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, 319 insertions, 0 deletions

diff --git a/pack2b.c b/pack2b.c
new file mode 100644
index 0000000..25e154d
--- /dev/null
+++ b/pack2b.c
@@ -0,0 +1,319 @@
+#include <stdio.h>
+#include <ctype.h>
+#include <stdarg.h>
+#include <string.h>
+#include <stdint.h>
+#include <inttypes.h>
+#include "pack2b.h"
+
+/*
+** pack754() -- pack a floating point number into IEEE-754 format
+*/ 
+uint64_t pack754(long double f, unsigned bits, unsigned expbits)
+{
+	long double fnorm;
+	int shift;
+	long long sign, exp, significand;
+	unsigned significandbits = bits - expbits - 1; // -1 for sign bit
+
+	if (f == 0.0) return 0; // get this special case out of the way
+
+	// check sign and begin normalization
+	if (f < 0) { sign = 1; fnorm = -f; }
+	else { sign = 0; fnorm = f; }
+
+	// get the normalized form of f and track the exponent
+	shift = 0;
+	while(fnorm >= 2.0) { fnorm /= 2.0; shift++; }
+	while(fnorm < 1.0) { fnorm *= 2.0; shift--; }
+	fnorm = fnorm - 1.0;
+
+	// calculate the binary form (non-float) of the significand data
+	significand = fnorm * ((1LL<<significandbits) + 0.5f);
+
+	// get the biased exponent
+	exp = shift + ((1<<(expbits-1)) - 1); // shift + bias
+
+	// return the final answer
+	return (sign<<(bits-1)) | (exp<<(bits-expbits-1)) | significand;
+}
+
+/*
+** unpack754() -- unpack a floating point number from IEEE-754 format
+*/ 
+long double unpack754(uint64_t i, unsigned bits, unsigned expbits)
+{
+	long double result;
+	long long shift;
+	unsigned bias;
+	unsigned significandbits = bits - expbits - 1; // -1 for sign bit
+
+	if (i == 0) return 0.0;
+
+	// pull the significand
+	result = (i&((1LL<<significandbits)-1)); // mask
+	result /= (1LL<<significandbits); // convert back to float
+	result += 1.0f; // add the one back on
+
+	// deal with the exponent
+	bias = (1<<(expbits-1)) - 1;
+	shift = ((i>>significandbits)&((1LL<<expbits)-1)) - bias;
+	while(shift > 0) { result *= 2.0; shift--; }
+	while(shift < 0) { result /= 2.0; shift++; }
+
+	// sign it
+	result *= (i>>(bits-1))&1? -1.0: 1.0;
+
+	return result;
+}
+
+/*
+** packi16() -- store a 16-bit int into a char buffer (like htons())
+*/ 
+void packi16(uint8_t *buf, int16_t i)
+{
+	uint16_t i2 = i;
+
+	*buf++ = i2>>8; *buf++ = i2;
+}
+
+/*
+** packi32() -- store a 32-bit int into a char buffer (like htonl())
+*/ 
+void packi32(uint8_t *buf, int32_t i)
+{
+	uint32_t i2 = i;
+
+	*buf++ = i2>>24; *buf++ = i2>>16;
+	*buf++ = i2>>8;  *buf++ = i2;
+}
+
+/*
+** packi64() -- store a 64-bit int into a char buffer (like htonl())
+*/ 
+void packi64(uint8_t *buf, int64_t i)
+{
+	uint64_t i2 = i;
+
+	*buf++ = i2>>56; *buf++ = i2>>48;
+	*buf++ = i2>>40; *buf++ = i2>>32;
+	*buf++ = i2>>24; *buf++ = i2>>16;
+	*buf++ = i2>>8;  *buf++ = i2;
+}
+
+/*
+** unpacki16() -- unpack a 16-bit int from a char buffer (like ntohs())
+*/ 
+int16_t unpacki16(uint8_t *buf)
+{
+	uint16_t i2 = ((uint16_t)buf[0]<<8) | buf[1];
+	int16_t i;
+
+	// change unsigned numbers to signed
+	if (i2 <= 0x7fffu) { i = i2; }
+	//else { i = -(int16_t)((uint16_t)0xffff - i2 + (uint16_t)1u); }
+	else { i = -1 - (uint16_t)(0xffffu - i2); }
+
+	return i;
+}
+
+/*
+** unpacki32() -- unpack a 32-bit int from a char buffer (like ntohl())
+*/ 
+int32_t unpacki32(uint8_t *buf)
+{
+	uint32_t i2 = ((uint32_t)buf[0]<<24) | ((uint32_t)buf[1]<<16) |
+	              ((uint32_t)buf[2]<<8)  | buf[3];
+	int32_t i;
+
+	// change unsigned numbers to signed
+	if (i2 <= 0x7fffffffu) { i = i2; }
+	else { i = -1 - (int32_t)(0xffffffffu - i2); }
+
+	return i;
+}
+
+/*
+** unpacki64() -- unpack a 64-bit int from a char buffer (like ntohl())
+*/ 
+int64_t unpacki64(uint8_t *buf)
+{
+	uint64_t i2 = ((uint64_t)buf[0]<<56) | ((uint64_t)buf[1]<<48) |
+	              ((uint64_t)buf[2]<<40) | ((uint64_t)buf[3]<<32) |
+	              ((uint64_t)buf[4]<<24) | ((uint64_t)buf[5]<<16) |
+	              ((uint64_t)buf[6]<<8)  | buf[7];
+	int64_t i;
+
+	// change unsigned numbers to signed
+	if (i2 <= 0x7fffffffffffffffu) { i = i2; }
+	else { i = -1 -(int64_t)(0xffffffffffffffffu - i2); }
+
+	return i;
+}
+
+/*
+** pack() -- store data dictated by the format string in the buffer
+**
+**  c - 8-bit signed int     h - 16-bit signed int
+**  l - 32-bit signed int    f - 32-bit float
+**  L - 64-bit signed int    F - 64-bit float
+**  s - string (16-bit length is automatically prepended)
+*/ 
+int32_t pack(uint8_t *buf, char *format, ...)
+{
+	va_list ap;
+	int16_t h;
+	int32_t l;
+	int64_t L;
+	int8_t c;
+	float32_t f;
+	float64_t F;
+	char *s;
+	int32_t size = 0, len;
+
+	va_start(ap, format);
+
+	for(; *format != '\0'; format++) {
+		switch(*format) {
+		case 'h': // 16-bit
+			size += 2;
+			h = (int16_t)va_arg(ap, int); // promoted
+			packi16(buf, h);
+			buf += 2;
+			break;
+
+		case 'l': // 32-bit
+			size += 4;
+			l = va_arg(ap, int32_t);
+			packi32(buf, l);
+			buf += 4;
+			break;
+
+		case 'L': // 64-bit
+			size += 8;
+			L = va_arg(ap, int64_t);
+			packi64(buf, L);
+			buf += 8;
+			break;
+
+		case 'c': // 8-bit
+			size += 1;
+			c = (int8_t)va_arg(ap, int); // promoted
+			*buf++ = (c>>0)&0xff;
+			break;
+
+		case 'f': // float
+			size += 4;
+			f = (float32_t)va_arg(ap, double); // promoted
+			l = pack754_32(f); // convert to IEEE 754
+			packi32(buf, l);
+			buf += 4;
+			break;
+
+		case 'F': // float-64
+			size += 8;
+			F = (float64_t)va_arg(ap, float64_t);
+			L = pack754_64(F); // convert to IEEE 754
+			packi64(buf, L);
+			buf += 8;
+			break;
+
+		case 's': // string
+			s = va_arg(ap, char*);
+			len = strlen(s);
+			size += len + 2;
+			packi16(buf, len);
+			buf += 2;
+			memcpy(buf, s, len);
+			buf += len;
+			break;
+		}
+	}
+
+	va_end(ap);
+
+	return size;
+}
+
+/*
+** unpack() -- unpack data dictated by the format string into the buffer
+*/
+void unpack(uint8_t *buf, char *format, ...)
+{
+	va_list ap;
+	int16_t *h;
+	int32_t *l;
+	int64_t *L;
+	int32_t pf;
+	int64_t pF;
+	int8_t *c;
+	float32_t *f;
+	float64_t *F;
+	char *s;
+	int32_t len, count, maxstrlen=0;
+
+	va_start(ap, format);
+
+	for(; *format != '\0'; format++) {
+		switch(*format) {
+		case 'h': // 16-bit
+			h = va_arg(ap, int16_t*);
+			*h = unpacki16(buf);
+			buf += 2;
+			break;
+
+		case 'l': // 32-bit
+			l = va_arg(ap, int32_t*);
+			*l = unpacki32(buf);
+			buf += 4;
+			break;
+
+		case 'L': // 64-bit
+			L = va_arg(ap, int64_t*);
+			*L = unpacki64(buf);
+			buf += 8;
+			break;
+
+		case 'c': // 8-bit
+			c = va_arg(ap, int8_t*);
+			if (*buf <= 0x7f) { *c = *buf;}
+			else { *c = -1 - (uint8_t)(0xffu - *buf); }
+			buf++;
+			break;
+
+		case 'f': // float
+			f = va_arg(ap, float32_t*);
+			pf = unpacki32(buf);
+			buf += 4;
+			*f = unpack754_32(pf);
+			break;
+
+		case 'F': // float-64
+			F = va_arg(ap, float64_t*);
+			pF = unpacki64(buf);
+			buf += 8;
+			*F = unpack754_64(pF);
+			break;
+
+		case 's': // string
+			s = va_arg(ap, char*);
+			len = unpacki16(buf);
+			buf += 2;
+			if (maxstrlen > 0 && len > maxstrlen) count = maxstrlen - 1;
+			else count = len;
+			memcpy(s, buf, count);
+			s[count] = '\0';
+			buf += len;
+			break;
+
+		default:
+			if (isdigit(*format)) { // track max str len
+				maxstrlen = maxstrlen * 10 + (*format-'0');
+			}
+		}
+
+		if (!isdigit(*format)) maxstrlen = 0;
+	}
+
+	va_end(ap);
+}