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// This file is part of PLINK 1.90, copyright (C) 2005-2017 Shaun Purcell,
// Christopher Chang.
//
// 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 "plink_common.h"
#include "plink_matrix.h"
#ifndef NOLAPACK
#ifndef __APPLE__
void xerbla_(void) {} // fix static linking error
#endif
#endif
inline double SQR(const double a) {
return a * a;
}
#ifdef __cplusplus
inline double SIGN(const double &a, const double &b) {
// PLINK helper.h SIGN() template specialized to doubles.
return (b >= 0)? (a >= 0 ? a : -a) : (a >= 0 ? -a : a);
}
#else
inline double SIGN(const double a, const double b) {
// PLINK helper.h SIGN() template specialized to doubles.
return (b >= 0)? (a >= 0 ? a : -a) : (a >= 0 ? -a : a);
}
#endif
double pythag(const double a, const double b) {
// PLINK stats.cpp pythag().
double absa,absb;
absa=fabs(a);
absb=fabs(b);
if (absa > absb) return absa*sqrt(1.0+SQR(absb/absa));
else return (absb == 0.0 ? 0.0 : absb*sqrt(1.0+SQR(absa/absb)));
}
#ifdef NOLAPACK
int32_t svdcmp_c(int32_t m, double* a, double* w, double* v) {
// C port of PLINK stats.cpp svdcmp().
// now thread-safe.
double* rv1 = &(w[(uint32_t)m]);
int32_t n = m;
int32_t flag;
int32_t l = 0; // suppress compile warning
int32_t i,its,j,jj,k,nm;
double anorm,c,f,g,h,s,scale,x,y,z;
double temp;
g=scale=anorm=0.0;
for (i=0;i<n;i++) {
l=i+2;
rv1[i]=scale*g;
g=s=scale=0.0;
if (i < m) {
for (k=i;k<m;k++) scale += fabs(a[k * m + i]);
if (scale != 0.0) {
for (k=i;k<m;k++) {
a[k * m + i] /= scale;
s += a[k * m + i]*a[k * m + i];
}
f=a[i * m + i];
g = -SIGN(sqrt(s),f);
h=f*g-s;
a[i * m + i]=f-g;
for (j=l-1;j<n;j++) {
for (s=0.0,k=i;k<m;k++) s += a[k * m + i]*a[k * m + j];
f=s/h;
for (k=i;k<m;k++) a[k * m + j] += f*a[k * m + i];
}
for (k=i;k<m;k++) a[k * m + i] *= scale;
}
}
w[i]=scale *g;
g=s=scale=0.0;
if (i+1 <= m && i+1 != n) {
for (k=l-1;k<n;k++) scale += fabs(a[i * m + k]);
if (scale != 0.0) {
for (k=l-1;k<n;k++) {
a[i * m + k] /= scale;
s += a[i * m + k]*a[i * m + k];
}
f=a[i * m + l-1];
g = -SIGN(sqrt(s),f);
h=f*g-s;
a[i * m + l-1]=f-g;
for (k=l-1;k<n;k++) rv1[k]=a[i * m + k]/h;
for (j=l-1;j<m;j++) {
for (s=0.0,k=l-1;k<n;k++) s += a[j * m + k]*a[i * m + k];
for (k=l-1;k<n;k++) a[j * m + k] += s*rv1[k];
}
for (k=l-1;k<n;k++) a[i * m + k] *= scale;
}
}
anorm=MAXV(anorm,(fabs(w[i])+fabs(rv1[i])));
}
for (i=n-1;i>=0;i--) {
if (i < n-1) {
if (g != 0.0) {
for (j=l;j<n;j++)
v[j * m + i]=(a[i * m + j]/a[i * m + l])/g;
for (j=l;j<n;j++) {
for (s=0.0,k=l;k<n;k++) s += a[i * m + k]*v[k * m + j];
for (k=l;k<n;k++) v[k * m + j] += s*v[k * m + i];
}
}
for (j=l;j<n;j++) v[i * m + j]=v[j * m + i]=0.0;
}
v[i * m + i]=1.0;
g=rv1[i];
l=i;
}
for (i=MINV(m,n)-1;i>=0;i--) {
l=i+1;
g=w[i];
for (j=l;j<n;j++) a[i * m + j]=0.0;
if (g != 0.0) {
g=1.0/g;
for (j=l;j<n;j++) {
for (s=0.0,k=l;k<m;k++) s += a[k * m + i]*a[k * m + j];
f=(s/a[i * m + i])*g;
for (k=i;k<m;k++) a[k * m + j] += f*a[k * m + i];
}
for (j=i;j<m;j++) a[j * m + i] *= g;
} else for (j=i;j<m;j++) a[j * m + i]=0.0;
++a[i * m + i];
}
for (k=n-1;k>=0;k--) {
for (its=0;its<30;its++) {
flag=1;
for (l=k;l>=0;l--) {
nm=l-1;
temp=fabs(rv1[l])+anorm;
if (temp == anorm) {
flag=0;
break;
}
temp=fabs(w[nm])+anorm;
if (temp == anorm) break;
}
if (flag) {
c=0.0;
s=1.0;
for (i=l;i<k+1;i++) {
f=s*rv1[i];
rv1[i]=c*rv1[i];
temp = fabs(f)+anorm;
if (temp == anorm) break;
g=w[i];
h=pythag(f,g);
w[i]=h;
h=1.0/h;
c=g*h;
s = -f*h;
for (j=0;j<m;j++) {
y=a[j * m + nm];
z=a[j * m + i];
a[j * m + nm]=y*c+z*s;
a[j * m + i]=z*c-y*s;
}
}
}
z=w[k];
if (l == k) {
if (z < 0.0) {
w[k] = -z;
for (j=0;j<n;j++) v[j * m + k] = -v[j * m + k];
}
break;
}
if (its == 29)
return 0; // cannot converge: multi-collinearity?
x=w[l];
nm=k-1;
y=w[nm];
g=rv1[nm];
h=rv1[k];
f=((y-z)*(y+z)+(g-h)*(g+h))/(2.0*h*y);
g=pythag(f,1.0);
f=((x-z)*(x+z)+h*((y/(f+SIGN(g,f)))-h))/x;
c=s=1.0;
for (j=l;j<=nm;j++) {
i=j+1;
g=rv1[i];
y=w[i];
h=s*g;
g=c*g;
z=pythag(f,h);
rv1[j]=z;
c=f/z;
s=h/z;
f=x*c+g*s;
g=g*c-x*s;
h=y*s;
y *= c;
for (jj=0;jj<n;jj++) {
x=v[jj * m + j];
z=v[jj * m + i];
v[jj * m + j]=x*c+z*s;
v[jj * m + i]=z*c-x*s;
}
z=pythag(f,h);
w[j]=z;
if (z) {
z=1.0/z;
c=f*z;
s=h*z;
}
f=c*g+s*y;
x=c*y-s*g;
for (jj=0;jj<m;jj++) {
y=a[jj * m + j];
z=a[jj * m + i];
a[jj * m + j]=y*c+z*s;
a[jj * m + i]=z*c-y*s;
}
}
rv1[l]=0.0;
rv1[k]=f;
w[k]=x;
}
}
return 1;
}
int32_t invert_matrix(int32_t dim, double* matrix, MATRIX_INVERT_BUF1_TYPE* dbl_1d_buf, double* dbl_2d_buf) {
// C port of PLINK stats.cpp's svd_inverse() function.
// Now thread-safe in NOLAPACK case.
// w -> dbl_1d_buf
// v -> dbl_2d_buf
const double eps = 1e-24;
int32_t i;
int32_t j;
int32_t k;
i = svdcmp_c(dim, matrix, dbl_1d_buf, dbl_2d_buf);
if (i == -1) {
return -1;
} else if (!i) {
return 1;
}
// Look for singular values
double wmax = 0;
for (i=0; i<dim; i++) {
wmax = dbl_1d_buf[i] > wmax ? dbl_1d_buf[i] : wmax;
}
double wmin = wmax * eps;
for (i=0; i<dim; i++) {
dbl_1d_buf[i] = dbl_1d_buf[i] < wmin ? 0 : (1 / dbl_1d_buf[i]);
}
for (i=0; i<dim; i++) {
for (j=0; j<dim; j++) {
matrix[i * dim + j] = matrix[i * dim + j] * dbl_1d_buf[j];
}
}
// [nxn].[t(v)]
for (i=0; i<dim; i++) {
fill_double_zero(dim, dbl_1d_buf);
for (j=0; j<dim; j++) {
for (k=0; k<dim; k++) {
dbl_1d_buf[j] += matrix[i * dim + k] * dbl_2d_buf[j * dim + k];
}
}
for (j = 0; j < dim; j++) {
matrix[i * dim + j] = dbl_1d_buf[j];
}
}
return 0;
}
#else
int32_t invert_matrix(__CLPK_integer dim, double* matrix, MATRIX_INVERT_BUF1_TYPE* int_1d_buf, double* dbl_2d_buf) {
// dgetrf_/dgetri_ is more efficient than dpotrf_/dpotri_ on OS X.
__CLPK_integer lwork = dim * dim;
__CLPK_integer info;
dgetrf_(&dim, &dim, matrix, &dim, int_1d_buf, &info);
dgetri_(&dim, matrix, &dim, int_1d_buf, dbl_2d_buf, &lwork, &info);
if (info) {
return 1;
}
return 0;
}
int32_t invert_matrix_checked(__CLPK_integer dim, double* matrix, MATRIX_INVERT_BUF1_TYPE* int_1d_buf, double* dbl_2d_buf) {
// This used to fall back on PLINK 1.07's SVD-based implementation when the
// rcond estimate was too small, but in practice that just slowed things down
// without meaningfully improving inversion of nonsingular matrices. So now
// this just exits a bit earlier, while leaving the old "binary search for
// the first row/column causing multicollinearity" logic to the caller.
__CLPK_integer lwork = dim * dim;
char cc = '1';
double norm = dlange_(&cc, &dim, &dim, matrix, &dim, dbl_2d_buf);
__CLPK_integer info;
double rcond;
dgetrf_(&dim, &dim, matrix, &dim, int_1d_buf, &info);
if (info > 0) {
return 1;
}
dgecon_(&cc, &dim, matrix, &dim, &norm, &rcond, dbl_2d_buf, &(int_1d_buf[dim]), &info);
if (rcond < MATRIX_SINGULAR_RCOND) {
return 1;
}
dgetri_(&dim, matrix, &dim, int_1d_buf, dbl_2d_buf, &lwork, &info);
return 0;
}
#endif
void col_major_matrix_multiply(__CLPK_integer row1_ct, __CLPK_integer col2_ct, __CLPK_integer common_ct, double* inmatrix1, double* inmatrix2, double* outmatrix) {
#ifdef NOLAPACK
uintptr_t row1_ct_l = row1_ct;
uintptr_t col2_ct_l = col2_ct;
uintptr_t common_ct_l = common_ct;
uintptr_t row_idx;
uintptr_t col_idx;
uintptr_t com_idx;
double* dptr;
double dxx;
// not optimized
for (col_idx = 0; col_idx < col2_ct_l; col_idx++) {
for (row_idx = 0; row_idx < row1_ct_l; row_idx++) {
dxx = 0;
dptr = &(inmatrix2[col_idx * common_ct]);
for (com_idx = 0; com_idx < common_ct_l; com_idx++) {
dxx += (*dptr++) * inmatrix1[com_idx * row1_ct_l + row_idx];
}
*outmatrix++ = dxx;
}
}
#else
#ifdef _WIN32
char blas_char = 'N';
double dyy = 1;
double dzz = 0;
dgemm_(&blas_char, &blas_char, &row1_ct, &col2_ct, &common_ct, &dyy, inmatrix1, &row1_ct, inmatrix2, &common_ct, &dzz, outmatrix, &row1_ct);
#else
cblas_dgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, row1_ct, col2_ct, common_ct, 1.0, inmatrix1, row1_ct, inmatrix2, common_ct, 0.0, outmatrix, row1_ct);
#endif // _WIN32
#endif // NOLAPACK
}
void col_major_fmatrix_multiply(__CLPK_integer row1_ct, __CLPK_integer col2_ct, __CLPK_integer common_ct, float* inmatrix1, float* inmatrix2, float* outmatrix) {
#ifdef NOLAPACK
uintptr_t row1_ct_l = row1_ct;
uintptr_t col2_ct_l = col2_ct;
uintptr_t common_ct_l = common_ct;
uintptr_t row_idx;
uintptr_t col_idx;
uintptr_t com_idx;
float* fptr;
float fxx;
// not optimized
for (col_idx = 0; col_idx < col2_ct_l; col_idx++) {
for (row_idx = 0; row_idx < row1_ct_l; row_idx++) {
fxx = 0;
fptr = &(inmatrix2[col_idx * common_ct]);
for (com_idx = 0; com_idx < common_ct_l; com_idx++) {
fxx += (*fptr++) * inmatrix1[com_idx * row1_ct_l + row_idx];
}
*outmatrix++ = fxx;
}
}
#else
#ifdef _WIN32
char blas_char = 'N';
float fyy = 1;
float fzz = 0;
sgemm_(&blas_char, &blas_char, &row1_ct, &col2_ct, &common_ct, &fyy, inmatrix1, &row1_ct, inmatrix2, &common_ct, &fzz, outmatrix, &row1_ct);
#else
cblas_sgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, row1_ct, col2_ct, common_ct, 1.0, inmatrix1, row1_ct, inmatrix2, common_ct, 0.0, outmatrix, row1_ct);
#endif // _WIN32
#endif // NOLAPACK
}
// Todo: replace these with cache-oblivious, or at least -friendlier,
// algorithms.
void transpose_copy(uintptr_t old_maj, uintptr_t new_maj, double* old_matrix, double* new_matrix) {
double* dptr;
uintptr_t new_maj_idx;
uintptr_t old_maj_idx;
for (new_maj_idx = 0; new_maj_idx < new_maj; new_maj_idx++) {
dptr = &(old_matrix[new_maj_idx]);
for (old_maj_idx = 0; old_maj_idx < old_maj; old_maj_idx++) {
*new_matrix++ = dptr[old_maj_idx * new_maj];
}
}
}
void transpose_copy_float(uintptr_t old_maj, uintptr_t new_maj, uint32_t new_maj_max, float* old_matrix, float* new_matrix) {
// new_maj = in-memory stride of old_matrix rows
// new_maj_max = actual number of rows in new_matrix
// (distinction is necessary for SSE alignment)
float* fptr;
uintptr_t new_maj_idx;
uintptr_t old_maj_idx;
for (new_maj_idx = 0; new_maj_idx < new_maj_max; new_maj_idx++) {
fptr = &(old_matrix[new_maj_idx]);
for (old_maj_idx = 0; old_maj_idx < old_maj; old_maj_idx++) {
*new_matrix++ = fptr[old_maj_idx * new_maj];
}
}
}
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