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-/*
- Genome-wide Efficient Mixed Model Association (GEMMA)
- Copyright (C) 2011 Xiang Zhou
-
- This program is free software: you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation, either version 3 of the License, or
- (at your option) any later version.
-
- This program is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with this program. If not, see <http://www.gnu.org/licenses/>.
- */
-
-
-#include <iostream>
-#include <fstream>
-#include <sstream>
-#include <string>
-#include <iomanip>
-#include <bitset>
-#include <vector>
-#include <map>
-#include <set>
-#include <cstring>
-#include <cmath>
-#include <stdio.h>
-#include <stdlib.h>
-
-#include "gsl/gsl_vector.h"
-#include "gsl/gsl_matrix.h"
-#include "gsl/gsl_linalg.h"
-#include "gsl/gsl_blas.h"
-#include "gsl/gsl_cdf.h"
-
-#ifdef FORCE_FLOAT
-#include "mathfunc_float.h"
-#else
-#include "mathfunc.h"
-#endif
-
-
-using namespace std;
-
-
-
-//calculate variance of a vector
-double VectorVar (const gsl_vector *v)
-{
- double d, m=0.0, m2=0.0;
- for (size_t i=0; i<v->size; ++i) {
- d=gsl_vector_get (v, i);
- m+=d;
- m2+=d*d;
- }
- m/=(double)v->size;
- m2/=(double)v->size;
- return m2-m*m;
-}
-
-
-
-//center the matrix G
-void CenterMatrix (gsl_matrix *G)
-{
- double d;
- gsl_vector *w=gsl_vector_alloc (G->size1);
- gsl_vector *Gw=gsl_vector_alloc (G->size1);
- gsl_vector_set_all (w, 1.0);
-
- gsl_blas_dgemv (CblasNoTrans, 1.0, G, w, 0.0, Gw);
- gsl_blas_dsyr2 (CblasUpper, -1.0/(double)G->size1, Gw, w, G);
- gsl_blas_ddot (w, Gw, &d);
- gsl_blas_dsyr (CblasUpper, d/((double)G->size1*(double)G->size1), w, G);
-
- for (size_t i=0; i<G->size1; ++i) {
- for (size_t j=0; j<i; ++j) {
- d=gsl_matrix_get (G, j, i);
- gsl_matrix_set (G, i, j, d);
- }
- }
-
- gsl_vector_free(w);
- gsl_vector_free(Gw);
-
- return;
-}
-
-
-//center the matrix G
-void CenterMatrix (gsl_matrix *G, gsl_vector *w)
-{
- double d, wtw;
- gsl_vector *Gw=gsl_vector_alloc (G->size1);
-
- gsl_blas_ddot (w, w, &wtw);
- gsl_blas_dgemv (CblasNoTrans, 1.0, G, w, 0.0, Gw);
- gsl_blas_dsyr2 (CblasUpper, -1.0/wtw, Gw, w, G);
- gsl_blas_ddot (w, Gw, &d);
- gsl_blas_dsyr (CblasUpper, d/(wtw*wtw), w, G);
-
- for (size_t i=0; i<G->size1; ++i) {
- for (size_t j=0; j<i; ++j) {
- d=gsl_matrix_get (G, j, i);
- gsl_matrix_set (G, i, j, d);
- }
- }
-
- gsl_vector_free(Gw);
-
- return;
-}
-
-
-//scale the matrix G such that the mean diagonal = 1
-void ScaleMatrix (gsl_matrix *G)
-{
- double d=0.0;
-
- for (size_t i=0; i<G->size1; ++i) {
- d+=gsl_matrix_get(G, i, i);
- }
- d/=(double)G->size1;
-
- gsl_matrix_scale (G, 1.0/d);
-
- return;
-}
-
-
-//center the vector y
-double CenterVector (gsl_vector *y)
-{
- double d=0.0;
-
- for (size_t i=0; i<y->size; ++i) {
- d+=gsl_vector_get (y, i);
- }
- d/=(double)y->size;
-
- gsl_vector_add_constant (y, -1.0*d);
-
- return d;
-}
-
-
-//calculate UtX
-void CalcUtX (const gsl_matrix *U, gsl_matrix *UtX)
-{
- gsl_vector *Utx_vec=gsl_vector_alloc (UtX->size1);
- for (size_t i=0; i<UtX->size2; ++i) {
- gsl_vector_view UtX_col=gsl_matrix_column (UtX, i);
- gsl_blas_dgemv (CblasTrans, 1.0, U, &UtX_col.vector, 0.0, Utx_vec);
- gsl_vector_memcpy (&UtX_col.vector, Utx_vec);
- }
- gsl_vector_free (Utx_vec);
- return;
-}
-
-
-void CalcUtX (const gsl_matrix *U, const gsl_matrix *X, gsl_matrix *UtX)
-{
- for (size_t i=0; i<X->size2; ++i) {
- gsl_vector_const_view X_col=gsl_matrix_const_column (X, i);
- gsl_vector_view UtX_col=gsl_matrix_column (UtX, i);
- gsl_blas_dgemv (CblasTrans, 1.0, U, &X_col.vector, 0.0, &UtX_col.vector);
- }
- return;
-}
-
-void CalcUtX (const gsl_matrix *U, const gsl_vector *x, gsl_vector *Utx)
-{
- gsl_blas_dgemv (CblasTrans, 1.0, U, x, 0.0, Utx);
- return;
-}
-
-
-//Kronecker product
-void Kronecker(const gsl_matrix *K, const gsl_matrix *V, gsl_matrix *H)
-{
- for (size_t i=0; i<K->size1; i++) {
- for (size_t j=0; j<K->size2; j++) {
- gsl_matrix_view H_sub=gsl_matrix_submatrix (H, i*V->size1, j*V->size2, V->size1, V->size2);
- gsl_matrix_memcpy (&H_sub.matrix, V);
- gsl_matrix_scale (&H_sub.matrix, gsl_matrix_get (K, i, j));
- }
- }
- return;
-}
-
-//symmetric K matrix
-void KroneckerSym(const gsl_matrix *K, const gsl_matrix *V, gsl_matrix *H)
-{
- for (size_t i=0; i<K->size1; i++) {
- for (size_t j=i; j<K->size2; j++) {
- gsl_matrix_view H_sub=gsl_matrix_submatrix (H, i*V->size1, j*V->size2, V->size1, V->size2);
- gsl_matrix_memcpy (&H_sub.matrix, V);
- gsl_matrix_scale (&H_sub.matrix, gsl_matrix_get (K, i, j));
-
- if (i!=j) {
- gsl_matrix_view H_sub_sym=gsl_matrix_submatrix (H, j*V->size1, i*V->size2, V->size1, V->size2);
- gsl_matrix_memcpy (&H_sub_sym.matrix, &H_sub.matrix);
- }
- }
- }
- return;
-}
-
-
-// this function calculates HWE p value with methods described in Wigginton et al., 2005 AJHG;
-// it is based on the code in plink 1.07
-double CalcHWE (const size_t n_hom1, const size_t n_hom2, const size_t n_ab)
-{
- if ( (n_hom1+n_hom2+n_ab)==0 ) {return 1;}
-
- //aa is the rare allele
- int n_aa=n_hom1 < n_hom2 ? n_hom1 : n_hom2;
- int n_bb=n_hom1 < n_hom2 ? n_hom2 : n_hom1;
-
- int rare_copies = 2 * n_aa + n_ab;
- int genotypes = n_ab + n_bb + n_aa;
-
- double * het_probs = (double *) malloc( (rare_copies + 1) * sizeof(double));
- if (het_probs == NULL)
- cout<<"Internal error: SNP-HWE: Unable to allocate array"<<endl;
-
- int i;
- for (i = 0; i <= rare_copies; i++)
- het_probs[i] = 0.0;
-
- /* start at midpoint */
- int mid = rare_copies * (2 * genotypes - rare_copies) / (2 * genotypes);
-
- /* check to ensure that midpoint and rare alleles have same parity */
- if ((rare_copies & 1) ^ (mid & 1))
- mid++;
-
- int curr_hets = mid;
- int curr_homr = (rare_copies - mid) / 2;
- int curr_homc = genotypes - curr_hets - curr_homr;
-
- het_probs[mid] = 1.0;
- double sum = het_probs[mid];
- for (curr_hets = mid; curr_hets > 1; curr_hets -= 2)
- {
- het_probs[curr_hets - 2] = het_probs[curr_hets] * curr_hets * (curr_hets - 1.0)
- / (4.0 * (curr_homr + 1.0) * (curr_homc + 1.0));
- sum += het_probs[curr_hets - 2];
-
- /* 2 fewer heterozygotes for next iteration -> add one rare, one common homozygote */
- curr_homr++;
- curr_homc++;
- }
-
- curr_hets = mid;
- curr_homr = (rare_copies - mid) / 2;
- curr_homc = genotypes - curr_hets - curr_homr;
- for (curr_hets = mid; curr_hets <= rare_copies - 2; curr_hets += 2)
- {
- het_probs[curr_hets + 2] = het_probs[curr_hets] * 4.0 * curr_homr * curr_homc
- /((curr_hets + 2.0) * (curr_hets + 1.0));
- sum += het_probs[curr_hets + 2];
-
- /* add 2 heterozygotes for next iteration -> subtract one rare, one common homozygote */
- curr_homr--;
- curr_homc--;
- }
-
- for (i = 0; i <= rare_copies; i++)
- het_probs[i] /= sum;
-
- /* alternate p-value calculation for p_hi/p_lo
- double p_hi = het_probs[n_ab];
- for (i = n_ab + 1; i <= rare_copies; i++)
- p_hi += het_probs[i];
-
- double p_lo = het_probs[n_ab];
- for (i = n_ab - 1; i >= 0; i--)
- p_lo += het_probs[i];
-
- double p_hi_lo = p_hi < p_lo ? 2.0 * p_hi : 2.0 * p_lo;
- */
-
- double p_hwe = 0.0;
- /* p-value calculation for p_hwe */
- for (i = 0; i <= rare_copies; i++)
- {
- if (het_probs[i] > het_probs[n_ab])
- continue;
- p_hwe += het_probs[i];
- }
-
- p_hwe = p_hwe > 1.0 ? 1.0 : p_hwe;
-
- free(het_probs);
-
- return p_hwe;
-}
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