void polyfit( polyfit_vector x, polyfit_vector y, polyfit_vector sigma, int M,
polyfit_vector& a_fit, polyfit_vector& sig_a, polyfit_vector& yy, double& chisqr) {
// Function to fit a polynomial to data
// Inputs
// x Independent variable
// y Dependent variable
// sigma Estimate error in y
// M Number of parameters used to fit data
// Outputs
// a_fit Fit parameters; a(0) is intercept, a(1) is slope
// sig_a Estimated error in the parameters a()
// yy Curve fit to the data
// chisqr Chi squared statistic
//* Form the vector b and design matrix A
int i, j, k, N = x.dim1();
polyfit_vector b(N);
polyfit_matrix A(N,M);
for( i=0; i<N; i++ ) {
b(i) = y(i)/sigma(i);
for( j=0; j<M; j++ )
if ( sigma(i) > 0.0 )
A(i,j) = pow(x(i),(double)(j))/sigma(i);
else
A(i,j) = 0.0;
}
//* Compute the correlation matrix C
polyfit_matrix C(M,M), Cinv(M,M);
for( i=0; i<M; i++ ) { // (C inverse) = (A transpose) * A
for( j=0; j<M; j++ ) {
Cinv(i,j) = 0.0;
for( k=0; k<N; k++ )
Cinv(i,j) += A(k,i)*A(k,j);
}
}
inverse( Cinv, C ); // C = ( (C inverse) inverse)
//* Compute the least squares polynomial coefficients a_fit
for( k=0; k<M; k++ ) {
a_fit(k) = 0.0;
for( j=0; j<M; j++ )
for( i=0; i<N; i++ ) {
a_fit(k) += C(k,j) * A(i,j) * b(i);
}
}
//* Compute the estimated error bars for the coefficients
for( j=0; j<M; j++ )
sig_a(j) = sqrt(C(j,j));
//* Evaluate curve fit at each data point and compute Chi^2
chisqr = 0.0;
for( i=0; i<N; i++ ) {
yy(i) = 0.0; // yy is the curve fit
for( j=0; j<M; j++ )
yy(i) += a_fit(j) * pow( x(i), (double)(j) );
double delta = (y(i)-yy(i))/sigma(i);
chisqr += delta*delta; // Chi square
}
}
// material electric tangent modulus
const dMatrixT& FSDEMatViscoT::B_IJ()
{
const dMatrixT& C = RightCauchyGreenDeformation();
double J = C.Det();
J = sqrt(J);
dMatrixT Cinv(3);
Cinv.Inverse(C);
fTangentElectrical = Cinv;
fTangentElectrical *= fElectricPermittivity;
fTangentElectrical *= J;
return fTangentElectrical;
}
int NeoHookeanCompressible3D::ComputeTrials()
{
tensor tensorI2("I", 2, def_dim_2);
tensor tsr1;
tensor tsr2;
// Cinv:
Cinv = C.inverse();
Cinv.symmetrize11();
// J:
J = sqrt(C.determinant());
// lame constants:
double lambda = K - 2.0*G/3.0;
double mu = G - lambda*log(J);
// Pk2Stress:
thisPK2Stress = (tensorI2-Cinv)*G + Cinv*lambda*log(J);
// Green Strain:
thisGreenStrain = (C - tensorI2) * 0.5;
// Langrangian Tangent Stiffness:
tsr1 = Cinv("ij")*Cinv("kl");
tsr1.null_indices();
tsr2 = tsr1.transpose0110() + tsr1.transpose0111();
Stiffness = tsr1*lambda + tsr2*mu;
return 0;
}
double
wald_method::run(const snp_row &row1, const snp_row &row2, float *output)
{
arma::mat n0 = arma::zeros<arma::mat>( 3, 3 );
arma::mat n1 = arma::zeros<arma::mat>( 3, 3 );
for(int i = 0; i < row1.size( ); i++)
{
unsigned char snp1 = row1[ i ];
unsigned char snp2 = row2[ i ];
if( snp1 == 3 || snp2 == 3 || m_missing[ i ] == 1 )
{
continue;
}
unsigned int pheno = m_pheno[ i ];
if( pheno == 0 )
{
n0( snp1, snp2 ) += 1;
}
else if( pheno == 1 )
{
n1( snp1, snp2 ) += 1;
}
}
arma::mat eta( 3, 3 );
double num_samples = 0.0;
for(int i = 0; i < 3; i++)
{
for(int j = 0; j < 3; j++)
{
if( n0( i, j ) < METHOD_SMALLEST_CELL_SIZE_BINOMIAL || n1( i, j ) < METHOD_SMALLEST_CELL_SIZE_BINOMIAL )
{
continue;
}
eta( i, j ) = log( n1( i, j ) / n0( i, j ) );
num_samples += n1( i, j ) + n0( i, j );
}
}
/* Find valid parameters and estimate beta */
int num_valid = 0;
arma::uvec valid( 4 );
m_beta = arma::zeros<arma::vec>( 4 );
int i_map[] = { 1, 1, 2, 2 };
int j_map[] = { 1, 2, 1, 2 };
for(int i = 0; i < 4; i++)
{
int c_i = i_map[ i ];
int c_j = j_map[ i ];
if( n0( 0, 0 ) >= METHOD_SMALLEST_CELL_SIZE_NORMAL &&
n0( 0, c_j ) >= METHOD_SMALLEST_CELL_SIZE_NORMAL &&
n0( c_i, 0 ) >= METHOD_SMALLEST_CELL_SIZE_NORMAL &&
n0( c_i, c_j) >= METHOD_SMALLEST_CELL_SIZE_NORMAL &&
n1( 0, 0 ) >= METHOD_SMALLEST_CELL_SIZE_NORMAL &&
n1( 0, c_j ) >= METHOD_SMALLEST_CELL_SIZE_NORMAL &&
n1( c_i, 0 ) >= METHOD_SMALLEST_CELL_SIZE_NORMAL &&
n1( c_i, c_j) >= METHOD_SMALLEST_CELL_SIZE_NORMAL )
{
valid[ num_valid ] = i;
m_beta[ num_valid ] = eta( 0, 0 ) - eta( 0, c_j ) - eta( c_i, 0 ) + eta( c_i, c_j );
num_valid++;
}
}
set_num_ok_samples( (size_t)num_samples );
if( num_valid <= 0 )
{
return -9;
}
valid.resize( num_valid );
m_beta.resize( num_valid );
/* Construct covariance matrix */
m_C = arma::zeros<arma::mat>( num_valid, num_valid );
for(int iv = 0; iv < num_valid; iv++)
{
int i = valid[ iv ];
int c_i = i_map[ i ];
int c_j = j_map[ i ];
for(int jv = 0; jv < num_valid; jv++)
{
int j = valid[ jv ];
int o_i = i_map[ j ];
int o_j = j_map[ j ];
int same_row = c_i == o_i;
int same_col = c_j == o_j;
int in_cell = i == j;
m_C( iv, jv ) = 1.0 / n0( 0, 0 ) + same_col / n0( 0, c_j ) + same_row / n0( c_i, 0 ) + in_cell / n0( c_i, c_j );
m_C( iv, jv ) += 1.0 / n1( 0, 0 ) + same_col / n1( 0, c_j ) + same_row / n1( c_i, 0 ) + in_cell / n1( c_i, c_j );
}
}
arma::mat Cinv( num_valid, num_valid );
if( !inv( Cinv, m_C ) )
{
return -9;
}
/* Test if b != 0 with Wald test */
double chi = dot( m_beta, Cinv * m_beta );
output[ 0 ] = chi;
output[ 1 ] = 1.0 - chi_square_cdf( chi, num_valid );
output[ 2 ] = valid.n_elem;
return output[ 1 ];
}
