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