Matrix BaseController::pseudoInverse(const Matrix M)
{
Matrix result;
//int rows = this->rows();
//int cols = this->columns();
// calculate SVD decomposition
Matrix U,V;
DiagonalMatrix D;
NEWMAT::SVD(M,D,U,V, true, true);
Matrix Dinv = D.i();
result = V * Dinv * U.t();
return result;
}
void getGeneralizedInverse(Matrix& G, Matrix& Gi) {
#ifdef DEBUG
cout << "\n\ngetGeneralizedInverse - Singular Value\n";
#endif
// Singular value decomposition method
// do SVD
Matrix U, V;
DiagonalMatrix D;
SVD(G,D,U,V); // X = U * D * V.t()
#ifdef DEBUG
cout << "D:\n";
cout << setw(9) << setprecision(6) << (D);
cout << "\n\n";
#endif
DiagonalMatrix Di;
Di << D.i();
#ifdef DEBUG
cout << "Di:\n";
cout << setw(9) << setprecision(6) << (Di);
cout << "\n\n";
#endif
int i=Di.Nrows();
for (; i>=1; i--) {
if (Di(i) > 1000.0) {
Di(i) = 0.0;
}
}
#ifdef DEBUG
cout << "Di with biggies zeroed out:\n";
cout << setw(9) << setprecision(6) << (Di);
cout << "\n\n";
#endif
//Matrix Gi;
Gi << (U * (Di * V.t()));
return;
}
void test5(Real* y, Real* x1, Real* x2, int nobs, int npred)
{
cout << "\n\nTest 5 - singular value\n";
// Singular value decomposition method
// load data - 1s into col 1 of matrix
int npred1 = npred+1;
Matrix X(nobs,npred1); ColumnVector Y(nobs);
X.Column(1) = 1.0; X.Column(2) << x1; X.Column(3) << x2; Y << y;
// do SVD
Matrix U, V; DiagonalMatrix D;
SVD(X,D,U,V); // X = U * D * V.t()
ColumnVector Fitted = U.t() * Y;
ColumnVector A = V * ( D.i() * Fitted );
Fitted = U * Fitted;
ColumnVector Residual = Y - Fitted;
Real ResVar = Residual.SumSquare() / (nobs-npred1);
// get variances of estimates
D << V * (D * D).i() * V.t();
// Get diagonals of Hat matrix
DiagonalMatrix Hat; Hat << U * U.t();
// print out answers
cout << "\nEstimates and their standard errors\n\n";
ColumnVector SE(npred1);
for (int i=1; i<=npred1; i++) SE(i) = sqrt(D(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.Columns(2,3) | Y | Fitted | Residual | Hat.AsColumn());
cout << "\n\n";
}
/*
* Fits a weighted cubic regression on predictor(s)
*
* @param contrast - want to predict this value per snp
* @param strength - covariate of choice
* @param weights - weight of data points for this genotype
* @param Predictor - output, prediction function coefficients
* @param Predicted - output, predicted contrast per snp
*/
void
FitWeightedCubic(const std::vector<double> &contrast,
const std::vector<double> &strength,
const std::vector<double> &weights,
std::vector<double> &Predictor,
std::vector<double> &Predicted) {
// Singular value decomposition method
unsigned int i;
unsigned int nobs;
unsigned int npred;
npred = 3+1;
nobs= contrast.size();
// convert double into doubles to match newmat
vector<Real> tmp_vec(nobs);
Real* tmp_ptr = &tmp_vec[0];
vector<Real> obs_vec(nobs);
Real *obs_ptr = &obs_vec[0];
vector<Real> weight_vec(nobs);
Matrix covarMat(nobs,npred);
ColumnVector observedVec(nobs);
// fill in the data
// modified by weights
for (i=0; i<nobs; i++)
weight_vec[i] = sqrt(weights[i]);
// load data - 1s into col 1 of matrix
for (i=0; i<nobs; i++)
tmp_vec[i] = weight_vec[i];
covarMat.Column(1) << tmp_ptr;
for (i=0; i<nobs; i++)
tmp_vec[i] *= strength[i];
covarMat.Column(2) << tmp_ptr;
for (i=0; i<nobs; i++)
tmp_vec[i] *= strength[i];
covarMat.Column(3) << tmp_ptr;
for (i=0; i<nobs; i++)
tmp_vec[i] *= strength[i];
covarMat.Column(4) << tmp_ptr;
for (i=0; i<nobs; i++)
obs_vec[i] = contrast[i]*weight_vec[i];
observedVec << obs_ptr;
// do SVD
Matrix U, V;
DiagonalMatrix D;
ColumnVector Fitted(nobs);
ColumnVector A(npred);
SVD(covarMat,D,U,V);
Fitted = U.t() * observedVec;
A = V * ( D.i() * Fitted );
// this predicts "0" for low weights
// because of weighted regression
Fitted = U * Fitted;
// this is the predictor
Predictor.resize(npred);
for (i=0; i<npred; i++)
Predictor[i] = A.element(i);
// export data back to doubles
// and therefore this predicts "0" for low-weighted points
// which is >not< the desired outcome!!!!
// instead we need to predict all points at once
// >unweighted< as output
vector<double> Goofy;
Predicted.resize(nobs);
for (i = 0; i < nobs; ++i) {
Goofy.resize(npred);
Goofy[0] = 1;
Goofy[1] = strength[i];
Goofy[2] = strength[i]*Goofy[1];
Goofy[3] = strength[i]*Goofy[2];
Predicted[i] = vprod(Goofy,Predictor);
}
}
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";
}