mirror of
https://github.com/NGSolve/netgen.git
synced 2024-11-11 16:49:16 +05:00
1445 lines
27 KiB
C++
1445 lines
27 KiB
C++
#include <mystdlib.h>
|
|
|
|
#include <linalg.hpp>
|
|
|
|
|
|
namespace netgen
|
|
{
|
|
DenseMatrix :: DenseMatrix ()
|
|
{
|
|
data = NULL;
|
|
height = 0;
|
|
width = 0;
|
|
}
|
|
|
|
DenseMatrix :: DenseMatrix (int h, int w)
|
|
{
|
|
if (!w) w = h;
|
|
width = w;
|
|
height = h;
|
|
if (h*w)
|
|
data = new double[h*w];
|
|
else
|
|
data = 0;
|
|
|
|
for (int i = 0 ; i < (h * w); i++)
|
|
data[i] = 0;
|
|
}
|
|
|
|
/*
|
|
DenseMatrix :: DenseMatrix (int h, int w, const double * d)
|
|
: BaseMatrix (h, w)
|
|
{
|
|
int size = h * w;
|
|
int i;
|
|
|
|
if (size)
|
|
{
|
|
data = new double[size];
|
|
for (i = 0; i < size; i++)
|
|
data[i] = d[i];
|
|
}
|
|
else
|
|
data = NULL;
|
|
}
|
|
*/
|
|
|
|
DenseMatrix :: DenseMatrix (const DenseMatrix & m2)
|
|
{
|
|
data = NULL; height = width = 0;
|
|
SetSize (m2.Height(), m2.Width());
|
|
memcpy (data, m2.data, sizeof(double) * Height() * Width());
|
|
}
|
|
|
|
DenseMatrix :: ~DenseMatrix ()
|
|
{
|
|
delete [] data;
|
|
}
|
|
|
|
|
|
void DenseMatrix :: SetSize (int h, int w)
|
|
{
|
|
if (!w) w = h;
|
|
if (height == h && width == w)
|
|
return;
|
|
|
|
height = h;
|
|
width = w;
|
|
|
|
delete[] data;
|
|
|
|
if (h*w)
|
|
data = new double[h*w];
|
|
else
|
|
data = NULL;
|
|
}
|
|
|
|
|
|
/*
|
|
DenseMatrix & DenseMatrix :: operator= (const BaseMatrix & m2)
|
|
{
|
|
int i, j;
|
|
|
|
SetSize (m2.Height(), m2.Width());
|
|
|
|
if (data)
|
|
for (i = 1; i <= Height(); i++)
|
|
for (j = 1; j <= Width(); j++)
|
|
Set (i, j, m2(i, j));
|
|
else
|
|
(*myerr) << "DenseMatrix::Operator=: Matrix not allocated" << endl;
|
|
|
|
return *this;
|
|
}
|
|
*/
|
|
|
|
|
|
DenseMatrix & DenseMatrix :: operator= (const DenseMatrix & m2)
|
|
{
|
|
SetSize (m2.Height(), m2.Width());
|
|
|
|
if (data) memcpy (data, m2.data, sizeof(double) * m2.Height() * m2.Width());
|
|
return *this;
|
|
}
|
|
|
|
|
|
DenseMatrix & DenseMatrix :: operator+= (const DenseMatrix & m2)
|
|
{
|
|
int i;
|
|
double * p, * q;
|
|
|
|
if (Height() != m2.Height() || Width() != m2.Width())
|
|
{
|
|
(*myerr) << "DenseMatrix::Operator+=: Sizes don't fit" << endl;
|
|
return *this;
|
|
}
|
|
|
|
if (data)
|
|
{
|
|
p = data;
|
|
q = m2.data;
|
|
for (i = Width() * Height(); i > 0; i--)
|
|
{
|
|
*p += *q;
|
|
p++;
|
|
q++;
|
|
}
|
|
}
|
|
else
|
|
(*myerr) << "DenseMatrix::Operator+=: Matrix not allocated" << endl;
|
|
|
|
return *this;
|
|
}
|
|
|
|
|
|
DenseMatrix & DenseMatrix :: operator-= (const DenseMatrix & m2)
|
|
{
|
|
int i;
|
|
double * p, * q;
|
|
|
|
if (Height() != m2.Height() || Width() != m2.Width())
|
|
{
|
|
(*myerr) << "DenseMatrix::Operator-=: Sizes don't fit" << endl;
|
|
return *this;
|
|
}
|
|
|
|
if (data)
|
|
{
|
|
p = data;
|
|
q = m2.data;
|
|
for (i = Width() * Height(); i > 0; i--)
|
|
{
|
|
*p -= *q;
|
|
p++;
|
|
q++;
|
|
}
|
|
}
|
|
else
|
|
(*myerr) << "DenseMatrix::Operator-=: Matrix not allocated" << endl;
|
|
|
|
return *this;
|
|
}
|
|
|
|
|
|
|
|
|
|
/*
|
|
double & DenseMatrix :: operator() (int i, int j)
|
|
{
|
|
if (i >= 1 && j >= 1 && i <= height && j <= width)
|
|
return Elem(i,j);
|
|
else (*myerr) << "DenseMatrix: index (" << i << "," << j << ") out of range (1.."
|
|
<< height << ",1.." << width << ")\n";
|
|
static double dummy = 0;
|
|
return dummy;
|
|
}
|
|
|
|
double DenseMatrix :: operator() (int i, int j) const
|
|
{
|
|
if (i >= 1 && j >= 1 && i <= height && j <= width)
|
|
return Get(i,j);
|
|
else (*myerr) << "DenseMatrix: index (" << i << "," << j << ") out of range (1.."
|
|
<< height << ",1.." << width << ")\n";
|
|
|
|
static double dummy = 0;
|
|
return dummy;
|
|
}
|
|
*/
|
|
|
|
DenseMatrix & DenseMatrix :: operator= (double v)
|
|
{
|
|
int i;
|
|
double * p = data;
|
|
|
|
if (data)
|
|
for (i = width*height; i > 0; i--, p++)
|
|
*p = v;
|
|
|
|
return *this;
|
|
}
|
|
|
|
|
|
|
|
DenseMatrix & DenseMatrix :: operator*= (double v)
|
|
{
|
|
int i;
|
|
double * p = data;
|
|
|
|
if (data)
|
|
for (i = width*height; i > 0; i--, p++)
|
|
*p *= v;
|
|
|
|
return *this;
|
|
}
|
|
|
|
|
|
double DenseMatrix :: Det () const
|
|
{
|
|
if (width != height)
|
|
{
|
|
(*myerr) << "DenseMatrix :: Det: width != height" << endl;
|
|
return 0;
|
|
}
|
|
|
|
switch (width)
|
|
{
|
|
case 1: return Get(1, 1);
|
|
case 2: return Get(1) * Get(4) - Get(2) * Get(3);
|
|
|
|
case 3: return Get(1) * Get(5) * Get(9)
|
|
+ Get(2) * Get(6) * Get(7)
|
|
+ Get(3) * Get(4) * Get(8)
|
|
- Get(1) * Get(6) * Get(8)
|
|
- Get(2) * Get(4) * Get(9)
|
|
- Get(3) * Get(5) * Get(7);
|
|
default:
|
|
{
|
|
(*myerr) << "Matrix :: Det: general size not implemented (size=" << width << ")" << endl;
|
|
return 0;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
void CalcInverse (const DenseMatrix & m1, DenseMatrix & m2)
|
|
{
|
|
// int i, j, k, n;
|
|
double det;
|
|
// DenseMatrix m1 = hm1;
|
|
|
|
if (m1.width != m1.height)
|
|
{
|
|
(*myerr) << "CalcInverse: matrix not symmetric" << endl;
|
|
return;
|
|
}
|
|
if (m1.width != m2.width || m1.height != m2.height)
|
|
{
|
|
(*myerr) << "CalcInverse: dim(m2) != dim(m1)" << endl;
|
|
return;
|
|
}
|
|
|
|
|
|
if (m1.Width() <= 3)
|
|
{
|
|
det = m1.Det();
|
|
if (det == 0)
|
|
{
|
|
(*myerr) << "CalcInverse: Matrix singular" << endl;
|
|
return;
|
|
}
|
|
|
|
det = 1e0 / det;
|
|
switch (m1.width)
|
|
{
|
|
case 1:
|
|
{
|
|
m2.Set(1, 1, det);
|
|
return;
|
|
}
|
|
case 2:
|
|
{
|
|
m2.Set(1, 1, det * m1.Get(4));
|
|
m2.Set(2, 2, det * m1.Get(1));
|
|
m2.Set(1, 2, - det * m1.Get(2));
|
|
m2.Set(2, 1, - det * m1.Get(3));
|
|
return;
|
|
}
|
|
case 3:
|
|
{
|
|
m2.Set(1, 1, det * (m1.Get(5) * m1.Get(9) - m1.Get(6) * m1.Get(8)));
|
|
m2.Set(2, 1, -det * (m1.Get(4) * m1.Get(9) - m1.Get(6) * m1.Get(7)));
|
|
m2.Set(3, 1, det * (m1.Get(4) * m1.Get(8) - m1.Get(5) * m1.Get(7)));
|
|
|
|
m2.Set(1, 2, -det * (m1.Get(2) * m1.Get(9) - m1.Get(3) * m1.Get(8)));
|
|
m2.Set(2, 2, det * (m1.Get(1) * m1.Get(9) - m1.Get(3) * m1.Get(7)));
|
|
m2.Set(3, 2, -det * (m1.Get(1) * m1.Get(8) - m1.Get(2) * m1.Get(7)));
|
|
|
|
m2.Set(1, 3, det * (m1.Get(2) * m1.Get(6) - m1.Get(3) * m1.Get(5)));
|
|
m2.Set(2, 3, -det * (m1.Get(1) * m1.Get(6) - m1.Get(3) * m1.Get(4)));
|
|
m2.Set(3, 3, det * (m1.Get(1) * m1.Get(5) - m1.Get(2) * m1.Get(4)));
|
|
return;
|
|
}
|
|
}
|
|
}
|
|
|
|
else
|
|
{
|
|
int i, j, k, n;
|
|
n = m1.Height();
|
|
|
|
|
|
#ifdef CHOL
|
|
int dots = (n > 200);
|
|
|
|
// Cholesky
|
|
|
|
double x;
|
|
Vector p(n);
|
|
|
|
m2 = m1;
|
|
/*
|
|
m2.SetSymmetric();
|
|
if (!m2.Symmetric())
|
|
cerr << "m should be symmetric for Cholesky" << endl;
|
|
*/
|
|
|
|
for (i = 1; i <= n; i++)
|
|
for (j = 1; j < i; j++)
|
|
m2.Elem(j, i) = m2.Get(i, j);
|
|
|
|
for (i = 1; i <= n; i++)
|
|
{
|
|
if (dots && i % 10 == 0)
|
|
(*mycout) << "." << flush;
|
|
|
|
for (j = i; j <= n; j++)
|
|
{
|
|
x = m2.Get(i, j);
|
|
|
|
const double * pik = &m2.Get(i, 1);
|
|
const double * pjk = &m2.Get(j, 1);
|
|
|
|
for (k = i-2; k >= 0; --k, ++pik, ++pjk)
|
|
x -= (*pik) * (*pjk);
|
|
|
|
// for (k = i-1; k >= 1; --k)
|
|
// x -= m2.Get(j, k) * m2.Get(i, k);
|
|
|
|
if (i == j)
|
|
{
|
|
if (x <= 0)
|
|
{
|
|
cerr << "Matrix indefinite 1" << endl;
|
|
return;
|
|
}
|
|
|
|
p.Elem(i) = 1 / sqrt(x);
|
|
}
|
|
else
|
|
{
|
|
m2.Elem(j, i) = x * p.Get(i);
|
|
}
|
|
}
|
|
}
|
|
|
|
for (i = 1; i <= n; i++)
|
|
m2.Elem(i, i) = 1 / p.Get(i);
|
|
|
|
// check: A = L L^t
|
|
|
|
// for (i = 1; i <= n; i++)
|
|
// for (j = 1; j <= n; j++)
|
|
// {
|
|
// x = 0;
|
|
// for (k = 1; k <= i && k <= j; k++)
|
|
// x += m2.Get(i, k) * m2.Get(j, k);
|
|
// (*testout) << "err " << i << "," << j << " = " << (m1.Get(i, j) - x) << endl;
|
|
// }
|
|
|
|
|
|
|
|
// calc L^{-1}, store upper triangle
|
|
|
|
// DenseMatrix hm(n);
|
|
// hm = m2;
|
|
|
|
for (i = 1; i <= n; i++)
|
|
{
|
|
if (dots && i % 10 == 0)
|
|
(*mycout) << "+" << flush;
|
|
|
|
for (j = i; j <= n; j++)
|
|
{
|
|
x = 0;
|
|
if (j == i) x = 1;
|
|
|
|
const double * pjk = &m2.Get(j, i);
|
|
const double * pik = &m2.Get(i, i);
|
|
for (k = i; k < j; k++, ++pjk, ++pik)
|
|
x -= *pik * *pjk;
|
|
|
|
// for (k = i; k < j; k++)
|
|
// x -= m2.Get(j, k) * m2.Get(i, k);
|
|
|
|
m2.Elem(i, j) = x / m2.Get(j, j);
|
|
}
|
|
}
|
|
|
|
// (*testout) << "check L^-1" << endl;
|
|
// for (i = 1; i <= n; i++)
|
|
// for (j = 1; j <= n; j++)
|
|
// {
|
|
// x = 0;
|
|
// for (k = j; k <= i; k++)
|
|
// x += hm.Get(i, k) * m2.Get(j, k);
|
|
// (*testout) << "i, j = " << i << "," << j << " x = " << x << endl;
|
|
// }
|
|
|
|
|
|
// calc A^-1 = L^-T * L^-1
|
|
|
|
for (i = 1; i <= n; i++)
|
|
{
|
|
if (dots && i % 10 == 0)
|
|
(*mycout) << "-" << flush;
|
|
|
|
for (j = 1; j <= i; j++)
|
|
{
|
|
x = 0;
|
|
k = i;
|
|
if (j > i) k = j;
|
|
|
|
const double * pik = &m2.Get(i, k);
|
|
const double * pjk = &m2.Get(j, k);
|
|
|
|
for ( ; k <= n; ++k, ++pik, ++pjk)
|
|
x += *pik * *pjk;
|
|
// for ( ; k <= n; k++)
|
|
// x += m2.Get(i, k) * m2.Get(j, k);
|
|
|
|
m2.Elem(i, j) = x;
|
|
}
|
|
}
|
|
|
|
for (i = 1; i <= n; i++)
|
|
for (j = 1; j < i; j++)
|
|
m2.Elem(j, i) = m2.Get(i, j);
|
|
|
|
if (dots) (*mycout) << endl;
|
|
#endif
|
|
|
|
|
|
|
|
// Gauss - Jordan - algorithm
|
|
|
|
int r, hi;
|
|
double max, hr;
|
|
|
|
|
|
ARRAY<int> p(n); // pivot-permutation
|
|
Vector hv(n);
|
|
|
|
|
|
m2 = m1;
|
|
|
|
/*
|
|
if (m2.Symmetric())
|
|
for (i = 1; i <= n; i++)
|
|
for (j = 1; j < i; j++)
|
|
m2.Elem(j, i) = m2.Get(i, j);
|
|
*/
|
|
|
|
// Algorithm of Stoer, Einf. i. d. Num. Math, S 145
|
|
|
|
for (j = 1; j <= n; j++)
|
|
p.Set(j, j);
|
|
|
|
for (j = 1; j <= n; j++)
|
|
{
|
|
// pivot search
|
|
|
|
max = fabs(m2.Get(j, j));
|
|
r = j;
|
|
|
|
for (i = j+1; i <= n ;i++)
|
|
if (fabs (m2.Get(i, j)) > max)
|
|
{
|
|
r = i;
|
|
max = fabs (m2.Get(i, j));
|
|
}
|
|
|
|
if (max < 1e-20)
|
|
{
|
|
cerr << "Inverse matrix: matrix singular" << endl;
|
|
return;
|
|
}
|
|
|
|
r = j;
|
|
|
|
// exchange rows
|
|
if (r > j)
|
|
{
|
|
for (k = 1; k <= n; k++)
|
|
{
|
|
hr = m2.Get(j, k);
|
|
m2.Elem(j, k) = m2.Get(r, k);
|
|
m2.Elem(r, k) = hr;
|
|
}
|
|
hi = p.Get(j);
|
|
p.Elem(j) = p.Get(r);
|
|
p.Elem(r) = hi;
|
|
}
|
|
|
|
|
|
// transformation
|
|
|
|
hr = 1 / m2.Get(j, j);
|
|
for (i = 1; i <= n; i++)
|
|
m2.Elem(i, j) *= hr;
|
|
m2.Elem(j, j) = hr;
|
|
|
|
for (k = 1; k <= n; k++)
|
|
if (k != j)
|
|
{
|
|
for (i = 1; i <= n; i++)
|
|
if (i != j)
|
|
m2.Elem(i, k) -= m2.Elem(i, j) * m2.Elem(j, k);
|
|
m2.Elem(j, k) *= -hr;
|
|
}
|
|
}
|
|
|
|
// col exchange
|
|
|
|
for (i = 1; i <= n; i++)
|
|
{
|
|
for (k = 1; k <= n; k++)
|
|
hv.Elem(p.Get(k)) = m2.Get(i, k);
|
|
for (k = 1; k <= n; k++)
|
|
m2.Elem(i, k) = hv.Get(k);
|
|
}
|
|
|
|
|
|
|
|
/*
|
|
if (m1.Symmetric())
|
|
for (i = 1; i <= n; i++)
|
|
for (j = 1; j < i; j++)
|
|
m1.Elem(j, i) = m1.Get(i, j);
|
|
|
|
m2 = 0;
|
|
|
|
for (i = 1; i <= n; i++)
|
|
m2.Elem(i, i) = 1;
|
|
|
|
for (i = 1; i <= n; i++)
|
|
{
|
|
// (*mycout) << '.' << flush;
|
|
q = m1.Get(i, i);
|
|
for (k = 1; k <= n; k++)
|
|
{
|
|
m1.Elem(i, k) /= q;
|
|
m2.Elem(i, k) /= q;
|
|
}
|
|
|
|
for (j = i+1; j <= n; j++)
|
|
{
|
|
q = m1.Elem(j, i);
|
|
|
|
double * m1pi = &m1.Elem(i, i);
|
|
double * m1pj = &m1.Elem(j, i);
|
|
|
|
for (k = n; k >= i; --k, ++m1pi, ++m1pj)
|
|
*m1pj -= q * (*m1pi);
|
|
|
|
double * m2pi = &m2.Elem(i, 1);
|
|
double * m2pj = &m2.Elem(j, 1);
|
|
|
|
for (k = i; k > 0; --k, ++m2pi, ++m2pj)
|
|
*m2pj -= q * (*m2pi);
|
|
|
|
// for (k = 1; k <= n; k++)
|
|
// {
|
|
// m1.Elem(j, k) -= q * m1.Elem(i, k);
|
|
// m2.Elem(j, k) -= q * m2.Elem(i, k);
|
|
// }
|
|
|
|
}
|
|
}
|
|
|
|
for (i = n; i >= 1; i--)
|
|
{
|
|
// (*mycout) << "+" << flush;
|
|
for (j = 1; j < i; j++)
|
|
{
|
|
q = m1.Elem(j, i);
|
|
|
|
double * m2pi = &m2.Elem(i, 1);
|
|
double * m2pj = &m2.Elem(j, 1);
|
|
|
|
for (k = n; k > 0; --k, ++m2pi, ++m2pj)
|
|
*m2pj -= q * (*m2pi);
|
|
|
|
|
|
// for (k = 1; k <= n; k++)
|
|
// {
|
|
// m1.Elem(j, k) -= q * m1.Elem(i, k);
|
|
// m2.Elem(j, k) -= q * m2.Elem(i, k);
|
|
// }
|
|
}
|
|
}
|
|
|
|
if (m2.Symmetric())
|
|
{
|
|
for (i = 1; i <= n; i++)
|
|
for (j = 1; j < i; j++)
|
|
m2.Elem(i, j) = m2.Elem(j, i);
|
|
}
|
|
*/
|
|
}
|
|
}
|
|
|
|
|
|
void CalcAAt (const DenseMatrix & a, DenseMatrix & m2)
|
|
{
|
|
int n1 = a.Height();
|
|
int n2 = a.Width();
|
|
int i, j, k;
|
|
double sum;
|
|
const double *p, *q, *p0;
|
|
|
|
if (m2.Height() != n1 || m2.Width() != n1)
|
|
{
|
|
(*myerr) << "CalcAAt: sizes don't fit" << endl;
|
|
return;
|
|
}
|
|
|
|
for (i = 1; i <= n1; i++)
|
|
{
|
|
sum = 0;
|
|
p = &a.ConstElem(i, 1);
|
|
for (k = 1; k <= n2; k++)
|
|
{
|
|
sum += *p * *p;
|
|
p++;
|
|
}
|
|
m2.Set(i, i, sum);
|
|
|
|
p0 = &a.ConstElem(i, 1);
|
|
q = a.data;
|
|
for (j = 1; j < i; j++)
|
|
{
|
|
sum = 0;
|
|
p = p0;
|
|
|
|
for (k = 1; k <= n2; k++)
|
|
{
|
|
sum += *p * *q;
|
|
p++;
|
|
q++;
|
|
}
|
|
m2.Set(i, j, sum);
|
|
m2.Set(j, i, sum);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
|
|
#ifdef ABC
|
|
BaseMatrix * DenseMatrix :: InverseMatrix (const BitArray * /* inner */) const
|
|
{
|
|
if (Height() != Width())
|
|
{
|
|
(*myerr) << "BaseMatrix::InverseMatrix(): Matrix not symmetric" << endl;
|
|
return new DenseMatrix(1);
|
|
}
|
|
else
|
|
{
|
|
if (Symmetric())
|
|
{
|
|
(*mycout) << "Invmat not available" << endl;
|
|
BaseMatrix * invmat = NULL;
|
|
return invmat;
|
|
}
|
|
|
|
DenseMatrix * invmat = new DenseMatrix (Height());
|
|
|
|
CalcInverse (*this, *invmat);
|
|
return invmat;
|
|
}
|
|
}
|
|
#endif
|
|
|
|
|
|
|
|
void CalcAtA (const DenseMatrix & a, DenseMatrix & m2)
|
|
{
|
|
int n1 = a.Height();
|
|
int n2 = a.Width();
|
|
int i, j, k;
|
|
double sum;
|
|
|
|
if (m2.Height() != n2 || m2.Width() != n2)
|
|
{
|
|
(*myerr) << "CalcAtA: sizes don't fit" << endl;
|
|
return;
|
|
}
|
|
|
|
for (i = 1; i <= n2; i++)
|
|
for (j = 1; j <= n2; j++)
|
|
{
|
|
sum = 0;
|
|
for (k = 1; k <= n1; k++)
|
|
sum += a.Get(k, i) * a.Get(k, j);
|
|
m2.Elem(i, j) = sum;
|
|
}
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
void CalcABt (const DenseMatrix & a, const DenseMatrix & b, DenseMatrix & m2)
|
|
{
|
|
int n1 = a.Height();
|
|
int n2 = a.Width();
|
|
int n3 = b.Height();
|
|
int i, j, k;
|
|
double sum;
|
|
|
|
if (m2.Height() != n1 || m2.Width() != n3 || b.Width() != n2)
|
|
{
|
|
(*myerr) << "CalcABt: sizes don't fit" << endl;
|
|
return;
|
|
}
|
|
|
|
double * pm2 = &m2.Elem(1, 1);
|
|
const double * pa1 = &a.Get(1, 1);
|
|
|
|
for (i = 1; i <= n1; i++)
|
|
{
|
|
const double * pb = &b.Get(1, 1);
|
|
for (j = 1; j <= n3; j++)
|
|
{
|
|
sum = 0;
|
|
const double * pa = pa1;
|
|
|
|
for (k = 1; k <= n2; k++)
|
|
{
|
|
sum += *pa * *pb;
|
|
pa++; pb++;
|
|
}
|
|
|
|
*pm2 = sum;
|
|
pm2++;
|
|
}
|
|
pa1 += n2;
|
|
}
|
|
}
|
|
|
|
|
|
void CalcAtB (const DenseMatrix & a, const DenseMatrix & b, DenseMatrix & m2)
|
|
{
|
|
int n1 = a.Height();
|
|
int n2 = a.Width();
|
|
int n3 = b.Width();
|
|
int i, j, k;
|
|
|
|
if (m2.Height() != n2 || m2.Width() != n3 || b.Height() != n1)
|
|
{
|
|
(*myerr) << "CalcAtB: sizes don't fit" << endl;
|
|
return;
|
|
}
|
|
|
|
for (i = 1; i <= n2 * n3; i++)
|
|
m2.data[i-1] = 0;
|
|
|
|
for (i = 1; i <= n1; i++)
|
|
for (j = 1; j <= n2; j++)
|
|
{
|
|
const double va = a.Get(i, j);
|
|
double * pm2 = &m2.Elem(j, 1);
|
|
const double * pb = &b.Get(i, 1);
|
|
|
|
for (k = 1; k <= n3; ++k, ++pm2, ++pb)
|
|
*pm2 += va * *pb;
|
|
// for (k = 1; k <= n3; k++)
|
|
// m2.Elem(j, k) += va * b.Get(i, k);
|
|
}
|
|
/*
|
|
for (i = 1; i <= n2; i++)
|
|
for (j = 1; j <= n3; j++)
|
|
{
|
|
sum = 0;
|
|
for (k = 1; k <= n1; k++)
|
|
sum += a.Get(k, i) * b.Get(k, j);
|
|
m2.Elem(i, j) = sum;
|
|
}
|
|
*/
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
DenseMatrix operator* (const DenseMatrix & m1, const DenseMatrix & m2)
|
|
{
|
|
DenseMatrix temp (m1.Height(), m2.Width());
|
|
|
|
if (m1.Width() != m2.Height())
|
|
{
|
|
(*myerr) << "DenseMatrix :: operator*: Matrix Size does not fit" << endl;
|
|
}
|
|
else if (temp.Height() != m1.Height())
|
|
{
|
|
(*myerr) << "DenseMatrix :: operator*: temp not allocated" << endl;
|
|
}
|
|
else
|
|
{
|
|
Mult (m1, m2, temp);
|
|
}
|
|
return temp;
|
|
}
|
|
|
|
|
|
void Mult (const DenseMatrix & m1, const DenseMatrix & m2, DenseMatrix & m3)
|
|
{
|
|
double sum;
|
|
double *p1, *p1s, *p1sn, *p1snn, *p2, *p2s, *p2sn, *p3;
|
|
|
|
if (m1.Width() != m2.Height() || m1.Height() != m3.Height() ||
|
|
m2.Width() != m3.Width() )
|
|
{
|
|
(*myerr) << "DenseMatrix :: Mult: Matrix Size does not fit" << endl;
|
|
(*myerr) << "m1: " << m1.Height() << " x " << m1.Width() << endl;
|
|
(*myerr) << "m2: " << m2.Height() << " x " << m2.Width() << endl;
|
|
(*myerr) << "m3: " << m3.Height() << " x " << m3.Width() << endl;
|
|
return;
|
|
}
|
|
/*
|
|
else if (m1.Symmetric() || m2.Symmetric() || m3.Symmetric())
|
|
{
|
|
(*myerr) << "DenseMatrix :: Mult: not implemented for symmetric matrices" << endl;
|
|
return;
|
|
}
|
|
*/
|
|
else
|
|
{
|
|
// int i, j, k;
|
|
int n1 = m1.Height();
|
|
int n2 = m2.Width();
|
|
int n3 = m1.Width();
|
|
|
|
/*
|
|
for (i = n1 * n2-1; i >= 0; --i)
|
|
m3.data[i] = 0;
|
|
|
|
const double * pm1 = &m1.Get(1, 1);
|
|
for (i = 1; i <= n1; i++)
|
|
{
|
|
const double * pm2 = &m2.Get(1, 1);
|
|
double * pm3i = &m3.Elem(i, 1);
|
|
|
|
for (j = 1; j <= n3; j++)
|
|
{
|
|
const double vm1 = *pm1;
|
|
++pm1;
|
|
// const double vm1 = m1.Get(i, j);
|
|
double * pm3 = pm3i;
|
|
// const double * pm2 = &m2.Get(j, 1);
|
|
|
|
for (k = 0; k < n2; k++)
|
|
{
|
|
*pm3 += vm1 * *pm2;
|
|
++pm2;
|
|
++pm3;
|
|
}
|
|
|
|
// for (k = 1; k <= n2; k++)
|
|
// m3.Elem(i, k) += m1.Get(i, j) * m2.Get(j, k);
|
|
}
|
|
}
|
|
*/
|
|
|
|
/*
|
|
for (i = 1; i <= n1; i++)
|
|
for (j = 1; j <= n2; j++)
|
|
{
|
|
sum = 0;
|
|
for (k = 1; k <= n3; k++)
|
|
sum += m1.Get(i, k) * m2.Get(k, j);
|
|
m3.Set(i, j, sum);
|
|
}
|
|
*/
|
|
|
|
|
|
/*
|
|
for (i = 1; i <= n1; i++)
|
|
{
|
|
const double pm1i = &m1.Get(i, 1);
|
|
const double pm2j = &m2.Get(1, 1);
|
|
|
|
for (j = 1; j <= n2; j++)
|
|
{
|
|
double sum = 0;
|
|
const double * pm1 = pm1i;
|
|
const double * pm2 = pm2j;
|
|
pm2j++;
|
|
|
|
for (k = 1; k <= n3; k++)
|
|
{
|
|
sum += *pm1 * *pm2;
|
|
++pm1;
|
|
pm2 += n2;
|
|
}
|
|
|
|
m3.Set (i, j, sum);
|
|
}
|
|
}
|
|
*/
|
|
|
|
|
|
p3 = m3.data;
|
|
p1s = m1.data;
|
|
p2sn = m2.data + n2;
|
|
p1snn = p1s + n1 * n3;
|
|
|
|
while (p1s != p1snn)
|
|
{
|
|
p1sn = p1s + n3;
|
|
p2s = m2.data;
|
|
|
|
while (p2s != p2sn)
|
|
{
|
|
sum = 0;
|
|
p1 = p1s;
|
|
p2 = p2s;
|
|
p2s++;
|
|
|
|
while (p1 != p1sn)
|
|
{
|
|
sum += *p1 * *p2;
|
|
p1++;
|
|
p2 += n2;
|
|
}
|
|
*p3++ = sum;
|
|
}
|
|
p1s = p1sn;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
|
|
DenseMatrix operator+ (const DenseMatrix & m1, const DenseMatrix & m2)
|
|
{
|
|
DenseMatrix temp (m1.Height(), m1.Width());
|
|
int i, j;
|
|
|
|
if (m1.Width() != m2.Width() || m1.Height() != m2.Height())
|
|
{
|
|
(*myerr) << "BaseMatrix :: operator+: Matrix Size does not fit" << endl;
|
|
}
|
|
else if (temp.Height() != m1.Height())
|
|
{
|
|
(*myerr) << "BaseMatrix :: operator+: temp not allocated" << endl;
|
|
}
|
|
else
|
|
{
|
|
for (i = 1; i <= m1.Height(); i++)
|
|
for (j = 1; j <= m1.Width(); j++)
|
|
{
|
|
temp.Set(i, j, m1.Get(i, j) + m2.Get(i, j));
|
|
}
|
|
}
|
|
return temp;
|
|
}
|
|
|
|
|
|
|
|
|
|
void Transpose (const DenseMatrix & m1, DenseMatrix & m2)
|
|
{
|
|
int w = m1.Width();
|
|
int h = m1.Height();
|
|
int i, j;
|
|
|
|
m2.SetSize (w, h);
|
|
|
|
double * pm2 = &m2.Elem(1, 1);
|
|
for (j = 1; j <= w; j++)
|
|
{
|
|
const double * pm1 = &m1.Get(1, j);
|
|
for (i = 1; i <= h; i++)
|
|
{
|
|
*pm2 = *pm1;
|
|
pm2 ++;
|
|
pm1 += w;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
/*
|
|
void DenseMatrix :: Mult (const Vector & v, Vector & prod) const
|
|
{
|
|
double sum, val;
|
|
const double * mp, * sp;
|
|
double * dp;
|
|
// const Vector & v = bv.CastToVector();
|
|
// Vector & prod = bprod.CastToVector();
|
|
|
|
|
|
int n = Height();
|
|
int m = Width();
|
|
|
|
if (prod.Size() != n)
|
|
prod.SetSize (n);
|
|
|
|
#ifdef DEVELOP
|
|
if (!n)
|
|
{
|
|
cout << "DenseMatrix::Mult mheight = 0" << endl;
|
|
}
|
|
if (!m)
|
|
{
|
|
cout << "DenseMatrix::Mult mwidth = 0" << endl;
|
|
}
|
|
|
|
if (m != v.Size())
|
|
{
|
|
(*myerr) << "\nMatrix and Vector don't fit" << endl;
|
|
}
|
|
else if (Height() != prod.Size())
|
|
{
|
|
(*myerr) << "Base_Matrix::operator*(Vector): prod vector not ok" << endl;
|
|
}
|
|
else
|
|
#endif
|
|
{
|
|
if (Symmetric())
|
|
{
|
|
int i, j;
|
|
|
|
|
|
for (i = 1; i <= n; i++)
|
|
{
|
|
sp = &v.Get(1);
|
|
dp = &prod.Elem(1);
|
|
mp = &Get(i, 1);
|
|
|
|
val = v.Get(i);
|
|
sum = Get(i, i) * val;
|
|
|
|
for (j = 1; j < i; ++j, ++mp, ++sp, ++dp)
|
|
{
|
|
sum += *mp * *sp;
|
|
*dp += val * *mp;
|
|
}
|
|
|
|
prod.Elem(i) = sum;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
mp = data;
|
|
dp = &prod.Elem(1);
|
|
for (int i = 1; i <= n; i++)
|
|
{
|
|
sum = 0;
|
|
sp = &v.Get(1);
|
|
|
|
for (int j = 1; j <= m; j++)
|
|
{
|
|
// sum += Get(i,j) * v.Get(j);
|
|
sum += *mp * *sp;
|
|
mp++;
|
|
sp++;
|
|
}
|
|
|
|
// prod.Set (i, sum);
|
|
*dp = sum;
|
|
dp++;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
*/
|
|
|
|
void DenseMatrix :: MultTrans (const Vector & v, Vector & prod) const
|
|
{
|
|
// const Vector & v = (const Vector&)bv; // .CastToVector();
|
|
// Vector & prod = (Vector & )bprod; // .CastToVector();
|
|
|
|
/*
|
|
if (Height() != v.Size())
|
|
{
|
|
(*myerr) << "\nMatrix and Vector don't fit" << endl;
|
|
}
|
|
else if (Width() != prod.Size())
|
|
{
|
|
(*myerr) << "Base_Matrix::operator*(Vector): prod vector not ok" << endl;
|
|
}
|
|
else
|
|
*/
|
|
{
|
|
int i, j;
|
|
int w = Width(), h = Height();
|
|
if (prod.Size() != w)
|
|
prod.SetSize (w);
|
|
|
|
const double * pmat = &Get(1, 1);
|
|
const double * pv = &v.Get(1);
|
|
|
|
prod = 0;
|
|
|
|
for (i = 1; i <= h; i++)
|
|
{
|
|
double val = *pv;
|
|
++pv;
|
|
|
|
double * pprod = &prod.Elem(1);
|
|
|
|
for (j = w-1; j >= 0; --j, ++pmat, ++pprod)
|
|
{
|
|
*pprod += val * *pmat;
|
|
}
|
|
}
|
|
|
|
/*
|
|
double sum;
|
|
|
|
for (i = 1; i <= Width(); i++)
|
|
{
|
|
sum = 0;
|
|
|
|
for (int j = 1; j <= Height(); j++)
|
|
sum += Get(j, i) * v.Get(j);
|
|
|
|
prod.Set (i, sum);
|
|
}
|
|
*/
|
|
}
|
|
}
|
|
|
|
|
|
void DenseMatrix :: Residuum (const Vector & x, const Vector & b,
|
|
Vector & res) const
|
|
{
|
|
double sum;
|
|
// const Vector & x = bx.CastToVector();
|
|
// const Vector & b = bb.CastToVector();
|
|
// Vector & res = bres.CastToVector();
|
|
|
|
res.SetSize (Height());
|
|
|
|
if (Width() != x.Size() || Height() != b.Size())
|
|
{
|
|
(*myerr) << "\nMatrix and Vector don't fit" << endl;
|
|
}
|
|
else if (Height() != res.Size())
|
|
{
|
|
(*myerr) << "Base_Matrix::operator*(Vector): prod vector not ok" << endl;
|
|
}
|
|
else
|
|
{
|
|
int i, j;
|
|
int h = Height();
|
|
int w = Width();
|
|
const double * mp = &Get(1, 1);
|
|
|
|
for (i = 1; i <= h; i++)
|
|
{
|
|
sum = b.Get(i);
|
|
const double * xp = &x.Get(1);
|
|
|
|
for (j = 1; j <= w; ++j, ++mp, ++xp)
|
|
sum -= *mp * *xp;
|
|
|
|
res.Elem(i) = sum;
|
|
}
|
|
}
|
|
}
|
|
|
|
#ifdef ABC
|
|
double DenseMatrix :: EvaluateBilinearform (const Vector & hx) const
|
|
{
|
|
double sum = 0, hsum;
|
|
// const Vector & hx = x.CastToVector();
|
|
int i, j;
|
|
|
|
if (Width() != hx.Size() || Height() != hx.Size())
|
|
{
|
|
(*myerr) << "Matrix::EvaluateBilinearForm: sizes don't fit" << endl;
|
|
}
|
|
else
|
|
{
|
|
for (i = 1; i <= Height(); i++)
|
|
{
|
|
hsum = 0;
|
|
for (j = 1; j <= Height(); j++)
|
|
{
|
|
hsum += Get(i, j) * hx.Get(j);
|
|
}
|
|
sum += hsum * hx.Get(i);
|
|
}
|
|
}
|
|
|
|
// testout << "sum = " << sum << endl;
|
|
return sum;
|
|
}
|
|
|
|
|
|
void DenseMatrix :: MultElementMatrix (const ARRAY<int> & pnum,
|
|
const Vector & hx, Vector & hy)
|
|
{
|
|
int i, j;
|
|
// const Vector & hx = x.CastToVector();
|
|
// Vector & hy = y.CastToVector();
|
|
|
|
if (Symmetric())
|
|
{
|
|
for (i = 1; i <= Height(); i++)
|
|
{
|
|
for (j = 1; j < i; j++)
|
|
{
|
|
hy.Elem(pnum.Get(i)) += Get(i, j) * hx.Get(pnum.Get(j));
|
|
hy.Elem(pnum.Get(j)) += Get(i, j) * hx.Get(pnum.Get(i));
|
|
}
|
|
hy.Elem(pnum.Get(j)) += Get(i, i) * hx.Get(pnum.Get(i));
|
|
}
|
|
}
|
|
else
|
|
for (i = 1; i <= Height(); i++)
|
|
for (j = 1; j <= Width(); j++)
|
|
hy.Elem(pnum.Get(i)) += Get(i, j) * hx.Get(pnum.Get(j));
|
|
|
|
}
|
|
|
|
void DenseMatrix :: MultTransElementMatrix (const ARRAY<int> & pnum,
|
|
const Vector & hx, Vector & hy)
|
|
{
|
|
int i, j;
|
|
// const Vector & hx = x.CastToVector();
|
|
// Vector & hy = y.CastToVector();
|
|
|
|
if (Symmetric())
|
|
MultElementMatrix (pnum, hx, hy);
|
|
else
|
|
for (i = 1; i <= Height(); i++)
|
|
for (j = 1; j <= Width(); j++)
|
|
hy.Elem(pnum.Get(i)) += Get(j, i) * hx.Get(pnum.Get(j));
|
|
}
|
|
#endif
|
|
|
|
|
|
void DenseMatrix :: Solve (const Vector & v, Vector & sol) const
|
|
{
|
|
DenseMatrix temp (*this);
|
|
temp.SolveDestroy (v, sol);
|
|
}
|
|
|
|
|
|
void DenseMatrix :: SolveDestroy (const Vector & v, Vector & sol)
|
|
{
|
|
double q;
|
|
|
|
if (Width() != Height())
|
|
{
|
|
(*myerr) << "SolveDestroy: Matrix not square";
|
|
return;
|
|
}
|
|
if (Width() != v.Size())
|
|
{
|
|
(*myerr) << "SolveDestroy: Matrix and Vector don't fit";
|
|
return;
|
|
}
|
|
|
|
sol = v;
|
|
if (Height() != sol.Size())
|
|
{
|
|
(*myerr) << "SolveDestroy: Solution Vector not ok";
|
|
return;
|
|
}
|
|
|
|
|
|
if (0 /* Symmetric() */)
|
|
{
|
|
|
|
// Cholesky factorization
|
|
|
|
int i, j, k, n;
|
|
n = Height();
|
|
|
|
// Cholesky
|
|
|
|
double x;
|
|
Vector p(n);
|
|
|
|
for (i = 1; i <= n; i++)
|
|
for (j = 1; j < i; j++)
|
|
Elem(j, i) = Get(i, j);
|
|
|
|
for (i = 1; i <= n; i++)
|
|
{
|
|
// (*mycout) << "." << flush;
|
|
for (j = i; j <= n; j++)
|
|
{
|
|
x = Get(i, j);
|
|
|
|
const double * pik = &Get(i, 1);
|
|
const double * pjk = &Get(j, 1);
|
|
|
|
for (k = i-2; k >= 0; --k, ++pik, ++pjk)
|
|
x -= (*pik) * (*pjk);
|
|
|
|
// for (k = i-1; k >= 1; --k)
|
|
// x -= Get(j, k) * Get(i, k);
|
|
|
|
if (i == j)
|
|
{
|
|
if (x <= 0)
|
|
{
|
|
cerr << "Matrix indefinite" << endl;
|
|
return;
|
|
}
|
|
|
|
p.Elem(i) = 1 / sqrt(x);
|
|
}
|
|
else
|
|
{
|
|
Elem(j, i) = x * p.Get(i);
|
|
}
|
|
}
|
|
}
|
|
|
|
for (i = 1; i <= n; i++)
|
|
Elem(i, i) = 1 / p.Get(i);
|
|
|
|
// A = L L^t
|
|
// L stored in left-lower triangle
|
|
|
|
|
|
sol = v;
|
|
|
|
// Solve L sol = sol
|
|
|
|
for (i = 1; i <= n; i++)
|
|
{
|
|
double val = sol.Get(i);
|
|
|
|
const double * pij = &Get(i, 1);
|
|
const double * solj = &sol.Get(1);
|
|
|
|
for (j = 1; j < i; j++, ++pij, ++solj)
|
|
val -= *pij * *solj;
|
|
// for (j = 1; j < i; j++)
|
|
// val -= Get(i, j) * sol.Get(j);
|
|
|
|
sol.Elem(i) = val / Get(i, i);
|
|
}
|
|
|
|
// Solve L^t sol = sol
|
|
|
|
for (i = n; i >= 1; i--)
|
|
{
|
|
double val = sol.Get(i) / Get(i, i);
|
|
sol.Elem(i) = val;
|
|
|
|
double * solj = &sol.Elem(1);
|
|
const double * pij = &Get(i, 1);
|
|
|
|
for (j = 1; j < i; ++j, ++pij, ++solj)
|
|
*solj -= val * *pij;
|
|
// for (j = 1; j < i; j++)
|
|
// sol.Elem(j) -= Get(i, j) * val;
|
|
}
|
|
|
|
|
|
}
|
|
else
|
|
{
|
|
// (*mycout) << "gauss" << endl;
|
|
int i, j, k, n = Height();
|
|
for (i = 1; i <= n; i++)
|
|
{
|
|
for (j = i+1; j <= n; j++)
|
|
{
|
|
q = Get(j,i) / Get(i,i);
|
|
if (q)
|
|
{
|
|
const double * pik = &Get(i, i+1);
|
|
double * pjk = &Elem(j, i+1);
|
|
|
|
for (k = i+1; k <= n; ++k, ++pik, ++pjk)
|
|
*pjk -= q * *pik;
|
|
|
|
// for (k = i+1; k <= Height(); k++)
|
|
// Elem(j, k) -= q * Get(i,k);
|
|
|
|
|
|
sol.Elem(j) -= q * sol.Get(i);
|
|
}
|
|
}
|
|
}
|
|
|
|
for (i = n; i >= 1; i--)
|
|
{
|
|
q = sol.Get(i);
|
|
for (j = i+1; j <= n; j++)
|
|
q -= Get(i,j) * sol.Get(j);
|
|
|
|
sol.Elem(i) = q / Get(i,i);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
/*
|
|
BaseMatrix * DenseMatrix :: Copy () const
|
|
{
|
|
return new DenseMatrix (*this);
|
|
}
|
|
*/
|
|
|
|
|
|
|
|
|
|
ostream & operator<< (ostream & ost, const DenseMatrix & m)
|
|
{
|
|
for (int i = 0; i < m.Height(); i++)
|
|
{
|
|
for (int j = 0; j < m.Width(); j++)
|
|
ost << m.Get(i+1,j+1) << " ";
|
|
ost << endl;
|
|
}
|
|
return ost;
|
|
}
|
|
|
|
|
|
|
|
}
|