/// \ingroup newmat
///@{
/// \file tmt9.cpp
/// Part of matrix library test program.
//#define WANT_STREAM
#include "include.h"
#include "newmatap.h"
#include "tmt.h"
#ifdef use_namespace
using namespace NEWMAT;
#endif
/**************************** test program ******************************/
void trymat9()
{
Tracer et("Ninth test of Matrix package");
Tracer::PrintTrace();
int i; int j;
Matrix A(7,7); Matrix X(7,3);
for (i=1;i<=7;i++) for (j=1;j<=7;j++) A(i,j)=i*i+j+((i==j) ? 1 : 0);
for (i=1;i<=7;i++) for (j=1;j<=3;j++) X(i,j)=i-j;
Matrix B = A.i(); DiagonalMatrix D(7); D=1.0;
{
Tracer et1("Stage 1");
Matrix Q = B*A-D; Clean(Q, 0.000000001); Print(Q);
Q=A; Q = Q.i() * X; Q = A*Q - X; Clean(Q, 0.000000001); Print(Q);
Q=X; Q = A.i() * Q; Q = A*Q - X; Clean(Q, 0.000000001); Print(Q);
}
for (i=1;i<=7;i++) D(i,i)=i*i+1;
DiagonalMatrix E(3); for (i=1;i<=3;i++) E(i,i)=i+23;
{
Tracer et1("Stage 2");
Matrix DXE = D.i() * X * E;
DXE = E.i() * DXE.t() * D - X.t(); Clean(DXE, 0.00000001); Print(DXE);
E=D; for (i=1;i<=7;i++) E(i,i)=i*3+1;
}
DiagonalMatrix F=D;
{
Tracer et1("Stage 3");
F=E.i()*F; F=F*E-D; Clean(F,0.00000001); Print(F);
F=E.i()*D; F=F*E-D; Clean(F,0.00000001); Print(F);
}
{
Tracer et1("Stage 4");
F=E; F=F.i()*D; F=F*E-D; Clean(F,0.00000001); Print(F);
}
{
Tracer et1("Stage 5");
// testing equal
ColumnVector A(18), B(18);
Matrix X(3,3);
X << 3 << 5 << 7 << 5 << 8 << 2 << 7 << 2 << 9;
SymmetricMatrix S; S << X;
B(1) = S == X; A(1) = true;
B(2) = S == (X+1); A(2) = false;
B(3) = (S+2) == (X+2); A(3) = true;
Matrix Y = X;
B(4) = X == Y; A(4) = true;
B(5) = (X*2) == (Y*2); A(5) = true;
Y(3,3) = 10;
B(6) = X == Y; A(6) = false;
B(7) = (X*2) == (Y*2); A(7) = false;
B(8) = S == Y; A(8) = false;
B(9) = S == S; A(9) = true;
Matrix Z = X.SubMatrix(1,2,2,3);
B(10) = X == Z; A(10) = false;
GenericMatrix GS = S;
GenericMatrix GX = X;
GenericMatrix GY = Y;
B(11) = GS == GX; A(11) = true;
B(12) = GS == GY; A(12) = false;
CroutMatrix CS = S;
CroutMatrix CX = X;
CroutMatrix CY = Y;
B(13) = CS == CX; A(13) = true;
B(14) = CS == CY; A(14) = false;
B(15) = X == CX; A(15) = false;
B(16) = X == A; A(16) = false;
B(17) = X == (X | X); A(17) = false;
B(18) = CX == X; A(18) = false;
A = A - B; Print(A);
}
{
Tracer et1("Stage 6");
// testing equal
ColumnVector A(22), B(22);
BandMatrix X(6,2,1);
X(1,1)=23; X(1,2)=21;
X(2,1)=12; X(2,2)=17; X(2,3)=45;
X(3,1)=35; X(3,2)=19; X(3,3)=24; X(3,4)=29;
X(4,2)=17; X(4,3)=11; X(4,4)=19; X(4,5)=35;
X(5,3)=10; X(5,4)=44; X(5,5)=23; X(5,6)=31;
X(6,4)=49; X(6,5)=41; X(6,6)=17;
SymmetricBandMatrix S1(6,2); S1.Inject(X);
BandMatrix U(6,2,3); U = 0.0; U.Inject(X);
B(1) = U == X; A(1) = true;
B(2) = U == (X*3); A(2) = false;
B(3) = (U*5) == (X*5); A(3) = true;
Matrix Y = X;
B(4) = X == Y; A(4) = true;
B(5) = (X*2) == (Y*2); A(5) = true;
Y(6,6) = 10;
B(6) = X == Y; A(6) = false;
B(7) = (X*2) == (Y*2); A(7) = false;
B(8) = U == Y; A(8) = false;
B(9) = U == U; A(9) = true;
Matrix Z = X.SubMatrix(1,2,2,3);
B(10) = X == Z; A(10) = false;
GenericMatrix GU = U;
GenericMatrix GX = X;
GenericMatrix GY = Y;
B(11) = GU == GX; A(11) = true;
B(12) = GU == GY; A(12) = false;
X = X + X.t(); U = U + U.t();
SymmetricBandMatrix S(6,2); S.Inject(X);
Matrix D = S-X; Print(D);
BandLUMatrix BS = S;
BandLUMatrix BX = X;
BandLUMatrix BU = U;
CroutMatrix CX = X;
B(13) = BS == BX; A(13) = true;
B(14) = BX == BU; A(14) = false;
B(15) = X == BX; A(15) = false;
B(16) = X != BX; A(16) = true;
B(17) = BX != BS; A(17) = false;
B(18) = (2*X) != (X*2);A(18) = false;
B(19) = (X*2) != (X+2);A(19) = true;
B(20) = BX == CX; A(20) = false;
B(21) = CX == BX; A(21) = false;
B(22) = BX == X; A(22) = false;
A = A - B; Print(A);
DiagonalMatrix I(6); I=1.0;
D = BS.i() * X - I; Clean(D,0.00000001); Print(D);
D = BX.i() * X - I; Clean(D,0.00000001); Print(D);
D = BU.i() * X - I; Clean(D,0.00000001); Print(D);
// test row wise load
SymmetricBandMatrix X1(6,2);
X1.Row(1) << 23;
X1.Row(2) << 12 << 17;
X1.Row(3) << 35 << 19 << 24;
X1.Row(4) << 17 << 11 << 19;
X1.Row(5) << 10 << 44 << 23;
X1.Row(6) << 49 << 41 << 17;
Matrix M = X1 - S1; Print(M);
// check out submatrix
SymmetricBandMatrix X2(20,3); X2 = 0.0;
X2.SubMatrix(2,7,2,7) = X1; X2.SymSubMatrix(11,16) = 2 * X1;
Matrix MX1 = X1;
Matrix MX2(20,20); MX2 = 0;
MX2.SymSubMatrix(2,7) = MX1; MX2.SubMatrix(11,16,11,16) = MX1 * 2;
MX2 -= X2; Print(MX2);
BandMatrix X4(20,3,3); X4 = 0.0;
X4.SubMatrix(2,7,3,8) = X1; X4.SubMatrix(11,16,10,15) = 2 * X1;
MX1 = X1;
Matrix MX4(20,20); MX4 = 0;
MX4.SubMatrix(2,7,3,8) = MX1; MX4.SubMatrix(11,16,10,15) = MX1 * 2;
MX4 -= X4; Print(MX4);
MX1 = X1.i() * X1 - IdentityMatrix(6);
Clean(MX1,0.00000001); Print(MX1);
}
{
Tracer et1("Stage 7");
// testing equal
ColumnVector A(12), B(12);
BandMatrix X(6,2,1);
X(1,1)=23; X(1,2)=21;
X(2,1)=12; X(2,2)=17; X(2,3)=45;
X(3,1)=35; X(3,2)=19; X(3,3)=24; X(3,4)=29;
X(4,2)=17; X(4,3)=11; X(4,4)=19; X(4,5)=35;
X(5,3)=10; X(5,4)=44; X(5,5)=23; X(5,6)=31;
X(6,4)=49; X(6,5)=41; X(6,6)=17;
Matrix Y = X;
LinearEquationSolver LX = X;
LinearEquationSolver LY = Y;
CroutMatrix CX = X;
CroutMatrix CY = Y;
BandLUMatrix BX = X;
B(1) = LX == CX; A(1) = false;
B(2) = LY == CY; A(2) = true;
B(3) = X == Y; A(3) = true;
B(4) = BX == LX; A(4) = true;
B(5) = CX == CY; A(5) = true;
B(6) = LX == LY; A(6) = false;
B(7) = BX == BX; A(7) = true;
B(8) = CX == CX; A(8) = true;
B(9) = LX == LX; A(9) = true;
B(10) = LY == LY; A(10) = true;
CroutMatrix CX1 = X.SubMatrix(1,4,1,4);
B(11) = CX == CX1; A(11) = false;
BandLUMatrix BX1 = X.SymSubMatrix(1,4); // error with SubMatrix
B(12) = BX == BX1; A(12) = false;
A = A - B; Print(A);
DiagonalMatrix I(6); I=1.0; Matrix D;
D = LX.i() * X - I; Clean(D,0.00000001); Print(D);
D = LY.i() * X - I; Clean(D,0.00000001); Print(D);
I.ReSize(4); I = 1;
D = CX1.i() * X.SymSubMatrix(1,4) - I; Clean(D,0.00000001); Print(D);
D = BX1.i() * X.SubMatrix(1,4,1,4) - I; Clean(D,0.00000001); Print(D);
}
{
Tracer et1("Stage 8");
// test copying CroutMatrix and BandLUMatrix - see also tmtd.cpp
MultWithCarry MWC;
SymmetricBandMatrix SBM(50, 10);
for (int i = 1; i <= 50; ++i) for (int j = 1; j <= i; ++j)
if (i - j <= 10) SBM(i, j) = MWC.Next();
CroutMatrix CM = SBM; BandLUMatrix BM = SBM;
CroutMatrix CM1 = CM; BandLUMatrix BM1; BM1 = BM;
CM1.release(); BM1.release();
CroutMatrix CM2; CM2 = CM1; BandLUMatrix BM2 = BM1;
Matrix X = SBM.i(); Matrix Y = CM2.i() - X; Matrix Z = BM2.i() - X;
Clean(Y,0.00000001); Print(Y); Clean(Z,0.00000001); Print(Z);
X *= SBM; X -= IdentityMatrix(50); Clean(X,0.00000001); Print(X);
LogAndSign x = log_determinant(SBM);
LogAndSign y = log_determinant(CM2);
LogAndSign z = log_determinant(BM2);
RowVector D(4);
D(1) = y.value() - x.value();
D(2) = z.value() - x.value();
D(3) = y.sign() - x.sign();
D(4) = z.sign() - x.sign();
Clean(D,0.00000001); Print(D);
}
{
Tracer et1("Stage 9");
// do it again odd matrix size
MultWithCarry MWC;
SymmetricBandMatrix SBM(51, 10);
for (int i = 1; i <= 51; ++i) for (int j = 1; j <= i; ++j)
if (i - j <= 10) SBM(i, j) = MWC.Next();
CroutMatrix CM = SBM; BandLUMatrix BM = SBM;
CroutMatrix CM1 = CM; BandLUMatrix BM1; BM1 = BM;
CM1.release(); BM1.release();
CroutMatrix CM2; CM2 = CM1; BandLUMatrix BM2 = BM1;
Matrix X = SBM.i(); Matrix Y = CM2.i() - X; Matrix Z = BM2.i() - X;
Clean(Y,0.00000001); Print(Y); Clean(Z,0.00000001); Print(Z);
X *= SBM; X -= IdentityMatrix(51); Clean(X,0.00000001); Print(X);
LogAndSign x = log_determinant(SBM);
LogAndSign y = log_determinant(CM2);
LogAndSign z = log_determinant(BM2);
RowVector D(4);
D(1) = y.value() - x.value();
D(2) = z.value() - x.value();
D(3) = y.sign() - x.sign();
D(4) = z.sign() - x.sign();
Clean(D,0.00000001); Print(D);
}
// cout << "\nEnd of ninth test\n";
}
///@}
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