double SpinAdapted::dotproduct(const RowVector& a, const RowVector& b)
{
assert(a.Ncols() == b.Ncols());
#ifdef BLAS
return DDOT(a.Storage(), a.Store(), 1, b.Store(), 1);
#else
return a * b.t();
#endif
}
void test3(Real* y, Real* x1, Real* x2, int nobs, int npred)
{
cout << "\n\nTest 3 - Cholesky\n";
// traditional sum of squares and products method of calculation
// with subtraction of means - using Cholesky decomposition
Matrix X(nobs,npred);
X.Column(1) << x1; X.Column(2) << x2;
ColumnVector Y(nobs); Y << y;
ColumnVector Ones(nobs); Ones = 1.0;
RowVector M = Ones.t() * X / nobs;
Matrix XC(nobs,npred);
XC = X - Ones * M;
ColumnVector YC(nobs);
Real m = Sum(Y) / nobs; YC = Y - Ones * m;
SymmetricMatrix SSQ; SSQ << XC.t() * XC;
// Cholesky decomposition of SSQ
LowerTriangularMatrix L = Cholesky(SSQ);
// calculate estimate
ColumnVector A = L.t().i() * (L.i() * (XC.t() * YC));
// calculate estimate of constant term
Real a = m - (M * A).AsScalar();
// Get variances of estimates from diagonal elements of invoice of SSQ
DiagonalMatrix D; D << L.t().i() * L.i();
ColumnVector V = D.AsColumn();
Real v = 1.0/nobs + (L.i() * M.t()).SumSquare();
// Calculate fitted values and residuals
int npred1 = npred+1;
ColumnVector Fitted = X * A + a;
ColumnVector Residual = Y - Fitted;
Real ResVar = Residual.SumSquare() / (nobs-npred1);
// Get diagonals of Hat matrix (an expensive way of doing this)
Matrix X1(nobs,npred1); X1.Column(1)<<Ones; X1.Columns(2,npred1)<<X;
DiagonalMatrix Hat; Hat << X1 * (X1.t() * X1).i() * X1.t();
// print out answers
cout << "\nEstimates and their standard errors\n\n";
cout.setf(ios::fixed, ios::floatfield);
cout << setw(11) << setprecision(5) << a << " ";
cout << setw(11) << setprecision(5) << sqrt(v*ResVar) << endl;
ColumnVector SE(npred);
for (int i=1; i<=npred; i++) SE(i) = sqrt(V(i)*ResVar);
cout << setw(11) << setprecision(5) << (A | SE) << endl;
cout << "\nObservations, fitted value, residual value, hat value\n";
cout << setw(9) << setprecision(3) <<
(X | Y | Fitted | Residual | Hat.AsColumn());
cout << "\n\n";
}
void trymatc()
{
// cout << "\nTwelfth test of Matrix package\n";
Tracer et("Twelfth test of Matrix package");
Tracer::PrintTrace();
DiagonalMatrix D(15); D=1.5;
Matrix A(15,15);
int i,j;
for (i=1;i<=15;i++) for (j=1;j<=15;j++) A(i,j)=i*i+j-150;
{ A = A + D; }
ColumnVector B(15);
for (i=1;i<=15;i++) B(i)=i+i*i-150.0;
{
Tracer et1("Stage 1");
ColumnVector B1=B;
B=(A*2.0).i() * B1;
Matrix X = A*B-B1/2.0;
Clean(X, 0.000000001); Print(X);
A.ReSize(3,5);
for (i=1; i<=3; i++) for (j=1; j<=5; j++) A(i,j) = i+100*j;
B = A.AsColumn()+10000;
RowVector R = (A+10000).AsColumn().t();
Print( RowVector(R-B.t()) );
}
{
Tracer et1("Stage 2");
B = A.AsColumn()+10000;
Matrix XR = (A+10000).AsMatrix(15,1).t();
Print( RowVector(XR-B.t()) );
}
{
Tracer et1("Stage 3");
B = (A.AsMatrix(15,1)+A.AsColumn())/2.0+10000;
Matrix MR = (A+10000).AsColumn().t();
Print( RowVector(MR-B.t()) );
B = (A.AsMatrix(15,1)+A.AsColumn())/2.0;
MR = A.AsColumn().t();
Print( RowVector(MR-B.t()) );
}
{
Tracer et1("Stage 4");
B = (A.AsMatrix(15,1)+A.AsColumn())/2.0;
RowVector R = A.AsColumn().t();
Print( RowVector(R-B.t()) );
}
{
Tracer et1("Stage 5");
RowVector R = (A.AsColumn()-5000).t();
B = ((R.t()+10000) - A.AsColumn())-5000;
Print( RowVector(B.t()) );
}
{
Tracer et1("Stage 6");
B = A.AsColumn(); ColumnVector B1 = (A+10000).AsColumn() - 10000;
Print(ColumnVector(B1-B));
}
{
Tracer et1("Stage 7");
Matrix X = B.AsMatrix(3,5); Print(Matrix(X-A));
for (i=1; i<=3; i++) for (j=1; j<=5; j++) B(5*(i-1)+j) -= i+100*j;
Print(B);
}
{
Tracer et1("Stage 8");
A.ReSize(7,7); D.ReSize(7);
for (i=1; i<=7; i++) for (j=1; j<=7; j++) A(i,j) = i*j*j;
for (i=1; i<=7; i++) D(i,i) = i;
UpperTriangularMatrix U; U << A;
Matrix X = A; for (i=1; i<=7; i++) X(i,i) = i;
A.Inject(D); Print(Matrix(X-A));
X = U; U.Inject(D); A = U; for (i=1; i<=7; i++) X(i,i) = i;
Print(Matrix(X-A));
}
{
Tracer et1("Stage 9");
A.ReSize(7,5);
for (i=1; i<=7; i++) for (j=1; j<=5; j++) A(i,j) = i+100*j;
Matrix Y = A; Y = Y - ((const Matrix&)A); Print(Y);
Matrix X = A; // X.Release();
Y = A; Y = ((const Matrix&)X) - A; Print(Y); Y = 0.0;
Y = ((const Matrix&)X) - ((const Matrix&)A); Print(Y);
}
{
Tracer et1("Stage 10");
// some tests on submatrices
UpperTriangularMatrix U(20);
for (i=1; i<=20; i++) for (j=i; j<=20; j++) U(i,j)=100 * i + j;
UpperTriangularMatrix V = U.SymSubMatrix(1,5);
UpperTriangularMatrix U1 = U;
U1.SubMatrix(4,8,5,9) /= 2;
U1.SubMatrix(4,8,5,9) += 388 * V;
U1.SubMatrix(4,8,5,9) *= 2;
U1.SubMatrix(4,8,5,9) += V;
U1 -= U; UpperTriangularMatrix U2 = U1;
U1 << U1.SubMatrix(4,8,5,9);
U2.SubMatrix(4,8,5,9) -= U1; Print(U2);
U1 -= (777*V); Print(U1);
U1 = U; U1.SubMatrix(4,8,5,9) -= U.SymSubMatrix(1,5);
U1 -= U; U2 = U1; U1 << U1.SubMatrix(4,8,5,9);
U2.SubMatrix(4,8,5,9) -= U1; Print(U2);
U1 += V; Print(U1);
U1 = U;
U1.SubMatrix(3,10,15,19) += 29;
U1 -= U;
Matrix X = U1.SubMatrix(3,10,15,19); X -= 29; Print(X);
U1.SubMatrix(3,10,15,19) *= 0; Print(U1);
LowerTriangularMatrix L = U.t();
LowerTriangularMatrix M = L.SymSubMatrix(1,5);
LowerTriangularMatrix L1 = L;
L1.SubMatrix(5,9,4,8) /= 2;
L1.SubMatrix(5,9,4,8) += 388 * M;
L1.SubMatrix(5,9,4,8) *= 2;
L1.SubMatrix(5,9,4,8) += M;
L1 -= L; LowerTriangularMatrix L2 = L1;
L1 << L1.SubMatrix(5,9,4,8);
L2.SubMatrix(5,9,4,8) -= L1; Print(L2);
L1 -= (777*M); Print(L1);
L1 = L; L1.SubMatrix(5,9,4,8) -= L.SymSubMatrix(1,5);
L1 -= L; L2 =L1; L1 << L1.SubMatrix(5,9,4,8);
L2.SubMatrix(5,9,4,8) -= L1; Print(L2);
L1 += M; Print(L1);
L1 = L;
L1.SubMatrix(15,19,3,10) -= 29;
L1 -= L;
X = L1.SubMatrix(15,19,3,10); X += 29; Print(X);
L1.SubMatrix(15,19,3,10) *= 0; Print(L1);
}
{
Tracer et1("Stage 11");
// more tests on submatrices
Matrix M(20,30);
for (i=1; i<=20; i++) for (j=1; j<=30; j++) M(i,j)=100 * i + j;
Matrix M1 = M;
for (j=1; j<=30; j++)
{ ColumnVector CV = 3 * M1.Column(j); M.Column(j) += CV; }
for (i=1; i<=20; i++)
{ RowVector RV = 5 * M1.Row(i); M.Row(i) -= RV; }
M += M1; Print(M);
}
// cout << "\nEnd of twelfth test\n";
}
void test2(Real* y, Real* x1, Real* x2, int nobs, int npred)
{
cout << "\n\nTest 2 - traditional, OK\n";
// traditional sum of squares and products method of calculation
// with subtraction of means - less subject to round-off error
// than test1
// make matrix of predictor values
Matrix X(nobs,npred);
// load x1 and x2 into X
// [use << rather than = when loading arrays]
X.Column(1) << x1; X.Column(2) << x2;
// vector of Y values
ColumnVector Y(nobs); Y << y;
// make vector of 1s
ColumnVector Ones(nobs); Ones = 1.0;
// calculate means (averages) of x1 and x2 [ .t() takes transpose]
RowVector M = Ones.t() * X / nobs;
// and subtract means from x1 and x1
Matrix XC(nobs,npred);
XC = X - Ones * M;
// do the same to Y [use Sum to get sum of elements]
ColumnVector YC(nobs);
Real m = Sum(Y) / nobs; YC = Y - Ones * m;
// form sum of squares and product matrix
// [use << rather than = for copying Matrix into SymmetricMatrix]
SymmetricMatrix SSQ; SSQ << XC.t() * XC;
// calculate estimate
// [bracket last two terms to force this multiplication first]
// [ .i() means inverse, but inverse is not explicity calculated]
ColumnVector A = SSQ.i() * (XC.t() * YC);
// calculate estimate of constant term
// [AsScalar converts 1x1 matrix to Real]
Real a = m - (M * A).AsScalar();
// Get variances of estimates from diagonal elements of inverse of SSQ
// [ we are taking inverse of SSQ - we need it for finding D ]
Matrix ISSQ = SSQ.i(); DiagonalMatrix D; D << ISSQ;
ColumnVector V = D.AsColumn();
Real v = 1.0/nobs + (M * ISSQ * M.t()).AsScalar();
// for calc variance of const
// Calculate fitted values and residuals
int npred1 = npred+1;
ColumnVector Fitted = X * A + a;
ColumnVector Residual = Y - Fitted;
Real ResVar = Residual.SumSquare() / (nobs-npred1);
// Get diagonals of Hat matrix (an expensive way of doing this)
Matrix X1(nobs,npred1); X1.Column(1)<<Ones; X1.Columns(2,npred1)<<X;
DiagonalMatrix Hat; Hat << X1 * (X1.t() * X1).i() * X1.t();
// print out answers
cout << "\nEstimates and their standard errors\n\n";
cout.setf(ios::fixed, ios::floatfield);
cout << setw(11) << setprecision(5) << a << " ";
cout << setw(11) << setprecision(5) << sqrt(v*ResVar) << endl;
// make vector of standard errors
ColumnVector SE(npred);
for (int i=1; i<=npred; i++) SE(i) = sqrt(V(i)*ResVar);
// use concatenation function to form matrix and use matrix print
// to get two columns
cout << setw(11) << setprecision(5) << (A | SE) << endl;
cout << "\nObservations, fitted value, residual value, hat value\n";
cout << setw(9) << setprecision(3) <<
(X | Y | Fitted | Residual | Hat.AsColumn());
cout << "\n\n";
}
void trymatc()
{
// cout << "\nTwelfth test of Matrix package\n";
Tracer et("Twelfth test of Matrix package");
Tracer::PrintTrace();
DiagonalMatrix D(15); D=1.5;
Matrix A(15,15);
int i,j;
for (i=1;i<=15;i++) for (j=1;j<=15;j++) A(i,j)=i*i+j-150;
{ A = A + D; }
ColumnVector B(15);
for (i=1;i<=15;i++) B(i)=i+i*i-150.0;
{
Tracer et1("Stage 1");
ColumnVector B1=B;
B=(A*2.0).i() * B1;
Matrix X = A*B-B1/2.0;
Clean(X, 0.000000001); Print(X);
A.ReSize(3,5);
for (i=1; i<=3; i++) for (j=1; j<=5; j++) A(i,j) = i+100*j;
B = A.AsColumn()+10000;
RowVector R = (A+10000).AsColumn().t();
Print( RowVector(R-B.t()) );
}
{
Tracer et1("Stage 2");
B = A.AsColumn()+10000;
Matrix XR = (A+10000).AsMatrix(15,1).t();
Print( RowVector(XR-B.t()) );
}
{
Tracer et1("Stage 3");
B = (A.AsMatrix(15,1)+A.AsColumn())/2.0+10000;
Matrix MR = (A+10000).AsColumn().t();
Print( RowVector(MR-B.t()) );
B = (A.AsMatrix(15,1)+A.AsColumn())/2.0;
MR = A.AsColumn().t();
Print( RowVector(MR-B.t()) );
}
{
Tracer et1("Stage 4");
B = (A.AsMatrix(15,1)+A.AsColumn())/2.0;
RowVector R = A.AsColumn().t();
Print( RowVector(R-B.t()) );
}
{
Tracer et1("Stage 5");
RowVector R = (A.AsColumn()-5000).t();
B = ((R.t()+10000) - A.AsColumn())-5000;
Print( RowVector(B.t()) );
}
{
Tracer et1("Stage 6");
B = A.AsColumn(); ColumnVector B1 = (A+10000).AsColumn() - 10000;
Print(ColumnVector(B1-B));
}
{
Tracer et1("Stage 7");
Matrix X = B.AsMatrix(3,5); Print(Matrix(X-A));
for (i=1; i<=3; i++) for (j=1; j<=5; j++) B(5*(i-1)+j) -= i+100*j;
Print(B);
}
{
Tracer et1("Stage 8");
A.ReSize(7,7); D.ReSize(7);
for (i=1; i<=7; i++) for (j=1; j<=7; j++) A(i,j) = i*j*j;
for (i=1; i<=7; i++) D(i,i) = i;
UpperTriangularMatrix U; U << A;
Matrix X = A; for (i=1; i<=7; i++) X(i,i) = i;
A.Inject(D); Print(Matrix(X-A));
X = U; U.Inject(D); A = U; for (i=1; i<=7; i++) X(i,i) = i;
Print(Matrix(X-A));
}
{
Tracer et1("Stage 9");
A.ReSize(7,5);
for (i=1; i<=7; i++) for (j=1; j<=5; j++) A(i,j) = i+100*j;
Matrix Y = A; Y = Y - ((const Matrix&)A); Print(Y);
Matrix X = A;
Y = A; Y = ((const Matrix&)X) - A; Print(Y); Y = 0.0;
Y = ((const Matrix&)X) - ((const Matrix&)A); Print(Y);
}
{
Tracer et1("Stage 10");
// some tests on submatrices
UpperTriangularMatrix U(20);
for (i=1; i<=20; i++) for (j=i; j<=20; j++) U(i,j)=100 * i + j;
UpperTriangularMatrix V = U.SymSubMatrix(1,5);
UpperTriangularMatrix U1 = U;
U1.SubMatrix(4,8,5,9) /= 2;
U1.SubMatrix(4,8,5,9) += 388 * V;
U1.SubMatrix(4,8,5,9) *= 2;
U1.SubMatrix(4,8,5,9) += V;
U1 -= U; UpperTriangularMatrix U2 = U1;
U1 << U1.SubMatrix(4,8,5,9);
U2.SubMatrix(4,8,5,9) -= U1; Print(U2);
U1 -= (777*V); Print(U1);
U1 = U; U1.SubMatrix(4,8,5,9) -= U.SymSubMatrix(1,5);
U1 -= U; U2 = U1; U1 << U1.SubMatrix(4,8,5,9);
U2.SubMatrix(4,8,5,9) -= U1; Print(U2);
U1 += V; Print(U1);
U1 = U;
U1.SubMatrix(3,10,15,19) += 29;
U1 -= U;
Matrix X = U1.SubMatrix(3,10,15,19); X -= 29; Print(X);
U1.SubMatrix(3,10,15,19) *= 0; Print(U1);
LowerTriangularMatrix L = U.t();
LowerTriangularMatrix M = L.SymSubMatrix(1,5);
LowerTriangularMatrix L1 = L;
L1.SubMatrix(5,9,4,8) /= 2;
L1.SubMatrix(5,9,4,8) += 388 * M;
L1.SubMatrix(5,9,4,8) *= 2;
L1.SubMatrix(5,9,4,8) += M;
L1 -= L; LowerTriangularMatrix L2 = L1;
L1 << L1.SubMatrix(5,9,4,8);
L2.SubMatrix(5,9,4,8) -= L1; Print(L2);
L1 -= (777*M); Print(L1);
L1 = L; L1.SubMatrix(5,9,4,8) -= L.SymSubMatrix(1,5);
L1 -= L; L2 =L1; L1 << L1.SubMatrix(5,9,4,8);
L2.SubMatrix(5,9,4,8) -= L1; Print(L2);
L1 += M; Print(L1);
L1 = L;
L1.SubMatrix(15,19,3,10) -= 29;
L1 -= L;
X = L1.SubMatrix(15,19,3,10); X += 29; Print(X);
L1.SubMatrix(15,19,3,10) *= 0; Print(L1);
}
{
Tracer et1("Stage 11");
// more tests on submatrices
Matrix M(20,30);
for (i=1; i<=20; i++) for (j=1; j<=30; j++) M(i,j)=100 * i + j;
Matrix M1 = M;
for (j=1; j<=30; j++)
{ ColumnVector CV = 3 * M1.Column(j); M.Column(j) += CV; }
for (i=1; i<=20; i++)
{ RowVector RV = 5 * M1.Row(i); M.Row(i) -= RV; }
M += M1; Print(M);
}
{
Tracer et1("Stage 12");
// more tests on Release
Matrix M(20,30);
for (i=1; i<=20; i++) for (j=1; j<=30; j++) M(i,j)=100 * i + j;
Matrix M1 = M;
M.Release();
Matrix M2 = M;
Matrix X = M; Print(X);
X = M1 - M2; Print(X);
#ifndef DONT_DO_NRIC
nricMatrix N = M1;
nricMatrix N1 = N;
N.Release();
nricMatrix N2 = N;
nricMatrix Y = N; Print(Y);
Y = N1 - N2; Print(Y);
N = M1 / 2; N1 = N * 2; N.Release(); N2 = N * 2; Y = N; Print(N);
Y = (N1 - M1) | (N2 - M1); Print(Y);
#endif
}
{
Tracer et("Stage 13");
// test sum of squares of rows or columns
MultWithCarry mwc;
DiagonalMatrix DM; Matrix X;
// rectangular matrix
Matrix A(20, 15);
FillWithValues(mwc, A);
// sum of squares of rows
DM << A * A.t();
ColumnVector CV = A.sum_square_rows();
X = CV - DM.AsColumn(); Clean(X, 0.000000001); Print(X);
DM << A.t() * A;
RowVector RV = A.sum_square_columns();
X = RV - DM.AsRow(); Clean(X, 0.000000001); Print(X);
X = RV - A.t().sum_square_rows().t(); Clean(X, 0.000000001); Print(X);
X = CV - A.t().sum_square_columns().t(); Clean(X, 0.000000001); Print(X);
// UpperTriangularMatrix
A.ReSize(17,17); FillWithValues(mwc, A);
UpperTriangularMatrix UT; UT << A;
Matrix A1 = UT;
X = UT.sum_square_rows() - A1.sum_square_rows(); Print(X);
X = UT.sum_square_columns() - A1.sum_square_columns(); Print(X);
// LowerTriangularMatrix
LowerTriangularMatrix LT; LT << A;
A1 = LT;
X = LT.sum_square_rows() - A1.sum_square_rows(); Print(X);
X = LT.sum_square_columns() - A1.sum_square_columns(); Print(X);
// SymmetricMatrix
SymmetricMatrix SM; SM << A;
A1 = SM;
X = SM.sum_square_rows() - A1.sum_square_rows(); Print(X);
X = SM.sum_square_columns() - A1.sum_square_columns(); Print(X);
// DiagonalMatrix
DM << A;
A1 = DM;
X = DM.sum_square_rows() - A1.sum_square_rows(); Print(X);
X = DM.sum_square_columns() - A1.sum_square_columns(); Print(X);
// BandMatrix
BandMatrix BM(17, 3, 5); BM.Inject(A);
A1 = BM;
X = BM.sum_square_rows() - A1.sum_square_rows(); Print(X);
X = BM.sum_square_columns() - A1.sum_square_columns(); Print(X);
// SymmetricBandMatrix
SymmetricBandMatrix SBM(17, 4); SBM.Inject(A);
A1 = SBM;
X = SBM.sum_square_rows() - A1.sum_square_rows(); Print(X);
X = SBM.sum_square_columns() - A1.sum_square_columns(); Print(X);
// IdentityMatrix
IdentityMatrix IM(29);
X = IM.sum_square_rows() - 1; Print(X);
X = IM.sum_square_columns() - 1; Print(X);
// Matrix with zero rows
A1.ReSize(0,10);
X.ReSize(1,10); X = 0; X -= A1.sum_square_columns(); Print(X);
X.ReSize(0,1); X -= A1.sum_square_rows(); Print(X);
// Matrix with zero columns
A1.ReSize(10,0);
X.ReSize(10,1); X = 0; X -= A1.sum_square_rows(); Print(X);
X.ReSize(1,0); X -= A1.sum_square_columns(); Print(X);
}
{
Tracer et("Stage 14");
// test extend orthonormal
MultWithCarry mwc;
Matrix A(20,5); FillWithValues(mwc, A);
// Orthonormalise
UpperTriangularMatrix R;
Matrix A_old = A;
QRZ(A,R);
// Check decomposition
Matrix X = A * R - A_old; Clean(X, 0.000000001); Print(X);
// Check orthogonality
X = A.t() * A - IdentityMatrix(5);
Clean(X, 0.000000001); Print(X);
// Try orthonality extend
SquareMatrix A1(20);
A1.Columns(1,5) = A;
extend_orthonormal(A1,5);
// check columns unchanged
X = A - A1.Columns(1,5); Print(X);
// Check orthogonality
X = A1.t() * A1 - IdentityMatrix(20);
Clean(X, 0.000000001); Print(X);
X = A1 * A1.t() - IdentityMatrix(20);
Clean(X, 0.000000001); Print(X);
// Test with smaller number of columns
Matrix A2(20,15);
A2.Columns(1,5) = A;
extend_orthonormal(A2,5);
// check columns unchanged
X = A - A2.Columns(1,5); Print(X);
// Check orthogonality
X = A2.t() * A2 - IdentityMatrix(15);
Clean(X, 0.000000001); Print(X);
// check it works with no columns to start with
A2.ReSize(100,100);
extend_orthonormal(A2,0);
// Check orthogonality
X = A2.t() * A2 - IdentityMatrix(100);
Clean(X, 0.000000001); Print(X);
X = A2 * A2.t() - IdentityMatrix(100);
Clean(X, 0.000000001); Print(X);
}
// cout << "\nEnd of twelfth test\n";
}