int main(int argc, char *argv[])
{
int cost[R][C] = { {1, 2, 3},
{4, 8, 2},
{1, 5, 3} };
printf("Min Cost Path = %d\n",MCP(cost));
}
// Coordinate descent for binomial models
SEXP cdfit_binomial(SEXP X_, SEXP y_, SEXP penalty_, SEXP lambda, SEXP eps_, SEXP max_iter_, SEXP gamma_, SEXP multiplier, SEXP alpha_, SEXP dfmax_, SEXP user_, SEXP warn_) {
// Declarations
int n = length(y_);
int p = length(X_)/n;
int L = length(lambda);
SEXP res, beta0, beta, Dev, iter;
PROTECT(beta0 = allocVector(REALSXP, L));
double *b0 = REAL(beta0);
for (int i=0; i<L; i++) b0[i] = 0;
PROTECT(beta = allocVector(REALSXP, L*p));
double *b = REAL(beta);
for (int j=0; j<(L*p); j++) b[j] = 0;
PROTECT(Dev = allocVector(REALSXP, L));
PROTECT(iter = allocVector(INTSXP, L));
for (int i=0; i<L; i++) INTEGER(iter)[i] = 0;
double *a = Calloc(p, double); // Beta from previous iteration
for (int j=0; j<p; j++) a[j] = 0;
double a0 = 0; // Beta0 from previous iteration
double *X = REAL(X_);
double *y = REAL(y_);
const char *penalty = CHAR(STRING_ELT(penalty_, 0));
double *lam = REAL(lambda);
double eps = REAL(eps_)[0];
int max_iter = INTEGER(max_iter_)[0];
double gamma = REAL(gamma_)[0];
double *m = REAL(multiplier);
double alpha = REAL(alpha_)[0];
int dfmax = INTEGER(dfmax_)[0];
int user = INTEGER(user_)[0];
int warn = INTEGER(warn_)[0];
double *r = Calloc(n, double);
double *w = Calloc(n, double);
double *s = Calloc(n, double);
double *z = Calloc(p, double);
double *eta = Calloc(n, double);
int *e1 = Calloc(p, int);
for (int j=0; j<p; j++) e1[j] = 0;
int *e2 = Calloc(p, int);
for (int j=0; j<p; j++) e2[j] = 0;
double xwr, xwx, pi, u, v, cutoff, l1, l2, shift, si;
int converged, lstart;
// Initialization
double ybar = sum(y, n)/n;
a0 = b0[0] = log(ybar/(1-ybar));
double nullDev = 0;
for (int i=0;i<n;i++) nullDev = nullDev - y[i]*log(ybar) - (1-y[i])*log(1-ybar);
for (int i=0; i<n; i++) s[i] = y[i] - ybar;
for (int i=0; i<n; i++) eta[i] = a0;
for (int j=0; j<p; j++) z[j] = crossprod(X, s, n, j)/n;
// If lam[0]=lam_max, skip lam[0] -- closed form sol'n available
if (user) {
lstart = 0;
} else {
lstart = 1;
REAL(Dev)[0] = nullDev;
}
// Path
for (int l=lstart; l<L; l++) {
if (l != 0) {
// Assign a, a0
a0 = b0[l-1];
for (int j=0; j<p; j++) a[j] = b[(l-1)*p+j];
// Check dfmax
int nv = 0;
for (int j=0; j<p; j++) {
if (a[j] != 0) nv++;
}
if (nv > dfmax) {
for (int ll=l; ll<L; ll++) INTEGER(iter)[ll] = NA_INTEGER;
res = cleanupB(s, w, a, r, e1, e2, z, eta, beta0, beta, Dev, iter);
return(res);
}
// Determine eligible set
if (strcmp(penalty, "lasso")==0) cutoff = 2*lam[l] - lam[l-1];
if (strcmp(penalty, "MCP")==0) cutoff = lam[l] + gamma/(gamma-1)*(lam[l] - lam[l-1]);
if (strcmp(penalty, "SCAD")==0) cutoff = lam[l] + gamma/(gamma-2)*(lam[l] - lam[l-1]);
for (int j=0; j<p; j++) if (fabs(z[j]) > (cutoff * alpha * m[j])) e2[j] = 1;
} else {
// Determine eligible set
double lmax = 0;
for (int j=0; j<p; j++) if (fabs(z[j]) > lmax) lmax = fabs(z[j]);
if (strcmp(penalty, "lasso")==0) cutoff = 2*lam[l] - lmax;
if (strcmp(penalty, "MCP")==0) cutoff = lam[l] + gamma/(gamma-1)*(lam[l] - lmax);
if (strcmp(penalty, "SCAD")==0) cutoff = lam[l] + gamma/(gamma-2)*(lam[l] - lmax);
for (int j=0; j<p; j++) if (fabs(z[j]) > (cutoff * alpha * m[j])) e2[j] = 1;
}
while (INTEGER(iter)[l] < max_iter) {
while (INTEGER(iter)[l] < max_iter) {
while (INTEGER(iter)[l] < max_iter) {
INTEGER(iter)[l]++;
REAL(Dev)[l] = 0;
for (int i=0;i<n;i++) {
if (eta[i] > 10) {
pi = 1;
w[i] = .0001;
} else if (eta[i] < -10) {
pi = 0;
w[i] = .0001;
} else {
pi = exp(eta[i])/(1+exp(eta[i]));
w[i] = pi*(1-pi);
}
s[i] = y[i] - pi;
r[i] = s[i]/w[i];
if (y[i]==1) REAL(Dev)[l] = REAL(Dev)[l] - log(pi);
if (y[i]==0) REAL(Dev)[l] = REAL(Dev)[l] - log(1-pi);
}
if (REAL(Dev)[l]/nullDev < .01) {
if (warn) warning("Model saturated; exiting...");
for (int ll=l; ll<L; ll++) INTEGER(iter)[ll] = NA_INTEGER;
res = cleanupB(s, w, a, r, e1, e2, z, eta, beta0, beta, Dev, iter);
return(res);
}
// Intercept
xwr = crossprod(w, r, n, 0);
xwx = sum(w, n);
b0[l] = xwr/xwx + a0;
for (int i=0; i<n; i++) {
si = b0[l] - a0;
r[i] -= si;
eta[i] += si;
}
// Covariates
for (int j=0; j<p; j++) {
if (e1[j]) {
// Calculate u, v
xwr = wcrossprod(X, r, w, n, j);
xwx = wsqsum(X, w, n, j);
u = xwr/n + (xwx/n)*a[j];
v = xwx/n;
// Update b_j
l1 = lam[l] * m[j] * alpha;
l2 = lam[l] * m[j] * (1-alpha);
if (strcmp(penalty,"MCP")==0) b[l*p+j] = MCP(u, l1, l2, gamma, v);
if (strcmp(penalty,"SCAD")==0) b[l*p+j] = SCAD(u, l1, l2, gamma, v);
if (strcmp(penalty,"lasso")==0) b[l*p+j] = lasso(u, l1, l2, v);
// Update r
shift = b[l*p+j] - a[j];
if (shift !=0) {
/* for (int i=0;i<n;i++) r[i] -= shift*X[j*n+i]; */
/* for (int i=0;i<n;i++) eta[i] += shift*X[j*n+i]; */
for (int i=0;i<n;i++) {
si = shift*X[j*n+i];
r[i] -= si;
eta[i] += si;
}
}
}
}
// Check for convergence
converged = checkConvergence(b, a, eps, l, p);
a0 = b0[l];
for (int j=0; j<p; j++) a[j] = b[l*p+j];
if (converged) break;
}
// Scan for violations in strong set
int violations = 0;
for (int j=0; j<p; j++) {
if (e1[j]==0 & e2[j]==1) {
z[j] = crossprod(X, s, n, j)/n;
l1 = lam[l] * m[j] * alpha;
if (fabs(z[j]) > l1) {
e1[j] = e2[j] = 1;
violations++;
}
}
}
if (violations==0) break;
}
// Scan for violations in rest
int violations = 0;
for (int j=0; j<p; j++) {
if (e2[j]==0) {
z[j] = crossprod(X, s, n, j)/n;
l1 = lam[l] * m[j] * alpha;
if (fabs(z[j]) > l1) {
e1[j] = e2[j] = 1;
violations++;
}
}
}
if (violations==0) break;
}
}
res = cleanupB(s, w, a, r, e1, e2, z, eta, beta0, beta, Dev, iter);
return(res);
}
// Coordinate descent for gaussian models
SEXP cdfit_gaussian(SEXP X_, SEXP y_, SEXP penalty_, SEXP lambda, SEXP eps_, SEXP max_iter_, SEXP gamma_, SEXP multiplier, SEXP alpha_, SEXP dfmax_, SEXP user_) {
// Declarations
int n = length(y_);
int p = length(X_)/n;
int L = length(lambda);
SEXP res, beta, loss, iter;
PROTECT(beta = allocVector(REALSXP, L*p));
double *b = REAL(beta);
for (int j=0; j<(L*p); j++) b[j] = 0;
PROTECT(loss = allocVector(REALSXP, L));
PROTECT(iter = allocVector(INTSXP, L));
for (int i=0; i<L; i++) INTEGER(iter)[i] = 0;
double *a = Calloc(p, double); // Beta from previous iteration
for (int j=0; j<p; j++) a[j]=0;
double *X = REAL(X_);
double *y = REAL(y_);
const char *penalty = CHAR(STRING_ELT(penalty_, 0));
double *lam = REAL(lambda);
double eps = REAL(eps_)[0];
int max_iter = INTEGER(max_iter_)[0];
double gamma = REAL(gamma_)[0];
double *m = REAL(multiplier);
double alpha = REAL(alpha_)[0];
int dfmax = INTEGER(dfmax_)[0];
int user = INTEGER(user_)[0];
double *r = Calloc(n, double);
for (int i=0; i<n; i++) r[i] = y[i];
double *z = Calloc(p, double);
for (int j=0; j<p; j++) z[j] = crossprod(X, r, n, j)/n;
int *e1 = Calloc(p, int);
for (int j=0; j<p; j++) e1[j] = 0;
int *e2 = Calloc(p, int);
for (int j=0; j<p; j++) e2[j] = 0;
double cutoff, l1, l2;
int lstart;
// If lam[0]=lam_max, skip lam[0] -- closed form sol'n available
double rss = gLoss(r,n);
if (user) {
lstart = 0;
} else {
REAL(loss)[0] = rss;
lstart = 1;
}
double sdy = sqrt(rss/n);
// Path
for (int l=lstart;l<L;l++) {
R_CheckUserInterrupt();
if (l != 0) {
// Assign a
for (int j=0;j<p;j++) a[j] = b[(l-1)*p+j];
// Check dfmax
int nv = 0;
for (int j=0; j<p; j++) {
if (a[j] != 0) nv++;
}
if (nv > dfmax) {
for (int ll=l; ll<L; ll++) INTEGER(iter)[ll] = NA_INTEGER;
res = cleanupG(a, r, e1, e2, z, beta, loss, iter);
return(res);
}
// Determine eligible set
if (strcmp(penalty, "lasso")==0) cutoff = 2*lam[l] - lam[l-1];
if (strcmp(penalty, "MCP")==0) cutoff = lam[l] + gamma/(gamma-1)*(lam[l] - lam[l-1]);
if (strcmp(penalty, "SCAD")==0) cutoff = lam[l] + gamma/(gamma-2)*(lam[l] - lam[l-1]);
for (int j=0; j<p; j++) if (fabs(z[j]) > (cutoff * alpha * m[j])) e2[j] = 1;
} else {
// Determine eligible set
double lmax = 0;
for (int j=0; j<p; j++) if (fabs(z[j]) > lmax) lmax = fabs(z[j]);
if (strcmp(penalty, "lasso")==0) cutoff = 2*lam[l] - lmax;
if (strcmp(penalty, "MCP")==0) cutoff = lam[l] + gamma/(gamma-1)*(lam[l] - lmax);
if (strcmp(penalty, "SCAD")==0) cutoff = lam[l] + gamma/(gamma-2)*(lam[l] - lmax);
for (int j=0; j<p; j++) if (fabs(z[j]) > (cutoff * alpha * m[j])) e2[j] = 1;
}
while (INTEGER(iter)[l] < max_iter) {
while (INTEGER(iter)[l] < max_iter) {
while (INTEGER(iter)[l] < max_iter) {
// Solve over the active set
INTEGER(iter)[l]++;
double maxChange = 0;
for (int j=0; j<p; j++) {
if (e1[j]) {
z[j] = crossprod(X, r, n, j)/n + a[j];
// Update beta_j
l1 = lam[l] * m[j] * alpha;
l2 = lam[l] * m[j] * (1-alpha);
if (strcmp(penalty,"MCP")==0) b[l*p+j] = MCP(z[j], l1, l2, gamma, 1);
if (strcmp(penalty,"SCAD")==0) b[l*p+j] = SCAD(z[j], l1, l2, gamma, 1);
if (strcmp(penalty,"lasso")==0) b[l*p+j] = lasso(z[j], l1, l2, 1);
// Update r
double shift = b[l*p+j] - a[j];
if (shift !=0) {
for (int i=0;i<n;i++) r[i] -= shift*X[j*n+i];
if (fabs(shift) > maxChange) maxChange = fabs(shift);
}
}
}
// Check for convergence
for (int j=0; j<p; j++) a[j] = b[l*p+j];
if (maxChange < eps*sdy) break;
}
// Scan for violations in strong set
int violations = 0;
for (int j=0; j<p; j++) {
if (e1[j]==0 & e2[j]==1) {
z[j] = crossprod(X, r, n, j)/n;
// Update beta_j
l1 = lam[l] * m[j] * alpha;
l2 = lam[l] * m[j] * (1-alpha);
if (strcmp(penalty,"MCP")==0) b[l*p+j] = MCP(z[j], l1, l2, gamma, 1);
if (strcmp(penalty,"SCAD")==0) b[l*p+j] = SCAD(z[j], l1, l2, gamma, 1);
if (strcmp(penalty,"lasso")==0) b[l*p+j] = lasso(z[j], l1, l2, 1);
// If something enters the eligible set, update eligible set & residuals
if (b[l*p+j] !=0) {
e1[j] = e2[j] = 1;
for (int i=0; i<n; i++) r[i] -= b[l*p+j]*X[j*n+i];
a[j] = b[l*p+j];
violations++;
}
}
}
if (violations==0) break;
}
// Scan for violations in rest
int violations = 0;
for (int j=0; j<p; j++) {
if (e2[j]==0) {
z[j] = crossprod(X, r, n, j)/n;
// Update beta_j
l1 = lam[l] * m[j] * alpha;
l2 = lam[l] * m[j] * (1-alpha);
if (strcmp(penalty,"MCP")==0) b[l*p+j] = MCP(z[j], l1, l2, gamma, 1);
if (strcmp(penalty,"SCAD")==0) b[l*p+j] = SCAD(z[j], l1, l2, gamma, 1);
if (strcmp(penalty,"lasso")==0) b[l*p+j] = lasso(z[j], l1, l2, 1);
// If something enters the eligible set, update eligible set & residuals
if (b[l*p+j] !=0) {
e1[j] = e2[j] = 1;
for (int i=0; i<n; i++) r[i] -= b[l*p+j]*X[j*n+i];
a[j] = b[l*p+j];
violations++;
}
}
}
if (violations==0) {
break;
}
}
REAL(loss)[l] = gLoss(r, n);
}
res = cleanupG(a, r, e1, e2, z, beta, loss, iter);
return(res);
}
string& string::operator =(const string* s)
{
MCP(vbf_, STR(s->vbf_), LEN(s->vbf_));
TERM(vbf_);
return *this;
}