int rATL_dpotrfL(int N, double *A,int lda)
{
double *An, *Ar;
int Nleft, Nright, ierr;
if (N > 4) {
Nleft = N >> 1;
#if 0
int nb = ilaenv_f77(&IONE, "DPOTRF", "L", &N,
&IMONE,&IONE, &IMONE, strlen("DPOTRF"), strlen("L"));
if (Nleft > nb<<1) Nleft = (Nleft/nb)*nb;
#endif
#if 0
if (Nleft > 64) {
Nleft = 64;
}
#endif
Nright = N - Nleft;
ierr = rATL_dpotrfL(Nleft, A,lda);
if (!ierr) {
Ar = A + Nleft;
An = Ar + lda * Nleft;
dtrsm_f77 ((char *)"R",(char *)"L",(char *)"T",(char *)"N",
&Nright,&Nleft,&DONE,A,&lda,
Ar, &lda, strlen("R"),strlen("L"),
strlen("T"),strlen("N"));
dsyrk_f77 ((char *)"L",(char *)"N",&Nright,&Nleft,&DMONE,
Ar, &lda, &DONE,An,&lda,strlen("L"),strlen("N"));
ierr = rATL_dpotrfL(Nright, An,lda);
if (ierr) return(ierr+Nleft);
}
else return(ierr);
}
/*
* cpLapackDenseProjSetup does the setup operations for the dense
* linear solver.
* It calls the Jacobian evaluation routine and, depending on ftype,
* it performs various factorizations.
*/
static int cpLapackDenseProjSetup(CPodeMem cp_mem, N_Vector y, N_Vector cy,
N_Vector c_tmp1, N_Vector c_tmp2, N_Vector s_tmp1)
{
int ier;
CPDlsProjMem cpdlsP_mem;
realtype *col_i, rim1, ri;
int i, j, nd, one = 1;
int retval;
realtype coef_1 = ONE, coef_0 = ZERO;
cpdlsP_mem = (CPDlsProjMem) lmemP;
nd = ny-nc;
/* Call Jacobian function (G will contain the Jacobian transposed) */
retval = djacP(nc, ny, tn, y, cy, G, JP_data, c_tmp1, c_tmp2);
njeP++;
if (retval < 0) {
cpProcessError(cp_mem, CPDIRECT_JACFUNC_UNRECVR, "CPLAPACK", "cpLapackDenseProjSetup", MSGD_JACFUNC_FAILED);
return(-1);
} else if (retval > 0) {
return(1);
}
/* Save Jacobian before factorization for possible use by lmultP */
dcopy_f77(&(G->ldata), G->data, &one, savedG->data, &one);
/* Factorize G, depending on ftype */
switch (ftype) {
case CPDIRECT_LU:
/*
* LU factorization of G^T with partial pivoting
* P*G^T = | U1^T | * L^T
* | U2^T |
* After factorization, P is encoded in pivotsP and
* G^T is overwritten with U1 (nc by nc unit upper triangular),
* U2 ( nc by ny-nc rectangular), and L (nc by nc lower triangular).
* Return ier if factorization failed.
*/
dgetrf_f77(&ny, &nc, G->data, &ny, pivotsP, &ier);
if (ier != 0) return(ier);
/*
* Build S = U1^{-1} * U2 (in place, S overwrites U2)
* For each row j of G, j = nc,...,ny-1, perform
* a backward substitution (row version).
* After this step, G^T contains U1, S, and L.
*/
for (j=nc; j<ny; j++)
dtrsv_f77("L", "T", "U", &nc, G->data, &ny, (G->data + j), &ny, 1, 1, 1);
/*
* Build K = D1 + S^T * D2 * S
* S^T is stored in g_mat[nc...ny-1][0...nc]
* Compute and store only the lower triangular part of K.
*/
if (pnorm == CP_PROJ_L2NORM) {
dsyrk_f77("L", "N", &nd, &nc, &coef_1, (G->data + nc), &ny, &coef_0, K->data, &nd, 1, 1);
LapackDenseAddI(K);
} else {
cplLUcomputeKD(cp_mem, s_tmp1);
}
/*
* Perform Cholesky decomposition of K: K = C*C^T
* After factorization, the lower triangular part of K contains C.
* Return ier if factorization failed.
*/
dpotrf_f77("L", &nd, K->data, &nd, &ier, 1);
if (ier != 0) return(ier);
break;
case CPDIRECT_QR:
/*
* QR factorization of G^T: G^T = Q*R
* After factorization, the upper triangular part of G^T
* contains the matrix R. The lower trapezoidal part of
* G^T, together with the array beta, encodes the orthonormal
* columns of Q as elementary reflectors.
*/
dgeqrf_f77(&ny, &nc, G->data, &ny, beta, wrk, &len_wrk, &ier);
if (ier != 0) return(ier);
/* If projecting in WRMS norm */
if (pnorm == CP_PROJ_ERRNORM) {
/* Build K = Q^T * D^(-1) * Q */
cplQRcomputeKD(cp_mem, s_tmp1);
/* Perform Cholesky decomposition of K */
dpotrf_f77("L", &nc, K->data, &nc, &ier, 1);
if (ier != 0) return(ier);
}
break;
case CPDIRECT_QRP:
/*
* QR with pivoting factorization of G^T: G^T * P = Q * R.
* After factorization, the upper triangular part of G^T
* contains the matrix R. The lower trapezoidal part of
* G^T, together with the array beta, encodes the orthonormal
* columns of Q as elementary reflectors.
* The pivots are stored in 'pivotsP'.
*/
for (i=0; i<nc; i++) pivotsP[i] = 0;
dgeqp3_f77(&ny, &nc, G->data, &ny, pivotsP, beta, wrk, &len_wrk, &ier);
if (ier != 0) return(ier);
/*
* Determine the number of independent constraints.
* After the QR factorization, the diagonal elements of R should
* be in decreasing order of their absolute values.
*/
rim1 = ABS(G->data[0]);
for (i=1, nr=1; i<nc; i++, nr++) {
col_i = G->cols[i];
ri = ABS(col_i[i]);
if (ri < 100*uround) break;
if (ri/rim1 < RPowerR(uround, THREE/FOUR)) break;
}
/* If projecting in WRMS norm */
if (pnorm == CP_PROJ_ERRNORM) {
/* Build K = Q^T * D^(-1) * Q */
cplQRcomputeKD(cp_mem, s_tmp1);
/* Perform Cholesky decomposition of K */
dpotrf_f77("L", &nc, K->data, &nc, &ier, 1);
if (ier != 0) return(ier);
}
break;
case CPDIRECT_SC:
/*
* Build K = G*D^(-1)*G^T
* G^T is stored in g_mat[0...ny-1][0...nc]
* Compute and store only the lower triangular part of K.
*/
if (pnorm == CP_PROJ_L2NORM) {
dsyrk_f77("L", "T", &nc, &ny, &coef_1, G->data, &ny, &coef_0, K->data, &nc, 1, 1);
} else {
cplSCcomputeKD(cp_mem, s_tmp1);
}
/*
* Perform Cholesky decomposition of K: K = C*C^T
* After factorization, the lower triangular part of K contains C.
* Return 1 if factorization failed.
*/
dpotrf_f77("L", &nc, K->data, &nc, &ier, 1);
if (ier != 0) return(ier);
break;
}
return(0);
}