/* F11JB_A1W_F C++ Header Example Program.
*
* Copyright 2020 Numerical Algorithms Group.
* Mark 27.1, 2020.
*/
#include <dco_light.hpp>
#include <nag.h>
#include <nagx04.h>
#include <nagad.h>
#include <stdio.h>
#include <iostream>
using namespace std;
extern "C"
{
static void NAG_CALL do_rcm (void *&ad_handle,
Integer &n,
Integer &nnz,
Integer irow[], Integer icol[],
nagad_a1w_w_rtype a[], nagad_a1w_w_rtype y[],
Integer istr[],
Integer perm_fwd[], Integer perm_inv[],
Integer iwork[]);
}
int main(void)
{
int exit_status = 0;
void *ad_handle = 0;
Integer ifail = 0;
cout << "F11JB_A1W_F C++ Header Example Program Results\n\n";
// Skip heading in data file
string mystr;
getline (cin, mystr);
// Read order of matrix and number of nonzero entries
Integer n, nnz;
cin >> n;
cin >> nnz;
Integer la = 3*nnz;
Integer liwork = 2*la + 7*n + 1;
nagad_a1w_w_rtype *a=0, *x=0, *y=0;
double *ar=0, *yr=0, *dxdy=0;
Integer *icol=0, *ipiv=0, *irow=0, *istr=0, *iwork=0;
Integer *perm_fwd=0, *perm_inv=0;
a = new nagad_a1w_w_rtype [la];
x = new nagad_a1w_w_rtype [n];
y = new nagad_a1w_w_rtype [n];
icol = new Integer [la];
ipiv = new Integer [n];
irow = new Integer [la];
istr = new Integer [n+1];
iwork = new Integer [liwork];
perm_fwd = new Integer [n];
perm_inv = new Integer [n];
ar = new double [la];
yr = new double [n];
dxdy = new double [n*n];
// Read the matrix A
for (int i=0; i<nnz; i++) {
cin >> ar[i] >> irow[i] >> icol[i];
a[i] = ar[i];
}
// Create AD tape
nagad_a1w_ir_create();
// Read the vector y
for (int i=0; i<n; i++) {
cin >> yr[i];
y[i] = yr[i];
nagad_a1w_ir_register_variable(&y[i]);
}
// Create AD configuration data object
ifail = 0;
x10aa_a1w_f_(ad_handle,ifail);
// Calculate Cholesky factorization
Integer lfill = -1;
Integer nnzc, npivm;
nagad_a1w_w_rtype dscale, dtol;
dtol = 0.0;
dscale = 0.0;
// Compute reverse Cuthill-McKee permutation for bandwidth reduction
do_rcm(ad_handle,n,nnz,irow,icol,a,y,istr,perm_fwd,perm_inv,iwork);
ifail = 0;
f11ja_a1w_f_(ad_handle,n,nnz,a,la,irow,icol,lfill,dtol,"N",dscale,"M",
ipiv,istr,nnzc,npivm,iwork,liwork,ifail,1,1);
// Check the output value of NPIVM
if (npivm>0) {
cout << " Factorization is not complete" << endl;
goto END;
}
// Solve P L D L^T P^T x = y
ifail = 0;
f11jb_a1w_f_(ad_handle,n,a,la,irow,icol,ipiv,istr,"C",y,x,ifail,1);
// Output results
cout.setf(ios::scientific,ios::floatfield);
cout.precision(4);
cout << " Solution vector" << endl;
for (int i=0; i<n; ++i) {
cout.width(12);cout << nagad_a1w_get_value(x[perm_inv[i]]) << endl;
}
cout << "\n Derivatives calculated: First order adjoints\n";
cout << " Computational mode : algorithmic\n";
cout << "\n Derivatives of solution X w.r.t RHS Y:\n";
// Setup evaluation of derivatives via adjoints
for (int i=0; i<n; i++) {
// Reset adjoints, initialize derivative, and evaluate adjoint
nagad_a1w_ir_zero_adjoints();
double inc = 1.0;
nagad_a1w_inc_derivative(&x[perm_inv[i]],inc);
ifail = 0;
nagad_a1w_ir_interpret_adjoint(ifail);
for (int j=0; j<n; j++) {
Integer k = i + j*n;
dxdy[k] = nagad_a1w_get_derivative(y[perm_inv[j]]);
}
}
// Print derivatives
cout << endl;
NagError fail;
INIT_FAIL(fail);
x04cac(Nag_ColMajor,Nag_GeneralMatrix,Nag_NonUnitDiag,n,n,dxdy,n,
" dx_i/dy_j",0,&fail);
END:
// Remove computational data object and tape
ifail = 0;
x10ab_a1w_f_(ad_handle,ifail);
nagad_a1w_ir_remove();
delete [] a;
delete [] x;
delete [] y;
delete [] icol;
delete [] ipiv;
delete [] irow;
delete [] istr;
delete [] iwork;
delete [] ar;
delete [] yr;
delete [] dxdy;
delete [] perm_fwd;
delete [] perm_inv;
return exit_status;
}
static void NAG_CALL do_rcm(void *&ad_handle,
Integer &n,
Integer &nnz,
Integer irow[], Integer icol[],
nagad_a1w_w_rtype a[], nagad_a1w_w_rtype y[],
Integer istr[],
Integer perm_fwd[], Integer perm_inv[],
Integer iwork[]) {
logical lopts[5];
lopts[0] = 0;
lopts[1] = 0;
lopts[2] = 1;
lopts[3] = 1;
lopts[4] = 1;
nagad_a1w_w_rtype *rwork = 0;
Integer info[4], mask[1];
// SCS to CS, must add the upper triangle entries.
Integer j = nnz;
for (Integer i=0; i<nnz; i++) {
if (irow[i]>icol[i]) {
// strictly lower triangle, add the transposed
a[j] = a[i];
irow[j] = icol[i];
icol[j] = irow[i];
j++;
}
}
Integer nnz_cs = j;
// Reorder, CS to CCS, icolzp in istr
Integer ifail = 0;
f11za_a1w_f_(ad_handle,n,nnz_cs,a,icol,irow,"F","F",istr,iwork,ifail,1,1);
// Calculate reverse Cuthill-McKee
ifail = 0;
f11yef_(n,nnz_cs,istr,irow,lopts,mask,perm_fwd,info,ifail);
// compute inverse perm, in perm_inv
for (int i = 0; i<n; i++) {
perm_fwd[i] = perm_fwd[i] - 1;
perm_inv[perm_fwd[i]] = i;
}
// Apply permutation on column/row indices
Integer *iswapc=0, *iswapr=0;
iswapc = new Integer [nnz_cs];
iswapr = new Integer [nnz_cs];
for (int i=0; i<nnz_cs; i++) {
iswapc[i] = perm_inv[icol[i]-1];
iswapr[i] = perm_inv[irow[i]-1];
}
for (int i=0; i<nnz_cs; i++) {
icol[i] = iswapc[i] + 1;
irow[i] = iswapr[i] + 1;
}
delete [] iswapc;
delete [] iswapr;
// restrict to lower triangle, SCS format
// copying entries upwards
j = 0;
for (Integer i = 0; i<nnz_cs; i++) {
if (irow[i]>=icol[i]) {
// non-upper triangle, bubble up
a[j] = a[i];
icol[j] = icol[i];
irow[j] = irow[i];
j++;
}
}
Integer nnz_scs = j;
// sort
ifail = 0;
f11zb_a1w_f_(ad_handle,n,nnz_scs,a,irow,icol,"S","K",istr,iwork,ifail,1,1);
// permute rhs vector
rwork = new nagad_a1w_w_rtype [n];
for (int i=0; i<n; i++) {
rwork[i] = y[perm_fwd[i]];
}
for (int i=0; i<n; i++) {
y[i] = rwork[i];
}
delete [] rwork;
return;
}