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#define WANT_STREAM
#define WANT_MATH
#include "newmat.h"
#include "tmt.h"
#ifdef use_namespace
using namespace NEWMAT;
#endif
// test maxima and minima
Real TestMax(const GenericMatrix& GM)
{
Matrix M = GM;
ColumnVector CV = GM.AsColumn();
int c, i, j, k; int n = CV.Nrows(), nr = M.Nrows(), nc = M.Ncols();
Real x1, x2, x3;
MatrixBandWidth mbw = GM.BandWidth();
int u = mbw.Upper(); int l = mbw.Lower();
bool IsBandMatrix = u > 0 && l > 0 && !(u == 0 && l == 0);
x1 = GM.MaximumAbsoluteValue();
x2 = GM.MaximumAbsoluteValue1(i);
if (fabs(CV(i)) != x2) return 1.1;
x3 = GM.MaximumAbsoluteValue2(i,j);
if (fabs(M(i,j)) != x3) return 1.2;
if (x3 != x1) return 1.3;
if (x2 != x1) return 1.4;
c = 0;
for (k = 1; k <= n; k++)
{
Real cvk = fabs(CV(k));
if (x1 <= cvk) { if (x1 < cvk) return 1.5; else c++; }
}
if (c == 0) return 1.6;
x1 = GM.MinimumAbsoluteValue();
x2 = GM.MinimumAbsoluteValue1(i);
if (fabs(CV(i)) != x2) return 2.1;
x3 = GM.MinimumAbsoluteValue2(i,j);
if (fabs(M(i,j)) != x3) return 2.2;
if (x3 != x1) return 2.3;
if (x2 != CV.MinimumAbsoluteValue()) return 2.4;
c = 0;
if (IsBandMatrix)
{
for (i = 1; i <= nr; i++) for (j = 1; j <= nc; j++)
if (i - j <= l && j - i <= u)
{
Real mij = fabs(M(i,j));
if (x1 >= mij) { if (x1 > mij) return 2.51; else c++; }
}
}
else
{
for (k = 1; k <= n; k++)
{
Real cvk = fabs(CV(k));
if (x1 >= cvk) { if (x1 > cvk) return 2.52; else c++; }
}
}
if (c == 0) return 2.6;
x1 = GM.Maximum();
x2 = GM.Maximum1(i);
if (CV(i) != x2) return 3.1;
x3 = GM.Maximum2(i,j);
if (M(i,j) != x3) return 3.2;
if (x3 != x1) return 3.3;
if (x2 != CV.Maximum()) return 3.4;
c = 0;
if (IsBandMatrix)
{
for (i = 1; i <= nr; i++) for (j = 1; j <= nc; j++)
if (i - j <= l && j - i <= u)
{
Real mij = M(i,j);
if (x1 <= mij) { if (x1 < mij) return 3.51; else c++; }
}
}
else
{
for (k = 1; k <= n; k++)
{
Real cvk = CV(k);
if (x1 <= cvk) { if (x1 < cvk) return 3.52; else c++; }
}
}
if (c == 0) return 3.6;
x1 = GM.Minimum();
x2 = GM.Minimum1(i);
if (CV(i) != x2) return 4.1;
x3 = GM.Minimum2(i,j);
if (M(i,j) != x3) return 4.2;
if (x3 != x1) return 4.3;
if (x2 != CV.Minimum()) return 4.4;
c = 0;
if (IsBandMatrix)
{
for (i = 1; i <= nr; i++) for (j = 1; j <= nc; j++)
if (i - j <= l && j - i <= u)
{
Real mij = M(i,j);
if (x1 >= mij) { if (x1 > mij) return 4.51; else c++; }
}
}
else
{
for (k = 1; k <= n; k++)
{
Real cvk = CV(k);
if (x1 >= cvk) { if (x1 > cvk) return 4.52; else c++; }
}
}
if (c == 0) return 4.6;
return 0;
}
void trymatl()
{
Tracer et("Twenty first test of Matrix package");
Tracer::PrintTrace();
Matrix M(4, 4);
M << 1.5 << 1.0 << -4.0 << 4.5
<< 3.5 << 7.0 << 2.0 << -1.0
<< -1.5 << 7.5 << -6.0 << 5.0
<< 0.5 << -8.0 << 5.5 << 4.0;
UpperTriangularMatrix UM; UM << M;
LowerTriangularMatrix LM; LM << -M;
SymmetricMatrix SM; SM << (UM + UM.t());
BandMatrix BM(4, 1, 2); BM.Inject(M);
DiagonalMatrix DM; DM << M;
SymmetricBandMatrix SBM(4,1); SBM.Inject(M);
RowVector Test(28); int k = 0;
// tests for different shapes
Test(++k) = TestMax(GenericMatrix(M));
Test(++k) = TestMax(GenericMatrix(UM));
Test(++k) = TestMax(GenericMatrix(LM));
Test(++k) = TestMax(GenericMatrix(SM));
Test(++k) = TestMax(GenericMatrix(DM));
Test(++k) = TestMax(GenericMatrix(BM));
Test(++k) = TestMax(GenericMatrix(SBM));
// tests for constant matrices - don't put non-zeros in corners of BM
Matrix MX(4,4);
MX = 1; Test(++k) = TestMax(GenericMatrix(MX));
BM.Inject(MX); Test(++k) = TestMax(GenericMatrix(BM));
MX = 0; Test(++k) = TestMax(GenericMatrix(MX));
BM.Inject(MX); Test(++k) = TestMax(GenericMatrix(BM));
MX = -1; Test(++k) = TestMax(GenericMatrix(MX));
BM.Inject(MX); Test(++k) = TestMax(GenericMatrix(BM));
// test for non-square
MX = M | (2 * M).t(); Test(++k) = TestMax(GenericMatrix(MX));
// test on row and column vector
RowVector RV(6);
RV << 1 << 3 << -5 << 2 << -4 << 3;
Test(++k) = TestMax(GenericMatrix(RV));
Test(++k) = TestMax(GenericMatrix(RV.t()));
// test for function form
Test(++k) = (MaximumAbsoluteValue(RV) - 5);
Test(++k) = (MinimumAbsoluteValue(RV) - 1);
Test(++k) = (Maximum(RV) - 3);
Test(++k) = (Minimum(RV) + 5);
Test(++k) = (MaximumAbsoluteValue(-RV) - 5);
Test(++k) = (MinimumAbsoluteValue(-RV) - 1);
Test(++k) = (Maximum(-RV) - 5);
Test(++k) = (Minimum(-RV) + 3);
// test formulae
RowVector RV2(6);
RV2 << 2 << 8 << 1 << 9 << 3 << -1;
Test(++k) = (MaximumAbsoluteValue(RV+RV2) - 11);
Test(++k) = (MinimumAbsoluteValue(RV+RV2) - 1);
Test(++k) = (Maximum(RV+RV2) - 11);
Test(++k) = (Minimum(RV+RV2) + 4);
Print(Test);
}
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