/**********************************************************************
* step_bci
*
* Calculate transition probabilities (for all intervals) for
* the Stahl model
**********************************************************************/
void step_bci(int n_mar, int n_states, double ***tm, double *d,
int m, double p, int maxit, double tol)
{
int i, v1, v2;
double *the_distinct_tm;
double *fms_bci_result;
double lambda1, lambda2, rfp;
allocate_double(2*m+1, &fms_bci_result);
allocate_double(3*m+2, &the_distinct_tm);
for(i=0; i<n_mar-1; i++) {
R_CheckUserInterrupt(); /* check for ^C */
lambda1 = d[i]*(1-p)*(double)(m+1)*2.0;
lambda2 = d[i]*p*2.0;
rfp = 0.5*(1.0 - exp(-lambda2));
fms_bci(lambda1, fms_bci_result, m, tol, maxit);
distinct_tm_bci(lambda1, the_distinct_tm, m, fms_bci_result);
for(v1=0; v1<n_states; v1++) {
for(v2=0; v2<n_states; v2++) {
tm[v1][v2][i] = tm_bci(v1, v2, the_distinct_tm, m);
if(p > 0)
tm[v1][v2][i] = (1.0-rfp)*tm[v1][v2][i] +
rfp*tm_bci(v1, (v2+m+1) % (2*m+2), the_distinct_tm, m);
tm[v1][v2][i] = log(tm[v1][v2][i]);
}
}
}
}
void R_discan_mr(int *n_ind, int *n_pos, int *n_gen,
int *geno, int *pheno, double *result)
{
int **Geno;
double *means;
reorg_geno(*n_ind, *n_pos, geno, &Geno);
allocate_double(*n_gen, &means);
discan_mr(*n_ind, *n_pos, *n_gen, Geno, pheno, result, means);
}
void R_discan_im(int *n_ind, int *n_pos, int *n_gen,
double *genoprob, int *pheno, double *result,
int *maxit, double *tol)
{
double ***Genoprob, **work;
double *means;
reorg_genoprob(*n_ind, *n_pos, *n_gen, genoprob, &Genoprob);
allocate_dmatrix(3, *n_gen, &work);
allocate_double(*n_gen, &means);
discan_im(*n_ind, *n_pos, *n_gen, Genoprob, pheno, result,
*maxit, *tol, work, means);
}
void calc_errorlod(int n_ind, int n_mar, int n_gen, int *geno,
double error_prob, double *genoprob, double *errlod,
double errorlod(int, double *, double))
{
int i, j, k, **Geno;
double *p, ***Genoprob, **Errlod;
/* reorganize geno, genoprob and errlod */
reorg_geno(n_ind, n_mar, geno, &Geno);
reorg_genoprob(n_ind, n_mar, n_gen, genoprob, &Genoprob);
reorg_errlod(n_ind, n_mar, errlod, &Errlod);
allocate_double(n_gen, &p);
for(i=0; i<n_ind; i++) {
R_CheckUserInterrupt(); /* check for ^C */
for(j=0; j<n_mar; j++) {
for(k=0; k<n_gen; k++) p[k] = Genoprob[k][j][i];
Errlod[j][i] = errorlod(Geno[j][i], p, error_prob);
}
}
}
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 argmax_geno(int n_ind, int n_pos, int n_gen, int *geno,
double *rf, double *rf2,
double error_prob, int *argmax,
double initf(int, int *),
double emitf(int, int, double, int *),
double stepf(int, int, double, double, int *))
{
int i, j, v, v2;
double s, t, *gamma, *tempgamma, *tempgamma2;
int **Geno, **Argmax, **traceback;
int cross_scheme[2];
/* cross scheme hidden in argmax argument; used by hmm_bcsft */
cross_scheme[0] = argmax[0];
cross_scheme[1] = argmax[1];
argmax[0] = geno[0];
argmax[1] = geno[1];
/* Read R's random seed */
/* in the case of multiple "most likely" genotype sequences,
we pick from them at random */
GetRNGstate();
/* allocate space and
reorganize geno and argmax */
reorg_geno(n_ind, n_pos, geno, &Geno);
reorg_geno(n_ind, n_pos, argmax, &Argmax);
allocate_imatrix(n_pos, n_gen, &traceback);
allocate_double(n_gen, &gamma);
allocate_double(n_gen, &tempgamma);
allocate_double(n_gen, &tempgamma2);
for(i=0; i<n_ind; i++) { /* i = individual */
R_CheckUserInterrupt(); /* check for ^C */
/* begin viterbi algorithm */
if(n_pos > 1) { /* multiple markers */
for(v=0; v<n_gen; v++)
gamma[v] = initf(v+1, cross_scheme) + emitf(Geno[0][i], v+1, error_prob, cross_scheme);
for(j=0; j<n_pos-1; j++) {
for(v=0; v<n_gen; v++) {
tempgamma[v] = s = gamma[0] + stepf(1, v+1, rf[j], rf2[j], cross_scheme);
traceback[j][v] = 0;
for(v2=1; v2<n_gen; v2++) {
t = gamma[v2] + stepf(v2+1, v+1, rf[j], rf2[j], cross_scheme);
if(t > s || (fabs(t-s) < TOL && unif_rand() < 0.5)) {
tempgamma[v] = s = t;
traceback[j][v] = v2;
}
}
tempgamma2[v] = tempgamma[v] + emitf(Geno[j+1][i], v+1, error_prob, cross_scheme);
}
for(v=0; v<n_gen; v++) gamma[v] = tempgamma2[v];
}
/* finish off viterbi and then traceback to get most
likely sequence of genotypes */
Argmax[n_pos-1][i] = 0;
s = gamma[0];
for(v=1; v<n_gen; v++) {
if(gamma[v] > s || (fabs(gamma[v]-s) < TOL &&
unif_rand() < 0.5)) {
s = gamma[v];
Argmax[n_pos-1][i] = v;
}
}
for(j=n_pos-2; j >= 0; j--)
Argmax[j][i] = traceback[j][Argmax[j+1][i]];
}
else { /* for exactly one marker */
s = initf(1, cross_scheme) + emitf(Geno[0][i], 1, error_prob, cross_scheme);
Argmax[0][i] = 0;
for(v=1; v<n_gen; v++) {
t = initf(v+1, cross_scheme) + emitf(Geno[0][i], v+1, error_prob, cross_scheme);
if(t > s || (fabs(t-s) < TOL && unif_rand() < 0.5)) {
s = t;
Argmax[0][i] = v;
}
}
}
/* code genotypes as 1, 2, ... */
for(j=0; j<n_pos; j++) Argmax[j][i]++;
} /* loop over individuals */
/* write R's random seed */
PutRNGstate();
}
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 fitqtl_imp_binary(int n_ind, int n_qtl, int *n_gen, int n_draws,
int ***Draws, double **Cov, int n_cov,
int *model, int n_int, double *pheno, int get_ests,
double *lod, int *df, double *ests, double *ests_covar,
double *design_mat, double tol, int maxit, int *matrix_rank)
{
/* create local variables */
int i, j, ii, jj, n_qc, itmp; /* loop variants and temp variables */
double llik, llik0, *LOD_array;
double *the_ests, *the_covar, **TheEsts, ***TheCovar;
double *dwork, **Ests_covar, tot_wt=0.0, *wts;
double **Covar_mean, **Mean_covar, *mean_ests; /* for ests and cov matrix */
int *iwork, sizefull, n_trim, *index;
/* number to trim from each end of the imputations */
n_trim = (int) floor( 0.5*log(n_draws)/log(2.0) );
/* initialization */
sizefull = 1;
/* calculate the dimension of the design matrix for full model */
n_qc = n_qtl+n_cov; /* total number of QTLs and covariates */
/* for additive QTLs and covariates*/
for(i=0; i<n_qc; i++)
sizefull += n_gen[i];
/* for interactions, loop thru all interactions */
for(i=0; i<n_int; i++) {
for(j=0, itmp=1; j<n_qc; j++) {
if(model[i*n_qc+j])
itmp *= n_gen[j];
}
sizefull += itmp;
}
/* reorganize Ests_covar for easy use later */
/* and make space for estimates and covariance matrix */
if(get_ests) {
reorg_errlod(sizefull, sizefull, ests_covar, &Ests_covar);
allocate_double(sizefull*n_draws, &the_ests);
allocate_double(sizefull*sizefull*n_draws, &the_covar);
/* I need to save all of the estimates and covariance matrices */
reorg_errlod(sizefull, n_draws, the_ests, &TheEsts);
reorg_genoprob(sizefull, sizefull, n_draws, the_covar, &TheCovar);
allocate_dmatrix(sizefull, sizefull, &Mean_covar);
allocate_dmatrix(sizefull, sizefull, &Covar_mean);
allocate_double(sizefull, &mean_ests);
allocate_double(n_draws, &wts);
}
/* allocate memory for working arrays, total memory is
sizefull*n_ind+6*n_ind+4*sizefull for double array,
and sizefull for integer array.
All memory will be allocated one time and split later */
dwork = (double *)R_alloc(sizefull*n_ind+6*n_ind+4*sizefull,
sizeof(double));
iwork = (int *)R_alloc(sizefull, sizeof(int));
index = (int *)R_alloc(n_draws, sizeof(int));
LOD_array = (double *)R_alloc(n_draws, sizeof(double));
/* calculate null model log10 likelihood */
llik0 = nullLODbin(pheno, n_ind);
*matrix_rank = n_ind;
/* loop over imputations */
for(i=0; i<n_draws; i++) {
R_CheckUserInterrupt(); /* check for ^C */
/* calculate alternative model RSS */
llik = galtLODimpbin(pheno, n_ind, n_gen, n_qtl, Draws[i],
Cov, n_cov, model, n_int, dwork, iwork, sizefull,
get_ests, ests, Ests_covar, design_mat,
tol, maxit, matrix_rank);
/* calculate the LOD score in this imputation */
LOD_array[i] = (llik - llik0);
/* if getting estimates, calculate the weights */
if(get_ests) {
wts[i] = LOD_array[i]*log(10.0);
if(i==0) tot_wt = wts[i];
else tot_wt = addlog(tot_wt, wts[i]);
for(ii=0; ii<sizefull; ii++) {
TheEsts[i][ii] = ests[ii];
for(jj=ii; jj<sizefull; jj++)
TheCovar[i][ii][jj] = Ests_covar[ii][jj];
}
}
} /* end loop over imputations */
/* sort the lod scores, and trim the weights */
if(get_ests) {
for(i=0; i<n_draws; i++) {
index[i] = i;
wts[i] = exp(wts[i]-tot_wt);
}
rsort_with_index(LOD_array, index, n_draws);
for(i=0; i<n_trim; i++)
wts[index[i]] = wts[index[n_draws-i-1]] = 0.0;
/* re-scale wts */
tot_wt = 0.0;
for(i=0; i<n_draws; i++) tot_wt += wts[i];
for(i=0; i<n_draws; i++) wts[i] /= tot_wt;
}
/* calculate the result LOD score */
*lod = wtaverage(LOD_array, n_draws);
/* degree of freedom equals to the number of columns of x minus 1 (mean) */
*df = sizefull - 1;
/* get means and variances and covariances of estimates */
if(get_ests) {
for(i=0; i<n_draws; i++) {
if(i==0) {
for(ii=0; ii<sizefull; ii++) {
mean_ests[ii] = TheEsts[i][ii] * wts[i];
for(jj=ii; jj<sizefull; jj++) {
Mean_covar[ii][jj] = TheCovar[i][ii][jj] * wts[i];
Covar_mean[ii][jj] = 0.0;
}
}
}
else {
for(ii=0; ii<sizefull; ii++) {
mean_ests[ii] += TheEsts[i][ii]*wts[i];
for(jj=ii; jj<sizefull; jj++) {
Mean_covar[ii][jj] += TheCovar[i][ii][jj]*wts[i];
Covar_mean[ii][jj] += (TheEsts[i][ii]-TheEsts[0][ii])*
(TheEsts[i][jj]-TheEsts[0][jj])*wts[i];
}
}
}
}
for(i=0; i<sizefull; i++) {
ests[i] = mean_ests[i];
for(j=i; j<sizefull; j++) {
Covar_mean[i][j] = (Covar_mean[i][j] - (mean_ests[i]-TheEsts[0][i])*
(mean_ests[j]-TheEsts[0][j]))*(double)n_draws/(double)(n_draws-1);
Ests_covar[i][j] = Ests_covar[j][i] = Mean_covar[i][j] + Covar_mean[i][j];
}
}
} /* done getting estimates */
}
double discan_covar_em(int n_ind, int pos, int n_gen, int n_par,
double ***Genoprob, double **Addcov, int n_addcov,
double **Intcov, int n_intcov, int *pheno,
double *start, int maxit, double tol, int verbose,
int *ind_noqtl)
{
int i, j, k, kk, s, offset;
double *jac, **Jac, *grad;
double *temp, **wts;
double fit, **temp1, **temp2;
double *temp1s, *temp2s;
double *newpar, *curpar;
double newllik=0.0, curllik, sum;
int info;
double rcond, *junk;
/* allocate space */
allocate_double(n_par*n_par, &jac);
reorg_errlod(n_par, n_par, jac, &Jac);
allocate_double(n_par, &grad);
allocate_double(n_ind*n_gen, &temp);
reorg_errlod(n_gen, n_ind, temp, &wts);
allocate_double(n_ind*n_gen, &temp);
reorg_errlod(n_gen, n_ind, temp, &temp1);
allocate_double(n_ind*n_gen, &temp);
reorg_errlod(n_gen, n_ind, temp, &temp2);
allocate_double(n_ind, &temp1s);
allocate_double(n_ind, &temp2s);
allocate_double(n_par, &newpar);
allocate_double(n_par, &curpar);
allocate_double(n_par, &junk);
/* initial wts */
for(i=0; i<n_ind; i++)
for(j=0; j<n_gen; j++)
wts[i][j] = Genoprob[j][pos][i];
for(i=0; i<n_par; i++) curpar[i] = start[i];
curllik = discan_covar_loglik(n_ind, pos, n_gen, n_par, curpar, Genoprob,
Addcov, n_addcov, Intcov, n_intcov, pheno, ind_noqtl);
if(verbose)
Rprintf(" %10.5f\n", curllik);
for(s=0; s<maxit; s++) {
R_CheckUserInterrupt(); /* check for ^C */
/****** M STEP ******/
/* 0's in gradient and Jacobian */
for(j=0; j<n_par; j++) {
grad[j] = 0.0;
for(k=0; k<n_par; k++)
Jac[j][k] = 0.0;
}
/* calculate gradient and Jacobian */
for(i=0; i<n_ind; i++) {
temp1s[i] = temp2s[i] = 0.0;
for(j=0; j<n_gen; j++) {
if(!ind_noqtl[i])
fit = curpar[j];
else fit = 0.0;
if(n_addcov > 0) {
for(k=0; k<n_addcov; k++)
fit += Addcov[k][i] * curpar[n_gen+k];
}
if(!ind_noqtl[i] && n_intcov > 0 && j<n_gen-1) {
for(k=0; k<n_intcov; k++)
fit += Intcov[k][i] * curpar[n_gen+n_addcov+n_intcov*j+k];
}
fit = exp(fit)/(1.0+exp(fit));
temp1s[i] += (temp1[i][j] = wts[i][j]*((double)pheno[i] - fit));
temp2s[i] += (temp2[i][j] = wts[i][j]*fit*(1.0-fit));
}
}
for(j=0; j<n_gen; j++) {
for(i=0; i<n_ind; i++) {
if(!ind_noqtl[i]) {
grad[j] += temp1[i][j];
Jac[j][j] += temp2[i][j];
}
}
}
for(k=0; k<n_addcov; k++) {
for(i=0; i<n_ind; i++) {
grad[k + n_gen] += Addcov[k][i] * temp1s[i];
for(kk=k; kk<n_addcov; kk++)
Jac[kk+n_gen][k+n_gen] += Addcov[k][i]*Addcov[kk][i] * temp2s[i];
if(!ind_noqtl[i]) {
for(j=0; j<n_gen; j++)
Jac[k+n_gen][j] += Addcov[k][i] * temp2[i][j];
}
}
}
for(j=0; j<n_gen-1; j++) {
offset = n_gen + n_addcov + n_intcov*j;
for(k=0; k<n_intcov; k++) {
for(i=0; i<n_ind; i++) {
if(!ind_noqtl[i]) {
grad[k + offset] += Intcov[k][i] * temp1[i][j];
for(kk=k; kk<n_intcov; kk++)
Jac[kk+offset][k+offset] += Intcov[k][i]*Intcov[kk][i]*temp2[i][j];
for(kk=0; kk<n_addcov; kk++)
Jac[k+offset][kk+n_gen] += Intcov[k][i]*Addcov[kk][i]*temp2[i][j];
Jac[k+offset][j] += Intcov[k][i]*temp2[i][j];
}
}
}
}
if(verbose > 1) {
Rprintf("grad: ");
for(j=0; j<n_par; j++)
Rprintf("%f ", grad[j]);
Rprintf("\n");
Rprintf("Jac:\n");
for(j=0; j<n_par; j++) {
for(k=0; k<n_par; k++)
Rprintf("%f ", Jac[j][k]);
Rprintf("\n");
}
Rprintf("\n");
}
/* dpoco and dposl from Linpack to calculate Jac^-1 %*% grad */
F77_CALL(dpoco)(jac, &n_par, &n_par, &rcond, junk, &info);
if(fabs(rcond) < TOL || info != 0) {
warning("Jacobian matrix is singular\n");
return(NA_REAL);
}
F77_CALL(dposl)(jac, &n_par, &n_par, grad);
if(verbose > 1) {
Rprintf(" solution: ");
for(j=0; j<n_par; j++)
Rprintf(" %f", grad[j]);
Rprintf("\n");
}
/* revised estimates */
for(j=0; j<n_par; j++)
newpar[j] = curpar[j] + grad[j];
if(verbose>1) {
for(j=0; j<n_par; j++)
Rprintf("%f ", newpar[j]);
Rprintf("\n");
}
newllik = discan_covar_loglik(n_ind, pos, n_gen, n_par, newpar, Genoprob,
Addcov, n_addcov, Intcov, n_intcov, pheno, ind_noqtl);
if(verbose) {
Rprintf(" %3d %10.5f %10.5f", s+1, newllik, newllik - curllik);
if(newllik < curllik) Rprintf(" ***");
Rprintf("\n");
}
if(newllik - curllik < tol) return(newllik);
for(j=0; j<n_par; j++)
curpar[j] = newpar[j];
curllik = newllik;
/* e-step */
for(i=0; i<n_ind; i++) {
sum=0.0;
for(j=0; j<n_gen; j++) {
fit = curpar[j];
if(n_addcov > 0) {
for(k=0; k<n_addcov; k++)
fit += Addcov[k][i] * curpar[n_gen+k];
}
if(n_intcov > 0 && j<n_gen-1) {
for(k=0; k<n_intcov; k++)
fit += Intcov[k][i] * curpar[n_gen+n_addcov+n_intcov*j+k];
}
fit = exp(fit);
if(pheno[i]) sum += (wts[i][j] = Genoprob[j][pos][i] * fit/(1.0+fit));
else sum += (wts[i][j] = Genoprob[j][pos][i] / (1.0+fit));
}
for(j=0; j<n_gen; j++)
wts[i][j] /= sum;
}
} /* end of em-step */
/* didn't converge */
return(newllik);
}
/**********************************************************************
*
* summary_scantwo
*
* Function to pull out the major bits from scantwo output
*
* n_pos: Total number of positions
* n_phe: Number of phenotype columns
* Lod: Array of LOD scores indexed as [phe][pos2][pos1]
* diagonal = scanone results; upper.tri = add've LOD; lower = full
* n_chr Number of distinct chromosomes
* chr Index of chromosomes; length n_pos, taking values in 1..n_chr
* pos cM positions; length n_pos
* xchr Index of xchr; length n_chr; 0=autosome, 1=X chromosome
* ScanoneX special X scanone; matrix indexed as [phe][pos]
*
* n_chrpair Number of pairs of chromosomes
* Chrpair Matrix giving chrpair index for a pair of chromosomes
* Pos1_jnt, Pos2_jnt On output, positions of maximum joint LOD
* Matrices indexed as [phe][chrpair]
* Pos1_add, Pos2_add On output, positions of maximum add've LOD
* Matrices indexed as [phe][chrpair]
* Pos1_int, Pos2_int On output, positions of maximum int've LOD
* Matrices indexed as [phe][chrpair]
* JNT_lod_* On output, joint and add've LOD at pos'ns with
* maximum joint LOD; matrices indexed as [phe][chrpair]
* ADD_lod_* On output, joint and add've LOD at pos'ns with
* maximum add've LOD; matrices indexed as [phe][chrpair]
* INT_lod_* On output, joint and add've LOD at pos'ns with
* maximum int've LOD; matrices indexed as [phe][chrpair]
* LOD_1qtl On output, maximum 1-QTL LOD for each pair of chr
* (selected from either scanone or scanoneX
*
**********************************************************************/
void summary_scantwo(int n_pos, int n_phe, double ***Lod, int n_chr,
int *chr, double *pos, int *xchr, double **ScanoneX,
int n_chrpair, int **Chrpair,
double **Pos1_jnt, double **Pos2_jnt,
double **Pos1_add, double **Pos2_add,
double **Pos1_int, double **Pos2_int,
double **JNT_lod_full, double **JNT_lod_add,
double **ADD_lod_full, double **ADD_lod_add,
double **INT_lod_full, double **INT_lod_add,
double **LOD_1qtl)
{
int i, j, k, c1, c2, thepair;
double *maxone, *maxoneX;
allocate_double(n_chr, &maxone);
allocate_double(n_chr, &maxoneX);
for(i=0; i<n_phe; i++) { /* loop over phenotype columns */
/* get maximum single-QTL results */
for(j=0; j<n_chr; j++)
maxone[j] = maxoneX[j] = 0.0;
for(j=0; j<n_pos; j++) {
if(Lod[i][j][j] > maxone[chr[j]-1])
maxone[chr[j]-1] = Lod[i][j][j];
if(ScanoneX[i][j] > maxoneX[chr[j]-1])
maxoneX[chr[j]-1] = ScanoneX[i][j];
}
/* zero out the matrices for the maximum LOD scores */
for(j=0; j<n_chrpair; j++) {
JNT_lod_full[i][j] = JNT_lod_add[i][j] =
ADD_lod_full[i][j] = ADD_lod_add[i][j] =
INT_lod_full[i][j] = INT_lod_add[i][j] =
Pos1_add[i][j] = Pos2_add[i][j] =
Pos1_int[i][j] = Pos2_int[i][j] =
Pos1_jnt[i][j] = Pos2_jnt[i][j] = 0.0;
}
/* maximum joint, add've, and int've LOD scores */
for(j=0; j<n_pos; j++) {
for(k=j; k<n_pos; k++) {
R_CheckUserInterrupt(); /* check for ^C */
c1 = chr[j]-1;
c2 = chr[k]-1;
thepair = Chrpair[c1][c2];
if(Lod[i][j][k] > JNT_lod_full[i][thepair]) {
JNT_lod_full[i][thepair] = Lod[i][j][k];
JNT_lod_add[i][thepair] = Lod[i][k][j];
Pos1_jnt[i][thepair] = pos[j];
Pos2_jnt[i][thepair] = pos[k];
}
if(Lod[i][k][j] > ADD_lod_add[i][thepair]) {
ADD_lod_add[i][thepair] = Lod[i][k][j];
ADD_lod_full[i][thepair] = Lod[i][j][k];
Pos1_add[i][thepair] = pos[j];
Pos2_add[i][thepair] = pos[k];
}
if(Lod[i][j][k] - Lod[i][k][j] >
INT_lod_full[i][thepair] - INT_lod_add[i][thepair]) {
INT_lod_full[i][thepair] = Lod[i][j][k];
INT_lod_add[i][thepair] = Lod[i][k][j];
Pos1_int[i][thepair] = pos[j];
Pos2_int[i][thepair] = pos[k];
}
}
}
/* pull out biggest single-QTL LOD scores */
for(j=0; j<n_chr; j++) {
for(k=j; k<n_chr; k++) {
R_CheckUserInterrupt(); /* check for ^C */
thepair = Chrpair[j][k];
/* calculate the two 2 v 1 conditional LOD scores */
if(xchr[j] || xchr[k]) {
if(maxoneX[j] > maxoneX[k]) LOD_1qtl[i][thepair] = maxoneX[j];
else LOD_1qtl[i][thepair] = maxoneX[k];
}
else {
if(maxone[j] > maxone[k]) LOD_1qtl[i][thepair] = maxone[j];
else LOD_1qtl[i][thepair] = maxone[k];
}
}
}
} /* end loop over phenotype columns */
}
