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; SquareMatrix B = BMB; BandMatrix BMC = KP(BMA, BMB); BandMatrix BMC1 = KP(BMA, B); 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); } { Tracer et1("Stage 7"); IdentityMatrix I(3); ColumnVector CV(4); CV << 4 << 3 << 1 << 7; Matrix A = KP(I, CV) + 5; Matrix B(3,12); B.Row(1) << 9 << 8 << 6 << 12 << 5 << 5 << 5 << 5 << 5 << 5 << 5 << 5; B.Row(2) << 5 << 5 << 5 << 5 << 9 << 8 << 6 << 12 << 5 << 5 << 5 << 5; B.Row(3) << 5 << 5 << 5 << 5 << 5 << 5 << 5 << 5 << 9 << 8 << 6 << 12; B -= A.t(); Print(B); } { Tracer et1("Stage 8"); // SquareMatrix Matrix A(2,3), B(3,2); A << 2 << 6 << 7 << 4 << 3 << 9; B << 1 << 3 << 4 << 8 << 0 << 6; SquareMatrix AB = A * B; Matrix M = (B.t() * A.t()).t(); M -= AB; Print(M); AB = B * A; M = (A.t() * B.t()).t(); M -= AB; Print(M); AB.ReSize(5,5); AB = 0; AB.SubMatrix(1,2,1,3) = A; AB.SubMatrix(4,5,3,5) = A; AB.SubMatrix(1,3,4,5) = B; AB.SubMatrix(3,5,1,2) = B; SquareMatrix C(5); C.Row(1) << 2 << 6 << 7 << 1 << 3; C.Row(2) << 4 << 3 << 9 << 4 << 8; C.Row(3) << 1 << 3 << 0 << 0 << 6; C.Row(4) << 4 << 8 << 2 << 6 << 7; C.Row(5) << 0 << 6 << 4 << 3 << 9; C -= AB; Print(C); AB = A.SymSubMatrix(1,2); AB = (AB | AB) & (AB | AB); C.ReSize(4); C.Row(1) << 2 << 6 << 2 << 6; C.Row(2) << 4 << 3 << 4 << 3; C.Row(3) << 2 << 6 << 2 << 6; C.Row(4) << 4 << 3 << 4 << 3; M = AB; C -= M; Print(C); C << M; C += -M; Print(C); } }
void trymat8() { // cout << "\nEighth test of Matrix package\n"; Tracer et("Eighth test of Matrix package"); Tracer::PrintTrace(); int i; DiagonalMatrix D(6); for (i=1;i<=6;i++) D(i,i)=i*i+i-10; DiagonalMatrix D2=D; Matrix MD=D; DiagonalMatrix D1(6); for (i=1;i<=6;i++) D1(i,i)=-100+i*i*i; Matrix MD1=D1; Print(Matrix(D*D1-MD*MD1)); Print(Matrix((-D)*D1+MD*MD1)); Print(Matrix(D*(-D1)+MD*MD1)); DiagonalMatrix DX=D; { Tracer et1("Stage 1"); DX=(DX+D1)*DX; Print(Matrix(DX-(MD+MD1)*MD)); DX=D; DX=-DX*DX+(DX-(-D1))*((-D1)+DX); // Matrix MX = Matrix(MD1); // MD1=DX+(MX.t())*(MX.t()); Print(MD1); MD1=DX+(Matrix(MD1).t())*(Matrix(MD1).t()); Print(MD1); DX=D; DX=DX; DX=D2-DX; Print(DiagonalMatrix(DX)); DX=D; } { Tracer et1("Stage 2"); D.Release(2); D1=D; D2=D; Print(DiagonalMatrix(D1-DX)); Print(DiagonalMatrix(D2-DX)); MD1=1.0; Print(Matrix(MD1-1.0)); } { Tracer et1("Stage 3"); //GenericMatrix LowerTriangularMatrix LT(4); LT << 1 << 2 << 3 << 4 << 5 << 6 << 7 << 8 << 9 << 10; UpperTriangularMatrix UT = LT.t() * 2.0; GenericMatrix GM1 = LT; LowerTriangularMatrix LT1 = GM1-LT; Print(LT1); GenericMatrix GM2 = GM1; LT1 = GM2; LT1 = LT1-LT; Print(LT1); GM2 = GM1; LT1 = GM2; LT1 = LT1-LT; Print(LT1); GM2 = GM1*2; LT1 = GM2; LT1 = LT1-LT*2; Print(LT1); GM1.Release(); GM1=GM1; LT1=GM1-LT; Print(LT1); LT1=GM1-LT; Print(LT1); GM1.Release(); GM1=GM1*4; LT1=GM1-LT*4; Print(LT1); LT1=GM1-LT*4; Print(LT1); GM1.CleanUp(); GM1=LT; GM2=UT; GM1=GM1*GM2; Matrix M=GM1; M=M-LT*UT; Print(M); Transposer(LT,GM2); LT1 = LT - GM2.t(); Print(LT1); GM1=LT; Transposer(GM1,GM2); LT1 = LT - GM2.t(); Print(LT1); GM1 = LT; GM1 = GM1 + GM1; LT1 = LT*2-GM1; Print(LT1); DiagonalMatrix D; D << LT; GM1 = D; LT1 = GM1; LT1 -= D; Print(LT1); UpperTriangularMatrix UT1 = GM1; UT1 -= D; Print(UT1); } { Tracer et1("Stage 4"); // Another test of SVD Matrix M(12,12); M = 0; M(1,1) = M(2,2) = M(4,4) = M(6,6) = M(7,7) = M(8,8) = M(10,10) = M(12,12) = -1; M(1,6) = M(1,12) = -5.601594; M(3,6) = M(3,12) = -0.000165; M(7,6) = M(7,12) = -0.008294; DiagonalMatrix D; SVD(M,D); SortDescending(D); // answer given by matlab DiagonalMatrix DX(12); DX(1) = 8.0461; DX(2) = DX(3) = DX(4) = DX(5) = DX(6) = DX(7) = 1; DX(8) = 0.1243; DX(9) = DX(10) = DX(11) = DX(12) = 0; D -= DX; Clean(D,0.0001); Print(D); } #ifndef DONT_DO_NRIC { Tracer et1("Stage 5"); // test numerical recipes in C interface DiagonalMatrix D(10); D << 1 << 4 << 6 << 2 << 1 << 6 << 4 << 7 << 3 << 1; ColumnVector C(10); C << 3 << 7 << 5 << 1 << 4 << 2 << 3 << 9 << 1 << 3; RowVector R(6); R << 2 << 3 << 5 << 7 << 11 << 13; nricMatrix M(10, 6); DCR( D.nric(), C.nric(), 10, R.nric(), 6, M.nric() ); M -= D * C * R; Print(M); D.ReSize(5); D << 1.25 << 4.75 << 9.5 << 1.25 << 3.75; C.ReSize(5); C << 1.5 << 7.5 << 4.25 << 0.0 << 7.25; R.ReSize(9); R << 2.5 << 3.25 << 5.5 << 7 << 11.25 << 13.5 << 0.0 << 1.5 << 3.5; Matrix MX = D * C * R; M.ReSize(MX); DCR( D.nric(), C.nric(), 5, R.nric(), 9, M.nric() ); M -= MX; Print(M); // test swap nricMatrix A(3,4); nricMatrix B(4,5); A.Row(1) << 2 << 7 << 3 << 6; A.Row(2) << 6 << 2 << 5 << 9; A.Row(3) << 1 << 0 << 1 << 6; B.Row(1) << 2 << 8 << 4 << 5 << 3; B.Row(2) << 1 << 7 << 5 << 3 << 9; B.Row(3) << 7 << 8 << 2 << 1 << 6; B.Row(4) << 5 << 2 << 9 << 0 << 9; nricMatrix A1(1,2); nricMatrix B1; nricMatrix X(3,5); Matrix X1 = A * B; swap(A, A1); swap(B1, B); for (int i = 1; i <= 3; ++i) for (int j = 1; j <= 5; ++j) { X.nric()[i][j] = 0.0; for (int k = 1; k <= 4; ++k) X.nric()[i][j] += A1.nric()[i][k] * B1.nric()[k][j]; } X1 -= X; Print(X1); } #endif { Tracer et1("Stage 6"); // test dotproduct DiagonalMatrix test(5); test = 1; ColumnVector C(10); C << 3 << 7 << 5 << 1 << 4 << 2 << 3 << 9 << 1 << 3; RowVector R(10); R << 2 << 3 << 5 << 7 << 11 << 13 << -3 << -4 << 2 << 4; test(1) = (R * C).AsScalar() - DotProduct(C, R); test(2) = C.SumSquare() - DotProduct(C, C); test(3) = 6.0 * (C.t() * R.t()).AsScalar() - DotProduct(2.0 * C, 3.0 * R); Matrix MC = C.AsMatrix(2,5), MR = R.AsMatrix(5,2); test(4) = DotProduct(MC, MR) - (R * C).AsScalar(); UpperTriangularMatrix UT(5); UT << 3 << 5 << 2 << 1 << 7 << 1 << 1 << 8 << 2 << 7 << 0 << 1 << 3 << 5 << 6; LowerTriangularMatrix LT(5); LT << 5 << 2 << 3 << 1 << 0 << 7 << 9 << 8 << 1 << 2 << 0 << 2 << 1 << 9 << 2; test(5) = DotProduct(UT, LT) - Sum(SP(UT, LT)); Print(test); // check row-wise load; LowerTriangularMatrix LT1(5); LT1.Row(1) << 5; LT1.Row(2) << 2 << 3; LT1.Row(3) << 1 << 0 << 7; LT1.Row(4) << 9 << 8 << 1 << 2; LT1.Row(5) << 0 << 2 << 1 << 9 << 2; Matrix M = LT1 - LT; Print(M); // check solution with identity matrix IdentityMatrix IM(5); IM *= 2; LinearEquationSolver LES1(IM); LowerTriangularMatrix LTX = LES1.i() * LT; M = LTX * 2 - LT; Print(M); DiagonalMatrix D = IM; LinearEquationSolver LES2(IM); LTX = LES2.i() * LT; M = LTX * 2 - LT; Print(M); UpperTriangularMatrix UTX = LES1.i() * UT; M = UTX * 2 - UT; Print(M); UTX = LES2.i() * UT; M = UTX * 2 - UT; Print(M); } { Tracer et1("Stage 7"); // Some more GenericMatrix stuff with *= |= &= // but don't any additional checks BandMatrix BM1(6,2,3); BM1.Row(1) << 3 << 8 << 4 << 1; BM1.Row(2) << 5 << 1 << 9 << 7 << 2; BM1.Row(3) << 1 << 0 << 6 << 3 << 1 << 3; BM1.Row(4) << 4 << 2 << 5 << 2 << 4; BM1.Row(5) << 3 << 3 << 9 << 1; BM1.Row(6) << 4 << 2 << 9; BandMatrix BM2(6,1,1); BM2.Row(1) << 2.5 << 7.5; BM2.Row(2) << 1.5 << 3.0 << 8.5; BM2.Row(3) << 6.0 << 6.5 << 7.0; BM2.Row(4) << 2.5 << 2.0 << 8.0; BM2.Row(5) << 0.5 << 4.5 << 3.5; BM2.Row(6) << 9.5 << 7.5; Matrix RM1 = BM1, RM2 = BM2; Matrix X; GenericMatrix GRM1 = RM1, GBM1 = BM1, GRM2 = RM2, GBM2 = BM2; Matrix Z(6,0); Z = 5; Print(Z); GRM1 |= Z; GBM1 |= Z; GRM2 &= Z.t(); GBM2 &= Z.t(); X = GRM1 - BM1; Print(X); X = GBM1 - BM1; Print(X); X = GRM2 - BM2; Print(X); X = GBM2 - BM2; Print(X); GRM1 = RM1; GBM1 = BM1; GRM2 = RM2; GBM2 = BM2; GRM1 *= GRM2; GBM1 *= GBM2; X = GRM1 - BM1 * BM2; Print(X); X = RM1 * RM2 - GBM1; Print(X); GRM1 = RM1; GBM1 = BM1; GRM2 = RM2; GBM2 = BM2; GRM1 *= GBM2; GBM1 *= GRM2; // Bs and Rs swapped on LHS X = GRM1 - BM1 * BM2; Print(X); X = RM1 * RM2 - GBM1; Print(X); X = BM1.t(); BandMatrix BM1X = BM1.t(); GRM1 = RM1; X -= GRM1.t(); Print(X); X = BM1X - BM1.t(); Print(X); // check that linear equation solver works with Identity Matrix IdentityMatrix IM(6); IM *= 2; GBM1 = BM1; GBM1 *= 4; GRM1 = RM1; GRM1 *= 4; DiagonalMatrix D = IM; LinearEquationSolver LES1(D); BandMatrix BX; BX = LES1.i() * GBM1; BX -= BM1 * 2; X = BX; Print(X); LinearEquationSolver LES2(IM); BX = LES2.i() * GBM1; BX -= BM1 * 2; X = BX; Print(X); BX = D.i() * GBM1; BX -= BM1 * 2; X = BX; Print(X); BX = IM.i() * GBM1; BX -= BM1 * 2; X = BX; Print(X); BX = IM.i(); BX *= GBM1; BX -= BM1 * 2; X = BX; Print(X); // try symmetric band matrices SymmetricBandMatrix SBM; SBM << SP(BM1, BM1.t()); SBM << IM.i() * SBM; X = 2 * SBM - SP(RM1, RM1.t()); Print(X); // Do this again with more general D D << 2.5 << 7.5 << 2 << 5 << 4.5 << 7.5; BX = D.i() * BM1; X = BX - D.i() * RM1; Clean(X,0.00000001); Print(X); BX = D.i(); BX *= BM1; X = BX - D.i() * RM1; Clean(X,0.00000001); Print(X); SBM << SP(BM1, BM1.t()); BX = D.i() * SBM; X = BX - D.i() * SP(RM1, RM1.t()); Clean(X,0.00000001); Print(X); // test return BX = TestReturn(BM1); X = BX - BM1; if (BX.BandWidth() != BM1.BandWidth()) X = 5; Print(X); } // cout << "\nEnd of eighth test\n"; }
void UpperBandMatrix<TYPE>::Swap(BandMatrix<TYPE>& gm) { assert(gm.BandWidth().Lower() == 0); BandMatrix<TYPE>::Swap(gm); }