initial commit of likelihood fit for muons

This commit contains code to fit for the energy, position, and direction of
muons in the SNO detector. Currently, we read events from SNOMAN zebra files
and fill an event struct containing the PMT hits and fit it with the Nelder
Mead simplex algorithm from GSL.

I've also added code to read in ZEBRA title bank files to read in the DQXX
files for a specific run. Any problems with channels in the DQCH and DQCR banks
are flagged in the event struct by masking in a bit in the flags variable and
these PMT hits are not included in the likelihood calculation.

The likelihood for an event is calculated by integrating along the particle
track for each PMT and computing the expected number of PE. The charge
likelihood is then calculated by looping over all possible number of PE and
computing:

    P(q|n)*P(n|mu)

where q is the calibrated QHS charge, n is the number of PE, and mu is the
expected number of photoelectrons. The latter is calculated assuming the
distribution of PE at a given PMT follows a Poisson distribution (which I think
should be correct given the track, but is probably not perfect for tracks which
scatter a lot).

The time part of the likelihood is calculated by integrating over the track for
each PMT and calculating the average time at which the PMT is hit. We then
assume the PDF for the photons to arrive is approximately a delta function and
compute the first order statistic for a given time to compute the probability
that the first photon arrived at a given time. So far I've only tested this
with single tracks but the method was designed to be easy to use when you are
fitting for multiple particles.

1 files changed, 170 insertions, 0 deletions

diff --git a/mt19937ar.c b/mt19937ar.c
new file mode 100755
index 0000000..0dda925
--- /dev/null
+++ b/mt19937ar.c
@@ -0,0 +1,170 @@
+/* 
+   A C-program for MT19937, with initialization improved 2002/1/26.
+   Coded by Takuji Nishimura and Makoto Matsumoto.
+
+   Before using, initialize the state by using init_genrand(seed)  
+   or init_by_array(init_key, key_length).
+
+   Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
+   All rights reserved.                          
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
+
+     1. Redistributions of source code must retain the above copyright
+        notice, this list of conditions and the following disclaimer.
+
+     2. Redistributions in binary form must reproduce the above copyright
+        notice, this list of conditions and the following disclaimer in the
+        documentation and/or other materials provided with the distribution.
+
+     3. The names of its contributors may not be used to endorse or promote 
+        products derived from this software without specific prior written 
+        permission.
+
+   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+   "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+   LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+   A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+   CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+   EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+   PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+
+   Any feedback is very welcome.
+   http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
+   email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
+*/
+
+/* Period parameters */  
+#define N 624
+#define M 397
+#define MATRIX_A 0x9908b0dfUL   /* constant vector a */
+#define UPPER_MASK 0x80000000UL /* most significant w-r bits */
+#define LOWER_MASK 0x7fffffffUL /* least significant r bits */
+
+static unsigned long mt[N]; /* the array for the state vector  */
+static int mti=N+1; /* mti==N+1 means mt[N] is not initialized */
+
+/* initializes mt[N] with a seed */
+void init_genrand(unsigned long s)
+{
+    mt[0]= s & 0xffffffffUL;
+    for (mti=1; mti<N; mti++) {
+        mt[mti] = 
+	    (1812433253UL * (mt[mti-1] ^ (mt[mti-1] >> 30)) + mti); 
+        /* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
+        /* In the previous versions, MSBs of the seed affect   */
+        /* only MSBs of the array mt[].                        */
+        /* 2002/01/09 modified by Makoto Matsumoto             */
+        mt[mti] &= 0xffffffffUL;
+        /* for >32 bit machines */
+    }
+}
+
+/* initialize by an array with array-length */
+/* init_key is the array for initializing keys */
+/* key_length is its length */
+/* slight change for C++, 2004/2/26 */
+void init_by_array(unsigned long init_key[], int key_length)
+{
+    int i, j, k;
+    init_genrand(19650218UL);
+    i=1; j=0;
+    k = (N>key_length ? N : key_length);
+    for (; k; k--) {
+        mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1664525UL))
+          + init_key[j] + j; /* non linear */
+        mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
+        i++; j++;
+        if (i>=N) { mt[0] = mt[N-1]; i=1; }
+        if (j>=key_length) j=0;
+    }
+    for (k=N-1; k; k--) {
+        mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1566083941UL))
+          - i; /* non linear */
+        mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
+        i++;
+        if (i>=N) { mt[0] = mt[N-1]; i=1; }
+    }
+
+    mt[0] = 0x80000000UL; /* MSB is 1; assuring non-zero initial array */ 
+}
+
+/* generates a random number on [0,0xffffffff]-interval */
+unsigned long genrand_int32(void)
+{
+    unsigned long y;
+    static unsigned long mag01[2]={0x0UL, MATRIX_A};
+    /* mag01[x] = x * MATRIX_A  for x=0,1 */
+
+    if (mti >= N) { /* generate N words at one time */
+        int kk;
+
+        if (mti == N+1)   /* if init_genrand() has not been called, */
+            init_genrand(5489UL); /* a default initial seed is used */
+
+        for (kk=0;kk<N-M;kk++) {
+            y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
+            mt[kk] = mt[kk+M] ^ (y >> 1) ^ mag01[y & 0x1UL];
+        }
+        for (;kk<N-1;kk++) {
+            y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
+            mt[kk] = mt[kk+(M-N)] ^ (y >> 1) ^ mag01[y & 0x1UL];
+        }
+        y = (mt[N-1]&UPPER_MASK)|(mt[0]&LOWER_MASK);
+        mt[N-1] = mt[M-1] ^ (y >> 1) ^ mag01[y & 0x1UL];
+
+        mti = 0;
+    }
+  
+    y = mt[mti++];
+
+    /* Tempering */
+    y ^= (y >> 11);
+    y ^= (y << 7) & 0x9d2c5680UL;
+    y ^= (y << 15) & 0xefc60000UL;
+    y ^= (y >> 18);
+
+    return y;
+}
+
+/* generates a random number on [0,0x7fffffff]-interval */
+long genrand_int31(void)
+{
+    return (long)(genrand_int32()>>1);
+}
+
+/* generates a random number on [0,1]-real-interval */
+double genrand_real1(void)
+{
+    return genrand_int32()*(1.0/4294967295.0); 
+    /* divided by 2^32-1 */ 
+}
+
+/* generates a random number on [0,1)-real-interval */
+double genrand_real2(void)
+{
+    return genrand_int32()*(1.0/4294967296.0); 
+    /* divided by 2^32 */
+}
+
+/* generates a random number on (0,1)-real-interval */
+double genrand_real3(void)
+{
+    return (((double)genrand_int32()) + 0.5)*(1.0/4294967296.0); 
+    /* divided by 2^32 */
+}
+
+/* generates a random number on [0,1) with 53-bit resolution*/
+double genrand_res53(void) 
+{ 
+    unsigned long a=genrand_int32()>>5, b=genrand_int32()>>6; 
+    return(a*67108864.0+b)*(1.0/9007199254740992.0); 
+} 
+/* These real versions are due to Isaku Wada, 2002/01/09 added */