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//#define WANT_STREAM
#include "include.h"
#include "config.h"
#include "newmatap.h"
#include "tmt.h"
#ifdef use_namespace
using namespace NEWMAT;
#endif
ReturnMatrix Inverter(const CroutMatrix& X)
{
Matrix Y = X.i();
Y.Release();
return Y.ForReturn();
}
void trymatd()
{
Tracer et("Thirteenth test of Matrix package");
Tracer::PrintTrace();
Matrix X(5,20);
int i,j;
for (j=1;j<=20;j++) X(1,j) = j+1;
for (i=2;i<=5;i++) for (j=1;j<=20; j++) X(i,j) = (long)X(i-1,j) * j % 1001;
SymmetricMatrix S; S << X * X.t();
Matrix SM = X * X.t() - S;
Print(SM);
LowerTriangularMatrix L = Cholesky(S);
Matrix Diff = L*L.t()-S; Clean(Diff, 0.000000001);
Print(Diff);
{
Tracer et1("Stage 1");
LowerTriangularMatrix L1(5);
Matrix Xt = X.t(); Matrix Xt2 = Xt;
QRZT(X,L1);
Diff = L - L1; Clean(Diff,0.000000001); Print(Diff);
UpperTriangularMatrix Ut(5);
QRZ(Xt,Ut);
Diff = L - Ut.t(); Clean(Diff,0.000000001); Print(Diff);
Matrix Y(3,20);
for (j=1;j<=20;j++) Y(1,j) = 22-j;
for (i=2;i<=3;i++) for (j=1;j<=20; j++)
Y(i,j) = (long)Y(i-1,j) * j % 101;
Matrix Yt = Y.t(); Matrix M,Mt; Matrix Y2=Y;
QRZT(X,Y,M); QRZ(Xt,Yt,Mt);
Diff = Xt - X.t(); Clean(Diff,0.000000001); Print(Diff);
Diff = Yt - Y.t(); Clean(Diff,0.000000001); Print(Diff);
Diff = Mt - M.t(); Clean(Diff,0.000000001); Print(Diff);
Diff = Y2 * Xt2 * S.i() - M * L.i();
Clean(Diff,0.000000001); Print(Diff);
}
ColumnVector C1(5);
{
Tracer et1("Stage 2");
X.ReSize(5,5);
for (j=1;j<=5;j++) X(1,j) = j+1;
for (i=2;i<=5;i++) for (j=1;j<=5; j++)
X(i,j) = (long)X(i-1,j) * j % 1001;
for (i=1;i<=5;i++) C1(i) = i*i;
CroutMatrix A = X;
ColumnVector C2 = A.i() * C1; C1 = X.i() * C1;
X = C1 - C2; Clean(X,0.000000001); Print(X);
}
{
Tracer et1("Stage 3");
X.ReSize(7,7);
for (j=1;j<=7;j++) X(1,j) = j+1;
for (i=2;i<=7;i++) for (j=1;j<=7; j++)
X(i,j) = (long)X(i-1,j) * j % 1001;
C1.ReSize(7);
for (i=1;i<=7;i++) C1(i) = i*i;
RowVector R1 = C1.t();
Diff = R1 * X.i() - ( X.t().i() * R1.t() ).t(); Clean(Diff,0.000000001);
Print(Diff);
}
{
Tracer et1("Stage 4");
X.ReSize(5,5);
for (j=1;j<=5;j++) X(1,j) = j+1;
for (i=2;i<=5;i++) for (j=1;j<=5; j++)
X(i,j) = (long)X(i-1,j) * j % 1001;
C1.ReSize(5);
for (i=1;i<=5;i++) C1(i) = i*i;
CroutMatrix A1 = X*X;
ColumnVector C2 = A1.i() * C1; C1 = X.i() * C1; C1 = X.i() * C1;
X = C1 - C2; Clean(X,0.000000001); Print(X);
}
{
Tracer et1("Stage 5");
int n = 40;
SymmetricBandMatrix B(n,2); B = 0.0;
for (i=1; i<=n; i++)
{
B(i,i) = 6;
if (i<=n-1) B(i,i+1) = -4;
if (i<=n-2) B(i,i+2) = 1;
}
B(1,1) = 5; B(n,n) = 5;
SymmetricMatrix A = B;
ColumnVector X(n);
X(1) = 429;
for (i=2;i<=n;i++) X(i) = (long)X(i-1) * 31 % 1001;
X = X / 100000L;
// the matrix B is rather ill-conditioned so the difficulty is getting
// good agreement (we have chosen X very small) may not be surprising;
// maximum element size in B.i() is around 1400
ColumnVector Y1 = A.i() * X;
LowerTriangularMatrix C1 = Cholesky(A);
ColumnVector Y2 = C1.t().i() * (C1.i() * X) - Y1;
Clean(Y2, 0.000000001); Print(Y2);
UpperTriangularMatrix CU = C1.t().i();
LowerTriangularMatrix CL = C1.i();
Y2 = CU * (CL * X) - Y1;
Clean(Y2, 0.000000001); Print(Y2);
Y2 = B.i() * X - Y1; Clean(Y2, 0.000000001); Print(Y2);
LowerBandMatrix C2 = Cholesky(B);
Matrix M = C2 - C1; Clean(M, 0.000000001); Print(M);
ColumnVector Y3 = C2.t().i() * (C2.i() * X) - Y1;
Clean(Y3, 0.000000001); Print(Y3);
CU = C1.t().i();
CL = C1.i();
Y3 = CU * (CL * X) - Y1;
Clean(Y3, 0.000000001); Print(Y3);
Y3 = B.i() * X - Y1; Clean(Y3, 0.000000001); Print(Y3);
SymmetricMatrix AI = A.i();
Y2 = AI*X - Y1; Clean(Y2, 0.000000001); Print(Y2);
SymmetricMatrix BI = B.i();
BandMatrix C = B; Matrix CI = C.i();
M = A.i() - CI; Clean(M, 0.000000001); Print(M);
M = B.i() - CI; Clean(M, 0.000000001); Print(M);
M = AI-BI; Clean(M, 0.000000001); Print(M);
M = AI-CI; Clean(M, 0.000000001); Print(M);
M = A; AI << M; M = AI-A; Clean(M, 0.000000001); Print(M);
C = B; BI << C; M = BI-B; Clean(M, 0.000000001); Print(M);
}
{
Tracer et1("Stage 5");
SymmetricMatrix A(4), B(4);
A << 5
<< 1 << 4
<< 2 << 1 << 6
<< 1 << 0 << 1 << 7;
B << 8
<< 1 << 5
<< 1 << 0 << 9
<< 2 << 1 << 0 << 6;
LowerTriangularMatrix AB = Cholesky(A) * Cholesky(B);
Matrix M = Cholesky(A) * B * Cholesky(A).t() - AB*AB.t();
Clean(M, 0.000000001); Print(M);
M = A * Cholesky(B); M = M * M.t() - A * B * A;
Clean(M, 0.000000001); Print(M);
}
{
Tracer et1("Stage 6");
int N=49;
int i;
SymmetricBandMatrix S(N,1);
Matrix B(N,N+1); B=0;
for (i=1;i<=N;i++) { S(i,i)=1; B(i,i)=1; B(i,i+1)=-1; }
for (i=1;i<N; i++) S(i,i+1)=-.5;
DiagonalMatrix D(N+1); D = 1;
B = B.t()*S.i()*B - (D-1.0/(N+1))*2.0;
Clean(B, 0.000000001); Print(B);
}
{
Tracer et1("Stage 7");
// See if you can pass a CroutMatrix to a function
Matrix A(4,4);
A.Row(1) << 3 << 2 << -1 << 4;
A.Row(2) << -8 << 7 << 2 << 0;
A.Row(3) << 2 << -2 << 3 << 1;
A.Row(4) << -1 << 5 << 2 << 2;
CroutMatrix B = A;
Matrix C = A * Inverter(B) - IdentityMatrix(4);
Clean(C, 0.000000001); Print(C);
}
// cout << "\nEnd of Thirteenth test\n";
}
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