// called from package MatrixModels's R code:
SEXP dgCMatrix_cholsol(SEXP x, SEXP y)
{
/* Solve Sparse Least Squares X %*% beta ~= y with dense RHS y,
* where X = t(x) i.e. we pass x = t(X) as argument,
* via "Cholesky(X'X)" .. well not really:
* cholmod_factorize("x", ..) finds L in X'X = L'L directly */
CHM_SP cx = AS_CHM_SP(x);
/* FIXME: extend this to work in multivariate case, i.e. y a matrix with > 1 column ! */
CHM_DN cy = AS_CHM_DN(coerceVector(y, REALSXP)), rhs, cAns, resid;
CHM_FR L;
int n = cx->ncol;/* #{obs.} {x = t(X) !} */
double one[] = {1,0}, zero[] = {0,0}, neg1[] = {-1,0};
const char *nms[] = {"L", "coef", "Xty", "resid", ""};
SEXP ans = PROTECT(Rf_mkNamed(VECSXP, nms));
R_CheckStack();
if (n < cx->nrow || n <= 0)
error(_("dgCMatrix_cholsol requires a 'short, wide' rectangular matrix"));
if (cy->nrow != n)
error(_("Dimensions of system to be solved are inconsistent"));
rhs = cholmod_allocate_dense(cx->nrow, 1, cx->nrow, CHOLMOD_REAL, &c);
/* cholmod_sdmult(A, transp, alpha, beta, X, Y, &c):
* Y := alpha*(A*X) + beta*Y or alpha*(A'*X) + beta*Y ;
* here: rhs := 1 * x %*% y + 0 = x %*% y = X'y */
if (!(cholmod_sdmult(cx, 0 /* trans */, one, zero, cy, rhs, &c)))
error(_("cholmod_sdmult error (rhs)"));
L = cholmod_analyze(cx, &c);
if (!cholmod_factorize(cx, L, &c))
error(_("cholmod_factorize failed: status %d, minor %d from ncol %d"),
c.status, L->minor, L->n);
/* FIXME: Do this in stages so an "effects" vector can be calculated */
if (!(cAns = cholmod_solve(CHOLMOD_A, L, rhs, &c)))
error(_("cholmod_solve (CHOLMOD_A) failed: status %d, minor %d from ncol %d"),
c.status, L->minor, L->n);
/* L : */
SET_VECTOR_ELT(ans, 0, chm_factor_to_SEXP(L, 0));
/* coef : */
SET_VECTOR_ELT(ans, 1, allocVector(REALSXP, cx->nrow));
Memcpy(REAL(VECTOR_ELT(ans, 1)), (double*)(cAns->x), cx->nrow);
/* X'y : */
/* FIXME: Change this when the "effects" vector is available */
SET_VECTOR_ELT(ans, 2, allocVector(REALSXP, cx->nrow));
Memcpy(REAL(VECTOR_ELT(ans, 2)), (double*)(rhs->x), cx->nrow);
/* resid := y */
resid = cholmod_copy_dense(cy, &c);
/* cholmod_sdmult(A, transp, alp, bet, X, Y, &c):
* Y := alp*(A*X) + bet*Y or alp*(A'*X) + beta*Y ;
* here: resid := -1 * x' %*% coef + 1 * y = y - X %*% coef */
if (!(cholmod_sdmult(cx, 1/* trans */, neg1, one, cAns, resid, &c)))
error(_("cholmod_sdmult error (resid)"));
/* FIXME: for multivariate case, i.e. resid *matrix* with > 1 column ! */
SET_VECTOR_ELT(ans, 3, allocVector(REALSXP, n));
Memcpy(REAL(VECTOR_ELT(ans, 3)), (double*)(resid->x), n);
cholmod_free_factor(&L, &c);
cholmod_free_dense(&rhs, &c);
cholmod_free_dense(&cAns, &c);
UNPROTECT(1);
return ans;
}
int CholeskyFactorization::factorize() {
if (m_matrix_type == Matrix::MATRIX_SPARSE) {
/* Cholesky decomposition of a SPARSE matrix: */
if (m_matrix->m_sparse == NULL) {
m_matrix->_createSparse();
}
/* analyze */
m_factor = cholmod_analyze(m_matrix->m_sparse, Matrix::cholmod_handle());
/* factorize */
cholmod_factorize(m_matrix->m_sparse, m_factor, Matrix::cholmod_handle());
/* Success: status = 0, else 1*/
return (m_factor->minor == m_matrix->m_nrows) ? ForBESUtils::STATUS_OK : ForBESUtils::STATUS_NUMERICAL_PROBLEMS;
} else { /* If this is any non-sparse matrix: */
memcpy(m_L, m_matrix->getData(), m_matrix->length() * sizeof (double)); /* m_L := m_matrix.m_data */
int info = ForBESUtils::STATUS_OK;
if (m_matrix_type == Matrix::MATRIX_DENSE) { /* This is a dense matrix */
info = LAPACKE_dpotrf(LAPACK_COL_MAJOR, 'L', m_matrix_nrows, m_L, m_matrix_nrows);
#ifdef SET_L_OFFDIAG_TO_ZERO
for (size_t i = 0; i < m_matrix_nrows; i++) {
for (size_t j = i + 1; j < m_matrix_nrows; j++) {
L.set(i, j, 0.0);
}
}
#endif
} else if (m_matrix_type == Matrix::MATRIX_SYMMETRIC) { /* This is a symmetric matrix */
info = LAPACKE_dpptrf(LAPACK_COL_MAJOR, 'L', m_matrix_nrows, m_L);
}
return info;
}
}
int main (int argc, char **argv)
{
/* ---------------------------------------------------------------------- */
/* get the file containing the input matrix */
/* ---------------------------------------------------------------------- */
FILE *ff = NULL ;
FILE *fb = NULL ;
if (argc <= 1)
{
printf("Usage is: cholmod_simple A.tri [B.txt (dense)]\n");
exit(0);
}
if (argc > 1)
ff = fopen(argv[1],"r");
if (argc > 2)
fb = fopen(argv[2], "r");
cholmod_sparse *A ;
cholmod_dense *x, *b, *r ;
cholmod_factor *L ;
double one [2] = {1,0}, m1 [2] = {-1,0} ; // basic scalars
cholmod_common c ;
cholmod_start (&c) ; /* start CHOLMOD */
A = cholmod_read_sparse (ff, &c) ; /* read in a matrix */
cholmod_print_sparse (A, (char *)"A", &c) ; /* print the matrix */
if (A->dtype) printf("A is float\n");
else printf("A is double\n");
if (A == NULL || A->stype == 0) /* A must be symmetric */
{
cholmod_free_sparse (&A, &c) ;
cholmod_finish (&c) ;
if (ff) fclose(ff);
if (fb) fclose(fb);
return (0) ;
}
if (fb)
b = cholmod_read_dense(fb, &c);
else
b = cholmod_ones (A->nrow, 1, A->xtype, &c) ; /* b = ones(n,1) */
double t0 = CPUTIME;
L = cholmod_analyze (A, &c) ; /* analyze */
cholmod_factorize (A, L, &c) ; /* factorize */
x = cholmod_solve (CHOLMOD_A, L, b, &c) ; /* solve Ax=b */
double t1 = CPUTIME;
if (c.dtype) printf("Compute is float\n");
else printf("Compute is double\n");
printf("Time: %12.4f \n", t1-t0);
r = cholmod_copy_dense (b, &c) ; /* r = b */
cholmod_sdmult (A, 0, m1, one, x, r, &c) ; /* r = r-Ax */
printf ("norm(b-Ax) %8.1e\n",
cholmod_norm_dense (r, 0, &c)) ; /* print norm(r) */
cholmod_free_factor (&L, &c) ; /* free matrices */
cholmod_free_sparse (&A, &c) ;
cholmod_free_dense (&r, &c) ;
cholmod_free_dense (&x, &c) ;
cholmod_free_dense (&b, &c) ;
cholmod_finish (&c) ; /* finish CHOLMOD */
return (0) ;
}
int main (void)
{
cholmod_sparse *A ;
cholmod_dense *x, *b, *r ;
cholmod_factor *L ;
double one [2] = {1,0}, m1 [2] = {-1,0} ; /* basic scalars */
cholmod_common c ;
cholmod_start (&c) ; /* start CHOLMOD */
A = cholmod_read_sparse (stdin, &c) ; /* read in a matrix */
cholmod_print_sparse (A, "A", &c) ; /* print the matrix */
if (A == NULL || A->stype == 0) /* A must be symmetric */
{
cholmod_free_sparse (&A, &c) ;
cholmod_finish (&c) ;
return (0) ;
}
b = cholmod_ones (A->nrow, 1, A->xtype, &c) ; /* b = ones(n,1) */
L = cholmod_analyze (A, &c) ; /* analyze */
cholmod_factorize (A, L, &c) ; /* factorize */
x = cholmod_solve (CHOLMOD_A, L, b, &c) ; /* solve Ax=b */
r = cholmod_copy_dense (b, &c) ; /* r = b */
cholmod_sdmult (A, 0, m1, one, x, r, &c) ; /* r = r-Ax */
printf ("norm(b-Ax) %8.1e\n",
cholmod_norm_dense (r, 0, &c)) ; /* print norm(r) */
cholmod_free_factor (&L, &c) ; /* free matrices */
cholmod_free_sparse (&A, &c) ;
cholmod_free_dense (&r, &c) ;
cholmod_free_dense (&x, &c) ;
cholmod_free_dense (&b, &c) ;
cholmod_finish (&c) ; /* finish CHOLMOD */
return (0) ;
}
bool SparseOptimizerIncremental::computeCholeskyUpdate()
{
if (_cholmodFactor) {
cholmod_free_factor(&_cholmodFactor, &_cholmodCommon);
_cholmodFactor = 0;
}
const SparseBlockMatrix<MatrixXd>& A = _updateMat;
size_t m = A.rows();
size_t n = A.cols();
if (_cholmodSparse->columnsAllocated < n) {
//std::cerr << __PRETTY_FUNCTION__ << ": reallocating columns" << std::endl;
_cholmodSparse->columnsAllocated = _cholmodSparse->columnsAllocated == 0 ? n : 2 * n; // pre-allocate more space if re-allocating
delete[] (int*)_cholmodSparse->p;
_cholmodSparse->p = new int[_cholmodSparse->columnsAllocated+1];
}
size_t nzmax = A.nonZeros();
if (_cholmodSparse->nzmax < nzmax) {
//std::cerr << __PRETTY_FUNCTION__ << ": reallocating row + values" << std::endl;
_cholmodSparse->nzmax = _cholmodSparse->nzmax == 0 ? nzmax : 2 * nzmax; // pre-allocate more space if re-allocating
delete[] (double*)_cholmodSparse->x;
delete[] (int*)_cholmodSparse->i;
_cholmodSparse->i = new int[_cholmodSparse->nzmax];
_cholmodSparse->x = new double[_cholmodSparse->nzmax];
}
_cholmodSparse->ncol = n;
_cholmodSparse->nrow = m;
A.fillCCS((int*)_cholmodSparse->p, (int*)_cholmodSparse->i, (double*)_cholmodSparse->x, true);
//writeCCSMatrix("updatesparse.txt", _cholmodSparse->nrow, _cholmodSparse->ncol, (int*)_cholmodSparse->p, (int*)_cholmodSparse->i, (double*)_cholmodSparse->x, true);
_cholmodFactor = cholmod_analyze(_cholmodSparse, &_cholmodCommon);
cholmod_factorize(_cholmodSparse, _cholmodFactor, &_cholmodCommon);
#if 0
int* p = (int*)_cholmodFactor->Perm;
for (int i = 0; i < (int)n; ++i)
if (i != p[i])
cerr << "wrong permutation" << i << " -> " << p[i] << endl;
#endif
if (_cholmodCommon.status == CHOLMOD_NOT_POSDEF) {
//std::cerr << "Cholesky failure, writing debug.txt (Hessian loadable by Octave)" << std::endl;
//writeCCSMatrix("debug.txt", _cholmodSparse->nrow, _cholmodSparse->ncol, (int*)_cholmodSparse->p, (int*)_cholmodSparse->i, (double*)_cholmodSparse->x, true);
return false;
}
// change to the specific format we need to have a pretty normal L
int change_status = cholmod_change_factor(CHOLMOD_REAL, 1, 0, 1, 1, _cholmodFactor, &_cholmodCommon);
if (! change_status) {
return false;
}
return true;
}
SEXP dsCMatrix_Cholesky(SEXP Ap, SEXP permP, SEXP LDLp, SEXP superP)
{
char *fname = strdup("spdCholesky"); /* template for factorization name */
int perm = asLogical(permP),
LDL = asLogical(LDLp),
super = asLogical(superP);
SEXP Chol;
cholmod_sparse *A;
cholmod_factor *L;
int sup, ll;
if (super) fname[0] = 'S';
if (perm) fname[1] = 'P';
if (LDL) fname[2] = 'D';
Chol = get_factors(Ap, "fname");
if (Chol != R_NilValue) return Chol;
A = as_cholmod_sparse(Ap);
sup = c.supernodal;
ll = c.final_ll;
if (!A->stype) error("Non-symmetric matrix passed to dsCMatrix_chol");
c.final_ll = !LDL; /* leave as LL' or form LDL' */
c.supernodal = super ? CHOLMOD_SUPERNODAL : CHOLMOD_SIMPLICIAL;
if (perm) {
L = cholmod_analyze(A, &c); /* get fill-reducing permutation */
} else { /* require identity permutation */
int nmethods = c.nmethods, ord0 = c.method[0].ordering,
postorder = c.postorder;
c.nmethods = 1;
c.method[0].ordering = CHOLMOD_NATURAL;
c.postorder = FALSE;
L = cholmod_analyze(A, &c);
c.nmethods = nmethods; c.method[0].ordering = ord0;
c.postorder = postorder;
}
c.supernodal = sup; /* restore previous setting */
c.final_ll = ll;
if (!cholmod_factorize(A, L, &c))
error(_("Cholesky factorization failed"));
Free(A);
Chol = set_factors(Ap, chm_factor_to_SEXP(L, 1), fname);
free(fname); /* note, this must be free, not Free */
return Chol;
}
// doing cholesky decomposition
void Algebra::CK_decomp(Matrix &A, cholmod_factor *&L, cholmod_common *cm, size_t &peak_mem, size_t & CK_mem){
// doing factorization first
cholmod_triplet * T;
size_t n_row = A.get_row();
size_t n_col = A.get_row();
size_t nnz = A.size();
int *Ti;
int *Tj;
double *Tx;
int stype = -1;// lower triangular storage
T = cholmod_allocate_triplet(n_row, n_col, nnz, stype,
CHOLMOD_REAL, cm);
Ti = static_cast<int *>(T->i);
Tj = static_cast<int *>(T->j);
Tx = static_cast<double *>(T->x);
// copy data into T
for(size_t k=0;k<nnz;k++){
Ti[k] = A.Ti[k];
Tj[k] = A.Tj[k];
Tx[k] = A.Tx[k];
}
T->nnz = nnz;
A.Ti.clear();
A.Tj.clear();
A.Tx.clear();
cholmod_sparse * A_cholmod;
A_cholmod = cholmod_triplet_to_sparse(T, nnz, cm);
// free the triplet pointer
cholmod_free_triplet(&T, cm);
//cm->supernodal = -1;
L = cholmod_analyze(A_cholmod, cm);
//L->ordering = CHOLMOD_NATURAL;
cholmod_factorize(A_cholmod, L, cm);
//cholmod_print_factor(L, "L", cm);
//if(peak_mem < cm->memory_usage)
//peak_mem = cm->memory_usage;
//CK_mem += cm->lnz;
cholmod_free_sparse(&A_cholmod, cm);
}
int main (int argc, char **argv)
{
double resid, t, ta, tf, ts, tot, bnorm, xnorm, anorm, rnorm, fl, anz,
axbnorm, rnorm2, resid2 ;
FILE *f ;
cholmod_sparse *A ;
cholmod_dense *X, *B, *W, *R ;
double one [2], zero [2], minusone [2], beta [2], xlnz ;
cholmod_common Common, *cm ;
cholmod_factor *L ;
double *Bx, *Rx, *Xx ;
int i, n, isize, xsize, ordering, xtype, s, ss, lnz ;
/* ---------------------------------------------------------------------- */
/* get the file containing the input matrix */
/* ---------------------------------------------------------------------- */
ff = NULL ;
if (argc > 1)
{
if ((f = fopen (argv [1], "r")) == NULL)
{
my_handler (CHOLMOD_INVALID, __FILE__, __LINE__,
"unable to open file") ;
}
ff = f ;
}
else
{
f = stdin ;
}
/* ---------------------------------------------------------------------- */
/* start CHOLMOD and set parameters */
/* ---------------------------------------------------------------------- */
cm = &Common ;
cholmod_start (cm) ;
/* use default parameter settings, except for the error handler. This
* demo program terminates if an error occurs (out of memory, not positive
* definite, ...). It makes the demo program simpler (no need to check
* CHOLMOD error conditions). This non-default parameter setting has no
* effect on performance. */
cm->error_handler = my_handler ;
/* Note that CHOLMOD will do a supernodal LL' or a simplicial LDL' by
* default, automatically selecting the latter if flop/nnz(L) < 40. */
/* ---------------------------------------------------------------------- */
/* create basic scalars */
/* ---------------------------------------------------------------------- */
zero [0] = 0 ;
zero [1] = 0 ;
one [0] = 1 ;
one [1] = 0 ;
minusone [0] = -1 ;
minusone [1] = 0 ;
beta [0] = 1e-6 ;
beta [1] = 0 ;
/* ---------------------------------------------------------------------- */
/* read in a matrix */
/* ---------------------------------------------------------------------- */
printf ("\n---------------------------------- cholmod_demo:\n") ;
A = cholmod_read_sparse (f, cm) ;
if (ff != NULL) fclose (ff) ;
anorm = cholmod_norm_sparse (A, 0, cm) ;
xtype = A->xtype ;
printf ("norm (A,inf) = %g\n", anorm) ;
printf ("norm (A,1) = %g\n", cholmod_norm_sparse (A, 1, cm)) ;
cholmod_print_sparse (A, "A", cm) ;
if (A->nrow > A->ncol)
{
/* Transpose A so that A'A+beta*I will be factorized instead */
cholmod_sparse *C = cholmod_transpose (A, 2, cm) ;
cholmod_free_sparse (&A, cm) ;
A = C ;
printf ("transposing input matrix\n") ;
}
/* ---------------------------------------------------------------------- */
/* create an arbitrary right-hand-side */
/* ---------------------------------------------------------------------- */
n = A->nrow ;
B = cholmod_zeros (n, 1, xtype, cm) ;
Bx = B->x ;
#if GHS
{
/* b = A*ones(n,1), used by Gould, Hu, and Scott in their experiments */
cholmod_dense *X0 ;
X0 = cholmod_ones (A->ncol, 1, xtype, cm) ;
cholmod_sdmult (A, 0, one, zero, X0, B, cm) ;
cholmod_free_dense (&X0, cm) ;
}
#else
if (xtype == CHOLMOD_REAL)
{
/* real case */
for (i = 0 ; i < n ; i++)
{
double x = n ;
Bx [i] = 1 + i / x ;
}
}
else
{
/* complex case */
for (i = 0 ; i < n ; i++)
{
double x = n ;
Bx [2*i ] = 1 + i / x ; /* real part of B(i) */
Bx [2*i+1] = (x/2 - i) / (3*x) ; /* imag part of B(i) */
}
}
#endif
cholmod_print_dense (B, "B", cm) ;
bnorm = cholmod_norm_dense (B, 0, cm) ; /* max norm */
printf ("bnorm %g\n", bnorm) ;
/* ---------------------------------------------------------------------- */
/* analyze, factorize, and solve */
/* ---------------------------------------------------------------------- */
t = CPUTIME ;
L = cholmod_analyze (A, cm) ;
ta = CPUTIME - t ;
ta = MAX (ta, 0) ;
printf ("Analyze: flop %g lnz %g\n", cm->fl, cm->lnz) ;
if (A->stype == 0)
{
printf ("Factorizing A*A'+beta*I\n") ;
t = CPUTIME ;
cholmod_factorize_p (A, beta, NULL, 0, L, cm) ;
tf = CPUTIME - t ;
tf = MAX (tf, 0) ;
}
else
{
printf ("Factorizing A\n") ;
t = CPUTIME ;
cholmod_factorize (A, L, cm) ;
tf = CPUTIME - t ;
tf = MAX (tf, 0) ;
}
t = CPUTIME ;
X = cholmod_solve (CHOLMOD_A, L, B, cm) ;
ts = CPUTIME - t ;
ts = MAX (ts, 0) ;
tot = ta + tf + ts ;
/* ---------------------------------------------------------------------- */
/* compute the residual */
/* ---------------------------------------------------------------------- */
if (A->stype == 0)
{
/* (AA'+beta*I)x=b is the linear system that was solved */
/* W = A'*X */
W = cholmod_allocate_dense (A->ncol, 1, A->ncol, xtype, cm) ;
cholmod_sdmult (A, 2, one, zero, X, W, cm) ;
/* R = B - beta*X */
R = cholmod_zeros (n, 1, xtype, cm) ;
Rx = R->x ;
Xx = X->x ;
if (xtype == CHOLMOD_REAL)
{
for (i = 0 ; i < n ; i++)
{
Rx [i] = Bx [i] - beta [0] * Xx [i] ;
}
}
else
{
/* complex case */
for (i = 0 ; i < n ; i++)
{
Rx [2*i ] = Bx [2*i ] - beta [0] * Xx [2*i ] ;
Rx [2*i+1] = Bx [2*i+1] - beta [0] * Xx [2*i+1] ;
}
}
/* R = A*W - R */
cholmod_sdmult (A, 0, one, minusone, W, R, cm) ;
cholmod_free_dense (&W, cm) ;
}
else
{
/* Ax=b was factorized and solved, R = B-A*X */
R = cholmod_copy_dense (B, cm) ;
cholmod_sdmult (A, 0, minusone, one, X, R, cm) ;
}
rnorm = cholmod_norm_dense (R, 0, cm) ; /* max abs. entry */
xnorm = cholmod_norm_dense (X, 0, cm) ; /* max abs. entry */
axbnorm = (anorm * xnorm + bnorm + ((n == 0) ? 1 : 0)) ;
resid = rnorm / axbnorm ;
/* ---------------------------------------------------------------------- */
/* iterative refinement (real symmetric case only) */
/* ---------------------------------------------------------------------- */
resid2 = -1 ;
if (A->stype != 0 && A->xtype == CHOLMOD_REAL)
{
cholmod_dense *R2 ;
/* R2 = A\(B-A*X) */
R2 = cholmod_solve (CHOLMOD_A, L, R, cm) ;
/* compute X = X + A\(B-A*X) */
Xx = X->x ;
Rx = R2->x ;
for (i = 0 ; i < n ; i++)
{
Xx [i] = Xx [i] + Rx [i] ;
}
cholmod_free_dense (&R2, cm) ;
cholmod_free_dense (&R, cm) ;
/* compute the new residual, R = B-A*X */
R = cholmod_copy_dense (B, cm) ;
cholmod_sdmult (A, 0, minusone, one, X, R, cm) ;
rnorm2 = cholmod_norm_dense (R, 0, cm) ;
resid2 = rnorm2 / axbnorm ;
}
cholmod_free_dense (&R, cm) ;
/* ---------------------------------------------------------------------- */
/* print results */
/* ---------------------------------------------------------------------- */
cholmod_print_factor (L, "L", cm) ;
/* determine the # of integers's and reals's in L. See cholmod_free */
if (L->is_super)
{
s = L->nsuper + 1 ;
xsize = L->xsize ;
ss = L->ssize ;
isize =
n /* L->Perm */
+ n /* L->ColCount, nz in each column of 'pure' L */
+ s /* L->pi, column pointers for L->s */
+ s /* L->px, column pointers for L->x */
+ s /* L->super, starting column index of each supernode */
+ ss ; /* L->s, the pattern of the supernodes */
}
else
{
/* this space can increase if you change parameters to their non-
* default values (cm->final_pack, for example). */
lnz = L->nzmax ;
xsize = lnz ;
isize =
n /* L->Perm */
+ n /* L->ColCount, nz in each column of 'pure' L */
+ n+1 /* L->p, column pointers */
+ lnz /* L->i, integer row indices */
+ n /* L->nz, nz in each column of L */
+ n+2 /* L->next, link list */
+ n+2 ; /* L->prev, link list */
}
anz = cm->anz ;
for (i = 0 ; i < CHOLMOD_MAXMETHODS ; i++)
{
fl = cm->method [i].fl ;
xlnz = cm->method [i].lnz ;
cm->method [i].fl = -1 ;
cm->method [i].lnz = -1 ;
ordering = cm->method [i].ordering ;
if (fl >= 0)
{
printf ("Ordering: ") ;
if (ordering == CHOLMOD_POSTORDERED) printf ("postordered ") ;
if (ordering == CHOLMOD_NATURAL) printf ("natural ") ;
if (ordering == CHOLMOD_GIVEN) printf ("user ") ;
if (ordering == CHOLMOD_AMD) printf ("AMD ") ;
if (ordering == CHOLMOD_METIS) printf ("METIS ") ;
if (ordering == CHOLMOD_NESDIS) printf ("NESDIS ") ;
if (xlnz > 0)
{
printf ("fl/lnz %10.1f", fl / xlnz) ;
}
if (anz > 0)
{
printf (" lnz/anz %10.1f", xlnz / anz) ;
}
printf ("\n") ;
}
}
printf ("ints in L: %d, doubles in L: %d\n", isize, xsize) ;
printf ("factor flops %g nnz(L) %15.0f (w/no amalgamation)\n",
cm->fl, cm->lnz) ;
if (A->stype == 0)
{
printf ("nnz(A): %15.0f\n", cm->anz) ;
}
else
{
printf ("nnz(A*A'): %15.0f\n", cm->anz) ;
}
if (cm->lnz > 0)
{
printf ("flops / nnz(L): %8.1f\n", cm->fl / cm->lnz) ;
}
if (anz > 0)
{
printf ("nnz(L) / nnz(A): %8.1f\n", cm->lnz / cm->anz) ;
}
printf ("analyze cputime: %12.4f\n", ta) ;
printf ("factor cputime: %12.4f mflop: %8.1f\n", tf,
(tf == 0) ? 0 : (1e-6*cm->fl / tf)) ;
printf ("solve cputime: %12.4f mflop: %8.1f\n", ts,
(ts == 0) ? 0 : (1e-6*4*cm->lnz / ts)) ;
printf ("overall cputime: %12.4f mflop: %8.1f\n",
tot, (tot == 0) ? 0 : (1e-6 * (cm->fl + 4 * cm->lnz) / tot)) ;
printf ("peak memory usage: %12.0f (MB)\n",
(double) (cm->memory_usage) / 1048576.) ;
printf ("residual %8.1e (|Ax-b|/(|A||x|+|b|))\n", resid) ;
if (resid2 >= 0)
{
printf ("residual %8.1e (|Ax-b|/(|A||x|+|b|))"
" after iterative refinement\n", resid2) ;
}
printf ("rcond %8.1e\n\n", cholmod_rcond (L, cm)) ;
cholmod_free_factor (&L, cm) ;
cholmod_free_dense (&X, cm) ;
/* ---------------------------------------------------------------------- */
/* free matrices and finish CHOLMOD */
/* ---------------------------------------------------------------------- */
cholmod_free_sparse (&A, cm) ;
cholmod_free_dense (&B, cm) ;
cholmod_finish (cm) ;
return (0) ;
}
void MultivariateFNormalSufficientSparse::set_Sigma(
const SparseMatrix<double>& Sigma)
{
if (Sigma.cols() != Sigma.rows()) {
IMP_THROW("need a square matrix!", ModelException);
}
//std::cout << "set_sigma" << std::endl;
if (Sigma_) cholmod_free_sparse(&Sigma_, c_);
cholmod_sparse A(Eigen::viewAsCholmod(
Sigma.selfadjointView<Eigen::Upper>()));
Sigma_=cholmod_copy_sparse(&A, c_);
//cholmod_print_sparse(Sigma_,"Sigma",c_);
IMP_LOG(TERSE, "MVNsparse: set Sigma to new matrix" << std::endl);
IMP_LOG(TERSE, "MVNsparse: computing Cholesky decomposition"
<< std::endl);
// compute Cholesky decomposition for determinant and inverse
//c_->final_asis=1; // setup LDLT calculation
//c_->supernodal = CHOLMOD_SIMPLICIAL;
// convert matrix to cholmod format
//symbolic and numeric factorization
L_ = cholmod_analyze(Sigma_, c_);
int success = cholmod_factorize(Sigma_, L_, c_);
//cholmod_print_factor(L_,"L",c_);
if (success == 0 || L_->minor < L_->n)
IMP_THROW("Sigma matrix is not positive semidefinite!",
ModelException);
// determinant and derived constants
cholmod_factor *Lcp(cholmod_copy_factor(L_, c_));
cholmod_sparse *Lsp(cholmod_factor_to_sparse(Lcp,c_));
double logDetSigma=0;
if ((Lsp->itype != CHOLMOD_INT) &&
(Lsp->xtype != CHOLMOD_REAL))
IMP_THROW("types are not int and real, update them here first",
ModelException);
int *p=(int*) Lsp->p;
double *x=(double*) Lsp->x;
for (size_t i=0; i < (size_t) M_; ++i)
logDetSigma += std::log(x[p[i]]);
cholmod_free_sparse(&Lsp,c_);
cholmod_free_factor(&Lcp,c_);
IMP_LOG(TERSE, "MVNsparse: log det(Sigma) = "
<< logDetSigma << std::endl);
IMP_LOG(TERSE, "MVNsparse: det(Sigma) = "
<< exp(logDetSigma) << std::endl);
norm_= std::pow(2*IMP::PI, -double(N_*M_)/2.0)
* exp(-double(N_)/2.0*logDetSigma);
lnorm_=double(N_*M_)/2 * log(2*IMP::PI) + double(N_)/2 * logDetSigma;
IMP_LOG(TERSE, "MVNsparse: norm = " << norm_ << " lnorm = "
<< lnorm_ << std::endl);
//inverse
IMP_LOG(TERSE, "MVNsparse: solving for inverse" << std::endl);
cholmod_sparse* id = cholmod_speye(M_,M_,CHOLMOD_REAL,c_);
if (P_) cholmod_free_sparse(&P_, c_);
P_ = cholmod_spsolve(CHOLMOD_A, L_, id, c_);
cholmod_free_sparse(&id, c_);
if (!P_) IMP_THROW("Unable to solve for inverse!", ModelException);
//WP
IMP_LOG(TERSE, "MVNsparse: solving for PW" << std::endl);
if (PW_) cholmod_free_sparse(&PW_, c_);
PW_ = cholmod_spsolve(CHOLMOD_A, L_, W_, c_);
if (!PW_) IMP_THROW("Unable to solve for PW!", ModelException);
IMP_LOG(TERSE, "MVNsparse: done" << std::endl);
}
void tele2d::computeVectorField(){
unsigned time1, time2, time3 ;
time1 = clock() ;
std::vector<std::vector<double2>> allcurves = curves ;
vector_field.clear() ;
vector_field.resize(resolution*resolution) ;
// delete too short curves
for( int i=0; i<allcurves.size(); ++i ){
if( allcurves[i].size() < 5 )
allcurves.erase( allcurves.begin() + i ) ;
}
if( allcurves.size() == 0 ){
std::cout<<"no valid curves!" ;
exit(1) ;
}
// mark constrained vertices
constrained_vertices_mark.clear() ;
for( int i=0; i<resolution; ++i ) {
std::vector<int> a ;
for( int j=0;j<resolution; ++j )
a.push_back(0) ;
constrained_vertices_mark.push_back(a) ;
}
for( int i=0; i<allcurves.size(); ++ i){
for( int j =0; j<allcurves[i].size(); ++ j){
// get x index of closest vertices
float x = allcurves[i][j].x * resolution - 0.5 ;
int ix ;
if( x-floor(x) < 0.5 ) ix = floor(x) ;
else ix = ceil( x ) ;
// get y index of closest vertices
float y = allcurves[i][j].y * resolution - 0.5 ;
int iy ;
if( y-floor(y) < 0.5 ) iy = floor(y) ;
else iy = ceil( y ) ;
if( ix < 0 ) ix = 0;
if( ix > resolution-1) ix = resolution -1;
if( iy < 0 ) iy = 0;
if( iy > resolution-1) iy = resolution -1;
constrained_vertices_mark[ix][iy] = 1 ;
}
}
// compute b
std::vector<double2> b ;
b.resize(resolution*resolution) ;
for( int i=0; i<resolution; ++i ){
for( int j=0; j<resolution; ++j){
if(constrained_vertices_mark[i][j] == 0 ){
b[i+j*resolution].x = 0;
b[i+j*resolution].y = 0;
continue ;
}
// otherwise, the vertex indexed by (i,j) is constrained
double vx = ((double)i+0.5)/(double)resolution ;
double vy = ((double)j+0.5)/(double)resolution ;
// search for the closest points
int curveid_record = 0;
int pointid_record = 0;
double mindis = 1000.0f ;
for( int curveid=0; curveid<allcurves.size(); ++curveid ){
for( int pointid=0; pointid<allcurves[curveid].size(); ++pointid ){
double quadratic_dis = ( allcurves[curveid][pointid].x - vx )*( allcurves[curveid][pointid].x - vx ) + ( allcurves[curveid][pointid].y - vy )*( allcurves[curveid][pointid].y - vy ) ;
if( quadratic_dis < mindis ){
mindis = quadratic_dis ;
curveid_record = curveid ;
pointid_record = pointid ;
}
}
}
// compute the vector of the vertex indexed by (i,j)
int pid1 = pointid_record-1 > 0 ? pointid_record-1 : 0 ;
int pid2 = pointid_record+1 < allcurves[curveid_record].size()-1 ? pointid_record+1 : allcurves[curveid_record].size()-1;
double2 vector_of_vertex ;
vector_of_vertex.x = allcurves[curveid_record][pid2].x - allcurves[curveid_record][pid1].x ;
vector_of_vertex.y = allcurves[curveid_record][pid2].y - allcurves[curveid_record][pid1].y ;
double norm = sqrt( vector_of_vertex.x * vector_of_vertex.x + vector_of_vertex.y * vector_of_vertex.y) ;
vector_of_vertex.x /= norm ;
vector_of_vertex.y /= norm ;
assert( norm > 0 && norm < 1) ;
//std::cout<<"norm "<<norm<<std::endl;
b[i+j*resolution ] = vector_of_vertex ;
}
}
// compute Pb
std::vector<double2> Pb = b ;
for( int i=0; i<Pb.size(); ++i ){
Pb[i].x *= 1.0e8 ;
Pb[i].y *= 1.0e8 ;
}
// compute L+P
int vnum = resolution*resolution ;
sparse_matrix L_add_P(vnum) ; // create a sparse matrix of vnum rows
// L_add_P <- D - W
for( int id_x =0; id_x<resolution; ++id_x ){
for( int id_y =0; id_y<resolution; ++id_y ){
int vid = id_x + id_y * resolution ;
if( id_x != 0 && id_x != resolution-1 && id_y != 0 && id_y != resolution-1 ){ // inner area
//L_add_P[ vid + vid*vnum] += 6.8284 ;
L_add_P.pluse(vid,vid,6.8284 ) ;
int neibour_id_1 = id_x + id_y * resolution - 1 ;
int neibour_id_2 = id_x + id_y * resolution + 1 ;
int neibour_id_3 = id_x + (id_y-1) * resolution ;
int neibour_id_4 = id_x + (id_y+1) * resolution ;
int neibour_id_5 = id_x + (id_y+1) * resolution - 1 ;
int neibour_id_6 = id_x + (id_y+1) * resolution + 1 ;
int neibour_id_7 = id_x + (id_y-1) * resolution - 1 ;
int neibour_id_8 = id_x + (id_y-1) * resolution + 1 ;
//L_add_P[neibour_id_1+vid*vnum] -= 1 ;
L_add_P.pluse(vid,neibour_id_1, -1 ) ;
//L_add_P[neibour_id_2+vid*vnum] -= 1 ;
L_add_P.pluse(vid,neibour_id_2, -1 ) ;
//L_add_P[neibour_id_3+vid*vnum] -= 1 ;
L_add_P.pluse(vid,neibour_id_3, -1 ) ;
//L_add_P[neibour_id_4+vid*vnum] -= 1 ;
L_add_P.pluse(vid,neibour_id_4, -1 ) ;
//L_add_P[neibour_id_5+vid*vnum] -= 0.7071;
L_add_P.pluse(vid,neibour_id_5, -0.7071 ) ;
//L_add_P[neibour_id_6+vid*vnum] -= 0.7071;
L_add_P.pluse(vid,neibour_id_6, -0.7071 ) ;
//L_add_P[neibour_id_7+vid*vnum] -= 0.7071;
L_add_P.pluse(vid,neibour_id_7, -0.7071 ) ;
//L_add_P[neibour_id_8+vid*vnum] -= 0.7071;
L_add_P.pluse(vid,neibour_id_8, -0.7071 ) ;
}
else if((id_x == 0 || id_x==resolution-1) && (id_y == 0 || id_y==resolution-1) ){ // coners
//L_add_P[ vid + vid*vnum] += 2.7071 ;
L_add_P.pluse(vid,vid, 2.7071 ) ;
int neibour_id_1 = ( id_x == 0 ? ( id_x+id_y * resolution+1) : ( id_x+id_y * resolution - 1) );
int neibour_id_2 = ( id_y == 0 ? ( id_x+ (id_y+1) * resolution) : ( id_x+ (id_y-1) * resolution )) ;
int neibour_id_3 = ( id_x == 0 ? 1 : (resolution-2) ) + ( id_y == 0 ? 1 : (resolution - 2)) * resolution ;
//L_add_P[neibour_id_1+vid*vnum] -= 1 ;
L_add_P.pluse(vid,neibour_id_1, -1 ) ;
//L_add_P[neibour_id_2+vid*vnum] -= 1 ;
L_add_P.pluse(vid,neibour_id_2, -1 ) ;
//L_add_P[neibour_id_3+vid*vnum] -= 0.7071;
L_add_P.pluse(vid,neibour_id_3, -0.7071 ) ;
}
else { // boundaries
//L_add_P[ vid + vid*vnum] += 4.4142 ;
L_add_P.pluse(vid,vid, 4.4142 ) ;
int neibour_id_1, neibour_id_2, neibour_id_3, neibour_id_4, neibour_id_5 ;
if( id_x == 0){
neibour_id_1 = id_x + id_y * resolution + 1 ;
neibour_id_2 = id_x + (id_y+1) * resolution ;
neibour_id_3 = id_x + (id_y-1) * resolution ;
neibour_id_4 = id_x + (id_y+1) * resolution + 1;
neibour_id_5 = id_x + (id_y-1) * resolution + 1 ;
}
else if( id_x == resolution-1 ){
neibour_id_1 = id_x + id_y * resolution - 1 ;
neibour_id_2 = id_x + (id_y+1) * resolution ;
neibour_id_3 = id_x + (id_y-1) * resolution ;
neibour_id_4 = id_x + (id_y+1) * resolution - 1;
neibour_id_5 = id_x + (id_y-1) * resolution - 1 ;
}
else if( id_y == resolution-1 ){
neibour_id_1 = id_x + id_y * resolution + 1 ;
neibour_id_2 = id_x + id_y * resolution - 1 ;
neibour_id_3 = id_x + (id_y-1) * resolution ;
neibour_id_4 = id_x + (id_y-1) * resolution + 1;
neibour_id_5 = id_x + (id_y-1) * resolution - 1 ;
}
else {
neibour_id_1 = id_x + id_y * resolution + 1 ;
neibour_id_2 = id_x + id_y * resolution - 1 ;
neibour_id_3 = id_x + (id_y+1) * resolution ;
neibour_id_4 = id_x + (id_y+1) * resolution + 1;
neibour_id_5 = id_x + (id_y+1) * resolution - 1 ;
}
//L_add_P[neibour_id_1+vid*vnum] -= 1 ;
L_add_P.pluse(vid,neibour_id_1, -1 ) ;
//L_add_P[neibour_id_2+vid*vnum] -= 1 ;
L_add_P.pluse(vid,neibour_id_2, -1 ) ;
//L_add_P[neibour_id_3+vid*vnum] -= 1 ;
L_add_P.pluse(vid,neibour_id_3, -1 ) ;
//L_add_P[neibour_id_4+vid*vnum] -= 0.7071;
L_add_P.pluse(vid,neibour_id_4, -0.7071) ;
//L_add_P[neibour_id_5+vid*vnum] -= 0.7071;
L_add_P.pluse(vid,neibour_id_5, -0.7071 ) ;
}
}
}
// L_add_P <- D - W + P
for( int i=0; i<resolution; ++i ){
for( int j=0; j<resolution; ++j){
if(constrained_vertices_mark[i][j] == 1 ){
int vid = i + j*resolution ;
//L_add_P[vid+vid*vnum]+=1e8 ;
L_add_P.pluse(vid,vid, 1.0e8 ) ;
}
}
}
// solve the linear system with cholmod
cholmod_sparse *A ;
cholmod_dense *x, *y, *b1 ;
double one [2] = {1,0}, m1 [2] = {-1,0} ; /* basic scalars */
cholmod_factor *L ;
cholmod_common c ;
cholmod_start (&c) ;; /* start CHOLMOD */
//A = cholmod_read_sparse (pFile, &c) ; /* read in a matrix */
CMatrix *SM = new CMatrix( vnum, true, &c) ;
//for( int i=0; i<vnum; ++i ){
// for( int j=0; j<vnum; ++j ){
// if( L_add_P.getValue(j,i)!=0 )
// SM->set_coef(i, j,L_add_P.getValue(j,i) ) ;
// }
//}
for( int i=0; i<L_add_P.data.size(); ++i){
for( int j=0; j<L_add_P.data[i].size(); ++j)
SM->set_coef(L_add_P.data[i][j].row, i, L_add_P.data[i][j].val ) ;
}
A =(cholmod_sparse *) SM->get_cholmod_sparse();
time2 = clock() ;
//cholmod_print_sparse (A, "A", &c) ; /* print the matrix */
if (A == NULL || A->stype == 0) /* A must be symmetric */
{
cholmod_free_sparse (&A, &c) ;
cholmod_finish (&c) ;
std::cout << "fail to load the matrix or it's not symmeric!"<<std::endl;
exit(1) ;
}
b1 = cholmod_zeros(vnum, 1, CHOLMOD_REAL, &c);
// --------------------- x demension -----------------------
for( int i =0 ;i<Pb.size(); ++i ){
((double*)(b1->x))[i] = Pb[i].x ;
}
L = cholmod_analyze (A, &c) ; /* analyze */
cholmod_factorize (A, L, &c) ; /* factorize */
x = cholmod_solve (CHOLMOD_A, L, b1, &c) ; /* solve Ax=b */
// write x-values
for( int i=0; i<vector_field.size(); ++i)
vector_field[i].x = ((double*)(x->x))[i] ;
// --------------------- y demension -----------------------
for( int i =0 ;i<Pb.size(); ++i ){
((double*)(b1->x))[i] = Pb[i].y ;
}
y = cholmod_solve (CHOLMOD_A, L, b1, &c) ; /* solve Ay=b */
// write y-values
for( int i=0; i<vector_field.size(); ++i)
vector_field[i].y = ((double*)(y->x))[i] ;
cholmod_free_factor (&L, &c) ;
cholmod_free_dense (&x, &c) ;
cholmod_free_dense (&y, &c) ;
cholmod_free_dense (&b1, &c) ;
//delete L_add_P ;
delete SM ;
cholmod_finish (&c) ; /* finish CHOLMOD */
double normx2, normy2 ;
normx2 = normy2 = 0.0 ;
for( int i=0; i<vnum; ++i ){
normx2 += vector_field[i].x * vector_field[i].x ;
normy2 += vector_field[i].y * vector_field[i].y ;
}
//std::cout<<"|x| = "<<sqrt(normx2) <<"\n|y| = "<<sqrt(normy2) <<std::endl;
// normalize vector field
for( int i=0; i<vector_field.size(); ++i){
double norm = sqrt( vector_field[i].x * vector_field[i].x + vector_field[i].y * vector_field[i].y) ;
vector_field[i].x /= norm ;
vector_field[i].y /= norm ;
}
time3 = clock() ;
//std::cout<<"time consumed by computing A and b: " << (double)(time2-time1)/CLOCKS_PER_SEC <<" s" <<std::endl ;
//std::cout<<"time consumed by solving the system: " << (double)(time3-time2)/CLOCKS_PER_SEC <<" s" <<std::endl ;
//std::cout<<"vector field computing completed."<<std::endl; ;
int count = 0;
for( int i=0; i<L_add_P.data.size(); ++i)
count += L_add_P.data[i].size() ;
//std::cout << "nonzero number: " << count <<std::endl;
}
static int factorize(cholmod_sparse* A, cholmod_factor* L, cholmod_common* c) {
return cholmod_factorize(A, L, c);
}
int main (int argc, char **argv)
{
double resid [4], t, ta, tf, ts [3], tot, bnorm, xnorm, anorm, rnorm, fl,
anz, axbnorm, rnorm2, resid2, rcond ;
FILE *f ;
cholmod_sparse *A ;
cholmod_dense *X = NULL, *B, *W, *R ;
double one [2], zero [2], minusone [2], beta [2], xlnz ;
cholmod_common Common, *cm ;
cholmod_factor *L ;
double *Bx, *Rx, *Xx ;
int i, n, isize, xsize, ordering, xtype, s, ss, lnz ;
int trial, method, L_is_super ;
int ver [3] ;
ts[0] = 0.;
ts[1] = 0.;
ts[2] = 0.;
/* ---------------------------------------------------------------------- */
/* get the file containing the input matrix */
/* ---------------------------------------------------------------------- */
ff = NULL ;
if (argc > 1)
{
if ((f = fopen (argv [1], "r")) == NULL)
{
my_handler (CHOLMOD_INVALID, __FILE__, __LINE__,
"unable to open file") ;
}
ff = f ;
}
else
{
f = stdin ;
}
/* ---------------------------------------------------------------------- */
/* start CHOLMOD and set parameters */
/* ---------------------------------------------------------------------- */
cm = &Common ;
cholmod_start (cm) ;
CHOLMOD_FUNCTION_DEFAULTS (cm) ; /* just for testing (not required) */
/* use default parameter settings, except for the error handler. This
* demo program terminates if an error occurs (out of memory, not positive
* definite, ...). It makes the demo program simpler (no need to check
* CHOLMOD error conditions). This non-default parameter setting has no
* effect on performance. */
cm->error_handler = my_handler ;
/* Note that CHOLMOD will do a supernodal LL' or a simplicial LDL' by
* default, automatically selecting the latter if flop/nnz(L) < 40. */
/* ---------------------------------------------------------------------- */
/* create basic scalars */
/* ---------------------------------------------------------------------- */
zero [0] = 0 ;
zero [1] = 0 ;
one [0] = 1 ;
one [1] = 0 ;
minusone [0] = -1 ;
minusone [1] = 0 ;
beta [0] = 1e-6 ;
beta [1] = 0 ;
/* ---------------------------------------------------------------------- */
/* read in a matrix */
/* ---------------------------------------------------------------------- */
printf ("\n---------------------------------- cholmod_demo:\n") ;
cholmod_version (ver) ;
printf ("cholmod version %d.%d.%d\n", ver [0], ver [1], ver [2]) ;
SuiteSparse_version (ver) ;
printf ("SuiteSparse version %d.%d.%d\n", ver [0], ver [1], ver [2]) ;
A = cholmod_read_sparse (f, cm) ;
if (ff != NULL)
{
fclose (ff) ;
ff = NULL ;
}
anorm = cholmod_norm_sparse (A, 0, cm) ;
xtype = A->xtype ;
printf ("norm (A,inf) = %g\n", anorm) ;
printf ("norm (A,1) = %g\n", cholmod_norm_sparse (A, 1, cm)) ;
cholmod_print_sparse (A, "A", cm) ;
if (A->nrow > A->ncol)
{
/* Transpose A so that A'A+beta*I will be factorized instead */
cholmod_sparse *C = cholmod_transpose (A, 2, cm) ;
cholmod_free_sparse (&A, cm) ;
A = C ;
printf ("transposing input matrix\n") ;
}
/* ---------------------------------------------------------------------- */
/* create an arbitrary right-hand-side */
/* ---------------------------------------------------------------------- */
n = A->nrow ;
B = cholmod_zeros (n, 1, xtype, cm) ;
Bx = B->x ;
#if GHS
{
/* b = A*ones(n,1), used by Gould, Hu, and Scott in their experiments */
cholmod_dense *X0 ;
X0 = cholmod_ones (A->ncol, 1, xtype, cm) ;
cholmod_sdmult (A, 0, one, zero, X0, B, cm) ;
cholmod_free_dense (&X0, cm) ;
}
#else
if (xtype == CHOLMOD_REAL)
{
/* real case */
for (i = 0 ; i < n ; i++)
{
double x = n ;
Bx [i] = 1 + i / x ;
}
}
else
{
/* complex case */
for (i = 0 ; i < n ; i++)
{
double x = n ;
Bx [2*i ] = 1 + i / x ; /* real part of B(i) */
Bx [2*i+1] = (x/2 - i) / (3*x) ; /* imag part of B(i) */
}
}
#endif
cholmod_print_dense (B, "B", cm) ;
bnorm = cholmod_norm_dense (B, 0, cm) ; /* max norm */
printf ("bnorm %g\n", bnorm) ;
/* ---------------------------------------------------------------------- */
/* analyze and factorize */
/* ---------------------------------------------------------------------- */
t = CPUTIME ;
L = cholmod_analyze (A, cm) ;
ta = CPUTIME - t ;
ta = MAX (ta, 0) ;
printf ("Analyze: flop %g lnz %g\n", cm->fl, cm->lnz) ;
if (A->stype == 0)
{
printf ("Factorizing A*A'+beta*I\n") ;
t = CPUTIME ;
cholmod_factorize_p (A, beta, NULL, 0, L, cm) ;
tf = CPUTIME - t ;
tf = MAX (tf, 0) ;
}
else
{
printf ("Factorizing A\n") ;
t = CPUTIME ;
cholmod_factorize (A, L, cm) ;
tf = CPUTIME - t ;
tf = MAX (tf, 0) ;
}
cholmod_print_factor (L, "L", cm) ;
/* determine the # of integers's and reals's in L. See cholmod_free */
if (L->is_super)
{
s = L->nsuper + 1 ;
xsize = L->xsize ;
ss = L->ssize ;
isize =
n /* L->Perm */
+ n /* L->ColCount, nz in each column of 'pure' L */
+ s /* L->pi, column pointers for L->s */
+ s /* L->px, column pointers for L->x */
+ s /* L->super, starting column index of each supernode */
+ ss ; /* L->s, the pattern of the supernodes */
}
else
{
/* this space can increase if you change parameters to their non-
* default values (cm->final_pack, for example). */
lnz = L->nzmax ;
xsize = lnz ;
isize =
n /* L->Perm */
+ n /* L->ColCount, nz in each column of 'pure' L */
+ n+1 /* L->p, column pointers */
+ lnz /* L->i, integer row indices */
+ n /* L->nz, nz in each column of L */
+ n+2 /* L->next, link list */
+ n+2 ; /* L->prev, link list */
}
/* solve with Bset will change L from simplicial to supernodal */
rcond = cholmod_rcond (L, cm) ;
L_is_super = L->is_super ;
/* ---------------------------------------------------------------------- */
/* solve */
/* ---------------------------------------------------------------------- */
for (method = 0 ; method <= 3 ; method++)
{
double x = n ;
if (method == 0)
{
/* basic solve, just once */
t = CPUTIME ;
X = cholmod_solve (CHOLMOD_A, L, B, cm) ;
ts [0] = CPUTIME - t ;
ts [0] = MAX (ts [0], 0) ;
}
else if (method == 1)
{
/* basic solve, many times, but keep the last one */
t = CPUTIME ;
for (trial = 0 ; trial < NTRIALS ; trial++)
{
cholmod_free_dense (&X, cm) ;
Bx [0] = 1 + trial / x ; /* tweak B each iteration */
X = cholmod_solve (CHOLMOD_A, L, B, cm) ;
}
ts [1] = CPUTIME - t ;
ts [1] = MAX (ts [1], 0) / NTRIALS ;
}
else if (method == 2)
{
/* solve with reused workspace */
cholmod_dense *Ywork = NULL, *Ework = NULL ;
cholmod_free_dense (&X, cm) ;
t = CPUTIME ;
for (trial = 0 ; trial < NTRIALS ; trial++)
{
Bx [0] = 1 + trial / x ; /* tweak B each iteration */
cholmod_solve2 (CHOLMOD_A, L, B, NULL, &X, NULL,
&Ywork, &Ework, cm) ;
}
cholmod_free_dense (&Ywork, cm) ;
cholmod_free_dense (&Ework, cm) ;
ts [2] = CPUTIME - t ;
ts [2] = MAX (ts [2], 0) / NTRIALS ;
}
else
{
/* solve with reused workspace and sparse Bset */
cholmod_dense *Ywork = NULL, *Ework = NULL ;
cholmod_dense *X2 = NULL, *B2 = NULL ;
cholmod_sparse *Bset, *Xset = NULL ;
int *Bsetp, *Bseti, *Xsetp, *Xseti, xlen, j, k, *Lnz ;
double *X1x, *X2x, *B2x, err ;
FILE *timelog = fopen ("timelog.m", "w") ;
if (timelog) fprintf (timelog, "results = [\n") ;
B2 = cholmod_zeros (n, 1, xtype, cm) ;
B2x = B2->x ;
Bset = cholmod_allocate_sparse (n, 1, 1, FALSE, TRUE, 0,
CHOLMOD_PATTERN, cm) ;
Bsetp = Bset->p ;
Bseti = Bset->i ;
Bsetp [0] = 0 ; /* nnz(B) is 1 (it can be anything) */
Bsetp [1] = 1 ;
resid [3] = 0 ;
for (i = 0 ; i < MIN (100,n) ; i++)
{
/* B (i) is nonzero, all other entries are ignored
(implied to be zero) */
Bseti [0] = i ;
if (xtype == CHOLMOD_REAL)
{
B2x [i] = 3.1 * i + 0.9 ;
}
else
{
B2x [2*i ] = i + 0.042 ;
B2x [2*i+1] = i - 92.7 ;
}
/* first get the entire solution, to compare against */
cholmod_solve2 (CHOLMOD_A, L, B2, NULL, &X, NULL,
&Ywork, &Ework, cm) ;
/* now get the sparse solutions; this will change L from
supernodal to simplicial */
if (i == 0)
{
/* first solve can be slower because it has to allocate
space for X2, Xset, etc, and change L.
So don't time it */
cholmod_solve2 (CHOLMOD_A, L, B2, Bset, &X2, &Xset,
&Ywork, &Ework, cm) ;
}
t = CPUTIME ;
for (trial = 0 ; trial < NTRIALS ; trial++)
{
/* solve Ax=b but only to get x(i).
b is all zero except for b(i).
This takes O(xlen) time */
cholmod_solve2 (CHOLMOD_A, L, B2, Bset, &X2, &Xset,
&Ywork, &Ework, cm) ;
}
t = CPUTIME - t ;
t = MAX (t, 0) / NTRIALS ;
/* check the solution and log the time */
Xsetp = Xset->p ;
Xseti = Xset->i ;
xlen = Xsetp [1] ;
X1x = X->x ;
X2x = X2->x ;
Lnz = L->nz ;
/*
printf ("\ni %d xlen %d (%p %p)\n", i, xlen, X1x, X2x) ;
*/
if (xtype == CHOLMOD_REAL)
{
fl = 2 * xlen ;
for (k = 0 ; k < xlen ; k++)
{
j = Xseti [k] ;
fl += 4 * Lnz [j] ;
err = X1x [j] - X2x [j] ;
err = ABS (err) ;
resid [3] = MAX (resid [3], err) ;
}
}
else
{
fl = 16 * xlen ;
for (k = 0 ; k < xlen ; k++)
{
j = Xseti [k] ;
fl += 16 * Lnz [j] ;
err = X1x [2*j ] - X2x [2*j ] ;
err = ABS (err) ;
resid [3] = MAX (resid [3], err) ;
err = X1x [2*j+1] - X2x [2*j+1] ;
err = ABS (err) ;
resid [3] = MAX (resid [3], err) ;
}
}
if (timelog) fprintf (timelog, "%g %g %g %g\n",
(double) i, (double) xlen, fl, t);
/* clear B for the next test */
if (xtype == CHOLMOD_REAL)
{
B2x [i] = 0 ;
}
else
{
B2x [2*i ] = 0 ;
B2x [2*i+1] = 0 ;
}
}
if (timelog)
{
fprintf (timelog, "] ; resid = %g ;\n", resid [3]) ;
fprintf (timelog, "lnz = %g ;\n", cm->lnz) ;
fprintf (timelog, "t = %g ; %% dense solve time\n", ts [2]) ;
fclose (timelog) ;
}
resid [3] = resid [3] / cholmod_norm_dense (X, 1, cm) ;
cholmod_free_dense (&Ywork, cm) ;
cholmod_free_dense (&Ework, cm) ;
cholmod_free_dense (&X2, cm) ;
cholmod_free_dense (&B2, cm) ;
cholmod_free_sparse (&Xset, cm) ;
cholmod_free_sparse (&Bset, cm) ;
}
/* ------------------------------------------------------------------ */
/* compute the residual */
/* ------------------------------------------------------------------ */
if (method < 3)
{
if (A->stype == 0)
{
/* (AA'+beta*I)x=b is the linear system that was solved */
/* W = A'*X */
W = cholmod_allocate_dense (A->ncol, 1, A->ncol, xtype, cm) ;
cholmod_sdmult (A, 2, one, zero, X, W, cm) ;
/* R = B - beta*X */
R = cholmod_zeros (n, 1, xtype, cm) ;
Rx = R->x ;
Xx = X->x ;
if (xtype == CHOLMOD_REAL)
{
for (i = 0 ; i < n ; i++)
{
Rx [i] = Bx [i] - beta [0] * Xx [i] ;
}
}
else
{
/* complex case */
for (i = 0 ; i < n ; i++)
{
Rx [2*i ] = Bx [2*i ] - beta [0] * Xx [2*i ] ;
Rx [2*i+1] = Bx [2*i+1] - beta [0] * Xx [2*i+1] ;
}
}
/* R = A*W - R */
cholmod_sdmult (A, 0, one, minusone, W, R, cm) ;
cholmod_free_dense (&W, cm) ;
}
else
{
/* Ax=b was factorized and solved, R = B-A*X */
R = cholmod_copy_dense (B, cm) ;
cholmod_sdmult (A, 0, minusone, one, X, R, cm) ;
}
rnorm = cholmod_norm_dense (R, 0, cm) ; /* max abs. entry */
xnorm = cholmod_norm_dense (X, 0, cm) ; /* max abs. entry */
axbnorm = (anorm * xnorm + bnorm + ((n == 0) ? 1 : 0)) ;
resid [method] = rnorm / axbnorm ;
}
}
tot = ta + tf + ts [0] ;
/* ---------------------------------------------------------------------- */
/* iterative refinement (real symmetric case only) */
/* ---------------------------------------------------------------------- */
resid2 = -1 ;
if (A->stype != 0 && A->xtype == CHOLMOD_REAL)
{
cholmod_dense *R2 ;
/* R2 = A\(B-A*X) */
R2 = cholmod_solve (CHOLMOD_A, L, R, cm) ;
/* compute X = X + A\(B-A*X) */
Xx = X->x ;
Rx = R2->x ;
for (i = 0 ; i < n ; i++)
{
Xx [i] = Xx [i] + Rx [i] ;
}
cholmod_free_dense (&R2, cm) ;
cholmod_free_dense (&R, cm) ;
/* compute the new residual, R = B-A*X */
R = cholmod_copy_dense (B, cm) ;
cholmod_sdmult (A, 0, minusone, one, X, R, cm) ;
rnorm2 = cholmod_norm_dense (R, 0, cm) ;
resid2 = rnorm2 / axbnorm ;
}
cholmod_free_dense (&R, cm) ;
/* ---------------------------------------------------------------------- */
/* print results */
/* ---------------------------------------------------------------------- */
anz = cm->anz ;
for (i = 0 ; i < CHOLMOD_MAXMETHODS ; i++)
{
fl = cm->method [i].fl ;
xlnz = cm->method [i].lnz ;
cm->method [i].fl = -1 ;
cm->method [i].lnz = -1 ;
ordering = cm->method [i].ordering ;
if (fl >= 0)
{
printf ("Ordering: ") ;
if (ordering == CHOLMOD_POSTORDERED) printf ("postordered ") ;
if (ordering == CHOLMOD_NATURAL) printf ("natural ") ;
if (ordering == CHOLMOD_GIVEN) printf ("user ") ;
if (ordering == CHOLMOD_AMD) printf ("AMD ") ;
if (ordering == CHOLMOD_METIS) printf ("METIS ") ;
if (ordering == CHOLMOD_NESDIS) printf ("NESDIS ") ;
if (xlnz > 0)
{
printf ("fl/lnz %10.1f", fl / xlnz) ;
}
if (anz > 0)
{
printf (" lnz/anz %10.1f", xlnz / anz) ;
}
printf ("\n") ;
}
}
printf ("ints in L: %15.0f, doubles in L: %15.0f\n",
(double) isize, (double) xsize) ;
printf ("factor flops %g nnz(L) %15.0f (w/no amalgamation)\n",
cm->fl, cm->lnz) ;
if (A->stype == 0)
{
printf ("nnz(A): %15.0f\n", cm->anz) ;
}
else
{
printf ("nnz(A*A'): %15.0f\n", cm->anz) ;
}
if (cm->lnz > 0)
{
printf ("flops / nnz(L): %8.1f\n", cm->fl / cm->lnz) ;
}
if (anz > 0)
{
printf ("nnz(L) / nnz(A): %8.1f\n", cm->lnz / cm->anz) ;
}
printf ("analyze cputime: %12.4f\n", ta) ;
printf ("factor cputime: %12.4f mflop: %8.1f\n", tf,
(tf == 0) ? 0 : (1e-6*cm->fl / tf)) ;
printf ("solve cputime: %12.4f mflop: %8.1f\n", ts [0],
(ts [0] == 0) ? 0 : (1e-6*4*cm->lnz / ts [0])) ;
printf ("overall cputime: %12.4f mflop: %8.1f\n",
tot, (tot == 0) ? 0 : (1e-6 * (cm->fl + 4 * cm->lnz) / tot)) ;
printf ("solve cputime: %12.4f mflop: %8.1f (%d trials)\n", ts [1],
(ts [1] == 0) ? 0 : (1e-6*4*cm->lnz / ts [1]), NTRIALS) ;
printf ("solve2 cputime: %12.4f mflop: %8.1f (%d trials)\n", ts [2],
(ts [2] == 0) ? 0 : (1e-6*4*cm->lnz / ts [2]), NTRIALS) ;
printf ("peak memory usage: %12.0f (MB)\n",
(double) (cm->memory_usage) / 1048576.) ;
printf ("residual (|Ax-b|/(|A||x|+|b|)): ") ;
for (method = 0 ; method <= 3 ; method++)
{
printf ("%8.2e ", resid [method]) ;
}
printf ("\n") ;
if (resid2 >= 0)
{
printf ("residual %8.1e (|Ax-b|/(|A||x|+|b|))"
" after iterative refinement\n", resid2) ;
}
printf ("rcond %8.1e\n\n", rcond) ;
if (L_is_super)
{
cholmod_gpu_stats (cm) ;
}
cholmod_free_factor (&L, cm) ;
cholmod_free_dense (&X, cm) ;
/* ---------------------------------------------------------------------- */
/* free matrices and finish CHOLMOD */
/* ---------------------------------------------------------------------- */
cholmod_free_sparse (&A, cm) ;
cholmod_free_dense (&B, cm) ;
cholmod_finish (cm) ;
return (0) ;
}
void KVFModel::calculateVF(const std::set<DisplacedVertex> &disps, double alpha1)
{
TimeMeasurment total,t;
cholmod_common* cm = cholmod_get_common();
unsigned int numFaces = getNumFaces();
unsigned int numVertices = getNumVertices();
this->disps = disps;
std::set<DisplacedVertex> allDisplacements = disps;
for (auto iter = pinnedVertexes.begin(); iter != pinnedVertexes.end() ; iter++)
allDisplacements.insert(DisplacedVertex(*iter, Vector2(0,0)));
if (allDisplacements.size() <= 1)
return;
if (allDisplacements.size() != lastDispsSize) {
cholmod_free_factor(&L1, cholmod_get_common());
lastDispsSize = allDisplacements.size();
}
/************************************************/
/* BUILD P matrix */
P.startMatrixFill();
P.reshape(3*numFaces,2*numVertices,12*numFaces);
for (unsigned int f = 0; f < numFaces; f++)
{
int i = (*faces)[f][0];
int j = (*faces)[f][1];
int k = (*faces)[f][2];
if (i > j) { std::swap(i,j); }
if (i > k) { std::swap(i,k); }
if (j > k) { std::swap(j,k); }
Vector2 d1 = vertices[i] - vertices[k];
Vector2 d2 = vertices[j] - vertices[i];
double area = fabs(d1[1]*d2[0] - d1[0]*d2[1]);
Vector2 c1(-d1[1]/area,d1[0]/area);
Vector2 c2(-d2[1]/area,d2[0]/area);
double gix = -c1[0] - c2[0], gjx = c1[0], gkx = c2[0];
double giy = -c1[1] - c2[1], gjy = c1[1], gky = c2[1];
P.addElement(3*f+0,i,gix*2);
P.addElement(3*f+0,j,gjx*2);
P.addElement(3*f+0,k,gkx*2);
P.addElement(3*f+1,i,giy*M_SQRT2);
P.addElement(3*f+1,j,gjy*M_SQRT2);
P.addElement(3*f+1,k,gky*M_SQRT2);
P.addElement(3*f+1,i+numVertices,gix*M_SQRT2);
P.addElement(3*f+1,j+numVertices,gjx*M_SQRT2);
P.addElement(3*f+1,k+numVertices,gkx*M_SQRT2);
P.addElement(3*f+2,i+numVertices,giy*2);
P.addElement(3*f+2,j+numVertices,gjy*2);
P.addElement(3*f+2,k+numVertices,gky*2);
}
Pcopy.copy(P);
printf("KVF: P construct time: %f msec\n", t.measure_msec());
/*++++++++++++++++++++++++++++++++++++++++++++++*/
CholmodVector B = CholmodVector(2*numVertices);
std::vector<int> indices2;
double alpha = alpha1 / (2*allDisplacements.size()) * P.infinityNorm();
for (auto iter = allDisplacements.begin() ; iter != allDisplacements.end() ; iter++)
{
indices2.push_back(iter->v);
indices2.push_back(iter->v + numVertices);
B[iter->v] = iter->displacement[0]*alpha*alpha;
B[iter->v+numVertices] = iter->displacement[1]*alpha*alpha;
}
P.addConstraint(indices2, alpha);
printf("KVF: P constraint adding time: %f msec\n", t.measure_msec());
/*++++++++++++++++++++++++++++++++++++++++++++++*/
cholmod_sparse cSparse;
P.getCholmodMatrix(cSparse);
if (!L1) L1 = cholmod_analyze(&cSparse, cm);
cholmod_factorize(&cSparse, L1, cm);
cholmod_dense * Xcholmod = cholmod_solve(CHOLMOD_A, L1, B, cm);
double* Xx = (double*)Xcholmod->x;
for (unsigned int i = 0; i < numVertices; i++)
vfOrig[i] = Vector2D<double>(Xx[i],Xx[i+numVertices]);
printf("KVF: Solve time: %f msec\n", t.measure_msec());
/*+++++DIRICHLET SOLVE +++++++++++++++++++++++++++++++++++++++++*/
CholmodVector boundaryRHS = CholmodVector(2*numVertices);
for (std::set<int>::iterator it = boundaryVertices->begin(); it != boundaryVertices->end(); ++it)
{
boundaryRHS[*it] = Xx[*it];
boundaryRHS[*it + numVertices] = Xx[*it + numVertices];
}
CholmodVector rhsMove(Pcopy.numRows());
Pcopy.multiply(boundaryRHS, rhsMove);
for (unsigned int i = 0; i < rhsMove.size(); i++)
rhsMove[i] *= -1;
Pcopy.zeroOutColumns(*boundaryVertices, 0);
Pcopy.zeroOutColumns(*boundaryVertices, numVertices);
Pcopy.transposeMultiply(rhsMove,B);
std::vector<int> constrained;
for (std::set<int>::iterator it = boundaryVertices->begin(); it != boundaryVertices->end(); ++it)
{
int bv = *it;
constrained.push_back(*it);
constrained.push_back(*it+numVertices);
B[bv] += Xx[bv];
B[bv+numVertices] += Xx[bv+numVertices];
}
Pcopy.addConstraint(constrained,1);
printf("KVF: Dirichlet prepare time: %f msec\n", t.measure_msec());
/*++++++++++++++++++++++++++++++++++++++++++++++*/
Pcopy.getCholmodMatrix(cSparse);
if (!L2) L2 = cholmod_analyze(&cSparse, cm);
cholmod_factorize(&cSparse, L2, cm);
cholmod_dense *Xcholmod2 = cholmod_solve(CHOLMOD_A, L2, B, cm);
Xx = (double*)Xcholmod2->x;
printf("KVF: Dirichlet solve time: %f msec\n", t.measure_msec());
for (unsigned int i = 0; i < numVertices; i++)
vf[i] = Vector2D<double>(Xx[i],Xx[i+numVertices]);
cholmod_free_dense(&Xcholmod, cm);
cholmod_free_dense(&Xcholmod2, cm);
printf("KVF: Fini time: %f msec\n", t.measure_msec());
lastVFCalcTime = total.measure_msec();
}
/* Factorize - filling in rowsDropped and returning number dropped */
int
ClpCholeskyUfl::factorize(const double * diagonal, int * rowsDropped)
{
const CoinBigIndex * columnStart = model_->clpMatrix()->getVectorStarts();
const int * columnLength = model_->clpMatrix()->getVectorLengths();
const int * row = model_->clpMatrix()->getIndices();
const double * element = model_->clpMatrix()->getElements();
const CoinBigIndex * rowStart = rowCopy_->getVectorStarts();
const int * rowLength = rowCopy_->getVectorLengths();
const int * column = rowCopy_->getIndices();
const double * elementByRow = rowCopy_->getElements();
int numberColumns = model_->clpMatrix()->getNumCols();
int iRow;
double * work = new double[numberRows_];
CoinZeroN(work, numberRows_);
const double * diagonalSlack = diagonal + numberColumns;
int newDropped = 0;
double largest;
//double smallest;
//perturbation
double perturbation = model_->diagonalPerturbation() * model_->diagonalNorm();
perturbation = 0.0;
perturbation = perturbation * perturbation;
if (perturbation > 1.0) {
#ifdef COIN_DEVELOP
//if (model_->model()->logLevel()&4)
std::cout << "large perturbation " << perturbation << std::endl;
#endif
perturbation = sqrt(perturbation);;
perturbation = 1.0;
}
double delta2 = model_->delta(); // add delta*delta to diagonal
delta2 *= delta2;
for (iRow = 0; iRow < numberRows_; iRow++) {
double * put = sparseFactor_ + choleskyStart_[iRow];
int * which = choleskyRow_ + choleskyStart_[iRow];
int number = choleskyStart_[iRow+1] - choleskyStart_[iRow];
if (!rowLength[iRow])
rowsDropped_[iRow] = 1;
if (!rowsDropped_[iRow]) {
CoinBigIndex startRow = rowStart[iRow];
CoinBigIndex endRow = rowStart[iRow] + rowLength[iRow];
work[iRow] = diagonalSlack[iRow] + delta2;
for (CoinBigIndex k = startRow; k < endRow; k++) {
int iColumn = column[k];
if (!whichDense_ || !whichDense_[iColumn]) {
CoinBigIndex start = columnStart[iColumn];
CoinBigIndex end = columnStart[iColumn] + columnLength[iColumn];
double multiplier = diagonal[iColumn] * elementByRow[k];
for (CoinBigIndex j = start; j < end; j++) {
int jRow = row[j];
if (jRow >= iRow && !rowsDropped_[jRow]) {
double value = element[j] * multiplier;
work[jRow] += value;
}
}
}
}
int j;
for (j = 0; j < number; j++) {
int jRow = which[j];
put[j] = work[jRow];
work[jRow] = 0.0;
}
} else {
// dropped
int j;
for (j = 1; j < number; j++) {
put[j] = 0.0;
}
put[0] = 1.0;
}
}
//check sizes
double largest2 = maximumAbsElement(sparseFactor_, sizeFactor_);
largest2 *= 1.0e-20;
largest = CoinMin(largest2, 1.0e-11);
int numberDroppedBefore = 0;
for (iRow = 0; iRow < numberRows_; iRow++) {
int dropped = rowsDropped_[iRow];
// Move to int array
rowsDropped[iRow] = dropped;
if (!dropped) {
CoinBigIndex start = choleskyStart_[iRow];
double diagonal = sparseFactor_[start];
if (diagonal > largest2) {
sparseFactor_[start] = CoinMax(diagonal, 1.0e-10);
} else {
sparseFactor_[start] = CoinMax(diagonal, 1.0e-10);
rowsDropped[iRow] = 2;
numberDroppedBefore++;
}
}
}
delete [] work;
cholmod_sparse A ;
A.nrow = numberRows_;
A.ncol = numberRows_;
A.nzmax = choleskyStart_[numberRows_];
A.p = choleskyStart_;
A.i = choleskyRow_;
A.x = sparseFactor_;
A.stype = -1;
A.itype = CHOLMOD_INT;
A.xtype = CHOLMOD_REAL;
A.dtype = CHOLMOD_DOUBLE;
A.sorted = 1;
A.packed = 1;
cholmod_factorize (&A, L_, c_) ; /* factorize */
choleskyCondition_ = 1.0;
bool cleanCholesky;
if (model_->numberIterations() < 2000)
cleanCholesky = true;
else
cleanCholesky = false;
if (cleanCholesky) {
//drop fresh makes some formADAT easier
//int oldDropped=numberRowsDropped_;
if (newDropped || numberRowsDropped_) {
//std::cout <<"Rank "<<numberRows_-newDropped<<" ( "<<
// newDropped<<" dropped)";
//if (newDropped>oldDropped)
//std::cout<<" ( "<<newDropped-oldDropped<<" dropped this time)";
//std::cout<<std::endl;
newDropped = 0;
for (int i = 0; i < numberRows_; i++) {
int dropped = rowsDropped[i];
rowsDropped_[i] = (char)dropped;
if (dropped == 2) {
//dropped this time
rowsDropped[newDropped++] = i;
rowsDropped_[i] = 0;
}
}
numberRowsDropped_ = newDropped;
newDropped = -(2 + newDropped);
}
} else {
if (newDropped) {
newDropped = 0;
for (int i = 0; i < numberRows_; i++) {
int dropped = rowsDropped[i];
rowsDropped_[i] = (char)dropped;
if (dropped == 2) {
//dropped this time
rowsDropped[newDropped++] = i;
rowsDropped_[i] = 1;
}
}
}
numberRowsDropped_ += newDropped;
if (numberRowsDropped_ && 0) {
std::cout << "Rank " << numberRows_ - numberRowsDropped_ << " ( " <<
numberRowsDropped_ << " dropped)";
if (newDropped) {
std::cout << " ( " << newDropped << " dropped this time)";
}
std::cout << std::endl;
}
}
status_ = 0;
return newDropped;
}
BasicMesh MeshTransferer::transfer(const vector<PhGUtils::Matrix3x3d> &S1grad)
{
if( !(S0set && T0set) ) {
throw "S0 or T0 not set.";
}
auto &S = S1grad;
auto &T = T0grad;
int nfaces = S0.faces.nrow;
int nverts = S0.verts.nrow;
// assemble sparse matrix A
int nrowsA = nfaces * 3;
int nsv = stationary_vertices.size();
int nrowsC = nsv;
int nrows = nrowsA + nrowsC;
int ncols = nverts;
int ntermsA = nfaces*9;
int ntermsC = stationary_vertices.size();
int nterms = ntermsA + ntermsC;
SparseMatrix A(nrows, ncols, nterms);
// fill in the deformation gradient part
for(int i=0, ioffset=0;i<nfaces;++i) {
/*
* Ai:
* 1 2 3 4 5 ... nfaces*3
* 1 2 3 4 5 ... nfaces*3
* 1 2 3 4 5 ... nfaces*3
* Ai = reshape(Ai, 1, nfaces*9)
*
* Aj = reshape(repmat(S0.faces', 3, 1), 1, nfaces*9)
* Av = reshape(cell2mat(T)', 1, nfaces*9)
*/
int *f = S0.faces.rowptr(i);
auto Ti = T[i];
A.append(ioffset, f[0], Ti(0));
A.append(ioffset, f[1], Ti(1));
A.append(ioffset, f[2], Ti(2));
++ioffset;
A.append(ioffset, f[0], Ti(3));
A.append(ioffset, f[1], Ti(4));
A.append(ioffset, f[2], Ti(5));
++ioffset;
A.append(ioffset, f[0], Ti(6));
A.append(ioffset, f[1], Ti(7));
A.append(ioffset, f[2], Ti(8));
++ioffset;
}
// fill in the lower part of A, stationary vertices part
for(int i=0;i<nsv;++i) {
A.append(nrowsA+i, stationary_vertices[i], 1);
}
ofstream fA("A.txt");
fA<<A;
fA.close();
// fill in c matrix
DenseMatrix c(nrows, 3);
for(int i=0;i<3;++i) {
for(int j=0, joffset=0;j<nfaces;++j) {
auto &Sj = S[j];
c(joffset, i) = Sj(0, i); ++joffset;
c(joffset, i) = Sj(1, i); ++joffset;
c(joffset, i) = Sj(2, i); ++joffset;
}
}
for(int i=0;i<3;++i) {
for(int j=0, joffset=nrowsA;j<nsv;++j,++joffset) {
auto vj = T0.verts.rowptr(stationary_vertices[j]);
c(joffset, i) = vj[i];
}
}
cholmod_sparse *G = A.to_sparse();
cholmod_sparse *Gt = cholmod_transpose(G, 2, global::cm);
// compute GtD
// just multiply Dsi to corresponding elemenets
double *Gtx = (double*)Gt->x;
const int* Gtp = (const int*)(Gt->p);
for(int i=0;i<nrowsA;++i) {
int fidx = i/3;
for(int j=Gtp[i];j<Gtp[i+1];++j) {
Gtx[j] *= Ds(fidx);
}
}
// compute GtDG
cholmod_sparse *GtDG = cholmod_ssmult(Gt, G, 0, 1, 1, global::cm);
GtDG->stype = 1;
// compute GtD * c
cholmod_dense *GtDc = cholmod_allocate_dense(ncols, 3, ncols, CHOLMOD_REAL, global::cm);
double alpha[2] = {1, 0}; double beta[2] = {0, 0};
cholmod_sdmult(Gt, 0, alpha, beta, c.to_dense(), GtDc, global::cm);
// solve for GtDG \ GtDc
cholmod_factor *L = cholmod_analyze(GtDG, global::cm);
cholmod_factorize(GtDG, L, global::cm);
cholmod_dense *x = cholmod_solve(CHOLMOD_A, L, GtDc, global::cm);
// make a copy of T0
BasicMesh Td = T0;
// change the vertices with x
double *Vx = (double*)x->x;
for(int i=0;i<nverts;++i) {
Td.verts(i, 0) = Vx[i];
Td.verts(i, 1) = Vx[i+nverts];
Td.verts(i, 2) = Vx[i+nverts*2];
}
// release memory
cholmod_free_sparse(&G, global::cm);
cholmod_free_sparse(&Gt, global::cm);
cholmod_free_sparse(&GtDG, global::cm);
cholmod_free_dense(&GtDc, global::cm);
cholmod_free_factor(&L, global::cm);
cholmod_free_dense(&x, global::cm);
return Td;
}
int main(int argc, char *argv[])
{
char *name = "main";
char *seperator = "**********************************************************";
// Setup the data structure with parameters of the problem
switch (argc)
{
case 1:
printf("No input file specified. Using dia1P.inp\n");
dia1P_initialize("dia1P.inp",name);
break;
case 2:
dia1P_initialize(argv[1],name);
break;
default:
dia1P_errHandler(errCode_TooManyArguments,name,name,errMesg_TooManyArguments);
}
// Print the problem to make sure
dia1P_printPD(name);
/* The prefix M_ is used for components that can be reused in several
failure simulations. For example, it is not necessary to compute
the first stiffness matrix M_M or its decomposition M_L for each
failure simulation. On the other hand, the matrix of fuse strengths,
S, needs to be repopulated every time.
*/
/* START REUSABLE COMPONENTS DECLARATIONS */
// Stiffness matrix M
cholmod_sparse *M_M;
// J = M_V2C*V; where J = current flowing into the bottom nodes,
// and V = vector of voltages of all nodes
cholmod_sparse *M_V2C;
// Voltages at top and bottom nodes
cholmod_sparse *M_vTop, *M_vBot;
// Cholesky factor of the stiffness matrix M
cholmod_factor *M_L;
// Cholmod Common object
cholmod_common Common;
// Basic scalars, one and minus one
double one [2] = {1,0}, m1 [2] = {-1,0} ;
/* END REUSABLE COMPONENTS DECLARATIONS */
/* START REUSABLE COMPONENTS INITIALIZATIONS */
// Start cholmod, and the cholmod_common object
cholmod_start(&Common);
// Populated the top and bottom node voltages
// Bottom row is "grounded", thus has zero
// voltage by convention.
// cholmod_spzeros(NRow,NCol,stype,xtype,*common)
M_vBot = cholmod_spzeros(pD.gridSize/2,1,0,CHOLMOD_REAL,&Common);
// The top row has voltage = 1. Since cholmod has no inbuild
// function to return a sparse vector of all ones (makes sense)
// so we first create a dense vector of ones and then
// convert it to a sparse vector
{ // limit the scope of temporary variables
cholmod_dense *temp;
temp = cholmod_ones(pD.gridSize/2,1,CHOLMOD_REAL,&Common);
M_vTop = cholmod_dense_to_sparse(temp,1,&Common);
cholmod_free_dense(&temp,&Common);
}
// Polulate voltage to current matrix and check it for
// consistency
M_V2C = dia1P_voltageToCurrentMatrix(&Common,name);
cholmod_check_sparse(M_V2C,&Common);
// Populate stiffness matrix
M_M = dia1P_stiffnessMatrix(&Common,name);
// Check it for consistency
cholmod_check_sparse(M_M,&Common);
// Analyze and factorise the stiffness matrix
M_L = cholmod_analyze(M_M,&Common);
cholmod_factorize(M_M,M_L,&Common);
// Check the factor for consistency
cholmod_check_factor(M_L,&Common);
/* END REUSABLE COMPONENTS INITIALIZATIONS */
// Depending on the mode in which the program is run
// various levels of output are given to the user.
// The three modes implemented so far are:
// 0: Silent,
// 1: minimal,
// 2: normal
// 3: verbose
switch (pD.diagMode)
{
case 0:
break;
case 1:
fprintf(pD.diagFile,"NSim\tnF\t\tnAv\t\tV\t\tC\n");
fflush(pD.diagFile);
break;
case 2:
break;
case 3:
fprintf(pD.diagFile,"Initial Stiffness Matrix\n");
cholmod_write_sparse(pD.diagFile,M_M,NULL,NULL,&Common);
fflush(pD.diagFile);
break;
default:
dia1P_errHandler(errCode_UnknownDiagMode,name,name,errMesg_UnknownDiagMode);
}
/* START MAIN SIMULATIONS LOOP */
// Number of simulations performed
int countSims = 0;
while (countSims < pD.NSim)
{
/* START LOOP COMPONENTS DECLARATIONS */
// The sampleFailed flag remains zeros as long as
// the sample is not broken (a spanning crack is
// not encountered; it becomes 1 otherwise.
int sampleFailed = 0;
// nFail counts the number of bonds snapped till
// sample failure
int nFail = 0;
// Cholesky factor L will hold the cholesky factor that will be updated after each bond snapping
cholmod_factor *L;
// Vector of random fuse strengths
double *S;
// Matrix that maps the node voltages to the vector of
// currents flowing into the bottom nodes.
// This matrix is update after every bond breaking
cholmod_sparse *V2C;
// Load vector b. This vector is to be updated after
// every bond breaking
cholmod_sparse *b;
// A data structure that will store information about the
// most recently failed bond
dia1P_failureSite FD;
// A data structure that will store information about the
// sequence of failures in a particular simulation
dia1P_brokenBonds *BB;
/* END LOOP COMPONENTS DECLARATIONS */
/* START LOOP COMPONENTS INITIALIZATIONS */
// Copy the pre-calculated cholesky factor into the local
// cholesky factor
L = cholmod_copy_factor(M_L,&Common);
// Populate fuse strength vector
S = dia1P_strengthVector(name);
//FILE *pf = fopen("16.S","r"); S = cholmod_read_sparse(pf,&Common); fclose(pf);
// Copy the initial voltage to current matrix
V2C = cholmod_copy_sparse(M_V2C,&Common);
// Initialize the structure for keeping records of broken bonds
BB = dia1P_initializeBrokenBonds(name);
// Polulate the load vector b
b = dia1P_loadVector(&Common,name);
// Check to ensure consistency...
cholmod_check_sparse(b,&Common);
/* END LOOP COMPONENTS INITIALIZATIONS */
// Write diagonistic output as requested
switch (pD.diagMode)
{
case 0: break;
case 1: break;
case 2:
fprintf(pD.diagFile,"%s\n",seperator);
fprintf(pD.diagFile,"Starting Simulation Number %d\n",countSims+1);
fprintf(pD.diagFile,"I\t\tJ\t\tV\t\tC\n");
fflush(pD.diagFile);
break;
case 3:
fprintf(pD.diagFile,"%s\n",seperator);
fprintf(pD.diagFile,"Starting Simulation Number %d\n",countSims+1);
fprintf(pD.diagFile,"Matrix of Random Fuse Strengths:\n");
{
int count = 0;
for(count = 0; count < (pD.gridSize)*(pD.gridSize); count++)
{
int n1, n2;
dia1P_getNodeNumbers(&n1,&n2,count,name);
fprintf(pD.diagFile,"%d\t%d\t%G\n",n1,n2,S[count]);
}
fprintf(pD.diagFile,"\n");
}
//cholmod_write_sparse(pD.diagFile,S,NULL,NULL,&Common);
fflush(pD.diagFile);
break;
default: dia1P_errHandler(errCode_UnknownDiagMode,name,name,errMesg_UnknownDiagMode);
}
while(sampleFailed == 0)
{
/* START INNER LOOP COMPONENTS INITIALIZATIONS */
// Vector x will hold the unknown voltages
cholmod_sparse *x;
// Vectors VNode_s and VNode_d hold the full set
// of node voltages (knowns appended to the calculated unknowns)
cholmod_sparse *VNode_s;
cholmod_dense *VNode_d;
// This vector will be used to update the stiffness matrix M
// as M_new = M_old - stiffUpdate*transpose(stiffUpdate)
// Ofcouse, M is not update, rather its cholesky factor L is
cholmod_sparse *stiffUpdate;
// This vector updates the load vector as
// b_new = b_old + loadUpdate
cholmod_sparse *loadUpdate;
// This vector is needed for internal cholmod use.
// We L = PMP^T, where P is the permuation matrix.
// Thus, if U updates M, then PU will update L.
// uper = PU.
cholmod_sparse *uper;
/* END INNER LOOP COMPONENTS INITIALIZATIONS */
// Solve for the unknown voltages
x = cholmod_spsolve(CHOLMOD_A,L,b,&Common);
// Append the known vectors top and the bottom
// row voltages to x to construct the complete
// vector of voltages.
{ // Limit the score of temporary variables
cholmod_sparse *temp1;
temp1 = cholmod_vertcat(M_vBot,x,1,&Common);
VNode_s = cholmod_vertcat(temp1,M_vTop,1,&Common);
cholmod_free_sparse(&temp1,&Common);
}
// Check if the sample is broken, if it is then
// we are done
if(dia1P_isBroken(VNode_s,V2C,&Common,name))
{
sampleFailed = 1;
{
int count = 0;
for(count = 0; count < BB->nFail; count++)
{
fprintf(pD.outFile,"%d\t%d\t%G\t%G\t%G\n",BB->i[count]+1,BB->j[count]+1,BB->v[count],BB->c[count],BB->bondStrength[count]);
}
fprintf(pD.outFile,"%d\t%d\t%G\t%G\t%G\n",0,0,0.f,0.f,0.f);
}
}
else
{ // If the sample is not broken yet, then we need to
// to find which bond will be snapped next.
// Increment the number of failed bonds, since we know
// that one is going to snap
nFail++;
// Make a dense vector of voltages
VNode_d = cholmod_sparse_to_dense(VNode_s,&Common);
// Find which bond to break and store the information
// in the data structure FD.
dia1P_bondToSnap(S,VNode_d,VNode_s,V2C,BB,&FD,&Common,name);
// Update the data structure BB, which stores the entire
// sequence of broken bonds
dia1P_updateBrokenBonds(BB,&FD,name);
// Update the voltage to current matrix.
// This matrix will change only if a fuse connected to the
// bottom edge is blown.
dia1P_updateVoltageToCurrentMatrix(V2C,&FD,&Common,name);
// Find the vector to update the stiffness matrix.
// This vector is never empty, it has either 1 or 2 nonzero components
// depending on weather a boundary node is involved in the snapping or not
stiffUpdate = dia1P_stiffnessUpdateVector(&FD,&Common,name);
// Find the vector to update the load vector.
// This vector is non-zero only if a fuse connected to the
// top edge is blown.
loadUpdate = dia1P_loadUpdateVector(&FD,&Common,name);
// Update the load vector
{ // Limit the score of temporary variables
cholmod_sparse *temp;
temp = cholmod_copy_sparse(b,&Common);
// Free the current memory occupied by b before reallocating
cholmod_free_sparse(&b,&Common);
// Reallocate b
b = cholmod_add(temp,loadUpdate,one,one,1,0,&Common);
// Free temp
cholmod_free_sparse(&temp,&Common);
}
// Calculate the permuted update vector for updating the cholesky factor
uper = cholmod_submatrix(stiffUpdate,L->Perm,L->n,NULL,-1,1,1,&Common);
// update (downdate) the cholesky factor
cholmod_updown(0,uper,L,&Common);
// Write appropriate diagnostic output
switch (pD.diagMode)
{
case 0: break;
case 1: break;
case 2:
fprintf(pD.diagFile,"%d\t\t%d\t\t%.3f\t%.3f\n",FD.node1+1,FD.node2+1,FD.fVol,FD.fCur);
break;
case 3:
fprintf(pD.diagFile,"\nPass No. %d\nUnknown Node Voltages:\n",nFail);
cholmod_write_sparse(pD.diagFile,x,NULL,NULL,&Common);
fprintf(pD.diagFile,"\nSnapped Bond: \nI\t\tJ\t\tV\t\tC\n");
fprintf(pD.diagFile,"%d\t\t%d\t\t%.3f\t%.3f\n\n",FD.node1+1,FD.node2+1,FD.fVol,FD.fCur);
fprintf(pD.diagFile,"\nStiffNess Update Vector\n");
cholmod_write_sparse(pD.diagFile,stiffUpdate,NULL,NULL,&Common);
fprintf(pD.diagFile,"\nLoad Update Vector\n");
cholmod_write_sparse(pD.diagFile,loadUpdate,NULL,NULL,&Common);
break;
default: dia1P_errHandler(errCode_UnknownDiagMode,name,name,errMesg_UnknownDiagMode);
}
//Free memory
cholmod_free_dense(&VNode_d,&Common);
cholmod_free_sparse(&stiffUpdate,&Common);
cholmod_free_sparse(&loadUpdate,&Common);
cholmod_free_sparse(&uper,&Common);
}//ESLE
cholmod_free_sparse(&x,&Common);
cholmod_free_sparse(&VNode_s,&Common);
}//ELIHW, loop for nth simulation
// Free memory
free(S);
cholmod_free_sparse(&b,&Common);
cholmod_free_sparse(&V2C,&Common);
cholmod_free_factor(&L,&Common);
dia1P_freeBrokenBonds(&BB,name);
countSims++;
}//ELIHW, main loop for NSim simulations
// This completes the requested set of NSim simulations.
// Free memory
cholmod_free_sparse(&M_M,&Common);
cholmod_free_sparse(&M_V2C,&Common);
cholmod_free_sparse(&M_vBot,&Common);
cholmod_free_sparse(&M_vTop,&Common);
cholmod_free_factor(&M_L,&Common);
// Close dia1P and cholmod
dia1P_finish(name);
// cholmod_print_common("FuseNet Statistics",&Common);
cholmod_finish(&Common);
return(0);
}
int main(void)
{
int N = 2 ;
int i, j, n ;
int nz = 0;
double *Ax ;
double x, error ;
cholmod_dense *A, *invK, *spinvK, *I ;
cholmod_sparse *K, *V ;
cholmod_factor *L ;
cholmod_common Common,*cm ;
clock_t start, end;
double cpu_time_used;
cm=&Common;
// Start using CHOLMOD
cholmod_start(cm) ;
cm->print=5;
/* SPARSE COVARIANCE MATRIX CONSTRUCTION */
// Generate random symmetric positive (semi)definite matrix
A = cholmod_zeros(N, N, CHOLMOD_REAL, &Common) ;
Ax =(double*) A->x ;
nz = N ;
// Make positive-definite by adding something positive to the
// diagonal
for (n = 0; n < N; n++)
{
Ax[n+n*N] += 5;
}
// Make the matrix sparse
K = cholmod_dense_to_sparse(A, TRUE, &Common) ;
K->stype = 1 ; // NEED TO MAKE THE MATRIX SYMMETRIC
// Identity matrix
I = cholmod_eye(N,N,CHOLMOD_REAL,&Common) ;
/* SIMPLICIAL */
// Factorize
Common.supernodal = CHOLMOD_SIMPLICIAL ;
L = cholmod_analyze(K, &Common) ;
cholmod_factorize(K, L, &Common) ;
invK = cholmod_solve(CHOLMOD_A, L, I, &Common) ;
// Compute the sparse inverse and the full inverse
start = clock();
V = cholmod_spinv(L, &Common) ;
end = clock();
cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC;
// Show results
cholmod_print_sparse(K,"Original",&Common) ;
cholmod_print_factor(L,"Factor",&Common) ;
cholmod_print_sparse(V,"Sparse inverse",&Common) ;
cholmod_print_dense(invK,"Dense inverse",&Common);
// Free memory
cholmod_free_factor(&L, &Common) ;
cholmod_free_sparse(&K, &Common) ;
cholmod_free_dense(&I, &Common) ;
cholmod_free_dense(&A, &Common) ;
cholmod_finish(&Common) ;
return 0 ;
}
