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-rw-r--r--src/mathfunc.cpp274
1 files changed, 211 insertions, 63 deletions
diff --git a/src/mathfunc.cpp b/src/mathfunc.cpp
index 09e58dc..e9560ad 100644
--- a/src/mathfunc.cpp
+++ b/src/mathfunc.cpp
@@ -1,17 +1,17 @@
/*
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/>.
*/
@@ -29,13 +29,17 @@
#include <cstring>
#include <cmath>
#include <stdio.h>
-#include <stdlib.h>
+#include <stdlib.h>
+#include <limits.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"
+#include "Eigen/Dense"
+
+#include "lapack.h"
#ifdef FORCE_FLOAT
#include "mathfunc_float.h"
@@ -45,7 +49,7 @@
using namespace std;
-
+using namespace Eigen;
//calculate variance of a vector
@@ -64,105 +68,197 @@ double VectorVar (const gsl_vector *v)
-//center the matrix G
+//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_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_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)
-{
+//center the matrix G
+void CenterMatrix (gsl_matrix *G, const 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_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_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;
+}
+
+
+
+//center the matrix G
+void CenterMatrix (gsl_matrix *G, const gsl_matrix *W)
+{
+ gsl_matrix *WtW=gsl_matrix_alloc (W->size2, W->size2);
+ gsl_matrix *WtWi=gsl_matrix_alloc (W->size2, W->size2);
+ gsl_matrix *WtWiWt=gsl_matrix_alloc (W->size2, G->size1);
+ gsl_matrix *GW=gsl_matrix_alloc (G->size1, W->size2);
+ gsl_matrix *WtGW=gsl_matrix_alloc (W->size2, W->size2);
+ gsl_matrix *Gtmp=gsl_matrix_alloc (G->size1, G->size1);
+
+ gsl_blas_dgemm (CblasTrans, CblasNoTrans, 1.0, W, W, 0.0, WtW);
+
+ int sig;
+ gsl_permutation * pmt=gsl_permutation_alloc (W->size2);
+ LUDecomp (WtW, pmt, &sig);
+ LUInvert (WtW, pmt, WtWi);
+
+ gsl_blas_dgemm (CblasNoTrans, CblasTrans, 1.0, WtWi, W, 0.0, WtWiWt);
+ gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, G, W, 0.0, GW);
+ gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, GW, WtWiWt, 0.0, Gtmp);
+
+ gsl_matrix_sub (G, Gtmp);
+ gsl_matrix_transpose (Gtmp);
+ gsl_matrix_sub (G, Gtmp);
+
+ gsl_blas_dgemm (CblasTrans, CblasNoTrans, 1.0, W, GW, 0.0, WtGW);
+ //GW is destroyed
+ gsl_blas_dgemm (CblasTrans, CblasNoTrans, 1.0, WtWiWt, WtGW, 0.0, GW);
+ gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, GW, WtWiWt, 0.0, Gtmp);
+
+ gsl_matrix_add (G, Gtmp);
+
+ gsl_matrix_free(WtW);
+ gsl_matrix_free(WtWi);
+ gsl_matrix_free(WtWiWt);
+ gsl_matrix_free(GW);
+ gsl_matrix_free(WtGW);
+ gsl_matrix_free(Gtmp);
+
return;
}
//scale the matrix G such that the mean diagonal = 1
-void ScaleMatrix (gsl_matrix *G)
-{
+double 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;
+
+ if (d!=0) {
+ gsl_matrix_scale (G, 1.0/d);
+ }
+
+ return d;
}
//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;
}
+//center the vector y
+void CenterVector (gsl_vector *y, const gsl_matrix *W)
+{
+ gsl_matrix *WtW=gsl_matrix_alloc (W->size2, W->size2);
+ gsl_vector *Wty=gsl_vector_alloc (W->size2);
+ gsl_vector *WtWiWty=gsl_vector_alloc (W->size2);
+
+ gsl_blas_dgemm (CblasTrans, CblasNoTrans, 1.0, W, W, 0.0, WtW);
+ gsl_blas_dgemv (CblasTrans, 1.0, W, y, 0.0, Wty);
+
+ int sig;
+ gsl_permutation * pmt=gsl_permutation_alloc (W->size2);
+ LUDecomp (WtW, pmt, &sig);
+ LUSolve (WtW, pmt, Wty, WtWiWty);
+
+ gsl_blas_dgemv (CblasNoTrans, -1.0, W, WtWiWty, 1.0, y);
+
+ gsl_matrix_free(WtW);
+ gsl_vector_free(Wty);
+ gsl_vector_free(WtWiWty);
+
+ return;
+}
+
+
+//standardize vector y to have mean 0 and y^ty/n=1
+void StandardizeVector (gsl_vector *y)
+{
+ double d=0.0, m=0.0, v=0.0;
+
+ for (size_t i=0; i<y->size; ++i) {
+ d=gsl_vector_get (y, i);
+ m+=d;
+ v+=d*d;
+ }
+ m/=(double)y->size;
+ v/=(double)y->size;
+ v-=m*m;
+
+ gsl_vector_add_constant (y, -1.0*m);
+ gsl_vector_scale (y, 1.0/sqrt(v));
+
+ return;
+}
+
+
//calculate UtX
-void CalcUtX (const gsl_matrix *U, gsl_matrix *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)
+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);
@@ -172,7 +268,7 @@ void CalcUtX (const gsl_matrix *U, const gsl_matrix *X, gsl_matrix *UtX)
return;
}
-void CalcUtX (const gsl_matrix *U, const gsl_vector *x, gsl_vector *Utx)
+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;
@@ -180,7 +276,7 @@ void CalcUtX (const gsl_matrix *U, const gsl_vector *x, gsl_vector *Utx)
//Kronecker product
-void Kronecker(const gsl_matrix *K, const gsl_matrix *V, gsl_matrix *H)
+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++) {
@@ -193,14 +289,14 @@ void Kronecker(const gsl_matrix *K, const gsl_matrix *V, gsl_matrix *H)
}
//symmetric K matrix
-void KroneckerSym(const gsl_matrix *K, const gsl_matrix *V, gsl_matrix *H)
+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);
@@ -211,38 +307,38 @@ void KroneckerSym(const gsl_matrix *K, const gsl_matrix *V, gsl_matrix *H)
}
-// this function calculates HWE p value with methods described in Wigginton et al., 2005 AJHG;
+// 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)
+ 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)
@@ -250,12 +346,12 @@ double CalcHWE (const size_t n_hom1, const size_t n_hom2, const size_t n_ab)
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;
@@ -264,27 +360,27 @@ double CalcHWE (const size_t n_hom1, const size_t n_hom2, const size_t n_ab)
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++)
@@ -293,18 +389,70 @@ double CalcHWE (const size_t n_hom1, const size_t n_hom2, const size_t n_ab)
continue;
p_hwe += het_probs[i];
}
-
+
p_hwe = p_hwe > 1.0 ? 1.0 : p_hwe;
-
+
free(het_probs);
-
+
return p_hwe;
}
+double UcharToDouble02(const unsigned char c) {
+ return (double)c*0.01;
+ // return (double)c*2/(double)UCHAR_MAX;
+}
+
+unsigned char Double02ToUchar(const double dosage) {
+ return (int) (dosage*100);
+ // return (int) (dosage/2*UCHAR_MAX);
+}
+
+
+
+
+
+void uchar_matrix_get_row (const vector<vector<unsigned char> > &X, const size_t i_row, VectorXd &x_row)
+{
+ if (i_row<X.size()) {
+ for (size_t j=0; j<x_row.size(); j++) {
+ x_row(j)=UcharToDouble02(X[i_row][j]);
+ }
+ } else {
+ std::cerr << "Error return genotype vector...\n";
+ exit(1);
+ }
+}
+
+
+/*
+void getGTgslVec(uchar ** X, gsl_vector *xvec, size_t marker_i, const size_t ni_test, const size_t ns_test){
+
+ double geno, geno_mean = 0.0;
+ if (marker_i < ns_test ) {
+ for (size_t j=0; j<ni_test; j++) {
+ geno = UcharToDouble(X[marker_i][j]);
+ //cout << geno << ", ";
+ if (geno < 0.0 || geno > 2.0) {
+ cerr << "wrong genotype value = " << geno << endl;
+ exit(1);
+ }
+ gsl_vector_set(xvec, j, geno);
+ geno_mean += geno;
+ }
+ geno_mean /= (double)ni_test;
+ geno_mean = -geno_mean;
+ gsl_vector_add_constant(xvec, geno_mean); // center genotypes here
+ }
+ else {
+ std::cerr << "Error return genotype vector...\n";
+ exit(1);
+ }
+ //cout << endl;
+}
+*/
-
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