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Started work on Potential

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Unrolled powers
removed duplicate array access on k for
tried starting using omp parallel
This commit is contained in:
Afonso Franco 2023-10-15 00:56:00 +01:00
parent 898e7eeea7
commit da20f7966e
Signed by: afonso
SSH key fingerprint: SHA256:JiuxZNdA5bRWXPMUJChI0AQ75yC+cXY4xM0IaVwEVys
31 changed files with 4777 additions and 0 deletions
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BasedOnStyle: GNU
IndentWidth: 4
TabWidth: 4
UseTab: Always
BreakBeforeBraces: Attach

29
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CC = gcc
SRC = src/
CFLAGS = # none
ts := $(shell /usr/bin/date "+%d-%m__%H_%M_%S")
.DEFAULT_GOAL = MD
MD: $(SRC)/MD.cpp
$(CC) $(CFLAGS) $(SRC)MD.cpp -lm -O2 -fopenmp -pg -o ./out/MD
MDorig: $(SRC)/MD-original.cpp
$(CC) $(CFLAGS) $(SRC)MD-original.cpp -lm -O2 -fopenmp -pg -o ./out/MD-original
clean:
rm ./out/* gmon.out
run:
./out/MD < input/inputdata.txt
runorig:
./out/MD-original < input/inputdata.txt
gprof:
gprof out/MD gmon.out > analysis/$(ts).txt
gproforig:
gprof out/MD-original gmon.out > analysis/$(ts).txt
runfull: clean MD run gprof

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1 [color="#fe0500", fontcolor="#ffffff", fontsize="10.00", label="main\n99.56%\n(0.00%)"];
1 -> 2 [arrowsize="0.74", color="#2abc09", fontcolor="#2abc09", fontsize="10.00", label="54.56%\n201×", labeldistance="2.18", penwidth="2.18"];
1 -> 3 [arrowsize="0.35", color="#0d0e73", fontcolor="#0d0e73", fontsize="10.00", label="0.22%\n1×", labeldistance="0.50", penwidth="0.50"];
1 -> 4 [arrowsize="0.67", color="#0aae2c", fontcolor="#0aae2c", fontsize="10.00", label="44.79%\n201×", labeldistance="1.79", penwidth="1.79"];
2 [color="#2abc09", fontcolor="#ffffff", fontsize="10.00", label="Potential()\n54.56%\n(54.56%)\n201×"];
3 [color="#0aaf2b", fontcolor="#ffffff", fontsize="10.00", label="computeAccelerations()\n45.01%\n(35.43%)\n202×"];
3 -> 5 [arrowsize="0.35", color="#0d397f", fontcolor="#0d397f", fontsize="10.00", label="9.58%\n942014880×", labeldistance="0.50", penwidth="0.50"];
4 [color="#0aae2c", fontcolor="#ffffff", fontsize="10.00", label="VelocityVerlet(double, int, _IO_FILE*)\n44.79%\n(0.00%)\n201×"];
4 -> 3 [arrowsize="0.67", color="#0aae2c", fontcolor="#0aae2c", fontsize="10.00", label="44.79%\n201×", labeldistance="1.79", penwidth="1.79"];
5 [color="#0d397f", fontcolor="#ffffff", fontsize="10.00", label="__gnu_cxx::__promote_2<decltype (((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0))+((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0))), std::__is_integer<decltype (((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0))+((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0)))>::__value>::__type std::pow<double, int>(double, int)\n9.58%\n(9.58%)\n942014880×"];
}

204
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Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls ms/call ms/call name
54.61 15.03 15.03 201 74.79 74.79 Potential()
35.45 24.79 9.76 202 48.31 61.39 computeAccelerations()
9.60 27.43 2.64 942014880 0.00 0.00 __gnu_cxx::__promote_2<decltype (((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0))+((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0))), std::__is_integer<decltype (((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0))+((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0)))>::__value>::__type std::pow<double, int>(double, int)
0.44 27.55 0.12 _init
0.00 27.55 0.00 6480 0.00 0.00 gaussdist()
0.00 27.55 0.00 201 0.00 61.39 VelocityVerlet(double, int, _IO_FILE*)
0.00 27.55 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 27.55 0.00 201 0.00 0.00 Kinetic()
0.00 27.55 0.00 1 0.00 0.00 initialize()
0.00 27.55 0.00 1 0.00 0.00 initializeVelocities()
0.00 27.55 0.00 1 0.00 0.00 __gnu_cxx::__promote_2<decltype (((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0))+((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0))), std::__is_integer<decltype (((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0))+((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0)))>::__value>::__type std::pow<int, double>(int, double)
0.00 27.55 0.00 1 0.00 0.00 __gnu_cxx::__enable_if<std::__is_integer<int>::__value, double>::__type std::floor<int>(int)
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.04% of 27.55 seconds
index % time self children called name
<spontaneous>
[1] 99.6 0.00 27.43 main [1]
15.03 0.00 201/201 Potential() [2]
0.00 12.34 201/201 VelocityVerlet(double, int, _IO_FILE*) [4]
0.05 0.01 1/202 computeAccelerations() [3]
0.00 0.00 201/201 MeanSquaredVelocity() [11]
0.00 0.00 201/201 Kinetic() [12]
0.00 0.00 1/1 initialize() [13]
0.00 0.00 1/1 __gnu_cxx::__enable_if<std::__is_integer<int>::__value, double>::__type std::floor<int>(int) [16]
-----------------------------------------------
15.03 0.00 201/201 main [1]
[2] 54.6 15.03 0.00 201 Potential() [2]
-----------------------------------------------
0.05 0.01 1/202 main [1]
9.71 2.63 201/202 VelocityVerlet(double, int, _IO_FILE*) [4]
[3] 45.0 9.76 2.64 202 computeAccelerations() [3]
2.64 0.00 942014880/942014880 __gnu_cxx::__promote_2<decltype (((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0))+((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0))), std::__is_integer<decltype (((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0))+((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0)))>::__value>::__type std::pow<double, int>(double, int) [5]
-----------------------------------------------
0.00 12.34 201/201 main [1]
[4] 44.8 0.00 12.34 201 VelocityVerlet(double, int, _IO_FILE*) [4]
9.71 2.63 201/202 computeAccelerations() [3]
-----------------------------------------------
2.64 0.00 942014880/942014880 computeAccelerations() [3]
[5] 9.6 2.64 0.00 942014880 __gnu_cxx::__promote_2<decltype (((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0))+((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0))), std::__is_integer<decltype (((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0))+((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0)))>::__value>::__type std::pow<double, int>(double, int) [5]
-----------------------------------------------
<spontaneous>
[6] 0.4 0.12 0.00 _init [6]
-----------------------------------------------
0.00 0.00 6480/6480 initializeVelocities() [14]
[10] 0.0 0.00 0.00 6480 gaussdist() [10]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[11] 0.0 0.00 0.00 201 MeanSquaredVelocity() [11]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[12] 0.0 0.00 0.00 201 Kinetic() [12]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[13] 0.0 0.00 0.00 1 initialize() [13]
0.00 0.00 1/1 __gnu_cxx::__promote_2<decltype (((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0))+((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0))), std::__is_integer<decltype (((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0))+((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0)))>::__value>::__type std::pow<int, double>(int, double) [15]
0.00 0.00 1/1 initializeVelocities() [14]
-----------------------------------------------
0.00 0.00 1/1 initialize() [13]
[14] 0.0 0.00 0.00 1 initializeVelocities() [14]
0.00 0.00 6480/6480 gaussdist() [10]
-----------------------------------------------
0.00 0.00 1/1 initialize() [13]
[15] 0.0 0.00 0.00 1 __gnu_cxx::__promote_2<decltype (((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0))+((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0))), std::__is_integer<decltype (((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0))+((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0)))>::__value>::__type std::pow<int, double>(int, double) [15]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[16] 0.0 0.00 0.00 1 __gnu_cxx::__enable_if<std::__is_integer<int>::__value, double>::__type std::floor<int>(int) [16]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[13] initialize() [14] initializeVelocities() [5] __gnu_cxx::__promote_2<decltype (((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0))+((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0))), std::__is_integer<decltype (((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0))+((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0)))>::__value>::__type std::pow<double, int>(double, int)
[4] VelocityVerlet(double, int, _IO_FILE*) [12] Kinetic() [15] __gnu_cxx::__promote_2<decltype (((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0))+((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0))), std::__is_integer<decltype (((__gnu_cxx::__promote_2<int, std::__is_integer<int>::__value>::__type)(0))+((__gnu_cxx::__promote_2<double, std::__is_integer<double>::__value>::__type)(0)))>::__value>::__type std::pow<int, double>(int, double)
[11] MeanSquaredVelocity() [2] Potential() [16] __gnu_cxx::__enable_if<std::__is_integer<int>::__value, double>::__type std::floor<int>(int)
[3] computeAccelerations() [10] gaussdist() [6] _init

14
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2 [color="#f82f01", fontcolor="#ffffff", fontsize="10.00", label="_dl_relocate_static_pie\n95.37%\n(95.37%)\n3240×"];
3 [color="#f82f01", fontcolor="#ffffff", fontsize="10.00", label="initializeVelocities()\n95.37%\n(0.00%)\n1×"];
3 -> 2 [arrowsize="0.98", color="#f82f01", fontcolor="#f82f01", fontsize="10.00", label="95.37%\n3240×", labeldistance="3.81", penwidth="3.81"];
4 [color="#0d2078", fontcolor="#ffffff", fontsize="10.00", label="computeAccelerations()\n4.49%\n(4.49%)\n202×"];
5 [color="#0d2078", fontcolor="#ffffff", fontsize="10.00", label="VelocityVerlet(double, int, _IO_FILE*)\n4.47%\n(0.00%)\n201×"];
5 -> 4 [arrowsize="0.35", color="#0d2078", fontcolor="#0d2078", fontsize="10.00", label="4.47%\n201×", labeldistance="0.50", penwidth="0.50"];
}

178
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Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls s/call s/call name
95.46 33.14 33.14 3240 0.01 0.01 _dl_relocate_static_pie
4.50 34.71 1.56 202 0.01 0.01 computeAccelerations()
0.12 34.75 0.04 _init
0.03 34.76 0.01 201 0.00 0.00 MeanSquaredVelocity()
0.00 34.76 0.00 201 0.00 0.01 VelocityVerlet(double, int, _IO_FILE*)
0.00 34.76 0.00 1 0.00 0.00 initialize()
0.00 34.76 0.00 1 0.00 33.14 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.03% of 34.76 seconds
index % time self children called name
<spontaneous>
[1] 99.9 0.00 34.72 main [1]
0.00 33.14 1/1 initializeVelocities() [3]
0.00 1.55 201/201 VelocityVerlet(double, int, _IO_FILE*) [5]
0.01 0.00 201/201 MeanSquaredVelocity() [7]
0.01 0.00 1/202 computeAccelerations() [4]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
33.14 0.00 3240/3240 initializeVelocities() [3]
[2] 95.4 33.14 0.00 3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.00 33.14 1/1 main [1]
[3] 95.4 0.00 33.14 1 initializeVelocities() [3]
33.14 0.00 3240/3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.55 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [5]
[4] 4.5 1.56 0.00 202 computeAccelerations() [4]
-----------------------------------------------
0.00 1.55 201/201 main [1]
[5] 4.5 0.00 1.55 201 VelocityVerlet(double, int, _IO_FILE*) [5]
1.55 0.00 201/202 computeAccelerations() [4]
-----------------------------------------------
<spontaneous>
[6] 0.1 0.04 0.00 _init [6]
-----------------------------------------------
0.01 0.00 201/201 main [1]
[7] 0.0 0.01 0.00 201 MeanSquaredVelocity() [7]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [4] computeAccelerations() [6] _init
[5] VelocityVerlet(double, int, _IO_FILE*) [3] initializeVelocities()
[7] MeanSquaredVelocity() [2] _dl_relocate_static_pie

14
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1 -> 3 [arrowsize="0.71", color="#10b709", fontcolor="#10b709", fontsize="10.00", label="51.01%\n201×", labeldistance="2.04", penwidth="2.04"];
1 -> 4 [arrowsize="0.65", color="#0aab3b", fontcolor="#0aab3b", fontsize="10.00", label="42.41%\n201×", labeldistance="1.70", penwidth="1.70"];
2 [color="#12b709", fontcolor="#ffffff", fontsize="10.00", label="computeAccelerations()\n51.27%\n(51.27%)\n202×"];
3 [color="#10b709", fontcolor="#ffffff", fontsize="10.00", label="VelocityVerlet(double, int, _IO_FILE*)\n51.01%\n(0.00%)\n201×"];
3 -> 2 [arrowsize="0.71", color="#10b709", fontcolor="#10b709", fontsize="10.00", label="51.01%\n201×", labeldistance="2.04", penwidth="2.04"];
4 [color="#0aab3b", fontcolor="#ffffff", fontsize="10.00", label="Potential()\n42.41%\n(42.41%)\n201×"];
5 [color="#0d297b", fontcolor="#ffffff", fontsize="10.00", label="_init\n6.33%\n(6.33%)"];
}

183
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Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls ms/call ms/call name
51.16 1.62 1.62 202 8.00 8.00 computeAccelerations()
42.45 2.96 1.34 201 6.67 6.67 Potential()
6.34 3.16 0.20 _init
0.00 3.16 0.00 3240 0.00 0.00 _dl_relocate_static_pie
0.00 3.16 0.00 201 0.00 8.00 VelocityVerlet(double, int, _IO_FILE*)
0.00 3.16 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 3.16 0.00 1 0.00 0.00 initialize()
0.00 3.16 0.00 1 0.00 0.00 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.32% of 3.16 seconds
index % time self children called name
<spontaneous>
[1] 93.7 0.00 2.96 main [1]
0.00 1.61 201/201 VelocityVerlet(double, int, _IO_FILE*) [3]
1.34 0.00 201/201 Potential() [4]
0.01 0.00 1/202 computeAccelerations() [2]
0.00 0.00 201/201 MeanSquaredVelocity() [10]
0.00 0.00 1/1 initializeVelocities() [12]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.61 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [3]
[2] 51.2 1.62 0.00 202 computeAccelerations() [2]
-----------------------------------------------
0.00 1.61 201/201 main [1]
[3] 50.9 0.00 1.61 201 VelocityVerlet(double, int, _IO_FILE*) [3]
1.61 0.00 201/202 computeAccelerations() [2]
-----------------------------------------------
1.34 0.00 201/201 main [1]
[4] 42.5 1.34 0.00 201 Potential() [4]
-----------------------------------------------
<spontaneous>
[5] 6.3 0.20 0.00 _init [5]
-----------------------------------------------
0.00 0.00 3240/3240 initializeVelocities() [12]
[9] 0.0 0.00 0.00 3240 _dl_relocate_static_pie [9]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[10] 0.0 0.00 0.00 201 MeanSquaredVelocity() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[12] 0.0 0.00 0.00 1 initializeVelocities() [12]
0.00 0.00 3240/3240 _dl_relocate_static_pie [9]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [2] computeAccelerations() [9] _dl_relocate_static_pie
[3] VelocityVerlet(double, int, _IO_FILE*) [12] initializeVelocities() [5] _init
[10] MeanSquaredVelocity() [4] Potential()

14
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@ -0,0 +1,14 @@
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1 [color="#fe0400", fontcolor="#ffffff", fontsize="10.00", label="main\n99.62%\n(0.00%)"];
1 -> 3 [arrowsize="0.96", color="#f44902", fontcolor="#f44902", fontsize="10.00", label="92.69%\n1×", labeldistance="3.71", penwidth="3.71"];
1 -> 5 [arrowsize="0.35", color="#0d2b7c", fontcolor="#0d2b7c", fontsize="10.00", label="6.89%\n201×", labeldistance="0.50", penwidth="0.50"];
2 [color="#f44902", fontcolor="#ffffff", fontsize="10.00", label="_dl_relocate_static_pie\n92.69%\n(92.69%)\n3240×"];
3 [color="#f44902", fontcolor="#ffffff", fontsize="10.00", label="initializeVelocities()\n92.69%\n(0.00%)\n1×"];
3 -> 2 [arrowsize="0.96", color="#f44902", fontcolor="#f44902", fontsize="10.00", label="92.69%\n3240×", labeldistance="3.71", penwidth="3.71"];
4 [color="#0d2b7c", fontcolor="#ffffff", fontsize="10.00", label="computeAccelerations()\n6.93%\n(6.93%)\n202×"];
5 [color="#0d2b7c", fontcolor="#ffffff", fontsize="10.00", label="VelocityVerlet(double, int, _IO_FILE*)\n6.89%\n(0.00%)\n201×"];
5 -> 4 [arrowsize="0.35", color="#0d2b7c", fontcolor="#0d2b7c", fontsize="10.00", label="6.89%\n201×", labeldistance="0.50", penwidth="0.50"];
}

178
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Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls s/call s/call name
92.78 19.53 19.53 3240 0.01 0.01 _dl_relocate_static_pie
6.94 20.99 1.46 202 0.01 0.01 computeAccelerations()
0.38 21.07 0.08 _init
0.00 21.07 0.00 201 0.00 0.01 VelocityVerlet(double, int, _IO_FILE*)
0.00 21.07 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 21.07 0.00 1 0.00 0.00 initialize()
0.00 21.07 0.00 1 0.00 19.53 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.05% of 21.07 seconds
index % time self children called name
<spontaneous>
[1] 99.6 0.00 20.99 main [1]
0.00 19.53 1/1 initializeVelocities() [3]
0.00 1.45 201/201 VelocityVerlet(double, int, _IO_FILE*) [5]
0.01 0.00 1/202 computeAccelerations() [4]
0.00 0.00 201/201 MeanSquaredVelocity() [10]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
19.53 0.00 3240/3240 initializeVelocities() [3]
[2] 92.7 19.53 0.00 3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.00 19.53 1/1 main [1]
[3] 92.7 0.00 19.53 1 initializeVelocities() [3]
19.53 0.00 3240/3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.45 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [5]
[4] 6.9 1.46 0.00 202 computeAccelerations() [4]
-----------------------------------------------
0.00 1.45 201/201 main [1]
[5] 6.9 0.00 1.45 201 VelocityVerlet(double, int, _IO_FILE*) [5]
1.45 0.00 201/202 computeAccelerations() [4]
-----------------------------------------------
<spontaneous>
[6] 0.4 0.08 0.00 _init [6]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[10] 0.0 0.00 0.00 201 MeanSquaredVelocity() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [4] computeAccelerations() [6] _init
[5] VelocityVerlet(double, int, _IO_FILE*) [3] initializeVelocities()
[10] MeanSquaredVelocity() [2] _dl_relocate_static_pie

15
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@ -0,0 +1,15 @@
digraph {
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edge [fontname=Arial];
1 [color="#fe0700", fontcolor="#ffffff", fontsize="10.00", label="main\n99.31%\n(0.00%)"];
1 -> 3 [arrowsize="0.96", color="#f25302", fontcolor="#f25302", fontsize="10.00", label="91.53%\n1×", labeldistance="3.66", penwidth="3.66"];
1 -> 5 [arrowsize="0.35", color="#0d2f7d", fontcolor="#0d2f7d", fontsize="10.00", label="7.74%\n201×", labeldistance="0.50", penwidth="0.50"];
2 [color="#f25302", fontcolor="#ffffff", fontsize="10.00", label="_dl_relocate_static_pie\n91.53%\n(91.53%)\n3240×"];
3 [color="#f25302", fontcolor="#ffffff", fontsize="10.00", label="initializeVelocities()\n91.53%\n(0.00%)\n1×"];
3 -> 2 [arrowsize="0.96", color="#f25302", fontcolor="#f25302", fontsize="10.00", label="91.53%\n3240×", labeldistance="3.66", penwidth="3.66"];
4 [color="#0d307d", fontcolor="#ffffff", fontsize="10.00", label="computeAccelerations()\n7.78%\n(7.78%)\n202×"];
5 [color="#0d2f7d", fontcolor="#ffffff", fontsize="10.00", label="VelocityVerlet(double, int, _IO_FILE*)\n7.74%\n(0.00%)\n201×"];
5 -> 4 [arrowsize="0.35", color="#0d2f7d", fontcolor="#0d2f7d", fontsize="10.00", label="7.74%\n201×", labeldistance="0.50", penwidth="0.50"];
6 [color="#0d1074", fontcolor="#ffffff", fontsize="10.00", label="_init\n0.69%\n(0.69%)"];
}

178
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Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls s/call s/call name
91.62 16.00 16.00 3240 0.00 0.00 _dl_relocate_static_pie
7.80 17.36 1.36 202 0.01 0.01 computeAccelerations()
0.69 17.48 0.12 _init
0.00 17.48 0.00 201 0.00 0.01 VelocityVerlet(double, int, _IO_FILE*)
0.00 17.48 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 17.48 0.00 1 0.00 0.00 initialize()
0.00 17.48 0.00 1 0.00 16.00 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.06% of 17.48 seconds
index % time self children called name
<spontaneous>
[1] 99.3 0.00 17.36 main [1]
0.00 16.00 1/1 initializeVelocities() [3]
0.00 1.35 201/201 VelocityVerlet(double, int, _IO_FILE*) [5]
0.01 0.00 1/202 computeAccelerations() [4]
0.00 0.00 201/201 MeanSquaredVelocity() [10]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
16.00 0.00 3240/3240 initializeVelocities() [3]
[2] 91.5 16.00 0.00 3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.00 16.00 1/1 main [1]
[3] 91.5 0.00 16.00 1 initializeVelocities() [3]
16.00 0.00 3240/3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.35 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [5]
[4] 7.8 1.36 0.00 202 computeAccelerations() [4]
-----------------------------------------------
0.00 1.35 201/201 main [1]
[5] 7.8 0.00 1.35 201 VelocityVerlet(double, int, _IO_FILE*) [5]
1.35 0.00 201/202 computeAccelerations() [4]
-----------------------------------------------
<spontaneous>
[6] 0.7 0.12 0.00 _init [6]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[10] 0.0 0.00 0.00 201 MeanSquaredVelocity() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [4] computeAccelerations() [6] _init
[5] VelocityVerlet(double, int, _IO_FILE*) [3] initializeVelocities()
[10] MeanSquaredVelocity() [2] _dl_relocate_static_pie

178
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Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls s/call s/call name
94.75 24.45 24.45 3240 0.01 0.01 _dl_relocate_static_pie
5.24 25.80 1.35 202 0.01 0.01 computeAccelerations()
0.12 25.83 0.03 _init
0.00 25.83 0.00 201 0.00 0.01 VelocityVerlet(double, int, _IO_FILE*)
0.00 25.83 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 25.83 0.00 1 0.00 0.00 initialize()
0.00 25.83 0.00 1 0.00 24.45 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.04% of 25.83 seconds
index % time self children called name
<spontaneous>
[1] 99.9 0.00 25.80 main [1]
0.00 24.45 1/1 initializeVelocities() [3]
0.00 1.34 201/201 VelocityVerlet(double, int, _IO_FILE*) [5]
0.01 0.00 1/202 computeAccelerations() [4]
0.00 0.00 201/201 MeanSquaredVelocity() [10]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
24.45 0.00 3240/3240 initializeVelocities() [3]
[2] 94.7 24.45 0.00 3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.00 24.45 1/1 main [1]
[3] 94.7 0.00 24.45 1 initializeVelocities() [3]
24.45 0.00 3240/3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.34 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [5]
[4] 5.2 1.35 0.00 202 computeAccelerations() [4]
-----------------------------------------------
0.00 1.34 201/201 main [1]
[5] 5.2 0.00 1.34 201 VelocityVerlet(double, int, _IO_FILE*) [5]
1.34 0.00 201/202 computeAccelerations() [4]
-----------------------------------------------
<spontaneous>
[6] 0.1 0.03 0.00 _init [6]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[10] 0.0 0.00 0.00 201 MeanSquaredVelocity() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [4] computeAccelerations() [6] _init
[5] VelocityVerlet(double, int, _IO_FILE*) [3] initializeVelocities()
[10] MeanSquaredVelocity() [2] _dl_relocate_static_pie

178
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Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls s/call s/call name
92.56 20.01 20.01 3240 0.01 0.01 _dl_relocate_static_pie
7.22 21.57 1.56 202 0.01 0.01 computeAccelerations()
0.32 21.64 0.07 _init
0.00 21.64 0.00 201 0.00 0.01 VelocityVerlet(double, int, _IO_FILE*)
0.00 21.64 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 21.64 0.00 1 0.00 0.00 initialize()
0.00 21.64 0.00 1 0.00 20.01 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.05% of 21.64 seconds
index % time self children called name
<spontaneous>
[1] 99.7 0.00 21.57 main [1]
0.00 20.01 1/1 initializeVelocities() [3]
0.00 1.55 201/201 VelocityVerlet(double, int, _IO_FILE*) [5]
0.01 0.00 1/202 computeAccelerations() [4]
0.00 0.00 201/201 MeanSquaredVelocity() [10]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
20.01 0.00 3240/3240 initializeVelocities() [3]
[2] 92.5 20.01 0.00 3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.00 20.01 1/1 main [1]
[3] 92.5 0.00 20.01 1 initializeVelocities() [3]
20.01 0.00 3240/3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.55 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [5]
[4] 7.2 1.56 0.00 202 computeAccelerations() [4]
-----------------------------------------------
0.00 1.55 201/201 main [1]
[5] 7.2 0.00 1.55 201 VelocityVerlet(double, int, _IO_FILE*) [5]
1.55 0.00 201/202 computeAccelerations() [4]
-----------------------------------------------
<spontaneous>
[6] 0.3 0.07 0.00 _init [6]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[10] 0.0 0.00 0.00 201 MeanSquaredVelocity() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [4] computeAccelerations() [6] _init
[5] VelocityVerlet(double, int, _IO_FILE*) [3] initializeVelocities()
[10] MeanSquaredVelocity() [2] _dl_relocate_static_pie

178
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Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls s/call s/call name
88.74 13.28 13.28 3240 0.00 0.00 _dl_relocate_static_pie
10.70 14.89 1.60 202 0.01 0.01 computeAccelerations()
0.67 14.99 0.10 _init
0.00 14.99 0.00 201 0.00 0.01 VelocityVerlet(double, int, _IO_FILE*)
0.00 14.99 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 14.99 0.00 1 0.00 0.00 initialize()
0.00 14.99 0.00 1 0.00 13.28 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.07% of 14.99 seconds
index % time self children called name
<spontaneous>
[1] 99.3 0.00 14.89 main [1]
0.00 13.28 1/1 initializeVelocities() [3]
0.00 1.59 201/201 VelocityVerlet(double, int, _IO_FILE*) [5]
0.01 0.00 1/202 computeAccelerations() [4]
0.00 0.00 201/201 MeanSquaredVelocity() [10]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
13.28 0.00 3240/3240 initializeVelocities() [3]
[2] 88.6 13.28 0.00 3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.00 13.28 1/1 main [1]
[3] 88.6 0.00 13.28 1 initializeVelocities() [3]
13.28 0.00 3240/3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.59 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [5]
[4] 10.7 1.60 0.00 202 computeAccelerations() [4]
-----------------------------------------------
0.00 1.59 201/201 main [1]
[5] 10.6 0.00 1.59 201 VelocityVerlet(double, int, _IO_FILE*) [5]
1.59 0.00 201/202 computeAccelerations() [4]
-----------------------------------------------
<spontaneous>
[6] 0.7 0.10 0.00 _init [6]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[10] 0.0 0.00 0.00 201 MeanSquaredVelocity() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [4] computeAccelerations() [6] _init
[5] VelocityVerlet(double, int, _IO_FILE*) [3] initializeVelocities()
[10] MeanSquaredVelocity() [2] _dl_relocate_static_pie

178
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@ -0,0 +1,178 @@
Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls s/call s/call name
84.43 9.17 9.17 3240 0.00 0.00 _dl_relocate_static_pie
14.93 10.79 1.62 202 0.01 0.01 computeAccelerations()
0.46 10.84 0.05 _init
0.28 10.87 0.03 201 0.00 0.01 VelocityVerlet(double, int, _IO_FILE*)
0.00 10.87 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 10.87 0.00 1 0.00 0.00 initialize()
0.00 10.87 0.00 1 0.00 9.17 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.09% of 10.87 seconds
index % time self children called name
<spontaneous>
[1] 99.5 0.00 10.82 main [1]
0.00 9.17 1/1 initializeVelocities() [3]
0.03 1.61 201/201 VelocityVerlet(double, int, _IO_FILE*) [4]
0.01 0.00 1/202 computeAccelerations() [5]
0.00 0.00 201/201 MeanSquaredVelocity() [10]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
9.17 0.00 3240/3240 initializeVelocities() [3]
[2] 84.3 9.17 0.00 3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.00 9.17 1/1 main [1]
[3] 84.3 0.00 9.17 1 initializeVelocities() [3]
9.17 0.00 3240/3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.03 1.61 201/201 main [1]
[4] 15.1 0.03 1.61 201 VelocityVerlet(double, int, _IO_FILE*) [4]
1.61 0.00 201/202 computeAccelerations() [5]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.61 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [4]
[5] 14.9 1.62 0.00 202 computeAccelerations() [5]
-----------------------------------------------
<spontaneous>
[6] 0.5 0.05 0.00 _init [6]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[10] 0.0 0.00 0.00 201 MeanSquaredVelocity() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [5] computeAccelerations() [6] _init
[4] VelocityVerlet(double, int, _IO_FILE*) [3] initializeVelocities()
[10] MeanSquaredVelocity() [2] _dl_relocate_static_pie

183
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@ -0,0 +1,183 @@
Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls ms/call ms/call name
62.15 3.34 3.34 201 16.64 16.64 Potential()
36.10 5.29 1.94 202 9.61 9.61 computeAccelerations()
1.86 5.39 0.10 _init
0.00 5.39 0.00 3240 0.00 0.00 _dl_relocate_static_pie
0.00 5.39 0.00 201 0.00 9.61 VelocityVerlet(double, int, _IO_FILE*)
0.00 5.39 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 5.39 0.00 1 0.00 0.00 initialize()
0.00 5.39 0.00 1 0.00 0.00 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.19% of 5.39 seconds
index % time self children called name
<spontaneous>
[1] 98.1 0.00 5.29 main [1]
3.34 0.00 201/201 Potential() [2]
0.00 1.93 201/201 VelocityVerlet(double, int, _IO_FILE*) [4]
0.01 0.00 1/202 computeAccelerations() [3]
0.00 0.00 201/201 MeanSquaredVelocity() [10]
0.00 0.00 1/1 initializeVelocities() [12]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
3.34 0.00 201/201 main [1]
[2] 62.1 3.34 0.00 201 Potential() [2]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.93 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [4]
[3] 36.1 1.94 0.00 202 computeAccelerations() [3]
-----------------------------------------------
0.00 1.93 201/201 main [1]
[4] 35.9 0.00 1.93 201 VelocityVerlet(double, int, _IO_FILE*) [4]
1.93 0.00 201/202 computeAccelerations() [3]
-----------------------------------------------
<spontaneous>
[5] 1.9 0.10 0.00 _init [5]
-----------------------------------------------
0.00 0.00 3240/3240 initializeVelocities() [12]
[9] 0.0 0.00 0.00 3240 _dl_relocate_static_pie [9]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[10] 0.0 0.00 0.00 201 MeanSquaredVelocity() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[12] 0.0 0.00 0.00 1 initializeVelocities() [12]
0.00 0.00 3240/3240 _dl_relocate_static_pie [9]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [3] computeAccelerations() [9] _dl_relocate_static_pie
[4] VelocityVerlet(double, int, _IO_FILE*) [12] initializeVelocities() [5] _init
[10] MeanSquaredVelocity() [2] Potential()

178
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Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls s/call s/call name
93.03 19.47 19.47 3240 0.01 0.01 _dl_relocate_static_pie
6.74 20.88 1.41 202 0.01 0.01 computeAccelerations()
0.33 20.95 0.07 _init
0.00 20.95 0.00 201 0.00 0.01 VelocityVerlet(double, int, _IO_FILE*)
0.00 20.95 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 20.95 0.00 1 0.00 0.00 initialize()
0.00 20.95 0.00 1 0.00 19.47 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.05% of 20.95 seconds
index % time self children called name
<spontaneous>
[1] 99.7 0.00 20.88 main [1]
0.00 19.47 1/1 initializeVelocities() [3]
0.00 1.40 201/201 VelocityVerlet(double, int, _IO_FILE*) [5]
0.01 0.00 1/202 computeAccelerations() [4]
0.00 0.00 201/201 MeanSquaredVelocity() [10]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
19.47 0.00 3240/3240 initializeVelocities() [3]
[2] 92.9 19.47 0.00 3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.00 19.47 1/1 main [1]
[3] 92.9 0.00 19.47 1 initializeVelocities() [3]
19.47 0.00 3240/3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.40 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [5]
[4] 6.7 1.41 0.00 202 computeAccelerations() [4]
-----------------------------------------------
0.00 1.40 201/201 main [1]
[5] 6.7 0.00 1.40 201 VelocityVerlet(double, int, _IO_FILE*) [5]
1.40 0.00 201/202 computeAccelerations() [4]
-----------------------------------------------
<spontaneous>
[6] 0.3 0.07 0.00 _init [6]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[10] 0.0 0.00 0.00 201 MeanSquaredVelocity() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [4] computeAccelerations() [6] _init
[5] VelocityVerlet(double, int, _IO_FILE*) [3] initializeVelocities()
[10] MeanSquaredVelocity() [2] _dl_relocate_static_pie

178
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@ -0,0 +1,178 @@
Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls s/call s/call name
94.11 25.63 25.63 3240 0.01 0.01 _dl_relocate_static_pie
5.51 27.13 1.50 202 0.01 0.01 computeAccelerations()
0.48 27.26 0.13 _init
0.00 27.26 0.00 201 0.00 0.01 VelocityVerlet(double, int, _IO_FILE*)
0.00 27.26 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 27.26 0.00 1 0.00 0.00 initialize()
0.00 27.26 0.00 1 0.00 25.63 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.04% of 27.26 seconds
index % time self children called name
<spontaneous>
[1] 99.5 0.00 27.13 main [1]
0.00 25.63 1/1 initializeVelocities() [3]
0.00 1.49 201/201 VelocityVerlet(double, int, _IO_FILE*) [5]
0.01 0.00 1/202 computeAccelerations() [4]
0.00 0.00 201/201 MeanSquaredVelocity() [10]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
25.63 0.00 3240/3240 initializeVelocities() [3]
[2] 94.0 25.63 0.00 3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.00 25.63 1/1 main [1]
[3] 94.0 0.00 25.63 1 initializeVelocities() [3]
25.63 0.00 3240/3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.49 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [5]
[4] 5.5 1.50 0.00 202 computeAccelerations() [4]
-----------------------------------------------
0.00 1.49 201/201 main [1]
[5] 5.5 0.00 1.49 201 VelocityVerlet(double, int, _IO_FILE*) [5]
1.49 0.00 201/202 computeAccelerations() [4]
-----------------------------------------------
<spontaneous>
[6] 0.5 0.13 0.00 _init [6]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[10] 0.0 0.00 0.00 201 MeanSquaredVelocity() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [4] computeAccelerations() [6] _init
[5] VelocityVerlet(double, int, _IO_FILE*) [3] initializeVelocities()
[10] MeanSquaredVelocity() [2] _dl_relocate_static_pie

0
analysis/15-10__00_47_57.txt Normal file
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178
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@ -0,0 +1,178 @@
Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls s/call s/call name
71.39 4.30 4.30 3240 0.00 0.00 _dl_relocate_static_pie
27.89 5.99 1.68 202 0.01 0.01 computeAccelerations()
0.83 6.04 0.05 _init
0.00 6.04 0.00 201 0.00 0.01 VelocityVerlet(double, int, _IO_FILE*)
0.00 6.04 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 6.04 0.00 1 0.00 0.00 initialize()
0.00 6.04 0.00 1 0.00 4.30 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.17% of 6.04 seconds
index % time self children called name
<spontaneous>
[1] 99.2 0.00 5.99 main [1]
0.00 4.30 1/1 initializeVelocities() [3]
0.00 1.67 201/201 VelocityVerlet(double, int, _IO_FILE*) [5]
0.01 0.00 1/202 computeAccelerations() [4]
0.00 0.00 201/201 MeanSquaredVelocity() [10]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
4.30 0.00 3240/3240 initializeVelocities() [3]
[2] 71.3 4.30 0.00 3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.00 4.30 1/1 main [1]
[3] 71.3 0.00 4.30 1 initializeVelocities() [3]
4.30 0.00 3240/3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.67 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [5]
[4] 27.9 1.68 0.00 202 computeAccelerations() [4]
-----------------------------------------------
0.00 1.67 201/201 main [1]
[5] 27.7 0.00 1.67 201 VelocityVerlet(double, int, _IO_FILE*) [5]
1.67 0.00 201/202 computeAccelerations() [4]
-----------------------------------------------
<spontaneous>
[6] 0.8 0.05 0.00 _init [6]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[10] 0.0 0.00 0.00 201 MeanSquaredVelocity() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [4] computeAccelerations() [6] _init
[5] VelocityVerlet(double, int, _IO_FILE*) [3] initializeVelocities()
[10] MeanSquaredVelocity() [2] _dl_relocate_static_pie

183
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@ -0,0 +1,183 @@
Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls ms/call ms/call name
67.54 3.36 3.36 201 16.73 16.73 Potential()
31.16 4.92 1.55 202 7.68 7.68 computeAccelerations()
1.41 4.99 0.07 _init
0.00 4.99 0.00 3240 0.00 0.00 _dl_relocate_static_pie
0.00 4.99 0.00 201 0.00 7.68 VelocityVerlet(double, int, _IO_FILE*)
0.00 4.99 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 4.99 0.00 1 0.00 0.00 initialize()
0.00 4.99 0.00 1 0.00 0.00 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.20% of 4.99 seconds
index % time self children called name
<spontaneous>
[1] 98.6 0.00 4.92 main [1]
3.36 0.00 201/201 Potential() [2]
0.00 1.54 201/201 VelocityVerlet(double, int, _IO_FILE*) [4]
0.01 0.00 1/202 computeAccelerations() [3]
0.00 0.00 201/201 MeanSquaredVelocity() [10]
0.00 0.00 1/1 initializeVelocities() [12]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
3.36 0.00 201/201 main [1]
[2] 67.5 3.36 0.00 201 Potential() [2]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.54 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [4]
[3] 31.1 1.55 0.00 202 computeAccelerations() [3]
-----------------------------------------------
0.00 1.54 201/201 main [1]
[4] 31.0 0.00 1.54 201 VelocityVerlet(double, int, _IO_FILE*) [4]
1.54 0.00 201/202 computeAccelerations() [3]
-----------------------------------------------
<spontaneous>
[5] 1.4 0.07 0.00 _init [5]
-----------------------------------------------
0.00 0.00 3240/3240 initializeVelocities() [12]
[9] 0.0 0.00 0.00 3240 _dl_relocate_static_pie [9]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[10] 0.0 0.00 0.00 201 MeanSquaredVelocity() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[12] 0.0 0.00 0.00 1 initializeVelocities() [12]
0.00 0.00 3240/3240 _dl_relocate_static_pie [9]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [3] computeAccelerations() [9] _dl_relocate_static_pie
[4] VelocityVerlet(double, int, _IO_FILE*) [12] initializeVelocities() [5] _init
[10] MeanSquaredVelocity() [2] Potential()

178
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Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls s/call s/call name
56.17 2.34 2.34 3240 0.00 0.00 _dl_relocate_static_pie
42.25 4.10 1.76 202 0.01 0.01 computeAccelerations()
1.20 4.15 0.05 _init
0.48 4.17 0.02 201 0.00 0.01 VelocityVerlet(double, int, _IO_FILE*)
0.00 4.17 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 4.17 0.00 1 0.00 0.00 initialize()
0.00 4.17 0.00 1 0.00 2.34 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.24% of 4.17 seconds
index % time self children called name
<spontaneous>
[1] 98.8 0.00 4.12 main [1]
0.00 2.34 1/1 initializeVelocities() [3]
0.02 1.75 201/201 VelocityVerlet(double, int, _IO_FILE*) [4]
0.01 0.00 1/202 computeAccelerations() [5]
0.00 0.00 201/201 MeanSquaredVelocity() [10]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
2.34 0.00 3240/3240 initializeVelocities() [3]
[2] 56.1 2.34 0.00 3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.00 2.34 1/1 main [1]
[3] 56.1 0.00 2.34 1 initializeVelocities() [3]
2.34 0.00 3240/3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.02 1.75 201/201 main [1]
[4] 42.5 0.02 1.75 201 VelocityVerlet(double, int, _IO_FILE*) [4]
1.75 0.00 201/202 computeAccelerations() [5]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.75 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [4]
[5] 42.2 1.76 0.00 202 computeAccelerations() [5]
-----------------------------------------------
<spontaneous>
[6] 1.2 0.05 0.00 _init [6]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[10] 0.0 0.00 0.00 201 MeanSquaredVelocity() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [5] computeAccelerations() [6] _init
[4] VelocityVerlet(double, int, _IO_FILE*) [3] initializeVelocities()
[10] MeanSquaredVelocity() [2] _dl_relocate_static_pie

178
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@ -0,0 +1,178 @@
Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls s/call s/call name
73.01 4.42 4.42 3240 0.00 0.00 _dl_relocate_static_pie
25.44 5.97 1.54 202 0.01 0.01 computeAccelerations()
1.32 6.05 0.08 _init
0.33 6.07 0.02 201 0.00 0.01 VelocityVerlet(double, int, _IO_FILE*)
0.00 6.07 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 6.07 0.00 1 0.00 0.00 initialize()
0.00 6.07 0.00 1 0.00 4.42 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.16% of 6.07 seconds
index % time self children called name
<spontaneous>
[1] 98.7 0.00 5.99 main [1]
0.00 4.42 1/1 initializeVelocities() [3]
0.02 1.53 201/201 VelocityVerlet(double, int, _IO_FILE*) [4]
0.01 0.00 1/202 computeAccelerations() [5]
0.00 0.00 201/201 MeanSquaredVelocity() [10]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
4.42 0.00 3240/3240 initializeVelocities() [3]
[2] 72.9 4.42 0.00 3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.00 4.42 1/1 main [1]
[3] 72.9 0.00 4.42 1 initializeVelocities() [3]
4.42 0.00 3240/3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.02 1.53 201/201 main [1]
[4] 25.6 0.02 1.53 201 VelocityVerlet(double, int, _IO_FILE*) [4]
1.53 0.00 201/202 computeAccelerations() [5]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.53 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [4]
[5] 25.4 1.54 0.00 202 computeAccelerations() [5]
-----------------------------------------------
<spontaneous>
[6] 1.3 0.08 0.00 _init [6]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[10] 0.0 0.00 0.00 201 MeanSquaredVelocity() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [5] computeAccelerations() [6] _init
[4] VelocityVerlet(double, int, _IO_FILE*) [3] initializeVelocities()
[10] MeanSquaredVelocity() [2] _dl_relocate_static_pie

179
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@ -0,0 +1,179 @@
Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls s/call s/call name
74.12 4.65 4.65 3240 0.00 0.00 _dl_relocate_static_pie
24.87 6.22 1.56 202 0.01 0.01 computeAccelerations()
0.96 6.28 0.06 _init
0.16 6.29 0.01 main
0.00 6.29 0.00 201 0.00 0.01 VelocityVerlet(double, int, _IO_FILE*)
0.00 6.29 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 6.29 0.00 1 0.00 0.00 initialize()
0.00 6.29 0.00 1 0.00 4.65 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.16% of 6.29 seconds
index % time self children called name
<spontaneous>
[1] 99.0 0.01 6.22 main [1]
0.00 4.65 1/1 initializeVelocities() [3]
0.00 1.55 201/201 VelocityVerlet(double, int, _IO_FILE*) [5]
0.01 0.00 1/202 computeAccelerations() [4]
0.00 0.00 201/201 MeanSquaredVelocity() [10]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
4.65 0.00 3240/3240 initializeVelocities() [3]
[2] 74.0 4.65 0.00 3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.00 4.65 1/1 main [1]
[3] 74.0 0.00 4.65 1 initializeVelocities() [3]
4.65 0.00 3240/3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.55 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [5]
[4] 24.8 1.56 0.00 202 computeAccelerations() [4]
-----------------------------------------------
0.00 1.55 201/201 main [1]
[5] 24.7 0.00 1.55 201 VelocityVerlet(double, int, _IO_FILE*) [5]
1.55 0.00 201/202 computeAccelerations() [4]
-----------------------------------------------
<spontaneous>
[6] 1.0 0.06 0.00 _init [6]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[10] 0.0 0.00 0.00 201 MeanSquaredVelocity() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [4] computeAccelerations() [6] _init
[5] VelocityVerlet(double, int, _IO_FILE*) [3] initializeVelocities() [1] main
[10] MeanSquaredVelocity() [2] _dl_relocate_static_pie

178
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@ -0,0 +1,178 @@
Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls s/call s/call name
70.91 3.91 3.91 3240 0.00 0.00 _dl_relocate_static_pie
28.29 5.48 1.56 202 0.01 0.01 computeAccelerations()
0.91 5.53 0.05 _init
0.00 5.53 0.00 201 0.00 0.01 VelocityVerlet(double, int, _IO_FILE*)
0.00 5.53 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 5.53 0.00 1 0.00 0.00 initialize()
0.00 5.53 0.00 1 0.00 3.91 initializeVelocities()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.18% of 5.53 seconds
index % time self children called name
<spontaneous>
[1] 99.1 0.00 5.48 main [1]
0.00 3.91 1/1 initializeVelocities() [3]
0.00 1.55 201/201 VelocityVerlet(double, int, _IO_FILE*) [5]
0.01 0.00 1/202 computeAccelerations() [4]
0.00 0.00 201/201 MeanSquaredVelocity() [10]
0.00 0.00 1/1 initialize() [11]
-----------------------------------------------
3.91 0.00 3240/3240 initializeVelocities() [3]
[2] 70.8 3.91 0.00 3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.00 3.91 1/1 main [1]
[3] 70.8 0.00 3.91 1 initializeVelocities() [3]
3.91 0.00 3240/3240 _dl_relocate_static_pie [2]
-----------------------------------------------
0.01 0.00 1/202 main [1]
1.55 0.00 201/202 VelocityVerlet(double, int, _IO_FILE*) [5]
[4] 28.3 1.56 0.00 202 computeAccelerations() [4]
-----------------------------------------------
0.00 1.55 201/201 main [1]
[5] 28.1 0.00 1.55 201 VelocityVerlet(double, int, _IO_FILE*) [5]
1.55 0.00 201/202 computeAccelerations() [4]
-----------------------------------------------
<spontaneous>
[6] 0.9 0.05 0.00 _init [6]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[10] 0.0 0.00 0.00 201 MeanSquaredVelocity() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initialize() [11]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2023 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[11] initialize() [4] computeAccelerations() [6] _init
[5] VelocityVerlet(double, int, _IO_FILE*) [3] initializeVelocities()
[10] MeanSquaredVelocity() [2] _dl_relocate_static_pie

5
input/inputdata.txt Normal file
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@ -0,0 +1,5 @@
cp
Ar
100
35000

BIN
out/MD Executable file
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Binary file not shown.

BIN
src/.DS_Store vendored Normal file
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Binary file not shown.

702
src/MD-original.cpp Normal file
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@ -0,0 +1,702 @@
/*
MD.c - a simple molecular dynamics program for simulating real gas properties
of Lennard-Jones particles.
Copyright (C) 2016 Jonathan J. Foley IV, Chelsea Sweet, Oyewumi Akinfenwa
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
Electronic Contact: foleyj10@wpunj.edu
Mail Contact: Prof. Jonathan Foley
Department of Chemistry, William Paterson University
300 Pompton Road
Wayne NJ 07470
*/
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
// Number of particles
int N;
// Lennard-Jones parameters in natural units!
double sigma = 1.;
double epsilon = 1.;
double m = 1.;
double kB = 1.;
double NA = 6.022140857e23;
double kBSI = 1.38064852e-23; // m^2*kg/(s^2*K)
// Size of box, which will be specified in natural units
double L;
// Initial Temperature in Natural Units
double Tinit; // 2;
// Vectors!
//
const int MAXPART = 5001;
// Position
double r[MAXPART][3];
// Velocity
double v[MAXPART][3];
// Acceleration
double a[MAXPART][3];
// Force
double F[MAXPART][3];
// atom type
char atype[10];
// Function prototypes
// initialize positions on simple cubic lattice, also calls function to
// initialize velocities
void initialize ();
// update positions and velocities using Velocity Verlet algorithm
// print particle coordinates to file for rendering via VMD or other animation
// software return 'instantaneous pressure'
double VelocityVerlet (double dt, int iter, FILE *fp);
// Compute Force using F = -dV/dr
// solve F = ma for use in Velocity Verlet
void computeAccelerations ();
// Numerical Recipes function for generation gaussian distribution
double gaussdist ();
// Initialize velocities according to user-supplied initial Temperature
// (Tinit)
void initializeVelocities ();
// Compute total potential energy from particle coordinates
double Potential ();
// Compute mean squared velocity from particle velocities
double MeanSquaredVelocity ();
// Compute total kinetic energy from particle mass and velocities
double Kinetic ();
int
main () {
// variable delcarations
int i;
double dt, Vol, Temp, Press, Pavg, Tavg, rho;
double VolFac, TempFac, PressFac, timefac;
double KE, PE, mvs, gc, Z;
char trash[10000], prefix[1000], tfn[1000], ofn[1000], afn[1000];
FILE *infp, *tfp, *ofp, *afp;
printf (
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf (" WELCOME TO WILLY P CHEM MD!\n");
printf (
" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf ("\n ENTER A TITLE FOR YOUR CALCULATION!\n");
scanf ("%s", prefix);
strcpy (tfn, prefix);
strcat (tfn, "_traj.xyz");
strcpy (ofn, prefix);
strcat (ofn, "_output.txt");
strcpy (afn, prefix);
strcat (afn, "_average.txt");
printf (
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf (" TITLE ENTERED AS '%s'\n", prefix);
printf (
" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
/* Table of values for Argon relating natural units to SI units:
* These are derived from Lennard-Jones parameters from the article
* "Liquid argon: Monte carlo and molecular dynamics calculations"
* J.A. Barker , R.A. Fisher & R.O. Watts
* Mol. Phys., Vol. 21, 657-673 (1971)
*
* mass: 6.633e-26 kg = one natural unit of mass for
*argon, by definition energy: 1.96183e-21 J = one natural unit of
*energy for argon, directly from L-J parameters length: 3.3605e-10 m =
*one natural unit of length for argon, directly from L-J parameters
* volume: 3.79499-29 m^3 = one natural unit of volume for
*argon, by length^3 time: 1.951e-12 s = one natural unit of
*time for argon, by length*sqrt(mass/energy)
***************************************************************************************/
// !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// Edit these factors to be computed in terms of basic properties in
// natural units of the gas being simulated
printf (
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf (
" WHICH NOBLE GAS WOULD YOU LIKE TO SIMULATE? (DEFAULT IS ARGON)\n");
printf ("\n FOR HELIUM, TYPE 'He' THEN PRESS 'return' TO CONTINUE\n");
printf (" FOR NEON, TYPE 'Ne' THEN PRESS 'return' TO CONTINUE\n");
printf (" FOR ARGON, TYPE 'Ar' THEN PRESS 'return' TO CONTINUE\n");
printf (" FOR KRYPTON, TYPE 'Kr' THEN PRESS 'return' TO CONTINUE\n");
printf (" FOR XENON, TYPE 'Xe' THEN PRESS 'return' TO CONTINUE\n");
printf (
" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
scanf ("%s", atype);
if (strcmp (atype, "He") == 0) {
VolFac = 1.8399744000000005e-29;
PressFac = 8152287.336171632;
TempFac = 10.864459551225972;
timefac = 1.7572698825166272e-12;
} else if (strcmp (atype, "Ne") == 0) {
VolFac = 2.0570823999999997e-29;
PressFac = 27223022.27659913;
TempFac = 40.560648991243625;
timefac = 2.1192341945685407e-12;
} else if (strcmp (atype, "Ar") == 0) {
VolFac = 3.7949992920124995e-29;
PressFac = 51695201.06691862;
TempFac = 142.0950000000000;
timefac = 2.09618e-12;
// strcpy(atype,"Ar");
} else if (strcmp (atype, "Kr") == 0) {
VolFac = 4.5882712000000004e-29;
PressFac = 59935428.40275003;
TempFac = 199.1817584391428;
timefac = 8.051563913585078e-13;
} else if (strcmp (atype, "Xe") == 0) {
VolFac = 5.4872e-29;
PressFac = 70527773.72794868;
TempFac = 280.30305642163006;
timefac = 9.018957925790732e-13;
} else {
VolFac = 3.7949992920124995e-29;
PressFac = 51695201.06691862;
TempFac = 142.0950000000000;
timefac = 2.09618e-12;
strcpy (atype, "Ar");
}
printf (
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf ("\n YOU ARE SIMULATING %s GAS! \n", atype);
printf (
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf (
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf ("\n YOU WILL NOW ENTER A FEW SIMULATION PARAMETERS\n");
printf (
" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf ("\n\n ENTER THE INTIAL TEMPERATURE OF YOUR GAS IN KELVIN\n");
scanf ("%lf", &Tinit);
// Make sure temperature is a positive number!
if (Tinit < 0.) {
printf ("\n !!!!! ABSOLUTE TEMPERATURE MUST BE A POSITIVE NUMBER! "
"PLEASE TRY AGAIN WITH A POSITIVE TEMPERATURE!!!\n");
exit (0);
}
// Convert initial temperature from kelvin to natural units
Tinit /= TempFac;
printf ("\n\n ENTER THE NUMBER DENSITY IN moles/m^3\n");
printf (" FOR REFERENCE, NUMBER DENSITY OF AN IDEAL GAS AT STP IS ABOUT "
"40 moles/m^3\n");
printf (" NUMBER DENSITY OF LIQUID ARGON AT 1 ATM AND 87 K IS ABOUT "
"35000 moles/m^3\n");
scanf ("%lf", &rho);
N = 10 * 216;
Vol = N / (rho * NA);
Vol /= VolFac;
// Limiting N to MAXPART for practical reasons
if (N >= MAXPART) {
printf ("\n\n\n MAXIMUM NUMBER OF PARTICLES IS %i\n\n PLEASE ADJUST "
"YOUR INPUT FILE ACCORDINGLY \n\n",
MAXPART);
exit (0);
}
// Check to see if the volume makes sense - is it too small?
// Remember VDW radius of the particles is 1 natural unit of length
// and volume = L*L*L, so if V = N*L*L*L = N, then all the particles
// will be initialized with an interparticle separation equal to 2xVDW
// radius
if (Vol < N) {
printf ("\n\n\n YOUR DENSITY IS VERY HIGH!\n\n");
printf (" THE NUMBER OF PARTICLES IS %i AND THE AVAILABLE VOLUME IS "
"%f NATURAL UNITS\n",
N, Vol);
printf (" SIMULATIONS WITH DENSITY GREATER THAN 1 PARTCICLE/(1 "
"Natural Unit of Volume) MAY DIVERGE\n");
printf (" PLEASE ADJUST YOUR INPUT FILE ACCORDINGLY AND RETRY\n\n");
exit (0);
}
// Vol = L*L*L;
// Length of the box in natural units:
L = pow (Vol, (1. / 3));
// Files that we can write different quantities to
tfp = fopen (tfn, "w"); // The MD trajectory, coordinates of every
// particle at each timestep
ofp = fopen (
ofn,
"w"); // Output of other quantities (T, P, gc, etc) at every timestep
afp = fopen (afn, "w"); // Average T, P, gc, etc from the simulation
int NumTime;
if (strcmp (atype, "He") == 0) {
// dt in natural units of time s.t. in SI it is 5 f.s. for all other
// gasses
dt = 0.2e-14 / timefac;
// We will run the simulation for NumTime timesteps.
// The total time will be NumTime*dt in natural units
// And NumTime*dt multiplied by the appropriate conversion factor for
// time in seconds
NumTime = 50000;
} else {
dt = 0.5e-14 / timefac;
NumTime = 200;
}
// Put all the atoms in simple crystal lattice and give them random
// velocities that corresponds to the initial temperature we have
// specified
initialize ();
// Based on their positions, calculate the ininial intermolecular forces
// The accellerations of each particle will be defined from the forces and
// their mass, and this will allow us to update their positions via
// Newton's law
computeAccelerations ();
// Print number of particles to the trajectory file
fprintf (tfp, "%i\n", N);
// We want to calculate the average Temperature and Pressure for the
// simulation The variables need to be set to zero initially
Pavg = 0;
Tavg = 0;
int tenp = floor (NumTime / 10);
fprintf (
ofp,
" time (s) T(t) (K) P(t) (Pa) "
"Kinetic En. (n.u.) Potential En. (n.u.) Total En. (n.u.)\n");
printf (" PERCENTAGE OF CALCULATION COMPLETE:\n [");
for (i = 0; i < NumTime + 1; i++) {
// This just prints updates on progress of the calculation for the
// users convenience
if (i == tenp)
printf (" 10 |");
else if (i == 2 * tenp)
printf (" 20 |");
else if (i == 3 * tenp)
printf (" 30 |");
else if (i == 4 * tenp)
printf (" 40 |");
else if (i == 5 * tenp)
printf (" 50 |");
else if (i == 6 * tenp)
printf (" 60 |");
else if (i == 7 * tenp)
printf (" 70 |");
else if (i == 8 * tenp)
printf (" 80 |");
else if (i == 9 * tenp)
printf (" 90 |");
else if (i == 10 * tenp)
printf (" 100 ]\n");
fflush (stdout);
// This updates the positions and velocities using Newton's Laws
// Also computes the Pressure as the sum of momentum changes from wall
// collisions / timestep which is a Kinetic Theory of gasses concept of
// Pressure
Press = VelocityVerlet (dt, i + 1, tfp);
Press *= PressFac;
// !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// Now we would like to calculate somethings about the system:
// Instantaneous mean velocity squared, Temperature, Pressure
// Potential, and Kinetic Energy
// We would also like to use the IGL to try to see if we can extract
// the gas constant
mvs = MeanSquaredVelocity ();
KE = Kinetic ();
PE = Potential ();
// Temperature from Kinetic Theory
Temp = m * mvs / (3 * kB) * TempFac;
// Instantaneous gas constant and compressibility - not well defined
// because pressure may be zero in some instances because there will be
// zero wall collisions, pressure may be very high in some instances
// because there will be a number of collisions
gc = NA * Press * (Vol * VolFac) / (N * Temp);
Z = Press * (Vol * VolFac) / (N * kBSI * Temp);
Tavg += Temp;
Pavg += Press;
fprintf (ofp, " %8.4e %20.12f %20.12f %20.12f %20.12f %20.12f \n",
i * dt * timefac, Temp, Press, KE, PE, KE + PE);
}
// Because we have calculated the instantaneous temperature and pressure,
// we can take the average over the whole simulation here
Pavg /= NumTime;
Tavg /= NumTime;
Z = Pavg * (Vol * VolFac) / (N * kBSI * Tavg);
gc = NA * Pavg * (Vol * VolFac) / (N * Tavg);
fprintf (afp,
" Total Time (s) T (K) P (Pa) PV/nT "
"(J/(mol K)) Z V (m^3) N\n");
fprintf (
afp,
" -------------- ----------- --------------- "
"-------------- --------------- ------------ -----------\n");
fprintf (afp,
" %8.4e %15.5f %15.5f %10.5f %10.5f "
"%10.5e %i\n",
i * dt * timefac, Tavg, Pavg, gc, Z, Vol * VolFac, N);
printf ("\n TO ANIMATE YOUR SIMULATION, OPEN THE FILE \n '%s' WITH VMD "
"AFTER THE SIMULATION COMPLETES\n",
tfn);
printf ("\n TO ANALYZE INSTANTANEOUS DATA ABOUT YOUR MOLECULE, OPEN THE "
"FILE \n '%s' WITH YOUR FAVORITE TEXT EDITOR OR IMPORT THE DATA "
"INTO EXCEL\n",
ofn);
printf ("\n THE FOLLOWING THERMODYNAMIC AVERAGES WILL BE COMPUTED AND "
"WRITTEN TO THE FILE \n '%s':\n",
afn);
printf ("\n AVERAGE TEMPERATURE (K): %15.5f\n", Tavg);
printf ("\n AVERAGE PRESSURE (Pa): %15.5f\n", Pavg);
printf ("\n PV/nT (J * mol^-1 K^-1): %15.5f\n", gc);
printf ("\n PERCENT ERROR of pV/nT AND GAS CONSTANT: %15.5f\n",
100 * fabs (gc - 8.3144598) / 8.3144598);
printf ("\n THE COMPRESSIBILITY (unitless): %15.5f \n", Z);
printf ("\n TOTAL VOLUME (m^3): %10.5e \n",
Vol * VolFac);
printf ("\n NUMBER OF PARTICLES (unitless): %i \n", N);
fclose (tfp);
fclose (ofp);
fclose (afp);
return 0;
}
void
initialize () {
int n, p, i, j, k;
double pos;
// Number of atoms in each direction
n = int (ceil (pow (N, 1.0 / 3)));
// spacing between atoms along a given direction
pos = L / n;
// index for number of particles assigned positions
p = 0;
// initialize positions
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
for (k = 0; k < n; k++) {
if (p < N) {
r[p][0] = (i + 0.5) * pos;
r[p][1] = (j + 0.5) * pos;
r[p][2] = (k + 0.5) * pos;
}
p++;
}
}
}
// Call function to initialize velocities
initializeVelocities ();
/***********************************************
* Uncomment if you want to see what the initial positions and velocities
are printf(" Printing initial positions!\n"); for (i=0; i<N; i++) {
printf(" %6.3e %6.3e %6.3e\n",r[i][0],r[i][1],r[i][2]);
}
printf(" Printing initial velocities!\n");
for (i=0; i<N; i++) {
printf(" %6.3e %6.3e %6.3e\n",v[i][0],v[i][1],v[i][2]);
}
*/
}
// Function to calculate the averaged velocity squared
double
MeanSquaredVelocity () {
double vx2 = 0;
double vy2 = 0;
double vz2 = 0;
double v2;
for (int i = 0; i < N; i++) {
vx2 = vx2 + v[i][0] * v[i][0];
vy2 = vy2 + v[i][1] * v[i][1];
vz2 = vz2 + v[i][2] * v[i][2];
}
v2 = (vx2 + vy2 + vz2) / N;
// printf(" Average of x-component of velocity squared is %f\n",v2);
return v2;
}
// Function to calculate the kinetic energy of the system
double
Kinetic () { // Write Function here!
double v2, kin;
kin = 0.;
for (int i = 0; i < N; i++) {
v2 = 0.;
for (int j = 0; j < 3; j++) {
v2 += v[i][j] * v[i][j];
}
kin += m * v2 / 2.;
}
// printf(" Total Kinetic Energy is %f\n",N*mvs*m/2.);
return kin;
}
// Function to calculate the potential energy of the system
double
Potential () {
double quot, r2, rnorm, term1, term2, Pot;
int i, j, k;
Pot = 0.;
for (i = 0; i < N; i++) {
for (j = 0; j < N; j++) {
if (j != i) {
r2 = 0.;
for (k = 0; k < 3; k++) {
r2 += (r[i][k] - r[j][k]) * (r[i][k] - r[j][k]);
}
rnorm = sqrt (r2);
quot = sigma / rnorm;
term1 = pow (quot, 12.);
term2 = pow (quot, 6.);
Pot += 4 * epsilon * (term1 - term2);
}
}
}
return Pot;
}
// Uses the derivative of the Lennard-Jones potential to calculate
// the forces on each atom. Then uses a = F/m to calculate the
// accelleration of each atom.
void
computeAccelerations () {
int i, j, k;
double f, rSqd;
double rij[3]; // position of i relative to j
for (i = 0; i < N; i++) { // set all accelerations to zero
for (k = 0; k < 3; k++) {
a[i][k] = 0;
}
}
for (i = 0; i < N - 1; i++) { // loop over all distinct pairs i,j
for (j = i + 1; j < N; j++) {
// initialize r^2 to zero
rSqd = 0;
for (k = 0; k < 3; k++) {
// component-by-componenent position of i relative to j
rij[k] = r[i][k] - r[j][k];
// sum of squares of the components
rSqd += rij[k] * rij[k];
}
// From derivative of Lennard-Jones with sigma and epsilon set
// equal to 1 in natural units!
f = 24 * (2 * pow (rSqd, -7) - pow (rSqd, -4));
for (k = 0; k < 3; k++) {
// from F = ma, where m = 1 in natural units!
a[i][k] += rij[k] * f;
a[j][k] -= rij[k] * f;
}
}
}
}
// returns sum of dv/dt*m/A (aka Pressure) from elastic collisions with walls
double
VelocityVerlet (double dt, int iter, FILE *fp) {
int i, j, k;
double psum = 0.;
// Compute accelerations from forces at current position
// this call was removed (commented) for predagogical reasons
// computeAccelerations();
// Update positions and velocity with current velocity and acceleration
// printf(" Updated Positions!\n");
for (i = 0; i < N; i++) {
for (j = 0; j < 3; j++) {
r[i][j] += v[i][j] * dt + 0.5 * a[i][j] * dt * dt;
v[i][j] += 0.5 * a[i][j] * dt;
}
// printf(" %i %6.4e %6.4e %6.4e\n",i,r[i][0],r[i][1],r[i][2]);
}
// Update accellerations from updated positions
computeAccelerations ();
// Update velocity with updated acceleration
for (i = 0; i < N; i++) {
for (j = 0; j < 3; j++) {
v[i][j] += 0.5 * a[i][j] * dt;
}
}
// Elastic walls
for (i = 0; i < N; i++) {
for (j = 0; j < 3; j++) {
if (r[i][j] < 0.) {
v[i][j] *= -1.; //- elastic walls
psum += 2 * m * fabs (v[i][j])
/ dt; // contribution to pressure from "left" walls
}
if (r[i][j] >= L) {
v[i][j] *= -1.; //- elastic walls
psum += 2 * m * fabs (v[i][j])
/ dt; // contribution to pressure from "right" walls
}
}
}
/* removed, uncomment to save atoms positions */
/*for (i=0; i<N; i++) {
fprintf(fp,"%s",atype);
for (j=0; j<3; j++) {
fprintf(fp," %12.10e ",r[i][j]);
}
fprintf(fp,"\n");
}*/
// fprintf(fp,"\n \n");
return psum / (6 * L * L);
}
void
initializeVelocities () {
int i, j;
for (i = 0; i < N; i++) {
for (j = 0; j < 3; j++) {
// Pull a number from a Gaussian Distribution
v[i][j] = gaussdist ();
}
}
// Vcm = sum_i^N m*v_i/ sum_i^N M
// Compute center-of-mas velocity according to the formula above
double vCM[3] = { 0, 0, 0 };
for (i = 0; i < N; i++) {
for (j = 0; j < 3; j++) {
vCM[j] += m * v[i][j];
}
}
for (i = 0; i < 3; i++)
vCM[i] /= N * m;
// Subtract out the center-of-mass velocity from the
// velocity of each particle... effectively set the
// center of mass velocity to zero so that the system does
// not drift in space!
for (i = 0; i < N; i++) {
for (j = 0; j < 3; j++) {
v[i][j] -= vCM[j];
}
}
// Now we want to scale the average velocity of the system
// by a factor which is consistent with our initial temperature, Tinit
double vSqdSum, lambda;
vSqdSum = 0.;
for (i = 0; i < N; i++) {
for (j = 0; j < 3; j++) {
vSqdSum += v[i][j] * v[i][j];
}
}
lambda = sqrt (3 * (N - 1) * Tinit / vSqdSum);
for (i = 0; i < N; i++) {
for (j = 0; j < 3; j++) {
v[i][j] *= lambda;
}
}
}
// Numerical recipes Gaussian distribution number generator
double
gaussdist () {
static bool available = false;
static double gset;
double fac, rsq, v1, v2;
if (!available) {
do {
v1 = 2.0 * rand () / double (RAND_MAX) - 1.0;
v2 = 2.0 * rand () / double (RAND_MAX) - 1.0;
rsq = v1 * v1 + v2 * v2;
} while (rsq >= 1.0 || rsq == 0.0);
fac = sqrt (-2.0 * log (rsq) / rsq);
gset = v1 * fac;
available = true;
return v2 * fac;
} else {
available = false;
return gset;
}
}

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/*
MD.c - a simple molecular dynamics program for simulating real gas properties
of Lennard-Jones particles.
Copyright (C) 2016 Jonathan J. Foley IV, Chelsea Sweet, Oyewumi Akinfenwa
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
Electronic Contact: foleyj10@wpunj.edu
Mail Contact: Prof. Jonathan Foley
Department of Chemistry, William Paterson University
300 Pompton Road
Wayne NJ 07470
*/
#include <math.h>
#include <omp.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
// Number of particles
int N;
// Lennard-Jones parameters in natural units!
double sigma = 1.;
double epsilon = 1.;
double m = 1.;
double kB = 1.;
double NA = 6.022140857e23;
double kBSI = 1.38064852e-23; // m^2*kg/(s^2*K)
// Size of box, which will be specified in natural units
double L;
// Initial Temperature in Natural Units
double Tinit; // 2;
// Vectors!
//
const int MAXPART = 5001;
// Position
double r[MAXPART][3];
// Velocity
double v[MAXPART][3];
// Acceleration
double a[MAXPART][3];
// Force
double F[MAXPART][3];
// atom type
char atype[10];
// Function prototypes
// initialize positions on simple cubic lattice, also calls function to
// initialize velocities
void initialize ();
// update positions and velocities using Velocity Verlet algorithm
// print particle coordinates to file for rendering via VMD or other animation
// software return 'instantaneous pressure'
double VelocityVerlet (double dt, int iter, FILE *fp);
// Compute Force using F = -dV/dr
// solve F = ma for use in Velocity Verlet
void computeAccelerations ();
// Numerical Recipes function for generation gaussian distribution
double gaussdist ();
// Initialize velocities according to user-supplied initial Temperature
// (Tinit)
void initializeVelocities ();
// Compute total potential energy from particle coordinates
double Potential ();
// Compute mean squared velocity from particle velocities
double MeanSquaredVelocity ();
// Compute total kinetic energy from particle mass and velocities
double Kinetic ();
int
main () {
// variable delcarations
int i;
double dt, Vol, Temp, Press, Pavg, Tavg, rho;
double VolFac, TempFac, PressFac, timefac;
double KE, PE, mvs, gc, Z;
char trash[10000], prefix[1000], tfn[1000], ofn[1000], afn[1000];
FILE *infp, *tfp, *ofp, *afp;
printf (
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf (" WELCOME TO WILLY P CHEM MD!\n");
printf (
" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf ("\n ENTER A TITLE FOR YOUR CALCULATION!\n");
scanf ("%s", prefix);
strcpy (tfn, prefix);
strcat (tfn, "_traj.xyz");
strcpy (ofn, prefix);
strcat (ofn, "_output.txt");
strcpy (afn, prefix);
strcat (afn, "_average.txt");
printf (
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf (" TITLE ENTERED AS '%s'\n", prefix);
printf (
" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
/* Table of values for Argon relating natural units to SI units:
* These are derived from Lennard-Jones parameters from the article
* "Liquid argon: Monte carlo and molecular dynamics calculations"
* J.A. Barker , R.A. Fisher & R.O. Watts
* Mol. Phys., Vol. 21, 657-673 (1971)
*
* mass: 6.633e-26 kg = one natural unit of mass for
*argon, by definition energy: 1.96183e-21 J = one natural unit of
*energy for argon, directly from L-J parameters length: 3.3605e-10 m =
*one natural unit of length for argon, directly from L-J parameters
* volume: 3.79499-29 m^3 = one natural unit of volume for
*argon, by length^3 time: 1.951e-12 s = one natural unit of
*time for argon, by length*sqrt(mass/energy)
***************************************************************************************/
// !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// Edit these factors to be computed in terms of basic properties in
// natural units of the gas being simulated
printf (
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf (
" WHICH NOBLE GAS WOULD YOU LIKE TO SIMULATE? (DEFAULT IS ARGON)\n");
printf ("\n FOR HELIUM, TYPE 'He' THEN PRESS 'return' TO CONTINUE\n");
printf (" FOR NEON, TYPE 'Ne' THEN PRESS 'return' TO CONTINUE\n");
printf (" FOR ARGON, TYPE 'Ar' THEN PRESS 'return' TO CONTINUE\n");
printf (" FOR KRYPTON, TYPE 'Kr' THEN PRESS 'return' TO CONTINUE\n");
printf (" FOR XENON, TYPE 'Xe' THEN PRESS 'return' TO CONTINUE\n");
printf (
" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
scanf ("%s", atype);
if (strcmp (atype, "He") == 0) {
VolFac = 1.8399744000000005e-29;
PressFac = 8152287.336171632;
TempFac = 10.864459551225972;
timefac = 1.7572698825166272e-12;
} else if (strcmp (atype, "Ne") == 0) {
VolFac = 2.0570823999999997e-29;
PressFac = 27223022.27659913;
TempFac = 40.560648991243625;
timefac = 2.1192341945685407e-12;
} else if (strcmp (atype, "Ar") == 0) {
VolFac = 3.7949992920124995e-29;
PressFac = 51695201.06691862;
TempFac = 142.0950000000000;
timefac = 2.09618e-12;
// strcpy(atype,"Ar");
} else if (strcmp (atype, "Kr") == 0) {
VolFac = 4.5882712000000004e-29;
PressFac = 59935428.40275003;
TempFac = 199.1817584391428;
timefac = 8.051563913585078e-13;
} else if (strcmp (atype, "Xe") == 0) {
VolFac = 5.4872e-29;
PressFac = 70527773.72794868;
TempFac = 280.30305642163006;
timefac = 9.018957925790732e-13;
} else {
VolFac = 3.7949992920124995e-29;
PressFac = 51695201.06691862;
TempFac = 142.0950000000000;
timefac = 2.09618e-12;
strcpy (atype, "Ar");
}
printf (
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf ("\n YOU ARE SIMULATING %s GAS! \n", atype);
printf (
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf (
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf ("\n YOU WILL NOW ENTER A FEW SIMULATION PARAMETERS\n");
printf (
" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf ("\n\n ENTER THE INTIAL TEMPERATURE OF YOUR GAS IN KELVIN\n");
scanf ("%lf", &Tinit);
// Make sure temperature is a positive number!
if (Tinit < 0.) {
printf ("\n !!!!! ABSOLUTE TEMPERATURE MUST BE A POSITIVE "
"NUMBER! PLEASE "
"TRY AGAIN WITH A POSITIVE TEMPERATURE!!!\n");
exit (0);
}
// Convert initial temperature from kelvin to natural units
Tinit /= TempFac;
printf ("\n\n ENTER THE NUMBER DENSITY IN moles/m^3\n");
printf (
" FOR REFERENCE, NUMBER DENSITY OF AN IDEAL GAS AT STP IS ABOUT 40 "
"moles/m^3\n");
printf (
" NUMBER DENSITY OF LIQUID ARGON AT 1 ATM AND 87 K IS ABOUT 35000 "
"moles/m^3\n");
scanf ("%lf", &rho);
N = 10 * 216;
Vol = N / (rho * NA);
Vol /= VolFac;
// Limiting N to MAXPART for practical reasons
if (N >= MAXPART) {
printf ("\n\n\n MAXIMUM NUMBER OF PARTICLES IS %i\n\n PLEASE "
"ADJUST YOUR "
"INPUT FILE ACCORDINGLY \n\n",
MAXPART);
exit (0);
}
// Check to see if the volume makes sense - is it too small?
// Remember VDW radius of the particles is 1 natural unit of length
// and volume = L*L*L, so if V = N*L*L*L = N, then all the particles
// will be initialized with an interparticle separation equal to 2xVDW
// radius
if (Vol < N) {
printf ("\n\n\n YOUR DENSITY IS VERY HIGH!\n\n");
printf (" THE NUMBER OF PARTICLES IS %i AND THE AVAILABLE VOLUME "
"IS %f "
"NATURAL UNITS\n",
N, Vol);
printf (" SIMULATIONS WITH DENSITY GREATER THAN 1 PARTCICLE/(1 "
"Natural "
"Unit of Volume) MAY DIVERGE\n");
printf (" PLEASE ADJUST YOUR INPUT FILE ACCORDINGLY AND RETRY\n\n");
exit (0);
}
// Vol = L*L*L;
// Length of the box in natural units:
L = pow (Vol, (1. / 3));
// Files that we can write different quantities to
tfp = fopen (tfn, "w"); // The MD trajectory, coordinates of every
// particle at each timestep
ofp = fopen (
ofn,
"w"); // Output of other quantities (T, P, gc, etc) at every timestep
afp = fopen (afn, "w"); // Average T, P, gc, etc from the simulation
int NumTime;
if (strcmp (atype, "He") == 0) {
// dt in natural units of time s.t. in SI it is 5 f.s. for all
// other gasses
dt = 0.2e-14 / timefac;
// We will run the simulation for NumTime timesteps.
// The total time will be NumTime*dt in natural units
// And NumTime*dt multiplied by the appropriate conversion factor
// for time in seconds
NumTime = 50000;
} else {
dt = 0.5e-14 / timefac;
NumTime = 200;
}
// Put all the atoms in simple crystal lattice and give them random
// velocities that corresponds to the initial temperature we have
// specified
initialize ();
// Based on their positions, calculate the ininial intermolecular forces
// The accellerations of each particle will be defined from the forces and
// their mass, and this will allow us to update their positions via
// Newton's law
computeAccelerations ();
// Print number of particles to the trajectory file
fprintf (tfp, "%i\n", N);
// We want to calculate the average Temperature and Pressure for the
// simulation The variables need to be set to zero initially
Pavg = 0;
Tavg = 0;
int tenp = floor (NumTime / 10);
fprintf (
ofp,
" time (s) T(t) (K) P(t) (Pa) "
"Kinetic En. (n.u.) Potential En. (n.u.) Total En. (n.u.)\n");
printf (" PERCENTAGE OF CALCULATION COMPLETE:\n [");
for (i = 0; i < NumTime + 1; i++) {
// This just prints updates on progress of the calculation for the
// users convenience
if (i == tenp)
printf (" 10 |");
else if (i == 2 * tenp)
printf (" 20 |");
else if (i == 3 * tenp)
printf (" 30 |");
else if (i == 4 * tenp)
printf (" 40 |");
else if (i == 5 * tenp)
printf (" 50 |");
else if (i == 6 * tenp)
printf (" 60 |");
else if (i == 7 * tenp)
printf (" 70 |");
else if (i == 8 * tenp)
printf (" 80 |");
else if (i == 9 * tenp)
printf (" 90 |");
else if (i == 10 * tenp)
printf (" 100 ]\n");
fflush (stdout);
// This updates the positions and velocities using Newton's Laws
// Also computes the Pressure as the sum of momentum changes from
// wall collisions / timestep which is a Kinetic Theory of gasses
// concept of Pressure
Press = VelocityVerlet (dt, i + 1, tfp);
Press *= PressFac;
// !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// Now we would like to calculate somethings about the system:
// Instantaneous mean velocity squared, Temperature, Pressure
// Potential, and Kinetic Energy
// We would also like to use the IGL to try to see if we can
// extract the gas constant
mvs = MeanSquaredVelocity ();
KE = Kinetic ();
PE = Potential ();
// Temperature from Kinetic Theory
Temp = m * mvs / (3 * kB) * TempFac;
// Instantaneous gas constant and compressibility - not well
// defined because pressure may be zero in some instances because
// there will be zero wall collisions, pressure may be very high in
// some instances because there will be a number of collisions
gc = NA * Press * (Vol * VolFac) / (N * Temp);
Z = Press * (Vol * VolFac) / (N * kBSI * Temp);
Tavg += Temp;
Pavg += Press;
fprintf (ofp, " %8.4e %20.12f %20.12f %20.12f %20.12f %20.12f \n",
i * dt * timefac, Temp, Press, KE, PE, KE + PE);
}
// Because we have calculated the instantaneous temperature and pressure,
// we can take the average over the whole simulation here
Pavg /= NumTime;
Tavg /= NumTime;
Z = Pavg * (Vol * VolFac) / (N * kBSI * Tavg);
gc = NA * Pavg * (Vol * VolFac) / (N * Tavg);
fprintf (afp,
" Total Time (s) T (K) P (Pa) PV/nT "
"(J/(mol K)) Z V (m^3) N\n");
fprintf (
afp,
" -------------- ----------- --------------- "
"-------------- --------------- ------------ -----------\n");
fprintf (
afp,
" %8.4e %15.5f %15.5f %10.5f %10.5f %10.5e "
" %i\n",
i * dt * timefac, Tavg, Pavg, gc, Z, Vol * VolFac, N);
printf ("\n TO ANIMATE YOUR SIMULATION, OPEN THE FILE \n '%s' WITH VMD "
"AFTER THE SIMULATION COMPLETES\n",
tfn);
printf (
"\n TO ANALYZE INSTANTANEOUS DATA ABOUT YOUR MOLECULE, OPEN THE FILE "
"\n "
" '%s' WITH YOUR FAVORITE TEXT EDITOR OR IMPORT THE DATA INTO EXCEL\n",
ofn);
printf ("\n THE FOLLOWING THERMODYNAMIC AVERAGES WILL BE COMPUTED AND "
"WRITTEN TO THE FILE \n '%s':\n",
afn);
printf ("\n AVERAGE TEMPERATURE (K): %15.5f\n", Tavg);
printf ("\n AVERAGE PRESSURE (Pa): %15.5f\n", Pavg);
printf ("\n PV/nT (J * mol^-1 K^-1): %15.5f\n", gc);
printf ("\n PERCENT ERROR of pV/nT AND GAS CONSTANT: %15.5f\n",
100 * fabs (gc - 8.3144598) / 8.3144598);
printf ("\n THE COMPRESSIBILITY (unitless): %15.5f \n", Z);
printf ("\n TOTAL VOLUME (m^3): %10.5e \n",
Vol * VolFac);
printf ("\n NUMBER OF PARTICLES (unitless): %i \n", N);
fclose (tfp);
fclose (ofp);
fclose (afp);
return 0;
}
void
initialize () {
int n, p, i, j, k;
double pos;
// Number of atoms in each direction
n = int (ceil (pow (N, 1.0 / 3)));
// spacing between atoms along a given direction
pos = L / n;
// index for number of particles assigned positions
p = 0;
// initialize positions
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
for (k = 0; k < n; k++) {
if (p < N) {
r[p][0] = (i + 0.5) * pos;
r[p][1] = (j + 0.5) * pos;
r[p][2] = (k + 0.5) * pos;
}
p++;
}
}
}
// Call function to initialize velocities
initializeVelocities ();
/***********************************************
* Uncomment if you want to see what the initial positions and velocities
are printf(" Printing initial positions!\n"); for (i=0; i<N; i++) {
printf(" %6.3e %6.3e %6.3e\n",r[i][0],r[i][1],r[i][2]);
}
printf(" Printing initial velocities!\n");
for (i=0; i<N; i++) {
printf(" %6.3e %6.3e %6.3e\n",v[i][0],v[i][1],v[i][2]);
}
*/
}
// Function to calculate the averaged velocity squared
double
MeanSquaredVelocity () {
double vx2 = 0;
double vy2 = 0;
double vz2 = 0;
double v2;
for (int i = 0; i < N; i++) {
vx2 = vx2 + v[i][0] * v[i][0];
vy2 = vy2 + v[i][1] * v[i][1];
vz2 = vz2 + v[i][2] * v[i][2];
}
v2 = (vx2 + vy2 + vz2) / N;
// printf(" Average of x-component of velocity squared is %f\n",v2);
return v2;
}
// Function to calculate the kinetic energy of the system
double
Kinetic () { // Write Function here!
double v2, kin;
kin = 0.;
for (int i = 0; i < N; i++) {
v2 = 0.;
for (int j = 0; j < 3; j++) {
v2 += v[i][j] * v[i][j];
}
kin += m * v2 / 2.;
}
// printf(" Total Kinetic Energy is %f\n",N*mvs*m/2.);
return kin;
}
// Function to calculate the potential energy of the system
double
Potential () {
double quot, r2, rnorm, term1, term2, Pot;
int i, j, k;
Pot = 0.;
#pragma omp parallel for reduction(+ : Pot) private(j, k, r2, rnorm, quot, \
term1, term2)
for (i = 0; i < N; i++) {
for (j = 0; j < N; j++) {
if (j != i) {
r2 = 0.;
for (k = 0; k < 3; k++) {
double tmp = r[i][k] - r[j][k];
r2 += tmp * tmp;
}
rnorm = sqrt (r2);
quot = sigma / rnorm;
term2 = quot * quot;
term2 = term2 * term2 * term2;
term1 = term2 * term2;
double local_energy = 4 * epsilon * (term1 - term2);
#pragma omp atomic
Pot += local_energy;
}
}
}
return Pot;
}
// Uses the derivative of the Lennard-Jones potential to calculate
// the forces on each atom. Then uses a = F/m to calculate the
// accelleration of each atom.
void
computeAccelerations () {
int i, j, k;
double f, rSqd;
double rij[3]; // position of i relative to j
for (i = 0; i < N; i++) { // set all accelerations to zero
for (k = 0; k < 3; k++) {
a[i][k] = 0;
}
}
for (i = 0; i < N - 1; i++) { // loop over all distinct pairs i,j
for (j = i + 1; j < N; j++) {
// initialize r^2 to zero
rSqd = 0;
for (k = 0; k < 3; k++) {
// component-by-componenent position of i relative
// to j
rij[k] = r[i][k] - r[j][k];
// sum of squares of the components
rSqd += rij[k] * rij[k];
}
// From derivative of Lennard-Jones with sigma and epsilon
// set equal to 1 in natural units!
f = 24 * (2 * pow (rSqd, -7) - pow (rSqd, -4));
for (k = 0; k < 3; k++) {
// from F = ma, where m = 1 in natural units!
a[i][k] += rij[k] * f;
a[j][k] -= rij[k] * f;
}
}
}
}
// returns sum of dv/dt*m/A (aka Pressure) from elastic collisions with walls
double
VelocityVerlet (double dt, int iter, FILE *fp) {
int i, j, k;
double psum = 0.;
// Compute accelerations from forces at current position
// this call was removed (commented) for predagogical reasons
// computeAccelerations();
// Update positions and velocity with current velocity and acceleration
// printf(" Updated Positions!\n");
for (i = 0; i < N; i++) {
for (j = 0; j < 3; j++) {
r[i][j] += v[i][j] * dt + 0.5 * a[i][j] * dt * dt;
v[i][j] += 0.5 * a[i][j] * dt;
}
// printf(" %i %6.4e %6.4e %6.4e\n",i,r[i][0],r[i][1],r[i][2]);
}
// Update accellerations from updated positions
computeAccelerations ();
// Update velocity with updated acceleration
for (i = 0; i < N; i++) {
for (j = 0; j < 3; j++) {
v[i][j] += 0.5 * a[i][j] * dt;
}
}
// Elastic walls
for (i = 0; i < N; i++) {
for (j = 0; j < 3; j++) {
if (r[i][j] < 0.) {
v[i][j] *= -1.; //- elastic walls
psum
+= 2 * m * fabs (v[i][j]) / dt; // contribution to pressure
// from "left" walls
}
if (r[i][j] >= L) {
v[i][j] *= -1.; //- elastic walls
psum
+= 2 * m * fabs (v[i][j]) / dt; // contribution to pressure
// from "right" walls
}
}
}
/* removed, uncomment to save atoms positions */
/*for (i=0; i<N; i++) {
fprintf(fp,"%s",atype);
for (j=0; j<3; j++) {
fprintf(fp," %12.10e ",r[i][j]);
}
fprintf(fp,"\n");
}*/
// fprintf(fp,"\n \n");
return psum / (6 * L * L);
}
void
initializeVelocities () {
int i, j;
for (i = 0; i < N; i++) {
for (j = 0; j < 3; j++) {
// Pull a number from a Gaussian Distribution
v[i][j] = gaussdist ();
}
}
// Vcm = sum_i^N m*v_i/ sum_i^N M
// Compute center-of-mas velocity according to the formula above
double vCM[3] = { 0, 0, 0 };
for (i = 0; i < N; i++) {
for (j = 0; j < 3; j++) {
vCM[j] += m * v[i][j];
}
}
for (i = 0; i < 3; i++)
vCM[i] /= N * m;
// Subtract out the center-of-mass velocity from the
// velocity of each particle... effectively set the
// center of mass velocity to zero so that the system does
// not drift in space!
for (i = 0; i < N; i++) {
for (j = 0; j < 3; j++) {
v[i][j] -= vCM[j];
}
}
// Now we want to scale the average velocity of the system
// by a factor which is consistent with our initial temperature, Tinit
double vSqdSum, lambda;
vSqdSum = 0.;
for (i = 0; i < N; i++) {
for (j = 0; j < 3; j++) {
vSqdSum += v[i][j] * v[i][j];
}
}
lambda = sqrt (3 * (N - 1) * Tinit / vSqdSum);
for (i = 0; i < N; i++) {
for (j = 0; j < 3; j++) {
v[i][j] *= lambda;
}
}
}
// Numerical recipes Gaussian distribution number generator
double
gaussdist () {
static bool available = false;
static double gset;
double fac, rsq, v1, v2;
if (!available) {
do {
v1 = 2.0 * rand () / double (RAND_MAX) - 1.0;
v2 = 2.0 * rand () / double (RAND_MAX) - 1.0;
rsq = v1 * v1 + v2 * v2;
} while (rsq >= 1.0 || rsq == 0.0);
fac = sqrt (-2.0 * log (rsq) / rsq);
gset = v1 * fac;
available = true;
return v2 * fac;
} else {
available = false;
return gset;
}
}