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);
}
