void calc_markprob(int n_ind, int n_pos, int n_gen, int *geno,
double *rf, double *rf2,
double error_prob, double *markprob,
double initf(int),
double emitf(int, int, double),
double stepf(int, int, double, double))
{
int i, j, j2, v, v2;
double **betal, **betar; /* betas for left and right sides of the chromosome */
int **Geno;
double ***Markprob;
/* allocate space for betal and betar and
reorganize geno and markprob */
reorg_geno(n_ind, n_pos, geno, &Geno);
reorg_genoprob(n_ind, n_pos, n_gen, markprob, &Markprob);
allocate_alpha(n_pos, n_gen, &betal);
allocate_alpha(n_pos, n_gen, &betar);
for(i=0; i<n_ind; i++) { /* i = individual */
/* initialize betal and betar */
for(v=0; v<n_gen; v++) {
betal[v][0] = 0.0;
betar[v][n_pos-1] = 0.0;
}
/* backward equations */
for(j=1,j2=n_pos-2; j<n_pos; j++, j2--) {
for(v=0; v<n_gen; v++) {
betal[v][j] = betal[0][j-1] + stepf(v+1, 1, rf[j-1], rf2[j-1]) +
emitf(Geno[j-1][i],1,error_prob);
betar[v][j2] = betar[0][j2+1] + stepf(v+1,1,rf[j2], rf2[j2]) +
emitf(Geno[j2+1][i],1,error_prob);
for(v2=1; v2<n_gen; v2++) {
betal[v][j] = addlog(betal[v][j], betal[v2][j-1] +
stepf(v+1,v2+1,rf[j-1],rf2[j-1]) +
emitf(Geno[j-1][i],v2+1,error_prob));
betar[v][j2] = addlog(betar[v][j2], betar[v2][j2+1] +
stepf(v+1,v2+1,rf[j2],rf2[j2]) +
emitf(Geno[j2+1][i],v2+1,error_prob));
}
}
}
/* calculate genotype probabilities */
for(j=0; j<n_pos; j++)
for(v=0; v<n_gen; v++)
Markprob[v][j][i] = exp(betal[v][j] + betar[v][j] + emitf(Geno[j][i], v+1, error_prob));
} /* loop over individuals */
}
void est_map_bci(int n_ind, int n_mar, int *geno, double *d,
int m, double p, double error_prob,
double *loglik, int maxit, double tol, int verbose)
{
int i, j, j2, v, v2, it, flag=0, **Geno, n_states;
double s, **alpha, **beta, **gamma, *cur_d, *rf;
double ***tm, *temp;
double curloglik;
double initprob;
int ndigits;
double maxdif, tempdif;
char pattern[100], text[200];
n_states = 2*(m+1);
initprob = -log((double)n_states);
/* allocate space for beta and reorganize geno */
reorg_geno(n_ind, n_mar, geno, &Geno);
allocate_alpha(n_mar, n_states, &alpha);
allocate_alpha(n_mar, n_states, &beta);
allocate_dmatrix(n_states, n_states, &gamma);
allocate_double(n_mar-1, &cur_d);
allocate_double(n_mar-1, &rf);
/* allocate space for the transition matrices */
/* size n_states x n_states x (n_mar-1) */
/* tm[state1][state2][interval] */
tm = (double ***)R_alloc(n_states, sizeof(double **));
tm[0] = (double **)R_alloc(n_states * n_states, sizeof(double *));
for(i=1; i<n_states; i++) tm[i] = tm[i-1] + n_states;
tm[0][0] = (double *)R_alloc(n_states * n_states * (n_mar - 1),
sizeof(double));
temp = tm[0][0];
for(i=0; i < n_states; i++) {
for(j=0; j < n_states; j++) {
tm[i][j] = temp;
temp += n_mar-1;
}
}
/* digits in verbose output */
if(verbose) {
ndigits = (int)ceil(-log10(tol));
if(ndigits > 16) ndigits=16;
sprintf(pattern, "%s%d.%df", "%", ndigits+3, ndigits+1);
}
for(j=0; j<n_mar-1; j++) d[j] /= 100.0; /* convert to Morgans */
/* begin EM algorithm */
for(it=0; it<maxit; it++) {
for(j=0; j<n_mar-1; j++) {
cur_d[j] = d[j];
rf[j] = 0.0;
}
/* calculate the transition matrices */
step_bci(n_mar, n_states, tm, cur_d, m, p, maxit, tol);
for(i=0; i<n_ind; i++) { /* i = individual */
R_CheckUserInterrupt(); /* check for ^C */
/* initialize alpha and beta */
for(v=0; v<n_states; v++) {
alpha[v][0] = initprob + emit_bci(Geno[0][i], v, error_prob, m);
beta[v][n_mar-1] = 0.0;
}
/* forward-backward equations */
for(j=1,j2=n_mar-2; j<n_mar; j++, j2--) {
for(v=0; v<n_states; v++) {
alpha[v][j] = alpha[0][j-1] + tm[0][v][j-1];
beta[v][j2] = beta[0][j2+1] + tm[v][0][j2] +
emit_bci(Geno[j2+1][i], 0, error_prob, m);
for(v2=1; v2<n_states; v2++) {
alpha[v][j] = addlog(alpha[v][j], alpha[v2][j-1] +
tm[v2][v][j-1]);
beta[v][j2] = addlog(beta[v][j2], beta[v2][j2+1] +
tm[v][v2][j2] +
emit_bci(Geno[j2+1][i], v2, error_prob, m));
}
alpha[v][j] += emit_bci(Geno[j][i], v, error_prob, m);
}
}
for(j=0; j<n_mar-1; j++) {
/* calculate gamma = log Pr(v1, v2, O) */
for(v=0, s=0.0; v<n_states; v++) {
for(v2=0; v2<n_states; v2++) {
gamma[v][v2] = alpha[v][j] + beta[v2][j+1] +
emit_bci(Geno[j+1][i], v2, error_prob, m) +
tm[v][v2][j];
if(v==0 && v2==0) s = gamma[v][v2];
else s = addlog(s, gamma[v][v2]);
}
}
for(v=0; v<n_states; v++) {
for(v2=0; v2<n_states; v2++) {
rf[j] += nrec_bci(v, v2, m) * exp(gamma[v][v2] - s);
}
}
}
} /* loop over individuals */
/* rescale */
for(j=0; j<n_mar-1; j++) {
rf[j] /= (double)n_ind;
/*
if(rf[j] < tol/100.0) rf[j] = tol/100.0;
else if(rf[j] > 0.5-tol/100.0) rf[j] = 0.5-tol/100.0;
*/
}
/* use map function to convert back to distances */
for(j=0; j<n_mar-1; j++)
d[j] = imf_stahl(rf[j], m, p, 1e-10, 1000);
if(verbose>1) {
/* print estimates as we go along*/
Rprintf(" %4d ", it+1);
maxdif=0.0;
for(j=0; j<n_mar-1; j++) {
tempdif = fabs(d[j] - cur_d[j])/(cur_d[j]+tol*100.0);
if(maxdif < tempdif) maxdif = tempdif;
}
sprintf(text, "%s%s\n", " max rel've change = ", pattern);
Rprintf(text, maxdif);
}
/* check convergence */
for(j=0, flag=0; j<n_mar-1; j++) {
if(fabs(d[j] - cur_d[j]) > tol*(cur_d[j]+tol*100.0)) {
flag = 1;
break;
}
}
if(!flag) break;
} /* end EM algorithm */
if(flag) warning("Didn't converge!\n");
/* re-calculate transition matrices */
step_bci(n_mar, n_states, tm, d, m, p, maxit, tol);
/* calculate log likelihood */
*loglik = 0.0;
for(i=0; i<n_ind; i++) { /* i = individual */
R_CheckUserInterrupt(); /* check for ^C */
/* initialize alpha */
for(v=0; v<n_states; v++)
alpha[v][0] = initprob + emit_bci(Geno[0][i], v, error_prob, m);
/* forward equations */
for(j=1; j<n_mar; j++) {
for(v=0; v<n_states; v++) {
alpha[v][j] = alpha[0][j-1] + tm[0][v][j-1];
for(v2=1; v2<n_states; v2++)
alpha[v][j] = addlog(alpha[v][j], alpha[v2][j-1] +
tm[v2][v][j-1]);
alpha[v][j] += emit_bci(Geno[j][i], v, error_prob, m);
}
}
curloglik = alpha[0][n_mar-1];
for(v=1; v<n_states; v++)
curloglik = addlog(curloglik, alpha[v][n_mar-1]);
*loglik += curloglik;
}
if(verbose) {
if(verbose < 2) {
/* print final estimates */
Rprintf(" no. iterations = %d\n", it+1);
maxdif=0.0;
for(j=0; j<n_mar-1; j++) {
tempdif = fabs(d[j] - cur_d[j])/(cur_d[j]+tol*100.0);
if(maxdif < tempdif) maxdif = tempdif;
}
sprintf(text, "%s%s\n", " max rel've change at last step = ", pattern);
Rprintf(text, maxdif);
}
Rprintf(" loglik: %10.4lf\n\n", *loglik);
}
/* convert distances back to cM */
for(j=0; j<n_mar-1; j++) d[j] *= 100.0;
}
void est_map_f2i(int n_ind, int n_mar, int *geno, double *d,
int m, double p, double error_prob,
double *loglik, int maxit, double tol, int verbose)
{
int i, j, j2, v, v2, it, flag=0, **Geno, n_states, n_bcstates;
double s, **alpha, **beta, **gamma, *cur_d, *rf;
double ***tm, *temp;
double curloglik;
double initprob;
n_bcstates = 2*(m+1);
n_states = n_bcstates*n_bcstates;
initprob = -log((double)n_states);
/* allocate space for beta and reorganize geno */
reorg_geno(n_ind, n_mar, geno, &Geno);
allocate_alpha(n_mar, n_states, &alpha);
allocate_alpha(n_mar, n_states, &beta);
allocate_dmatrix(n_states, n_states, &gamma);
allocate_double(n_mar-1, &cur_d);
allocate_double(n_mar-1, &rf);
/* allocate space for the [backcross] transition matrices */
/* size n_states x n_states x (n_mar-1) */
/* tm[state1][state2][interval] */
tm = (double ***)R_alloc(n_bcstates, sizeof(double **));
tm[0] = (double **)R_alloc(n_bcstates * n_bcstates, sizeof(double *));
for(i=1; i<n_bcstates; i++) tm[i] = tm[i-1] + n_bcstates;
tm[0][0] = (double *)R_alloc(n_bcstates * n_bcstates * (n_mar - 1),
sizeof(double));
temp = tm[0][0];
for(i=0; i < n_bcstates; i++) {
for(j=0; j < n_bcstates; j++) {
tm[i][j] = temp;
temp += n_mar-1;
}
}
if(verbose) {
/* print initial estimates */
Rprintf(" ");
for(j=0; j<n_mar-1; j++) Rprintf("%.3lf ", d[j]);
Rprintf("\n");
}
for(j=0; j<n_mar-1; j++) d[j] /= 100.0; /* convert to Morgans */
/* begin EM algorithm */
for(it=0; it<maxit; it++) {
for(j=0; j<n_mar-1; j++) {
cur_d[j] = d[j];
rf[j] = 0.0;
}
/* calculate the transition matrices [for BC] */
step_bci(n_mar, n_bcstates, tm, cur_d, m, p, maxit, tol);
for(i=0; i<n_ind; i++) { /* i = individual */
R_CheckUserInterrupt(); /* check for ^C */
/* initialize alpha and beta */
for(v=0; v<n_states; v++) {
alpha[v][0] = initprob + emit_f2i(Geno[0][i], v, error_prob, m, n_bcstates);
beta[v][n_mar-1] = 0.0;
}
/* forward-backward equations */
for(j=1,j2=n_mar-2; j<n_mar; j++, j2--) {
for(v=0; v<n_states; v++) {
alpha[v][j] = alpha[0][j-1] + step_f2i(0, v, j-1, tm, n_bcstates);
beta[v][j2] = beta[0][j2+1] + step_f2i(v, 0, j2, tm, n_bcstates) +
emit_f2i(Geno[j2+1][i], 0, error_prob, m, n_bcstates);
for(v2=1; v2<n_states; v2++) {
alpha[v][j] = addlog(alpha[v][j], alpha[v2][j-1] +
step_f2i(v2, v, j-1, tm, n_bcstates));
beta[v][j2] = addlog(beta[v][j2], beta[v2][j2+1] +
step_f2i(v, v2, j2, tm, n_bcstates) +
emit_f2i(Geno[j2+1][i], v2, error_prob, m, n_bcstates));
}
alpha[v][j] += emit_f2i(Geno[j][i], v, error_prob, m, n_bcstates);
}
}
for(j=0; j<n_mar-1; j++) {
/* calculate gamma = log Pr(v1, v2, O) */
for(v=0, s=0.0; v<n_states; v++) {
for(v2=0; v2<n_states; v2++) {
gamma[v][v2] = alpha[v][j] + beta[v2][j+1] +
emit_f2i(Geno[j+1][i], v2, error_prob, m, n_bcstates) +
step_f2i(v, v2, j, tm, n_bcstates);
if(v==0 && v2==0) s = gamma[v][v2];
else s = addlog(s, gamma[v][v2]);
}
}
for(v=0; v<n_states; v++) {
for(v2=0; v2<n_states; v2++) {
rf[j] += nrec_f2i(v, v2, m, n_bcstates) * exp(gamma[v][v2] - s);
}
}
}
} /* loop over individuals */
/* rescale */
for(j=0; j<n_mar-1; j++) {
rf[j] /= (double)n_ind;
/*
if(rf[j] < tol/100.0) rf[j] = tol/100.0;
else if(rf[j] > 0.5-tol/100.0) rf[j] = 0.5-tol/100.0;
*/
}
/* use map function to convert back to distances */
for(j=0; j<n_mar-1; j++)
d[j] = imf_stahl(rf[j], m, p, 1e-10, 1000);
if(verbose > 1) { /* print some debugging stuff */
if(verbose == 2) Rprintf("Iteration");
Rprintf(" %4d ", it+1);
if(verbose > 2)
for(j=0; j<n_mar-1; j++) Rprintf("%.3lf ", d[j]*100.0);
Rprintf("\n");
}
/* check convergence */
for(j=0, flag=0; j<n_mar-1; j++) {
if(fabs(d[j] - cur_d[j]) > tol*(cur_d[j]+tol*100.0)) {
flag = 1;
break;
}
}
if(!flag) break;
} /* end EM algorithm */
if(flag) warning("Didn't converge!\n");
/* re-calculate transition matrices */
step_bci(n_mar, n_bcstates, tm, d, m, p, maxit, tol);
/* calculate log likelihood */
*loglik = 0.0;
for(i=0; i<n_ind; i++) { /* i = individual */
/* initialize alpha */
for(v=0; v<n_states; v++)
alpha[v][0] = initprob + emit_f2i(Geno[0][i], v, error_prob, m, n_bcstates);
/* forward equations */
for(j=1; j<n_mar; j++) {
for(v=0; v<n_states; v++) {
alpha[v][j] = alpha[0][j-1] + step_f2i(0, v, j-1, tm, n_bcstates);
for(v2=1; v2<n_states; v2++)
alpha[v][j] = addlog(alpha[v][j], alpha[v2][j-1] +
step_f2i(v2, v, j-1, tm, n_bcstates));
alpha[v][j] += emit_f2i(Geno[j][i], v, error_prob, m, n_bcstates);
}
}
curloglik = alpha[0][n_mar-1];
for(v=1; v<n_states; v++)
curloglik = addlog(curloglik, alpha[v][n_mar-1]);
*loglik += curloglik;
}
/* convert distances back to cM */
for(j=0; j<n_mar-1; j++) d[j] *= 100.0;
if(verbose) {
/* print final estimates */
Rprintf(" %4d ", it+1);
for(j=0; j<n_mar-1; j++) Rprintf("%.3lf ", d[j]);
Rprintf("\n");
Rprintf("loglik: %10.4lf\n\n", *loglik);
}
}
void calc_pairprob(int n_ind, int n_pos, int n_gen, int *geno,
double *rf, double *rf2,
double error_prob, double *genoprob,
double *pairprob,
double initf(int, int *),
double emitf(int, int, double, int *),
double stepf(int, int, double, double, int *))
{
int i, j, j2, v, v2, v3;
double s=0.0, **alpha, **beta;
int **Geno;
double ***Genoprob, *****Pairprob;
int cross_scheme[2];
/* cross scheme hidden in genoprob argument; used by hmm_bcsft */
cross_scheme[0] = genoprob[0];
cross_scheme[1] = genoprob[1];
genoprob[0] = 0.0;
genoprob[1] = 0.0;
/* n_pos must be at least 2, or there are no pairs! */
if(n_pos < 2) error("n_pos must be > 1 in calc_pairprob");
/* allocate space for alpha and beta and
reorganize geno, genoprob, and pairprob */
reorg_geno(n_ind, n_pos, geno, &Geno);
reorg_genoprob(n_ind, n_pos, n_gen, genoprob, &Genoprob);
reorg_pairprob(n_ind, n_pos, n_gen, pairprob, &Pairprob);
allocate_alpha(n_pos, n_gen, &alpha);
allocate_alpha(n_pos, n_gen, &beta);
for(i=0; i<n_ind; i++) { /* i = individual */
R_CheckUserInterrupt(); /* check for ^C */
/* initialize alpha and beta */
for(v=0; v<n_gen; v++) {
alpha[v][0] = initf(v+1, cross_scheme) + emitf(Geno[0][i], v+1, error_prob, cross_scheme);
beta[v][n_pos-1] = 0.0;
}
/* forward-backward equations */
for(j=1,j2=n_pos-2; j<n_pos; j++, j2--) {
for(v=0; v<n_gen; v++) {
alpha[v][j] = alpha[0][j-1] + stepf(1, v+1, rf[j-1], rf2[j-1], cross_scheme);
beta[v][j2] = beta[0][j2+1] + stepf(v+1,1,rf[j2], rf2[j2], cross_scheme) +
emitf(Geno[j2+1][i],1,error_prob, cross_scheme);
for(v2=1; v2<n_gen; v2++) {
alpha[v][j] = addlog(alpha[v][j], alpha[v2][j-1] +
stepf(v2+1,v+1,rf[j-1],rf2[j-1], cross_scheme));
beta[v][j2] = addlog(beta[v][j2], beta[v2][j2+1] +
stepf(v+1,v2+1,rf[j2],rf2[j2], cross_scheme) +
emitf(Geno[j2+1][i],v2+1,error_prob, cross_scheme));
}
alpha[v][j] += emitf(Geno[j][i],v+1,error_prob, cross_scheme);
}
}
/* calculate genotype probabilities */
for(j=0; j<n_pos; j++) {
s = Genoprob[0][j][i] = alpha[0][j] + beta[0][j];
for(v=1; v<n_gen; v++) {
Genoprob[v][j][i] = alpha[v][j] + beta[v][j];
s = addlog(s, Genoprob[v][j][i]);
}
for(v=0; v<n_gen; v++)
Genoprob[v][j][i] = exp(Genoprob[v][j][i] - s);
}
/* calculate Pr(G[j], G[j+1] | marker data) for i = 1...n_pos-1 */
for(j=0; j<n_pos-1; j++) {
for(v=0; v<n_gen; v++) {
for(v2=0; v2<n_gen; v2++) {
Pairprob[v][v2][j][j+1][i] = alpha[v][j] + beta[v2][j+1] +
stepf(v+1,v2+1,rf[j],rf2[j], cross_scheme) +
emitf(Geno[j+1][i],v2+1,error_prob, cross_scheme);
if(v==0 && v2==0) s=Pairprob[v][v2][j][j+1][i];
else s = addlog(s,Pairprob[v][v2][j][j+1][i]);
}
}
/* scale to sum to 1 */
for(v=0; v<n_gen; v++)
for(v2=0; v2<n_gen; v2++)
Pairprob[v][v2][j][j+1][i] =
exp(Pairprob[v][v2][j][j+1][i] - s);
}
/* now calculate Pr(G[i], G[j] | marker data) for j > i+1 */
for(j=0; j<n_pos-2; j++) {
for(j2=j+2; j2<n_pos; j2++) {
for(v=0; v<n_gen; v++) { /* genotype at pos'n j */
for(v2=0; v2<n_gen; v2++) { /* genotype at pos'n j2 */
Pairprob[v][v2][j][j2][i] = 0.0;
for(v3=0; v3<n_gen; v3++) { /* genotype at pos'n j2-1 */
s = Genoprob[v3][j2-1][i];
if(fabs(s) > TOL) /* avoid 0/0 */
Pairprob[v][v2][j][j2][i] += Pairprob[v][v3][j][j2-1][i]*
Pairprob[v3][v2][j2-1][j2][i]/s;
}
}
} /* end loops over genotypes */
}
} /* end loops over pairs of positions */
} /* end loop over individuals */
}
void calc_genoprob(int n_ind, int n_pos, int n_gen, int *geno,
double *rf, double *rf2,
double error_prob, double *genoprob,
double initf(int, int *),
double emitf(int, int, double, int *),
double stepf(int, int, double, double, int *))
{
int i, j, j2, v, v2;
double s, **alpha, **beta;
int **Geno;
double ***Genoprob;
int cross_scheme[2];
/* cross scheme hidden in genoprob argument; used by hmm_bcsft */
cross_scheme[0] = genoprob[0];
cross_scheme[1] = genoprob[1];
genoprob[0] = 0.0;
genoprob[1] = 0.0;
/* allocate space for alpha and beta and
reorganize geno and genoprob */
reorg_geno(n_ind, n_pos, geno, &Geno);
reorg_genoprob(n_ind, n_pos, n_gen, genoprob, &Genoprob);
allocate_alpha(n_pos, n_gen, &alpha);
allocate_alpha(n_pos, n_gen, &beta);
for(i=0; i<n_ind; i++) { /* i = individual */
R_CheckUserInterrupt(); /* check for ^C */
/* initialize alpha and beta */
for(v=0; v<n_gen; v++) {
alpha[v][0] = initf(v+1, cross_scheme) + emitf(Geno[0][i], v+1, error_prob, cross_scheme);
beta[v][n_pos-1] = 0.0;
}
/* forward-backward equations */
for(j=1,j2=n_pos-2; j<n_pos; j++, j2--) {
for(v=0; v<n_gen; v++) {
alpha[v][j] = alpha[0][j-1] + stepf(1, v+1, rf[j-1], rf2[j-1], cross_scheme);
beta[v][j2] = beta[0][j2+1] + stepf(v+1,1,rf[j2], rf2[j2], cross_scheme) +
emitf(Geno[j2+1][i],1,error_prob, cross_scheme);
for(v2=1; v2<n_gen; v2++) {
alpha[v][j] = addlog(alpha[v][j], alpha[v2][j-1] +
stepf(v2+1,v+1,rf[j-1],rf2[j-1], cross_scheme));
beta[v][j2] = addlog(beta[v][j2], beta[v2][j2+1] +
stepf(v+1,v2+1,rf[j2],rf2[j2], cross_scheme) +
emitf(Geno[j2+1][i],v2+1,error_prob, cross_scheme));
}
alpha[v][j] += emitf(Geno[j][i],v+1,error_prob, cross_scheme);
}
}
/* calculate genotype probabilities */
for(j=0; j<n_pos; j++) {
s = Genoprob[0][j][i] = alpha[0][j] + beta[0][j];
for(v=1; v<n_gen; v++) {
Genoprob[v][j][i] = alpha[v][j] + beta[v][j];
s = addlog(s, Genoprob[v][j][i]);
}
for(v=0; v<n_gen; v++)
Genoprob[v][j][i] = exp(Genoprob[v][j][i] - s);
}
/* the following is the old version */
/* for(j=0; j<n_pos; j++) {
s = 0.0;
for(v=0; v<n_gen; v++)
s += (Genoprob[v][j][i] = exp(alpha[v][j] + beta[v][j]));
for(v=0; v<n_gen; v++)
Genoprob[v][j][i] /= s;
} */
} /* loop over individuals */
}
void est_map(int n_ind, int n_mar, int n_gen, int *geno, double *rf,
double *rf2, double error_prob, double initf(int, int *),
double emitf(int, int, double, int *),
double stepf(int, int, double, double, int *),
double nrecf1(int, int, double, int*), double nrecf2(int, int, double, int*),
double *loglik, int maxit, double tol, int sexsp,
int verbose)
{
int i, j, j2, v, v2, it, flag=0, **Geno, ndigits;
double s, **alpha, **beta, **gamma, *cur_rf, *cur_rf2;
double curloglik, maxdif, temp;
char pattern[100], text[200];
int cross_scheme[2];
/* cross scheme hidden in loglik argument; used by hmm_bcsft */
cross_scheme[0] = (int) ftrunc(*loglik / 1000.0);
cross_scheme[1] = ((int) *loglik) - 1000 * cross_scheme[0];
*loglik = 0.0;
/* allocate space for beta and reorganize geno */
reorg_geno(n_ind, n_mar, geno, &Geno);
allocate_alpha(n_mar, n_gen, &alpha);
allocate_alpha(n_mar, n_gen, &beta);
allocate_dmatrix(n_gen, n_gen, &gamma);
allocate_double(n_mar-1, &cur_rf);
allocate_double(n_mar-1, &cur_rf2);
/* digits in verbose output */
if(verbose) {
ndigits = (int)ceil(-log10(tol));
if(ndigits > 16) ndigits=16;
sprintf(pattern, "%s%d.%df", "%", ndigits+3, ndigits+1);
}
/* begin EM algorithm */
for(it=0; it<maxit; it++) {
for(j=0; j<n_mar-1; j++) {
cur_rf[j] = cur_rf2[j] = rf[j];
rf[j] = 0.0;
if(sexsp) {
cur_rf2[j] = rf2[j];
rf2[j] = 0.0;
}
}
for(i=0; i<n_ind; i++) { /* i = individual */
R_CheckUserInterrupt(); /* check for ^C */
/* initialize alpha and beta */
for(v=0; v<n_gen; v++) {
alpha[v][0] = initf(v+1, cross_scheme) + emitf(Geno[0][i], v+1, error_prob, cross_scheme);
beta[v][n_mar-1] = 0.0;
}
/* forward-backward equations */
for(j=1,j2=n_mar-2; j<n_mar; j++, j2--) {
for(v=0; v<n_gen; v++) {
alpha[v][j] = alpha[0][j-1] + stepf(1, v+1, cur_rf[j-1], cur_rf2[j-1], cross_scheme);
beta[v][j2] = beta[0][j2+1] + stepf(v+1,1,cur_rf[j2], cur_rf2[j2], cross_scheme) +
emitf(Geno[j2+1][i],1,error_prob, cross_scheme);
for(v2=1; v2<n_gen; v2++) {
alpha[v][j] = addlog(alpha[v][j], alpha[v2][j-1] +
stepf(v2+1,v+1,cur_rf[j-1],cur_rf2[j-1], cross_scheme));
beta[v][j2] = addlog(beta[v][j2], beta[v2][j2+1] +
stepf(v+1,v2+1,cur_rf[j2],cur_rf2[j2], cross_scheme) +
emitf(Geno[j2+1][i],v2+1,error_prob, cross_scheme));
}
alpha[v][j] += emitf(Geno[j][i],v+1,error_prob, cross_scheme);
}
}
for(j=0; j<n_mar-1; j++) {
/* calculate gamma = log Pr(v1, v2, O) */
for(v=0, s=0.0; v<n_gen; v++) {
for(v2=0; v2<n_gen; v2++) {
gamma[v][v2] = alpha[v][j] + beta[v2][j+1] +
emitf(Geno[j+1][i], v2+1, error_prob, cross_scheme) +
stepf(v+1, v2+1, cur_rf[j], cur_rf2[j], cross_scheme);
if(v==0 && v2==0) s = gamma[v][v2];
else s = addlog(s, gamma[v][v2]);
}
}
for(v=0; v<n_gen; v++) {
for(v2=0; v2<n_gen; v2++) {
rf[j] += nrecf1(v+1,v2+1, cur_rf[j], cross_scheme) * exp(gamma[v][v2] - s);
if(sexsp) rf2[j] += nrecf2(v+1,v2+1, cur_rf[j], cross_scheme) * exp(gamma[v][v2] - s);
}
}
}
} /* loop over individuals */
/* rescale */
for(j=0; j<n_mar-1; j++) {
rf[j] /= (double)n_ind;
if(rf[j] < tol/1000.0) rf[j] = tol/1000.0;
else if(rf[j] > 0.5-tol/1000.0) rf[j] = 0.5-tol/1000.0;
if(sexsp) {
rf2[j] /= (double)n_ind;
if(rf2[j] < tol/1000.0) rf2[j] = tol/1000.0;
else if(rf2[j] > 0.5-tol/1000.0) rf2[j] = 0.5-tol/1000.0;
}
else rf2[j] = rf[j];
}
if(verbose>1) {
/* print estimates as we go along*/
Rprintf(" %4d ", it+1);
maxdif=0.0;
for(j=0; j<n_mar-1; j++) {
temp = fabs(rf[j] - cur_rf[j])/(cur_rf[j]+tol*100.0);
if(maxdif < temp) maxdif = temp;
if(sexsp) {
temp = fabs(rf2[j] - cur_rf2[j])/(cur_rf2[j]+tol*100.0);
if(maxdif < temp) maxdif = temp;
}
/* bsy add */
if(verbose > 2)
Rprintf("%d %f %f\n", j+1, cur_rf[j], rf[j]);
/* bsy add */
}
sprintf(text, "%s%s\n", " max rel've change = ", pattern);
Rprintf(text, maxdif);
}
/* check convergence */
for(j=0, flag=0; j<n_mar-1; j++) {
if(fabs(rf[j] - cur_rf[j]) > tol*(cur_rf[j]+tol*100.0) ||
(sexsp && fabs(rf2[j] - cur_rf2[j]) > tol*(cur_rf2[j]+tol*100.0))) {
flag = 1;
break;
}
}
if(!flag) break;
} /* end EM algorithm */
if(flag) warning("Didn't converge!\n");
/* calculate log likelihood */
*loglik = 0.0;
for(i=0; i<n_ind; i++) { /* i = individual */
/* initialize alpha */
for(v=0; v<n_gen; v++) {
alpha[v][0] = initf(v+1, cross_scheme) + emitf(Geno[0][i], v+1, error_prob, cross_scheme);
}
/* forward equations */
for(j=1; j<n_mar; j++) {
for(v=0; v<n_gen; v++) {
alpha[v][j] = alpha[0][j-1] +
stepf(1, v+1, rf[j-1], rf2[j-1], cross_scheme);
for(v2=1; v2<n_gen; v2++)
alpha[v][j] = addlog(alpha[v][j], alpha[v2][j-1] +
stepf(v2+1,v+1,rf[j-1],rf2[j-1], cross_scheme));
alpha[v][j] += emitf(Geno[j][i],v+1,error_prob, cross_scheme);
}
}
curloglik = alpha[0][n_mar-1];
for(v=1; v<n_gen; v++)
curloglik = addlog(curloglik, alpha[v][n_mar-1]);
*loglik += curloglik;
}
if(verbose) {
if(verbose < 2) {
/* print final estimates */
Rprintf(" no. iterations = %d\n", it+1);
maxdif=0.0;
for(j=0; j<n_mar-1; j++) {
temp = fabs(rf[j] - cur_rf[j])/(cur_rf[j]+tol*100.0);
if(maxdif < temp) maxdif = temp;
if(sexsp) {
temp = fabs(rf2[j] - cur_rf2[j])/(cur_rf2[j]+tol*100.0);
if(maxdif < temp) maxdif = temp;
}
}
sprintf(text, "%s%s\n", " max rel've change at last step = ", pattern);
Rprintf(text, maxdif);
}
Rprintf(" loglik: %10.4lf\n\n", *loglik);
}
}
void sim_geno(int n_ind, int n_pos, int n_gen, int n_draws,
int *geno, double *rf, double *rf2,
double error_prob, int *draws,
double initf(int, int *),
double emitf(int, int, double, int *),
double stepf(int, int, double, double, int *))
{
int i, k, j, v, v2;
double s, **beta, *probs;
int **Geno, ***Draws, curstate;
int cross_scheme[2];
/* cross scheme hidden in draws argument; used by hmm_bcsft */
cross_scheme[0] = draws[0];
cross_scheme[1] = draws[1];
draws[0] = 0;
draws[1] = 0;
/* allocate space for beta and
reorganize geno and draws */
/* Geno indexed as Geno[pos][ind] */
/* Draws indexed as Draws[rep][pos][ind] */
reorg_geno(n_ind, n_pos, geno, &Geno);
reorg_draws(n_ind, n_pos, n_draws, draws, &Draws);
allocate_alpha(n_pos, n_gen, &beta);
allocate_double(n_gen, &probs);
/* Read R's random seed */
GetRNGstate();
for(i=0; i<n_ind; i++) { /* i = individual */
R_CheckUserInterrupt(); /* check for ^C */
/* do backward equations */
/* initialize beta */
for(v=0; v<n_gen; v++) beta[v][n_pos-1] = 0.0;
/* backward equations */
for(j=n_pos-2; j>=0; j--) {
for(v=0; v<n_gen; v++) {
beta[v][j] = beta[0][j+1] + stepf(v+1,1,rf[j], rf2[j], cross_scheme) +
emitf(Geno[j+1][i],1,error_prob, cross_scheme);
for(v2=1; v2<n_gen; v2++)
beta[v][j] = addlog(beta[v][j], beta[v2][j+1] +
stepf(v+1,v2+1,rf[j],rf2[j], cross_scheme) +
emitf(Geno[j+1][i],v2+1,error_prob, cross_scheme));
}
}
for(k=0; k<n_draws; k++) { /* k = simulation replicate */
/* first draw */
/* calculate probs */
s = (probs[0] = initf(1, cross_scheme)+emitf(Geno[0][i],1,error_prob, cross_scheme)+beta[0][0]);
for(v=1; v<n_gen; v++) {
probs[v] = initf(v+1, cross_scheme) + emitf(Geno[0][i], v+1, error_prob, cross_scheme) +
beta[v][0];
s = addlog(s, probs[v]);
}
for(v=0; v<n_gen; v++) probs[v] = exp(probs[v] - s);
/* make draw: returns a value from {1, 2, ..., n_gen} */
curstate = Draws[k][0][i] = sample_int(n_gen, probs);
/* move along chromosome */
for(j=1; j<n_pos; j++) {
/* calculate probs */
for(v=0; v<n_gen; v++)
probs[v] = exp(stepf(curstate,v+1,rf[j-1],rf2[j-1], cross_scheme) +
emitf(Geno[j][i],v+1,error_prob, cross_scheme) +
beta[v][j] - beta[curstate-1][j-1]);
/* make draw */
curstate = Draws[k][j][i] = sample_int(n_gen, probs);
}
} /* loop over replicates */
} /* loop over individuals */
/* write R's random seed */
PutRNGstate();
}
void calc_genoprob_special(int n_ind, int n_pos, int n_gen, int *geno,
double *rf, double *rf2,
double error_prob, double *genoprob,
double initf(int),
double emitf(int, int, double),
double stepf(int, int, double, double))
{
int i, j, j2, v, v2, curpos;
double s, **alpha, **beta;
int **Geno;
double ***Genoprob;
/* allocate space for alpha and beta and
reorganize geno and genoprob */
reorg_geno(n_ind, n_pos, geno, &Geno);
reorg_genoprob(n_ind, n_pos, n_gen, genoprob, &Genoprob);
allocate_alpha(n_pos, n_gen, &alpha);
allocate_alpha(n_pos, n_gen, &beta);
for(i=0; i<n_ind; i++) { /* i = individual */
for(curpos=0; curpos < n_pos; curpos++) {
if(!Geno[curpos][i]) continue;
R_CheckUserInterrupt(); /* check for ^C */
/* initialize alpha and beta */
for(v=0; v<n_gen; v++) {
if(curpos==0)
alpha[v][0] = initf(v+1) + emitf(Geno[0][i], v+1, error_prob);
else
alpha[v][0] = initf(v+1) + emitf(Geno[0][i], v+1, TOL);
beta[v][n_pos-1] = 0.0;
}
/* forward-backward equations */
for(j=1,j2=n_pos-2; j<n_pos; j++, j2--) {
for(v=0; v<n_gen; v++) {
alpha[v][j] = alpha[0][j-1] + stepf(1, v+1, rf[j-1], rf2[j-1]);
if(curpos==j2+1)
beta[v][j2] = beta[0][j2+1] + stepf(v+1,1,rf[j2], rf2[j2]) +
emitf(Geno[j2+1][i],1,error_prob);
else
beta[v][j2] = beta[0][j2+1] + stepf(v+1,1,rf[j2], rf2[j2]) +
emitf(Geno[j2+1][i],1,TOL);
for(v2=1; v2<n_gen; v2++) {
alpha[v][j] = addlog(alpha[v][j], alpha[v2][j-1] +
stepf(v2+1,v+1,rf[j-1],rf2[j-1]));
if(curpos==j2+1)
beta[v][j2] = addlog(beta[v][j2], beta[v2][j2+1] +
stepf(v+1,v2+1,rf[j2],rf2[j2]) +
emitf(Geno[j2+1][i],v2+1,error_prob));
else
beta[v][j2] = addlog(beta[v][j2], beta[v2][j2+1] +
stepf(v+1,v2+1,rf[j2],rf2[j2]) +
emitf(Geno[j2+1][i],v2+1,TOL));
}
if(curpos==j)
alpha[v][j] += emitf(Geno[j][i],v+1,error_prob);
else
alpha[v][j] += emitf(Geno[j][i],v+1,TOL);
}
}
/* calculate genotype probabilities */
s = Genoprob[0][curpos][i] = alpha[0][curpos] + beta[0][curpos];
for(v=1; v<n_gen; v++) {
Genoprob[v][curpos][i] = alpha[v][curpos] + beta[v][curpos];
s = addlog(s, Genoprob[v][curpos][i]);
}
for(v=0; v<n_gen; v++)
Genoprob[v][curpos][i] = exp(Genoprob[v][curpos][i] - s);
} /* end loop over current position */
} /* loop over individuals */
}
