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#define WANT_STREAM
#define WANT_MATH
#include "newmat.h"
#include "tmt.h"
#ifdef use_namespace
using namespace NEWMAT;
#endif
// test Kronecker Product
void trymatm()
{
Tracer et("Twenty second test of Matrix package");
Tracer::PrintTrace();
{
Tracer et1("Stage 1");
Matrix A(2,3);
A << 3 << 5 << 2
<< 4 << 1 << 6;
Matrix B(4,3);
B << 7 << 2 << 9
<< 1 << 3 << 6
<< 4 << 10 << 5
<< 11 << 8 << 12;
Matrix C(8, 9);
C.Row(1) << 21 << 6 << 27 << 35 << 10 << 45 << 14 << 4 << 18;
C.Row(2) << 3 << 9 << 18 << 5 << 15 << 30 << 2 << 6 << 12;
C.Row(3) << 12 << 30 << 15 << 20 << 50 << 25 << 8 << 20 << 10;
C.Row(4) << 33 << 24 << 36 << 55 << 40 << 60 << 22 << 16 << 24;
C.Row(5) << 28 << 8 << 36 << 7 << 2 << 9 << 42 << 12 << 54;
C.Row(6) << 4 << 12 << 24 << 1 << 3 << 6 << 6 << 18 << 36;
C.Row(7) << 16 << 40 << 20 << 4 << 10 << 5 << 24 << 60 << 30;
C.Row(8) << 44 << 32 << 48 << 11 << 8 << 12 << 66 << 48 << 72;
Matrix AB = KP(A,B) - C; Print(AB);
IdentityMatrix I1(10); IdentityMatrix I2(15); I2 *= 2;
DiagonalMatrix D = KP(I1, I2) - IdentityMatrix(150) * 2;
Print(D);
}
{
Tracer et1("Stage 2");
UpperTriangularMatrix A(3);
A << 3 << 8 << 5
<< 7 << 2
<< 4;
UpperTriangularMatrix B(4);
B << 4 << 1 << 7 << 2
<< 3 << 9 << 8
<< 1 << 5
<< 6;
UpperTriangularMatrix C(12);
C.Row(1) <<12<< 3<<21<< 6 <<32<< 8<<56<<16 <<20<< 5<<35<<10;
C.Row(2) << 9<<27<<24 << 0<<24<<72<<64 << 0<<15<<45<<40;
C.Row(3) << 3<<15 << 0<< 0<< 8<<40 << 0<< 0<< 5<<25;
C.Row(4) <<18 << 0<< 0<< 0<<48 << 0<< 0<< 0<<30;
C.Row(5) <<28<< 7<<49<<14 << 8<< 2<<14<< 4;
C.Row(6) <<21<<63<<56 << 0<< 6<<18<<16;
C.Row(7) << 7<<35 << 0<< 0<< 2<<10;
C.Row(8) <<42 << 0<< 0<< 0<<12;
C.Row(9) <<16<< 4<<28<< 8;
C.Row(10) <<12<<36<<32;
C.Row(11) << 4<<20;
C.Row(12) <<24;
UpperTriangularMatrix AB = KP(A,B) - C; Print(AB);
LowerTriangularMatrix BT = B.t(); Matrix N(12,12);
N.Row(1) <<12 << 0<< 0<< 0 <<32<< 0<< 0<< 0 <<20<< 0<< 0<< 0;
N.Row(2) << 3 << 9<< 0<< 0 << 8<<24<< 0<< 0 << 5<<15<< 0<< 0;
N.Row(3) <<21 <<27<< 3<< 0 <<56<<72<< 8<< 0 <<35<<45<< 5<< 0;
N.Row(4) << 6 <<24<<15<<18 <<16<<64<<40<<48 <<10<<40<<25<<30;
N.Row(5) << 0 << 0<< 0<< 0 <<28<< 0<< 0<< 0 << 8<< 0<< 0<< 0;
N.Row(6) << 0 << 0<< 0<< 0 << 7<<21<< 0<< 0 << 2<< 6<< 0<< 0;
N.Row(7) << 0 << 0<< 0<< 0 <<49<<63<< 7<< 0 <<14<<18<< 2<< 0;
N.Row(8) << 0 << 0<< 0<< 0 <<14<<56<<35<<42 << 4<<16<<10<<12;
N.Row(9) << 0 << 0<< 0<< 0 << 0<< 0<< 0<< 0 <<16<< 0<< 0<< 0;
N.Row(10)<< 0 << 0<< 0<< 0 << 0<< 0<< 0<< 0 << 4<<12<< 0<< 0;
N.Row(11)<< 0 << 0<< 0<< 0 << 0<< 0<< 0<< 0 <<28<<36<< 4<< 0;
N.Row(12)<< 0 << 0<< 0<< 0 << 0<< 0<< 0<< 0 << 8<<32<<20<<24;
Matrix N1 = KP(A, BT); N1 -= N; Print(N1);
AB << KP(A, BT); AB << (AB - N); Print(AB);
BT << KP(A, BT); BT << (BT - N); Print(BT);
LowerTriangularMatrix AT = A.t();
N1 = KP(AT, B); N1 -= N.t(); Print(N1);
AB << KP(AT, B); AB << (AB - N.t()); Print(AB);
BT << KP(AT, B); BT << (BT - N.t()); Print(BT);
}
{
Tracer et1("Stage 3");
BandMatrix BMA(6,2,3);
BMA.Row(1) << 5.25 << 4.75 << 2.25 << 1.75;
BMA.Row(2) << 1.25 << 9.75 << 4.50 << 0.25 << 1.50;
BMA.Row(3) << 7.75 << 1.50 << 3.00 << 4.25 << 0.50 << 5.50;
BMA.Row(4) << 2.75 << 9.00 << 8.00 << 3.25 << 3.50;
BMA.Row(5) << 8.75 << 6.25 << 5.00 << 5.75;
BMA.Row(6) << 3.75 << 6.75 << 6.00;
Matrix A = BMA;
BandMatrix BMB(4,2,1);
BMB.Row(1) << 4.5 << 9.5;
BMB.Row(2) << 1.5 << 6.0 << 2.0;
BMB.Row(3) << 0.5 << 2.5 << 8.5 << 7.5;
BMB.Row(4) << 3.0 << 4.0 << 6.5;
Matrix B = BMB;
BandMatrix BMC = KP(BMA, BMB);
BandMatrix BMC1(24,11,15);
BMC1.Inject(Matrix(KP(BMA, B))); // not directly Band Matrix
Matrix C2 = KP(A, BMB);
Matrix C = KP(A, B);
Matrix M = C - BMC; Print(M);
M = C - BMC1; Print(M);
M = C - C2; Print(M);
RowVector X(4);
X(1) = BMC.BandWidth().Lower() - 10;
X(2) = BMC.BandWidth().Upper() - 13;
X(3) = BMC1.BandWidth().Lower() - 11;
X(4) = BMC1.BandWidth().Upper() - 15;
Print(X);
UpperTriangularMatrix UT; UT << KP(BMA, BMB);
UpperTriangularMatrix UT1; UT1 << (C - UT); Print(UT1);
LowerTriangularMatrix LT; LT << KP(BMA, BMB);
LowerTriangularMatrix LT1; LT1 << (C - LT); Print(LT1);
}
{
Tracer et1("Stage 4");
SymmetricMatrix SM1(4);
SM1.Row(1) << 2;
SM1.Row(2) << 4 << 5;
SM1.Row(3) << 9 << 2 << 1;
SM1.Row(4) << 3 << 6 << 8 << 2;
SymmetricMatrix SM2(3);
SM2.Row(1) << 3;
SM2.Row(2) << -7 << -6;
SM2.Row(3) << 4 << -2 << -1;
SymmetricMatrix SM = KP(SM1, SM2);
Matrix M1 = SM1; Matrix M2 = SM2;
Matrix M = KP(SM1, SM2); M -= SM; Print(M);
M = KP(SM1, SM2) - SM; Print(M);
M = KP(M1, SM2) - SM; Print(M);
M = KP(SM1, M2) - SM; Print(M);
M = KP(M1, M2); M -= SM; Print(M);
}
{
Tracer et1("Stage 5");
Matrix A(2,3);
A << 3 << 5 << 2
<< 4 << 1 << 6;
Matrix B(3,4);
B << 7 << 2 << 9 << 11
<< 1 << 3 << 6 << 8
<< 4 << 10 << 5 << 12;
RowVector C(2); C << 3 << 7;
ColumnVector D(4); D << 0 << 5 << 13 << 11;
Matrix M = KP(C * A, B * D) - KP(C, B) * KP(A, D); Print(M);
}
{
Tracer et1("Stage 6");
RowVector A(3), B(5), C(15);
A << 5 << 2 << 4;
B << 3 << 2 << 0 << 1 << 6;
C << 15 << 10 << 0 << 5 << 30
<< 6 << 4 << 0 << 2 << 12
<< 12 << 8 << 0 << 4 << 24;
Matrix N = KP(A, B) - C; Print(N);
N = KP(A.t(), B.t()) - C.t(); Print(N);
N = KP(A.AsDiagonal(), B.AsDiagonal()) - C.AsDiagonal(); Print(N);
}
}
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