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admm.c
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admm.c
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#include <math.h>
#include "admm.h"
#include "cholmod.h" // sparse Cholesky solver
extern Parameters params;
extern double TIME;
extern double f; // opt. value of SDP
extern int M; // number of eigenvalues
extern double *Z; // contains the eigenvectors
/* primal and dual variables corresponding to cutting planes */
extern double *u;
extern double *t;
extern double *s;
/* dsyevr variables */
extern int *ISUPPZ;
extern double *WORK;
extern int *IWORK;
extern int sizeWORK, sizeIWORK;
/* vector of triangle inequality constraints */
extern Triangle_Inequality *Cuts;
extern Pentagonal_Inequality *Pent_Cuts;
extern Heptagonal_Inequality *Hepta_Cuts;
/* macro to handle the errors if Blas/Lapack routine failed */
#define ERROR_INFO(cond,message)\
if ((cond)) {\
fprintf(stderr, "\nError: "#message"\n");\
exit(1);\
}
/******************** ADMM solver *********************/
/* ADMM method for solving Max-Cut SDP relaxation strengthened
* with triangle inequality constraints.
*
* Additional variable s is introduced in the dual SDP to
* avoid solving QP for t. Now one linear system for t is
* solved, projection onto PSD cone to obtain Q and X,
* projection onto nonnegative orthant to obtain s + additional dual update to get u.
*
* variables:
* DUAL: y (free), t (free), Q (psd), s (nonnegative)
* PRIMAL: X (dual variable for equality constraint L-Diag(y)-BT(t)+Z = 0)
* u slack variable for triangle inequalities B(X) <= e
******************************************************/
void ADMM_solver(const Problem *PP, double *X, double *y, double *Q, double *sigma, double tol, int *nbit, int print) {
/* constraints:
* n equality constraints : diag(X) = e
* PP->NIneq + PP->NPentIneq + PP->NHeptaIneq inequality constraints: B(X) <= e */
// size of problem
int n = PP->n;
int nn = n*n;
// number of cutting planes
int m = PP->NIneq + PP->NPentIneq + PP->NHeptaIneq;
int inc = 1; // for BLAS/LAPACK
double alpha;
char NORM = 'F'; // Frobenious norm
char UPLO = 'L'; // only upper triangular part is referenced!
double primal;
double dual;
double gap;
double err_p; // primal error
double err_d; // dual error
double err; // overall error
double digits_d;
double digits_p;
double secs;
/**** Initialize t, s, and u ****/
for (int ineq = 0; ineq < PP->NIneq; ++ineq) {
s[ineq] = Cuts[ineq].y;
t[ineq] = Cuts[ineq].y;
u[ineq] = 0.0;
}
for (int ineq = 0; ineq < PP->NPentIneq; ++ineq) {
s[ineq + PP->NIneq] = Pent_Cuts[ineq].y;
t[ineq + PP->NIneq] = Pent_Cuts[ineq].y;
u[ineq + PP->NIneq] = 0.0;
}
for (int ineq = 0; ineq < PP->NHeptaIneq; ++ineq) {
s[ineq + PP->NIneq + PP->NPentIneq] = Hepta_Cuts[ineq].y;
t[ineq + PP->NIneq + PP->NPentIneq] = Hepta_Cuts[ineq].y;
u[ineq + PP->NIneq + PP->NPentIneq] = 0.0;
}
/******************** using CHOLMOD ********************/
cholmod_dense *b_cholmod = NULL;
cholmod_dense *t_cholmod = NULL;
cholmod_factor *L_cholmod;
cholmod_sparse *B_cholmod;
cholmod_triplet *triplet;
double beta[2] = {1, 0};
/* ---------------------------------------------------------------------- */
/* start CHOLMOD and set parameters */
/* ---------------------------------------------------------------------- */
cholmod_common Common;
cholmod_start(&Common);
/* ---------------------------------------------------------------------- */
/* create matrix B */
/* ---------------------------------------------------------------------- */
// allocate space for triple: m rows, n^2 columns, 6m + ... nonzero elements, 0 = unsymmetric
// nonzero elements (3 for triag + 10 for penta + 21 for hepta) x 2 for symmetrix matrices (lower part)
triplet = cholmod_allocate_triplet(m, n*n, 6*PP->NIneq + 20*PP->NPentIneq + 42*PP->NHeptaIneq, 0, CHOLMOD_REAL, &Common); // all pointers already initialized
// construct triplet using Cuts array
int ii, jj, kk, ll, mm, nnn, oo, type, l;
/* triangles */
for (int ineq = 0; ineq < PP->NIneq; ++ineq) {
type = Cuts[ineq].type;
ii = Cuts[ineq].i;
jj = Cuts[ineq].j;
kk = Cuts[ineq].k;
/*** rows ***/
for (l = 6*ineq; l < 6*(ineq+1); ++l){
((int*)triplet->i)[l] = ineq;
}
/*** columns ***/
((int*)triplet->j)[6*ineq] = jj * n + ii;
((int*)triplet->j)[6*ineq+1] = ii * n + jj;
((int*)triplet->j)[6*ineq+2] = ii * n + kk;
((int*)triplet->j)[6*ineq+3] = kk * n + ii;
((int*)triplet->j)[6*ineq+4] = kk * n + jj;
((int*)triplet->j)[6*ineq+5] = jj * n + kk;
/*** values ***/
if (type == 1){
for (l = 6*ineq; l < 6*(ineq+1); ++l){
((double*)triplet->x)[l] = -0.5;
}
}
else if (type == 2){
((double*)triplet->x)[6*ineq] = -0.5;
((double*)triplet->x)[6*ineq+1] = -0.5;
((double*)triplet->x)[6*ineq+2] = 0.5;
((double*)triplet->x)[6*ineq+3] = 0.5;
((double*)triplet->x)[6*ineq+4] = 0.5;
((double*)triplet->x)[6*ineq+5] = 0.5;
}
else if (type == 3){
((double*)triplet->x)[6*ineq] = 0.5;
((double*)triplet->x)[6*ineq+1] = 0.5;
((double*)triplet->x)[6*ineq+2] = -0.5;
((double*)triplet->x)[6*ineq+3] = -0.5;
((double*)triplet->x)[6*ineq+4] = 0.5;
((double*)triplet->x)[6*ineq+5] = 0.5;
}
else if (type == 4){
((double*)triplet->x)[6*ineq] = 0.5;
((double*)triplet->x)[6*ineq+1] = 0.5;
((double*)triplet->x)[6*ineq+2] = 0.5;
((double*)triplet->x)[6*ineq+3] = 0.5;
((double*)triplet->x)[6*ineq+4] = -0.5;
((double*)triplet->x)[6*ineq+5] = -0.5;
}
}
/* pentagonals */
for (int ineq = 0; ineq < PP->NPentIneq; ++ineq) {
type = Pent_Cuts[ineq].type;
ii = Pent_Cuts[ineq].permutation[0];
jj = Pent_Cuts[ineq].permutation[1];
kk = Pent_Cuts[ineq].permutation[2];
ll = Pent_Cuts[ineq].permutation[3];
mm = Pent_Cuts[ineq].permutation[4];
/*** rows ***/
for (l = 6*PP->NIneq + 20*ineq; l < 6*PP->NIneq + 20*(ineq+1); ++l){
((int*)triplet->i)[l] = PP->NIneq + ineq;
}
/*** columns ***/
((int*)triplet->j)[6*PP->NIneq + 20*ineq] = jj * n + ii;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+1] = ii * n + jj;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+2] = ii * n + kk;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+3] = kk * n + ii;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+4] = ii * n + ll;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+5] = ll * n + ii;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+6] = ii * n + mm;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+7] = mm * n + ii;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+8] = jj * n + kk;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+9] = kk * n + jj;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+10] = jj * n + ll;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+11] = ll * n + jj;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+12] = jj * n + mm;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+13] = mm * n + jj;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+14] = kk * n + ll;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+15] = ll * n + kk;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+16] = kk * n + mm;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+17] = mm * n + kk;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+18] = ll * n + mm;
((int*)triplet->j)[6*PP->NIneq + 20*ineq+19] = mm * n + ll;
/*** values ***/
if (type == 1){
for (l = 6*PP->NIneq + 20*ineq; l < 6*PP->NIneq + 20*(ineq+1); ++l){
((double*)triplet->x)[l] = -0.25;
}
}
else if (type == 2){
((double*)triplet->x)[6*PP->NIneq + 20*ineq] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 1] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 2] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 3] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 4] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 5] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 6] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 7] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 8] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 9] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 10] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 11] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 12] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 13] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 14] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 15] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 16] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 17] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 18] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 19] = -0.25;
}
else if (type == 3){
((double*)triplet->x)[6*PP->NIneq + 20*ineq] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 1] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 2] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 3] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 4] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 5] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 6] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 7] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 8] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 9] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 10] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 11] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 12] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 13] = 0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 14] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 15] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 16] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 17] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 18] = -0.25;
((double*)triplet->x)[6*PP->NIneq + 20*ineq + 19] = -0.25;
}
}
/* heptagonal */
for (int ineq = 0; ineq < PP->NHeptaIneq; ++ineq) {
type = Hepta_Cuts[ineq].type;
ii = Hepta_Cuts[ineq].permutation[0];
jj = Hepta_Cuts[ineq].permutation[1];
kk = Hepta_Cuts[ineq].permutation[2];
ll = Hepta_Cuts[ineq].permutation[3];
mm = Hepta_Cuts[ineq].permutation[4];
nnn = Hepta_Cuts[ineq].permutation[5];
oo = Hepta_Cuts[ineq].permutation[6];
/*** rows ***/
for (l = 6*PP->NIneq + 20*PP->NPentIneq + 42*ineq; l < 6*PP->NIneq + 20*PP->NPentIneq + 42*(ineq+1); ++l){
((int*)triplet->i)[l] = PP->NIneq + PP->NPentIneq + ineq;
}
/*** columns ***/
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq] = jj * n + ii;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 1] = ii * n + jj;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 2] = kk * n + ii;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 3] = ii * n + kk;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 4] = ll * n + ii;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 5] = ii * n + ll;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 6] = mm * n + ii;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 7] = ii * n + mm;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 8] = nnn * n + ii;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 9] = ii * n + nnn;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 10] = oo * n + ii;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 11] = ii * n + oo;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 12] = jj * n + kk;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 13] = kk * n + jj;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 14] = jj * n + ll;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 15] = ll * n + jj;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 16] = jj * n + mm;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 17] = mm * n + jj;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 18] = jj * n + nnn;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 19] = nnn * n + jj;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 20] = jj * n + oo;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 21] = oo * n + jj;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 22] = kk * n + ll;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 23] = ll * n + kk;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 24] = kk * n + mm;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 25] = mm * n + kk;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 26] = kk * n + nnn;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 27] = nnn * n + kk;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 28] = kk * n + oo;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 29] = oo * n + kk;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 30] = ll * n + mm;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 31] = mm * n + ll;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 32] = ll * n + nnn;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 33] = nnn * n + ll;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 34] = ll * n + oo;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 35] = oo * n + ll;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 36] = mm * n + nnn;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 37] = nnn * n + mm;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 38] = mm * n + oo;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 39] = oo * n + mm;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 40] = nnn * n + oo;
((int*)triplet->j)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 41] = oo * n + nnn;
/*** values ***/
if (type == 1){
for (l = 6*PP->NIneq + 20*PP->NPentIneq + 42*ineq; l < 6*PP->NIneq + 20*PP->NPentIneq + 42*(ineq+1); ++l){
((double*)triplet->x)[l] = -1.0/6.0;
}
}
else if (type == 2){
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 1] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 2] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 3] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 4] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 5] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 6] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 7] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 8] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 9] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 10] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 11] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 12] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 13] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 14] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 15] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 16] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 17] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 18] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 19] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 20] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 21] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 22] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 23] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 24] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 25] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 26] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 27] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 28] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 29] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 30] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 31] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 32] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 33] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 34] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 35] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 36] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 37] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 38] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 39] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 40] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 41] = -1.0/6.0;
}
else if (type == 3){
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 1] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 2] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 3] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 4] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 5] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 6] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 7] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 8] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 9] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 10] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 11] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 12] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 13] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 14] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 15] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 16] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 17] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 18] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 19] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 20] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 21] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 22] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 23] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 24] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 25] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 26] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 27] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 28] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 29] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 30] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 31] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 32] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 33] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 34] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 35] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 36] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 37] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 38] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 39] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 40] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 41] = -1.0/6.0;
}
else if (type == 4){
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 1] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 2] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 3] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 4] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 5] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 6] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 7] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 8] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 9] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 10] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 11] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 12] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 13] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 14] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 15] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 16] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 17] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 18] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 19] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 20] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 21] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 22] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 23] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 24] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 25] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 26] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 27] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 28] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 29] = 1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 30] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 31] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 32] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 33] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 34] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 35] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 36] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 37] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 38] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 39] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 40] = -1.0/6.0;
((double*)triplet->x)[6*PP->NIneq + 20*PP->NPentIneq + 42*ineq + 41] = -1.0/6.0;
}
}
triplet->nnz = 6*PP->NIneq + 20*PP->NPentIneq + 42*PP->NHeptaIneq;
// triplet to sparse and allocate space for rhs of linear system (BBt + I)t = b_cholmod
B_cholmod = cholmod_triplet_to_sparse(triplet, 6*PP->NIneq + 20*PP->NPentIneq + 42*PP->NHeptaIneq, &Common);
b_cholmod = cholmod_zeros(m, 1, B_cholmod->xtype, &Common);
/* ---------------------------------------------------------------------- */
/* analyze and factorize */
/* ---------------------------------------------------------------------- */
L_cholmod = cholmod_analyze(B_cholmod, &Common);
cholmod_factorize_p(B_cholmod, beta, NULL, 0, L_cholmod, &Common); // factorize BBt + I
/*******************************************************/
// counts number of ADMM iterations
*nbit = 0;
/* print output */
if (print) {
puts("======================================================================================");
printf("%4s %6s %8s %8s %5s %9s %9s %12s\n",
"iter", "time", "primal", "dual", "gap", "log10(rp)", "log10(rd)", "log10(sigma)");
puts("======================================================================================");
}
/* some temporary variables */
double *tmp;
alloc_matrix(tmp, n, double);
double *rhs;
alloc_vector(rhs, m, double);
double *res;
alloc_vector(res, n, double);
double *v;
alloc_vector(v, m, double);
// NOTE: we use the fact that operators diag and B are orthogonal
// --> diag(Bt(t)) = 0 and B(Diag(y)) = 0
/***** main loop *****/
while ( (*nbit) <= params.ADMM_itermax ) {
// increase iteration count
(*nbit)++;
/* compute y = diag(L + Q + X/sigma) - e/sigma */
for (int i = 0; i < n; ++i) {
y[i] = PP->L[i + i * n] + Q[i + i * n] + (X[i + i * n] - 1.0) / (*sigma);
}
/* compute tmp = L + Q + X/sigma */
for (int i = 0; i < nn; ++i) {
tmp[i] = PP->L[i] + Q[i] + X[i]/(*sigma);
}
/*** compute t ***/
// rhs = B(tmp) + s + (u-b)/sigma --> copy into t
dcopy_(&m,s,&inc,t,&inc); // copy s to t
op_B(PP, t, tmp); // t += B(tmp)
for (int i = 0; i < m; ++i) {
t[i] += (u[i] - 1) / (*sigma); // t += (u-b)/sigma
((double*)b_cholmod->x)[i] = t[i]; // copy t into cholmod object
}
/*** CHOLMOD: solve linear system (BBt + I)t = rhs ***/
t_cholmod = cholmod_solve(CHOLMOD_A, L_cholmod, b_cholmod, &Common);
// copy cholmod solution to t
for (int i = 0; i < m; ++i) {
t[i] = ((double*)t_cholmod->x)[i];
}
// free memory for t_cholmod --> otherwise memory leak
cholmod_free_dense(&t_cholmod, &Common);
/**** compute s = (t-u/sigma)_+ = v_+ ****/
for (int i = 0; i < m; ++i) {
v[i] = t[i] - u[i]/(*sigma);
s[i] = ( ( v[i] > 0 ) ? v[i] : 0 );
}
/**** compute W = L + X/sigma - Diag(y) - Bt(t) ****/
// NOTE: save it in X!
for (int i = 0; i < nn; ++i) {
X[i] = PP->L[i] + X[i]/(*sigma);
}
op_Diag(PP, X, y);
op_Bt(PP, X, t);
/*
* projection onto PSD cone:
* computes X_+ and Q = -(X_-)
*/
project_SDP(PP);
/**** update primal variables ****/
// Scale: X = sigma * X
dscal_(&nn, sigma, X, &inc);
// Update Z so that X = Z*Z'
double sca = sqrt(*sigma);
int nM = n * M;
dscal_(&nM, &sca, Z, &inc); // Z = Z * sqrt(sigma)
// update: u = u + sigma * (s-t)
// = -sigma * v_-
for (int i = 0; i < m; ++i) {
u[i] = ( ( v[i] < 0 ) ? -(*sigma) * v[i] : 0 );
}
/*
* compute inner (primal) error || Diag(X) - e || + || max(B(X)-e,0) ||)
* and divide it by 1 + sqrt(n)
*/
// || Diag(X) - e ||
diag(X, res, n);
for (int i = 0; i < n; ++i) {
res[i] -= 1.0;
}
err_p = dnrm2_(&n, res, &inc);
// || max(B(X)-b,0) ||
for (int i = 0; i < m; ++i) {
rhs[i] = -1.0;
}
// rhs += B(X)
op_B(PP, rhs, X);
for (int i = 0; i < m; ++i) {
rhs[i] = ( (rhs[i] > 0) ? rhs[i] : 0);
}
err_p += dnrm2_(&m, rhs, &inc);
err_p /= (1 + sqrt(n));
/*
* compute outer (dual) error || Z - Diag(y) - Bt(t) + L || + || s - t ||
* and divide it by 1 + norm(L, 'fro')
*/
dcopy_(&m,s,&inc,rhs,&inc); // copy s to rhs
alpha = -1.0;
daxpy_(&m,&alpha,t,&inc,rhs,&inc); // rhs -= t
err_d = dnrm2_(&m,rhs,&inc);
// tmp = L + Z - Diag(y) - Bt(t)
for (int i = 0; i < nn; ++i) {
tmp[i] = PP->L[i] + Q[i];
}
op_Diag(PP, tmp, y);
op_Bt(PP, tmp, t);
err_d += dlansy_(&NORM, &UPLO, &n, tmp, &n, WORK);
err_d /= (1 + dlansy_(&NORM, &UPLO, &n, PP->L, &n, WORK));
/**** compute primal and dual objective values ****/
// NOTE: do not use ddot_(&nn,PP->L,&inc,X,&inc)
// --> lower triangular part of X contains garbage
// and should not be referenced!
primal = 0.0;
for (int i = 0; i < n; ++i) {
for (int j = i; j < n; ++j) {
if (i==j) {
primal += PP->L[i + i*n] * X[i + i*n];
}
else {
primal += 2 * PP->L[j + i*n] * X[j + i*n];
}
}
}
dual = 0.0;
for (int i = 0; i < n; ++i) {
dual += y[i];
}
for (int ineq = 0; ineq < m; ++ineq) {
dual += t[ineq];
}
/**** duality gap ****/
gap = fabs(dual - primal) / (1 + fabs(dual) + fabs(primal));
/*** error = max(err_p, err_d, gap) ***/
err = ( err_p > err_d ? (err_p > gap ? err_p : gap) : (err_d > gap ? err_d : gap) );
/**** time ****/
secs = MPI_Wtime() - TIME;
/**** number of digits ****/
digits_p = log10(err_p);
digits_d = log10(err_d);
/**** print output (every 10 iterations) ****/
if (print) {
if ( (*nbit) % 10 == 0) {
printf("%4d %6.2f %8.2f %8.2f %5.2f %9.2f %9.2f %12.2f\n",
*nbit, secs, primal, dual, gap, digits_p, digits_d, log10(*sigma));
}
}
/**** adjust sigma ****/
if (digits_d - digits_p < -0.5)
*sigma /= params.scaleSigma;
else if (digits_d - digits_p > 0.5)
*sigma *= params.scaleSigma;
/* stopping condition */
if ( err < tol ) {
if (print) {
printf("%4d %6.2f %8.2f %8.2f %5.2f %9.2f %9.2f %12.2f\n",
*nbit, secs, primal, dual, gap, digits_p, digits_d, log10(*sigma));
}
break;
}
}
/* ---------------------------------------------------------------------- */
/* free matrices and finish CHOLMOD */
/* ---------------------------------------------------------------------- */
cholmod_free_dense(&b_cholmod, &Common);
cholmod_free_dense(&t_cholmod, &Common);
cholmod_free_factor(&L_cholmod, &Common);
cholmod_free_sparse (&B_cholmod, &Common);
cholmod_free_triplet(&triplet, &Common);
cholmod_finish (&Common);
/* ---------------------------------------------------------------------- */
/******************** POST-PROCESSING to obtain safe upper bound ********************/
/* STEPS:
* Z_new = L-diag(y)-mat(B'*s);
* y = y + max(eig(Z_new)) * e;
* f = sum(y) + sum(s);
*/
double *Z_new;
alloc_matrix(Z_new, n, double);
dcopy_(&nn,PP->L,&inc,Z_new,&inc); // copy L into Z_new
op_Diag(PP, Z_new, y);
op_Bt(PP, Z_new, s);
/**** compute largest eigenvalue ****/
char JOBZ = 'N';
char RANGE = 'I';
int LDA = n;
double VL, VU; // not referenced
int IL = n;
int IU = n;
double ABSTOL = 1e-8;
int NUM_EIG;
double lambda_max;
int LDZ = n;
int LWORK = sizeWORK;
int LIWORK = sizeIWORK;
int INFO;
dsyevr_(&JOBZ, &RANGE, &UPLO, &n, Z_new, &LDA, &VL, &VU, &IL, &IU, &ABSTOL,
&NUM_EIG, &lambda_max, Z, &LDZ, ISUPPZ, WORK, &LWORK, IWORK, &LIWORK, &INFO);
if (INFO != 0) {
fprintf(stderr, "Error: eigenvalue computation failed\n");
exit(1);
}
/*** safe bound ***/
free(Z_new);
f = n * lambda_max;
for (int i = 0; i < n; ++i) {
f += y[i];
}
for (int ineq = 0; ineq < m; ++ineq) {
f += s[ineq];
}
/*---------------------------------------*/
free(tmp);
free(rhs);
free(res);
free(v);
}