mass<FOD, T> operator()(const mass<FOD, T>& m) const
{
mass<FOD, T> m_out(m);
operator()(m_out);
return m_out;
}
void
mp_fmout(MINT *a, FILE *f)
{
m_out(a, 10, f);
}
void
mp_mout(MINT *a)
{
m_out(a, 10, stdout);
}
void
mp_omout(MINT *a)
{
m_out(a, 8, stdout);
}
void
test(const int n, const int lb, const int ub, bool dumpfull) {
// Generate a special-band-matrix mfull With lb lower diagonals, ub upper
// diagonals and the elements of the highest upper diagonal extended across
// each row
MAT *mfull = m_get(n, n);
//m_rand(mfull);
randlist(mfull->base, (mfull->n)*(mfull->n));
double **me = mfull->me;
for(int i = 0; i < n; i++) {
for(int j = 0; j < i - lb; j++)
me[i][j] = 0.0;
for(int j = i+ub+1; j < n; j++)
me[i][j] = me[i][i+ub];
}
// Copy matrix mfull to a compactly stored version
// mcmpct
// First lb columns padding for later use
// Next lb columns for lower diagonals
// Next column for diagonal
// Next ub columns for upper diagonals
// as the highest upper diagonal of the same row
const int mm = 2*lb+ub+1;
double mcmpct[n][mm];
zero(&mcmpct[0][0], n*mm);
for(int i = 0; i < n; i++)
for(int j = MAX(i-lb, 0); j < MIN(i+ub+1, n); j++)
mcmpct[i][j-i+lb+lb] = me[i][j];
// Replace unused values with NAN to be sure they aren't used
for(int k = 0; k < n; k++)
for(int i = 0; i < lb; i++)
mcmpct[k][i] = NAN;
for(int k = 0; k < lb; k++)
for(int i = 0; i < lb-k; i++)
mcmpct[k][i+lb] = NAN;
for(int k=n-1; k >= n-ub; k--)
for(int i = n-1-k+1+lb; i < mm; i++)
mcmpct[k][i+lb] = NAN;
// Generate start vector x1 for test
VEC *x1 = v_get(n);
randlist(x1->ve, n);
// Calculate mfull*x1 = dfull
VEC *dfull = v_get(n);
mv_mlt(mfull, x1, dfull);
// Calculate mcmpct*x1 = dcmpct
double dcmpct[n];
bdspecLUmlt(&mcmpct[0][0], n, lb, ub, x1->ve, dcmpct);
if(dumpfull) {
printf("Vector x (random values)\n");
printf("========================\n");
v_out(x1->ve, n);
printf("Matrix A (random values)\n");
printf("========================\n");
printf("Full NxN Meschach Matrix\n");
m_out(mfull->base, n, n);
printf("Compact bdspec Array\n");
m_out(&mcmpct[0][0], n, mm);
printf("Vector d = A*x\n");
printf("==============\n");
printf("Calculated from Full Meschach Matrix:\n");
v_out(dfull->ve, n);
printf("Calculated from Compact bdspec Array:\n");
v_out(dcmpct, n);
printf("L2 norm of difference between Meschach and bdspec calculations of d\n");
}
double ddiff = v_diff(dfull->ve, dcmpct, n);
printf("d diff=%6.0E ", ddiff);
if(ddiff*ddiff > DBL_EPSILON*v_normsq(dfull->ve, n))
printf("FAIL,");
else
printf("PASS,");
PERM *p = px_get(n);
LUfactor(mfull, p);
int indx[n];
bdspecLUfactormeschscale(&mcmpct[0][0], n, lb, ub, indx);
VEC *yfull = v_get(n);
catchall(LUsolve(mfull, p, dfull, yfull), printf("--matrix singular--:\n"));
double ycmpct[n];
for(int i = 0; i < n; i++)
ycmpct[i] = dcmpct[i];
bdspecLUsolve(&mcmpct[0][0], n, lb, ub, indx, ycmpct);
if(dumpfull) {
printf("\n\n");
printf("LU Factorization\n");
printf("================\n");
printf("Meschach LU Array\n");
m_out(mfull->base, n, n);
printf("Compact bdspec LU Array\n");
m_out(&mcmpct[0][0], n, mm);
printf("Permutation\n");
printf("===========\n");
printf("Meschach permutation vector\n");
p_out((int *) p->pe, n);
printf("bdspec indx vector\n");
p_out(indx, n);
printf("A*y = d Solved for y\n");
printf("====================\n");
printf("Meschach result\n");
v_out(yfull->ve, n);
printf("bdspec result\n");
v_out(ycmpct, n);
printf("L2 norm of difference between Meschach and bdspec calculations of y:\n");
}
double ydiff = v_diff(yfull->ve, ycmpct, n);
printf("y diff=%6.0E ", ydiff);
if(ydiff*ydiff > DBL_EPSILON*v_normsq(yfull->ve, n))
printf("FAIL,");
else
printf("PASS,");
if(dumpfull) {
printf("\n\n");
printf("L2 norm of error = y-x\n");
printf("======================\n");
}
double x1normsq = v_normsq(x1->ve, n);
double mescherr = v_diff(yfull->ve, x1->ve, n);
printf("mesch err=%6.0E ", mescherr);
if(mescherr*mescherr > DBL_EPSILON*x1normsq)
printf("FAIL,");
else
printf("PASS,");
double bdspecerr = v_diff(ycmpct, x1->ve, n);
printf("bdspec err=%6.0E ", bdspecerr);
if(bdspecerr*bdspecerr > DBL_EPSILON*x1normsq)
printf("FAIL ");
else
printf("PASS ");
if(dumpfull) {
printf("\n\n");
}
fflush(stdout);
}
