
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
LinearEquationSolver::LinearEquationSolver(const BaseMatrix& bm)
|
|
{
|
|
gm = ( ((BaseMatrix&)bm).Evaluate() )->MakeSolver();
|
|
if (gm==&bm) { REPORT gm = gm->Image(); }
|
|
// want a copy if *gm is actually bm
|
|
else { REPORT gm->Protect(); }
|
|
}
|
|
|
|
|
|
#ifdef use_namespace
|
|
}
|
|
#endif
|
|
|