#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); } }