Dear all,
I have downloaded the Mac OsX Version of mrmc and tried to run bin/mrmc, I get the following message:
dyld: Library not loaded: /opt/local/lib/libgsl.0.dylib
Referenced from: /Users/leitnerf/Documents/Uni/Research/Tools/mrmc_mac_v1.4.1/bin/mrmc
Reason: image not found
Trace/BPT trap
If I try to do "make all" I get the following error:
Best regards,
Florian
--
Florian Leitner-Fischer
Chair for Software Engineering
Department of Computer and Information Science
University of Konstanz, Box 67
D-78457 Konstanz, Germany
Office: Building E, Room 223
Phone: +49 (0)7531 88 4762
Fax: +49 (0)7531 88 3577
WWW: http://www.inf.uni-konstanz.de/soft

Dear MRMC developers,
I think I have found another (more severe) problem in the MRMC
FoxGlynn implementation.
The algorithm generates wrong Left Poisson tail values for lambdas in
interval [25; 40].
I send you a table of the expected values (L', R'), and the values
generated by MRMC (L, R) with epsilon = 1.0e-7.
L' R' L R
1 0 173 0 173
2 0 174 0 174
3 0 175 0 175
4 0 176 0 176
5 0 177 0 177
6 0 178 0 178
7 0 179 0 179
8 0 180 0 180
9 0 181 0 181
10 0 182 0 182
11 0 183 0 183
12 0 184 0 184
13 0 185 0 185
14 0 186 0 186
15 0 187 0 187
16 0 188 0 188
17 0 189 0 189
18 0 190 0 190
19 0 191 0 191
20 0 192 0 192
21 0 193 0 193
22 0 194 0 194
23 0 195 0 195
24 0 196 0 196
25 0 197 23 197
26 0 198 24 198
27 0 199 25 199
28 0 200 26 200
29 0 201 27 201
30 0 202 28 202
31 0 203 29 203
32 0 204 30 204
33 0 205 31 205
34 0 206 32 206
35 0 207 33 207
36 0 208 34 208
37 0 209 35 209
38 0 210 36 210
39 0 211 37 211
40 0 212 38 212
41 0 213 0 213
42 0 214 0 214
43 1 215 1 215
44 1 216 1 216
45 2 217 2 217
46 3 218 3 218
47 3 219 3 219
48 4 220 4 220
49 4 221 4 221
50 5 222 5 222
I send you also a PDF with an Excel plot of these values. As you can
see, the left tail is computed wrongly with lambda=[25 to 40].
I suspect that the problem lies in the following lines (132-157 of foxglynn.c):
if( lambda >= lambda_25 )
{
/*The starting point for looking for the left truncation point*/
const double start_k = 1.0 / ( sqrt( 2.0 * lambda ) );
/*Here we choose the max possible value of k such that
(m - k * sqrt_lambda - 3/2) >= 0*/
const double stop_k = ( m - 3.0/2.0 ) / sqrt_lambda;
/*Start looking for the left truncation point*/
double k, k_ltp = 0;
/*For lambda >= 25 we can use the upper bound for b_lambda,
here lambda is always at least 400:
b_lambda_sup = 1.05;
b_lambda = ( 1.0 + 1.0 / lambda ) * exp( 1.0 / ( 8.0*lambda ) ) <=
a_lambda_sup*/
const double b_lambda_sup = 1.05;
double k_prime, c_m_inf, result;
for( k = start_k; k <= stop_k; k = k + 1 )
if( b_lambda_sup * exp(- 1.0 / 2.0 * k*k) / ( k * sqrt_2_pi ) <
epsilon / 2.0 )
{
k_ltp = k;
break;
}
/*Finally the left truncation point is found*/
pFG->left = (int) floor( m - k_ltp * sqrt_lambda - 3.0 / 2.0 );
I dont know why stop_k is defined as:
const double stop_k = ( m - 3.0/2.0 ) / sqrt_lambda;
because I couldn't find it in the paper, however I believe that this
upper limit estimate is too small. Maybe a value of lambda would be
more appropriate, but I'm not sure. I think that this code should be
modified in this way:
if( lambda >= lambda_25 )
{
/*The starting point for looking for the left truncation point*/
const double start_k = 1.0 / ( sqrt( 2.0 * lambda ) );
/*Here we choose the max possible value of k such that
(m - k * sqrt_lambda - 3/2) >= 0*/
const double stop_k = lambda; //( m - 3.0/2.0 ) / sqrt_lambda;
<<<<<<<<<<<MODIFIED
/*Start looking for the left truncation point*/
double k, k_ltp = 0;
/*For lambda >= 25 we can use the upper bound for b_lambda,
here lambda is always at least 400:
b_lambda_sup = 1.05;
b_lambda = ( 1.0 + 1.0 / lambda ) * exp( 1.0 / ( 8.0*lambda ) ) <=
a_lambda_sup*/
const double b_lambda_sup = 1.05;
double k_prime, c_m_inf, result;
for( k = start_k; k <= stop_k; k = k + 1 )
if( b_lambda_sup * exp(- 1.0 / 2.0 * k*k) / ( k * sqrt_2_pi ) <
epsilon / 2.0 )
{
k_ltp = k;
break;
}
/*Finally the left truncation point is found*/
pFG->left = (int) floor( m - k_ltp * sqrt_lambda - 3.0 / 2.0 );
pFG->left = max(0, pFG->left); <<<<<<<<<<MODIFIED
With these changes the code seems to behave correctly, but I'm not
completely sure of the upper limit stop_k. Note also the last line,
that checks that pFG->left is never < 0.
P.S.: I don't know how to reply in the mailing list, so send me
e-mails to my email address elvio.amparore AT gmail.com if you have
any questions.

Dear MRMC developers,
I believe I've found a bug in mrmc. When using transient analysis, MRMC
outputs:
>>>>ERROR: Fox-Glynn: lambda >= 25, underflow. The results are
UNRELIABLE.
which, I think, is the result of a wrong formula in foxglynn.c, line 199:
k_prime = k_rtp * sqrt_2 + 3.0 / 2.0 * sqrt_lambda;
This line should be:
k_prime = k_rtp * sqrt_2 + 3.0 / (2.0 * sqrt_lambda);
as written in Corollary 3 of the "Computing Poisson Probabilities" paper.
Without this line, mrmc always thinks that the right Poisson tail will
underflow, writing the warning message.
Amparore Elvio