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bkgd_interp.c
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bkgd_interp.c
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#include <glib.h>
#include <gsl/gsl_integration.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_spline.h>
#include "util/config.h"
#include "numer/numer.h"
#include "bkgd_interp.h"
#include "bkgd_param.h"
#include "bkgd_point.h"
#include "bkgd.h"
#include "bkgd_intg.h"
/**
* Returns the location of the next sample that we want to take given
* the current location by fitting a quadratic at the current
* position.
*/
static double get_r_next(double x, double bkgd, double b_drv1, double b_drv2) {
double a, b, c, c_new, discr, sq, x1,x2,x3,x4, closest;
/* Fit a curve to B at x by finding a with the same value, 1st and
* 2nd derivates at this point.
*/
/* find coefficients of quadratic */
a = 0.5 * b_drv2;
b = b_drv1 - b_drv2 * x;
c = a*x*x - b_drv1*x + bkgd;
/* now we want to find point where we estimate B will have changed
* by BKGD_OFFSET offset using the quadratic equation
*/
/* find next point that is offset GREATER */
c_new = c - bkgd-BKGD_OFFSET;
discr = b*b - 4*a*c_new;
if(discr < 0.0) {
x1 = x2 = x + BKGD_INTERP_MAX_DIST;
} else {
sq = sqrt(discr);
x1 = (-b + sq)/(2.0*a);
x2 = (-b - sq)/(2.0*a);
}
/* find next point that is offset LOWER */
c_new = c - bkgd+BKGD_OFFSET;
discr = b*b - 4*a*c_new;
if(discr < 0.0) {
x3 = x4 = x + BKGD_INTERP_MAX_DIST;
} else {
sq = sqrt(discr);
x3 = (-b + sq)/(2.0*a);
x4 = (-b + sq)/(2.0*a);
}
/* take closest point which is greater than x */
closest = x+BKGD_INTERP_MAX_DIST;
if(x1 > x && x1 < closest) {
closest = x1;
}
if(x2 > x && x2 < closest) {
closest = x2;
}
if(x3 > x && x3 < closest) {
closest = x3;
}
if(x4 > x && x4 < closest) {
closest = x4;
}
/* fprintf(stderr, "x1=%g, x2=%g, x3=%g, x4=%g closest=%g\n", */
/* x1, x2, x3, x4, closest); */
return closest;
}
/**
* Decides on what position should be evaluated next using quadratic
* extrapolation from last_p, and sets the attributes of p
* appropriately.
*/
static void get_next_point(BkgdInterp *bgi, BkgdPoint *last_p, BkgdPoint *p) {
double next_r, r_delta, b_delta;
long pos_delta;
int keep_point;
ConsBlock *cblk;
BkgdPoint *saved_p;
/* predict a good next r position */
next_r = get_r_next(last_p->r_pos, last_p->b,
last_p->b_drv1, last_p->b_drv2);
r_delta = 0.0;
/* check the queue of saved positions before evaluating B at new positions */
if(bgi->p_queue->length > 0) {
saved_p = g_queue_peek_head(bgi->p_queue);
if(saved_p->r_pos <= next_r) {
/* saved position is closer than predicted position, so try
* it instead
*/
/* calculate differences in saved position and last position */
b_delta = fabs(saved_p->b - last_p->b);
pos_delta = saved_p->pos - last_p->pos;
r_delta = (saved_p->r_pos - last_p->r_pos);
if(pos_delta > 1 && b_delta > BKGD_CHANGE_THRESH && r_delta > 0.0) {
/* Don't use saved position because still too far away */
/* instead try a position that is 1/4 as far away */
next_r = last_p->r_pos + r_delta * 0.25;
keep_point = FALSE;
} else {
/* saved position is good */
g_queue_pop_head(bgi->p_queue);
/* fprintf(stderr, "using saved point at %g, queue len=%d\n", */
/* saved_p->r_pos, bgi->p_queue->length); */
/* fprintf(stderr, "last_p->b=%g, saved_p->b: %g, " */
/* "b_delta=%g, pos_delta=%ld, r_delta=%g\n", */
/* last_p->b, saved_p->b, b_delta, pos_delta, r_delta); */
bkgd_point_copy(saved_p, p);
g_free(saved_p);
keep_point = TRUE;
}
} else {
/* predicted position is closer, try it instead */
keep_point = FALSE;
}
} else {
/* there are no saved positions so try predicted position */
keep_point = FALSE;
}
/* keep trying closer points until there are no closer points,
* or the change threshold is within our tolerance
*/
while(!keep_point) {
p->pos = last_p->pos+1;
/* find first base that is greater than next r position */
while((p->pos < bgi->chr_len) &&
(rectab_rpos(bgi->rtab,p->pos) < next_r)) {
p->pos += 1;
}
if((p->pos > last_p->pos+1) &&
(rectab_rpos(bgi->rtab,p->pos) > next_r)) {
/* backup one base so we don't exceed r pos we were aiming for */
p->pos -= 1;
}
p->r_pos = rectab_rpos(bgi->rtab,p->pos);
/* Update next_cons so that it points to next conserved block.
* Remember that p can move backwards if we chose a site that
* was too far ahead. When this happens we may have to backup in
* the conserved block list instead of moving forwards.
*/
/* first backup */
while(bgi->next_cons != NULL) {
cblk = bgi->next_cons->data;
if(cblk->start <= p->pos) {
break;
}
bgi->next_cons = g_list_previous(bgi->next_cons);
}
if(bgi->next_cons == NULL) {
bgi->next_cons = bgi->cons_list;
}
/* now advance */
while(bgi->next_cons != NULL) {
cblk = bgi->next_cons->data;
if(cblk->end >= p->pos) {
break;
}
bgi->next_cons = g_list_next(bgi->next_cons);
}
/* calculate B value and 1st/2nd derivatives at new position */
bkgd_calc_b(p, bgi->cons_list, bgi->next_cons,
bgi->parm, bgi->rtab->chr_r_len);
/* calculate differences in position and b between points */
b_delta = fabs(p->b - last_p->b);
pos_delta = p->pos - last_p->pos;
r_delta = (p->r_pos - last_p->r_pos);
/* fprintf(stderr, "B EVAL:p->pos=%ld, p->r_pos=%g, p->b=%g, " */
/* "last_p->b=%g, pos_delta=%ld,r_delta=%g, b_delta=%g\n", */
/* p->pos, p->r_pos, p->b, last_p->b, pos_delta, r_delta, b_delta); */
if(pos_delta > 1 && b_delta > BKGD_CHANGE_THRESH && r_delta > 0.0) {
/* We don't want use this point because it is still too far
* away. Push it onto queue for later use.
*/
g_queue_push_head(bgi->p_queue, bkgd_point_dup(p));
/* Try a position that is 1/4 as far away as last position we
* aimed for. Do not use r_delta here (which is always less than
* or equal to the difference we were aiming for) because if
* there is a jump in rec-dist at a particular site, we can end
* up trying the same position over and over again.
*/
next_r = last_p->r_pos + (next_r - last_p->r_pos)*0.25;
} else {
/* keep this position */
keep_point = TRUE;
}
}
/* update slope */
if(r_delta == 0.0) {
/* This occurs when two points are immediately adjacent (at least
* in rec dist). In this case there is no change in the B values
* between the points, so just call slope 0.
*/
bgi->slope = 0.0;
} else {
bgi->slope = (p->b - last_p->b) / r_delta;
}
}
/**
* Creates a new BkgdInterp structure, that is intended to
* transparently decide on appropriate locations to evaluate the B
* function and to perform interpolation between the locations where B
* was actually evaluated.
*/
BkgdInterp *bkgd_interp_new(RecRateTable *rtab, long chr_len,
GList *cons_list, BkgdParam *parm) {
BkgdInterp *bgi;
bgi = g_new(BkgdInterp, 1);
bgi->rtab = rtab;
bgi->chr_len = chr_len;
bgi->cons_list = cons_list;
bgi->next_cons = cons_list;
bgi->parm = parm;
bgi->p_queue = g_queue_new();
/* use first base on chr as first point */
bgi->p1 = g_new(BkgdPoint, 1);
bgi->p1->pos = 1;
bgi->p1->r_pos = rectab_rpos(rtab,1);
bkgd_calc_b(bgi->p1, bgi->cons_list, bgi->next_cons, parm, rtab->chr_r_len);
bgi->p2 = g_new(BkgdPoint, 1);
/* compute position of second point */
get_next_point(bgi, bgi->p1, bgi->p2);
return bgi;
}
/**
* Frees memory allocated for BkgdInterp.
*/
void bkgd_interp_free(BkgdInterp *bgi) {
BkgdPoint *p;
g_free(bgi->p1);
g_free(bgi->p2);
while(bgi->p_queue->length > 0) {
p = g_queue_pop_head(bgi->p_queue);
g_free(p);
}
g_queue_free(bgi->p_queue);
g_free(bgi);
}
/**
* Calculates an interpolated value at the desired position using the
* provided initialised interpolator.
*/
double bkgd_interp_eval(BkgdInterp *bgi, long pos) {
double r_delta;
BkgdPoint *p;
if(bgi->p2->pos < pos) {
/* need to find next point and update slope */
p = bgi->p1;
bgi->p1 = bgi->p2; /* second point becomes first point */
get_next_point(bgi, bgi->p1, p);
bgi->p2 = p; /* new point becomes second point */
}
/* perform linear interpolation (in recombination space) */
r_delta = rectab_rpos(bgi->rtab, pos) - bgi->p1->r_pos;
/* fprintf(stderr, "prev=%g, next=%g, slope=%g, r_delta=%g\n", */
/* bgi->p1->b, bgi->p2->b, bgi->slope, r_delta); */
return bgi->p1->b + r_delta*bgi->slope;
}