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Removed Sqrt function and optimized multiplications

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Afonso Franco 2023-10-16 19:29:22 +01:00
parent 44e386f674
commit 4c27b3c774
Signed by: afonso
SSH key fingerprint: SHA256:JiuxZNdA5bRWXPMUJChI0AQ75yC+cXY4xM0IaVwEVys
9 changed files with 626 additions and 268 deletions
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1
.clang-format
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@ -3,3 +3,4 @@ IndentWidth: 4
TabWidth: 4 TabWidth: 4
UseTab: Always UseTab: Always
BreakBeforeBraces: Attach BreakBeforeBraces: Attach
ColumnLimit: 100

2
Makefile
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@ -6,7 +6,7 @@ ts := $(shell /usr/bin/date "+%d-%m__%H_%M_%S")
.DEFAULT_GOAL = MD .DEFAULT_GOAL = MD
MD: $(SRC)/MD.cpp MD: $(SRC)/MD.cpp
$(CC) $(CFLAGS) $(SRC)MD.cpp -lm -O2 -ftree-vectorize -funroll-loops -pg -o ./out/MD $(CC) $(CFLAGS) $(SRC)MD.cpp -lm -O2 -ftree-vectorize -funroll-loops -pg -g -o ./out/MD
MDorig: $(SRC)/MD-original.cpp MDorig: $(SRC)/MD-original.cpp
$(CC) $(CFLAGS) $(SRC)MD-original.cpp -lm -O2 -pg -o ./out/MD-original $(CC) $(CFLAGS) $(SRC)MD-original.cpp -lm -O2 -pg -o ./out/MD-original

10
analysis/16-10__16_36_40.dot Normal file
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@ -0,0 +1,10 @@
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1 -> 2 [arrowsize="1.00", color="#ff0000", fontcolor="#ff0000", fontsize="10.00", label="100.00%\n201×", labeldistance="4.00", penwidth="4.00"];
2 [color="#ff0000", fontcolor="#ffffff", fontsize="10.00", label="VelocityVerlet(double, int, double*, _IO_FILE*)\n100.00%\n(0.00%)\n201×"];
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3 [color="#ff0000", fontcolor="#ffffff", fontsize="10.00", label="PotentialAndAcceleration()\n100.00%\n(100.00%)\n201×"];
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177
analysis/16-10__16_36_40.txt Normal file
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@ -0,0 +1,177 @@
Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls ms/call ms/call name
100.06 2.83 2.83 201 14.09 14.09 PotentialAndAcceleration()
0.00 2.83 0.00 3240 0.00 0.00 _dl_relocate_static_pie
0.00 2.83 0.00 201 0.00 14.09 VelocityVerlet(double, int, double*, _IO_FILE*)
0.00 2.83 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 2.83 0.00 1 0.00 0.00 initialize()
0.00 2.83 0.00 1 0.00 0.00 computeAccelerations()
0.00 2.83 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 0.35% of 2.83 seconds
index % time self children called name
<spontaneous>
[1] 100.0 0.00 2.83 main [1]
0.00 2.83 201/201 VelocityVerlet(double, int, double*, _IO_FILE*) [2]
0.00 0.00 201/201 MeanSquaredVelocity() [8]
0.00 0.00 1/1 computeAccelerations() [10]
0.00 0.00 1/1 initializeVelocities() [11]
0.00 0.00 1/1 initialize() [9]
-----------------------------------------------
0.00 2.83 201/201 main [1]
[2] 100.0 0.00 2.83 201 VelocityVerlet(double, int, double*, _IO_FILE*) [2]
2.83 0.00 201/201 PotentialAndAcceleration() [3]
-----------------------------------------------
2.83 0.00 201/201 VelocityVerlet(double, int, double*, _IO_FILE*) [2]
[3] 100.0 2.83 0.00 201 PotentialAndAcceleration() [3]
-----------------------------------------------
0.00 0.00 3240/3240 initializeVelocities() [11]
[7] 0.0 0.00 0.00 3240 _dl_relocate_static_pie [7]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[8] 0.0 0.00 0.00 201 MeanSquaredVelocity() [8]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[9] 0.0 0.00 0.00 1 initialize() [9]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[10] 0.0 0.00 0.00 1 computeAccelerations() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initializeVelocities() [11]
0.00 0.00 3240/3240 _dl_relocate_static_pie [7]
-----------------------------------------------
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
[9] initialize() [10] computeAccelerations() [7] _dl_relocate_static_pie
[2] VelocityVerlet(double, int, double*, _IO_FILE*) [11] initializeVelocities()
[8] MeanSquaredVelocity() [3] PotentialAndAcceleration()

10
analysis/16-10__16_44_31.dot Normal file
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@ -0,0 +1,10 @@
digraph {
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node [fontcolor=white, fontname=Arial, height=0, shape=box, style=filled, width=0];
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}

177
analysis/16-10__16_44_31.txt Normal file
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@ -0,0 +1,177 @@
Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls ms/call ms/call name
100.06 2.87 2.87 201 14.29 14.29 PotentialAndAcceleration()
0.00 2.87 0.00 3240 0.00 0.00 _dl_relocate_static_pie
0.00 2.87 0.00 201 0.00 14.29 VelocityVerlet(double, int, double*, _IO_FILE*)
0.00 2.87 0.00 201 0.00 0.00 MeanSquaredVelocity()
0.00 2.87 0.00 1 0.00 0.00 initialize()
0.00 2.87 0.00 1 0.00 0.00 computeAccelerations()
0.00 2.87 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 0.35% of 2.87 seconds
index % time self children called name
<spontaneous>
[1] 100.0 0.00 2.87 main [1]
0.00 2.87 201/201 VelocityVerlet(double, int, double*, _IO_FILE*) [2]
0.00 0.00 201/201 MeanSquaredVelocity() [8]
0.00 0.00 1/1 computeAccelerations() [10]
0.00 0.00 1/1 initializeVelocities() [11]
0.00 0.00 1/1 initialize() [9]
-----------------------------------------------
0.00 2.87 201/201 main [1]
[2] 100.0 0.00 2.87 201 VelocityVerlet(double, int, double*, _IO_FILE*) [2]
2.87 0.00 201/201 PotentialAndAcceleration() [3]
-----------------------------------------------
2.87 0.00 201/201 VelocityVerlet(double, int, double*, _IO_FILE*) [2]
[3] 100.0 2.87 0.00 201 PotentialAndAcceleration() [3]
-----------------------------------------------
0.00 0.00 3240/3240 initializeVelocities() [11]
[7] 0.0 0.00 0.00 3240 _dl_relocate_static_pie [7]
-----------------------------------------------
0.00 0.00 201/201 main [1]
[8] 0.0 0.00 0.00 201 MeanSquaredVelocity() [8]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[9] 0.0 0.00 0.00 1 initialize() [9]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[10] 0.0 0.00 0.00 1 computeAccelerations() [10]
-----------------------------------------------
0.00 0.00 1/1 main [1]
[11] 0.0 0.00 0.00 1 initializeVelocities() [11]
0.00 0.00 3240/3240 _dl_relocate_static_pie [7]
-----------------------------------------------
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
[9] initialize() [10] computeAccelerations() [7] _dl_relocate_static_pie
[2] VelocityVerlet(double, int, double*, _IO_FILE*) [11] initializeVelocities()
[8] MeanSquaredVelocity() [3] PotentialAndAcceleration()

350
cp_output.txt
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@ -1,202 +1,202 @@
time (s) T(t) (K) P(t) (Pa) Kinetic En. (n.u.) Potential En. (n.u.) Total En. (n.u.) time (s) T(t) (K) P(t) (Pa) Kinetic En. (n.u.) Potential En. (n.u.) Total En. (n.u.)
0.0000e+00 99.823046157131 0.000000000000 2276.129839537671 -21170.987155723738 -18894.857316186066 0.0000e+00 99.823046157131 0.000000000000 2276.129839537671 -21170.987155723738 -18894.857316186070
5.0000e-15 99.430066433986 0.000000000000 2267.169254696612 -21153.065287023051 -18885.896032326440 5.0000e-15 99.430066433986 0.000000000000 2267.169254696612 -21153.065287023051 -18885.896032326440
1.0000e-14 98.775883795075 0.000000000000 2252.252813230883 -21123.229899936763 -18870.977086705880 1.0000e-14 98.775883795075 0.000000000000 2252.252813230883 -21123.229899936763 -18870.977086705880
1.5000e-14 97.862741911230 0.000000000000 2231.431674530326 -21081.582692909291 -18850.151018378965 1.5000e-14 97.862741911230 0.000000000000 2231.431674530326 -21081.582692909291 -18850.151018378965
2.0000e-14 96.694206918839 0.000000000000 2204.787152377214 -21028.285410402823 -18823.498258025611 2.0000e-14 96.694206918839 0.000000000000 2204.787152377213 -21028.285410402827 -18823.498258025615
2.5000e-14 95.275447081837 0.000000000000 2172.437091700281 -20963.572595040936 -18791.135503340654 2.5000e-14 95.275447081837 0.000000000000 2172.437091700281 -20963.572595040936 -18791.135503340654
3.0000e-14 93.613593183031 0.000000000000 2134.544086090446 -20887.768030660216 -18753.223944569771 3.0000e-14 93.613593183031 0.000000000000 2134.544086090446 -20887.768030660216 -18753.223944569771
3.5000e-14 91.718175307735 0.000000000000 2091.325437186824 -20801.304686508829 -18709.979249322005 3.5000e-14 91.718175307735 0.000000000000 2091.325437186824 -20801.304686508818 -18709.979249321994
4.0000e-14 89.601625625826 0.000000000000 2043.064618935748 -20704.747699715073 -18661.683080779327 4.0000e-14 89.601625625826 0.000000000000 2043.064618935748 -20704.747699715081 -18661.683080779334
4.5000e-14 87.279827237114 0.000000000000 1990.123792168963 -20598.819500558115 -18608.695708389150 4.5000e-14 87.279827237114 0.000000000000 1990.123792168963 -20598.819500558118 -18608.695708389154
5.0000e-14 84.772675394773 0.000000000000 1932.956601422036 -20484.425558998624 -18551.468957576588 5.0000e-14 84.772675394773 0.000000000000 1932.956601422036 -20484.425558998628 -18551.468957576591
5.5000e-14 82.104599400629 0.000000000000 1872.120075006427 -20362.678405372902 -18490.558330366475 5.5000e-14 82.104599400629 0.000000000000 1872.120075006427 -20362.678405372910 -18490.558330366483
6.0000e-14 79.304972601851 0.000000000000 1808.283973609195 -20234.916615244118 -18426.632641634922 6.0000e-14 79.304972601851 0.000000000000 1808.283973609195 -20234.916615244118 -18426.632641634922
6.5000e-14 76.408318150720 0.000000000000 1742.235481954568 -20102.714524491177 -18360.479042536608 6.5000e-14 76.408318150720 0.000000000000 1742.235481954568 -20102.714524491174 -18360.479042536605
7.0000e-14 73.454206638373 0.000000000000 1674.876874684737 -19967.877882713929 -18293.001008029190 7.0000e-14 73.454206638373 0.000000000000 1674.876874684737 -19967.877882713929 -18293.001008029190
7.5000e-14 70.486747936098 0.000000000000 1607.213929504612 -19832.420906091691 -18225.206976587080 7.5000e-14 70.486747936098 0.000000000000 1607.213929504612 -19832.420906091687 -18225.206976587076
8.0000e-14 67.553612281810 0.000000000000 1540.333606341292 -19698.521671778017 -18158.188065436723 8.0000e-14 67.553612281810 0.000000000000 1540.333606341292 -19698.521671778017 -18158.188065436723
8.5000e-14 64.704576976476 0.000000000000 1475.370909629343 -19568.455621743615 -18093.084712114272 8.5000e-14 64.704576976476 0.000000000000 1475.370909629343 -19568.455621743618 -18093.084712114276
9.0000e-14 61.989675229269 0.000000000000 1413.466678931914 -19444.510671202428 -18031.043992270515 9.0000e-14 61.989675229269 0.000000000000 1413.466678931913 -19444.510671202424 -18031.043992270512
9.5000e-14 59.457101039628 0.000000000000 1355.719816801386 -19328.891029127131 -17973.171212325746 9.5000e-14 59.457101039628 0.000000000000 1355.719816801386 -19328.891029127128 -17973.171212325742
1.0000e-13 57.151073500535 0.000000000000 1303.138591377119 -19223.619147223981 -17920.480555846862 1.0000e-13 57.151073500535 0.000000000000 1303.138591377119 -19223.619147223984 -17920.480555846865
1.0500e-13 55.109870455531 0.000000000000 1256.595800527268 -19130.445501260390 -17873.849700733124 1.0500e-13 55.109870455531 0.000000000000 1256.595800527268 -19130.445501260390 -17873.849700733124
1.1000e-13 53.364208054286 0.000000000000 1216.791823047155 -19050.774326345723 -17833.982503298568 1.1000e-13 53.364208054286 0.000000000000 1216.791823047154 -19050.774326345734 -17833.982503298579
1.1500e-13 51.936086547624 0.000000000000 1184.228300885332 -18985.610801552139 -17801.382500666808 1.1500e-13 51.936086547624 0.000000000000 1184.228300885332 -18985.610801552139 -17801.382500666808
1.2000e-13 50.838162498530 0.000000000000 1159.193824520485 -18935.532402510431 -17776.338577989947 1.2000e-13 50.838162498530 0.000000000000 1159.193824520485 -18935.532402510431 -17776.338577989947
1.2500e-13 50.073654330447 0.000000000000 1141.761779307151 -18900.684708343262 -17758.922929036111 1.2500e-13 50.073654330447 0.000000000000 1141.761779307151 -18900.684708343259 -17758.922929036107
1.3000e-13 49.636744184237 0.000000000000 1131.799508476207 -18880.799949101500 -17749.000440625292 1.3000e-13 49.636744184237 0.000000000000 1131.799508476207 -18880.799949101503 -17749.000440625296
1.3500e-13 49.513403842570 0.000000000000 1128.987145571103 -18875.234971146012 -17746.247825574908 1.3500e-13 49.513403842570 0.000000000000 1128.987145571103 -18875.234971146016 -17746.247825574912
1.4000e-13 49.682546840563 0.000000000000 1132.843884467593 -18883.024119881375 -17750.180235413784 1.4000e-13 49.682546840563 0.000000000000 1132.843884467593 -18883.024119881378 -17750.180235413787
1.4500e-13 50.117395092442 0.000000000000 1142.759140712276 -18902.941905318730 -17760.182764606456 1.4500e-13 50.117395092442 0.000000000000 1142.759140712276 -18902.941905318727 -17760.182764606452
1.5000e-13 50.786947776435 0.000000000000 1158.026044517046 -18933.570293319775 -17775.544248802729 1.5000e-13 50.786947776435 0.000000000000 1158.026044517046 -18933.570293319772 -17775.544248802726
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1.0000e-12 99.359604739027 0.000000000000 2265.562612016245 -21149.316492673424 -18883.753880657179 1.0000e-12 99.359604739027 0.000000000000 2265.562612016248 -21149.316492673417 -18883.753880657168

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out/MD
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137
src/MD.cpp
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@ -38,6 +38,7 @@ double sigma = 1.;
double epsilon = 1.; double epsilon = 1.;
double m = 1.; double m = 1.;
double kB = 1.; double kB = 1.;
double epsilon_8 = epsilon * 8.;
double NA = 6.022140857e23; double NA = 6.022140857e23;
double kBSI = 1.38064852e-23; // m^2*kg/(s^2*K) double kBSI = 1.38064852e-23; // m^2*kg/(s^2*K)
@ -95,11 +96,9 @@ main () {
char trash[10000], prefix[1000], tfn[1000], ofn[1000], afn[1000]; char trash[10000], prefix[1000], tfn[1000], ofn[1000], afn[1000];
FILE *infp, *tfp, *ofp, *afp; FILE *infp, *tfp, *ofp, *afp;
printf ( printf ("\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf (" WELCOME TO WILLY P CHEM MD!\n"); printf (" WELCOME TO WILLY P CHEM MD!\n");
printf ( printf (" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf ("\n ENTER A TITLE FOR YOUR CALCULATION!\n"); printf ("\n ENTER A TITLE FOR YOUR CALCULATION!\n");
scanf ("%s", prefix); scanf ("%s", prefix);
strcpy (tfn, prefix); strcpy (tfn, prefix);
@ -109,11 +108,9 @@ main () {
strcpy (afn, prefix); strcpy (afn, prefix);
strcat (afn, "_average.txt"); strcat (afn, "_average.txt");
printf ( printf ("\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf (" TITLE ENTERED AS '%s'\n", prefix); printf (" TITLE ENTERED AS '%s'\n", prefix);
printf ( printf (" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
/* Table of values for Argon relating natural units to SI units: /* Table of values for Argon relating natural units to SI units:
* These are derived from Lennard-Jones parameters from the article * These are derived from Lennard-Jones parameters from the article
@ -134,17 +131,14 @@ main () {
// Edit these factors to be computed in terms of basic properties in // Edit these factors to be computed in terms of basic properties in
// natural units of the gas being simulated // natural units of the gas being simulated
printf ( printf ("\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n"); printf (" WHICH NOBLE GAS WOULD YOU LIKE TO SIMULATE? (DEFAULT IS ARGON)\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 ("\n FOR HELIUM, TYPE 'He' THEN PRESS 'return' TO CONTINUE\n");
printf (" FOR NEON, TYPE 'Ne' 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 ARGON, TYPE 'Ar' THEN PRESS 'return' TO CONTINUE\n");
printf (" FOR KRYPTON, TYPE 'Kr' 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 (" FOR XENON, TYPE 'Xe' THEN PRESS 'return' TO CONTINUE\n");
printf ( printf (" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
scanf ("%s", atype); scanf ("%s", atype);
if (strcmp (atype, "He") == 0) { if (strcmp (atype, "He") == 0) {
@ -186,17 +180,13 @@ main () {
timefac = 2.09618e-12; timefac = 2.09618e-12;
strcpy (atype, "Ar"); strcpy (atype, "Ar");
} }
printf ( printf ("\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf ("\n YOU ARE SIMULATING %s GAS! \n", atype); printf ("\n YOU ARE SIMULATING %s GAS! \n", atype);
printf ( printf ("\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf ( printf ("\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
"\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf ("\n YOU WILL NOW ENTER A FEW SIMULATION PARAMETERS\n"); printf ("\n YOU WILL NOW ENTER A FEW SIMULATION PARAMETERS\n");
printf ( printf (" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");
printf ("\n\n ENTER THE INTIAL TEMPERATURE OF YOUR GAS IN KELVIN\n"); printf ("\n\n ENTER THE INTIAL TEMPERATURE OF YOUR GAS IN KELVIN\n");
scanf ("%lf", &Tinit); scanf ("%lf", &Tinit);
// Make sure temperature is a positive number! // Make sure temperature is a positive number!
@ -210,11 +200,9 @@ main () {
Tinit /= TempFac; Tinit /= TempFac;
printf ("\n\n ENTER THE NUMBER DENSITY IN moles/m^3\n"); printf ("\n\n ENTER THE NUMBER DENSITY IN moles/m^3\n");
printf ( printf (" FOR REFERENCE, NUMBER DENSITY OF AN IDEAL GAS AT STP IS ABOUT 40 "
" FOR REFERENCE, NUMBER DENSITY OF AN IDEAL GAS AT STP IS ABOUT 40 "
"moles/m^3\n"); "moles/m^3\n");
printf ( printf (" NUMBER DENSITY OF LIQUID ARGON AT 1 ATM AND 87 K IS ABOUT 35000 "
" NUMBER DENSITY OF LIQUID ARGON AT 1 ATM AND 87 K IS ABOUT 35000 "
"moles/m^3\n"); "moles/m^3\n");
scanf ("%lf", &rho); scanf ("%lf", &rho);
@ -258,8 +246,7 @@ main () {
// Files that we can write different quantities to // Files that we can write different quantities to
tfp = fopen (tfn, "w"); // The MD trajectory, coordinates of every tfp = fopen (tfn, "w"); // The MD trajectory, coordinates of every
// particle at each timestep // particle at each timestep
ofp = fopen ( ofp = fopen (ofn,
ofn,
"w"); // Output of other quantities (T, P, gc, etc) at every timestep "w"); // Output of other quantities (T, P, gc, etc) at every timestep
afp = fopen (afn, "w"); // Average T, P, gc, etc from the simulation afp = fopen (afn, "w"); // Average T, P, gc, etc from the simulation
@ -299,9 +286,7 @@ main () {
Tavg = 0; Tavg = 0;
int tenp = floor (NumTime / 10); int tenp = floor (NumTime / 10);
fprintf ( fprintf (ofp, " time (s) T(t) (K) P(t) (Pa) "
ofp,
" time (s) T(t) (K) P(t) (Pa) "
"Kinetic En. (n.u.) Potential En. (n.u.) Total En. (n.u.)\n"); "Kinetic En. (n.u.) Potential En. (n.u.) Total En. (n.u.)\n");
printf (" PERCENTAGE OF CALCULATION COMPLETE:\n ["); printf (" PERCENTAGE OF CALCULATION COMPLETE:\n [");
for (i = 0; i < NumTime + 1; i++) { for (i = 0; i < NumTime + 1; i++) {
@ -359,8 +344,8 @@ main () {
Tavg += Temp; Tavg += Temp;
Pavg += Press; Pavg += Press;
fprintf (ofp, " %8.4e %20.12f %20.12f %20.12f %20.12f %20.12f \n", fprintf (ofp, " %8.4e %20.12f %20.12f %20.12f %20.12f %20.12f \n", i * dt * timefac,
i * dt * timefac, Temp, Press, KE, PE, KE + PE); Temp, Press, KE, PE, KE + PE);
} }
// Because we have calculated the instantaneous temperature and pressure, // Because we have calculated the instantaneous temperature and pressure,
@ -369,15 +354,11 @@ main () {
Tavg /= NumTime; Tavg /= NumTime;
Z = Pavg * (Vol * VolFac) / (N * kBSI * Tavg); Z = Pavg * (Vol * VolFac) / (N * kBSI * Tavg);
gc = NA * Pavg * (Vol * VolFac) / (N * Tavg); gc = NA * Pavg * (Vol * VolFac) / (N * Tavg);
fprintf (afp, fprintf (afp, " Total Time (s) T (K) P (Pa) PV/nT "
" Total Time (s) T (K) P (Pa) PV/nT "
"(J/(mol K)) Z V (m^3) N\n"); "(J/(mol K)) Z V (m^3) N\n");
fprintf ( fprintf (afp, " -------------- ----------- --------------- "
afp,
" -------------- ----------- --------------- "
"-------------- --------------- ------------ -----------\n"); "-------------- --------------- ------------ -----------\n");
fprintf ( fprintf (afp,
afp,
" %8.4e %15.5f %15.5f %10.5f %10.5f %10.5e " " %8.4e %15.5f %15.5f %10.5f %10.5f %10.5e "
" %i\n", " %i\n",
i * dt * timefac, Tavg, Pavg, gc, Z, Vol * VolFac, N); i * dt * timefac, Tavg, Pavg, gc, Z, Vol * VolFac, N);
@ -385,8 +366,7 @@ main () {
printf ("\n TO ANIMATE YOUR SIMULATION, OPEN THE FILE \n '%s' WITH VMD " printf ("\n TO ANIMATE YOUR SIMULATION, OPEN THE FILE \n '%s' WITH VMD "
"AFTER THE SIMULATION COMPLETES\n", "AFTER THE SIMULATION COMPLETES\n",
tfn); tfn);
printf ( printf ("\n TO ANALYZE INSTANTANEOUS DATA ABOUT YOUR MOLECULE, OPEN THE FILE "
"\n TO ANALYZE INSTANTANEOUS DATA ABOUT YOUR MOLECULE, OPEN THE FILE "
"\n " "\n "
" '%s' WITH YOUR FAVORITE TEXT EDITOR OR IMPORT THE DATA INTO EXCEL\n", " '%s' WITH YOUR FAVORITE TEXT EDITOR OR IMPORT THE DATA INTO EXCEL\n",
ofn); ofn);
@ -399,8 +379,7 @@ main () {
printf ("\n PERCENT ERROR of pV/nT AND GAS CONSTANT: %15.5f\n", printf ("\n PERCENT ERROR of pV/nT AND GAS CONSTANT: %15.5f\n",
100 * fabs (gc - 8.3144598) / 8.3144598); 100 * fabs (gc - 8.3144598) / 8.3144598);
printf ("\n THE COMPRESSIBILITY (unitless): %15.5f \n", Z); printf ("\n THE COMPRESSIBILITY (unitless): %15.5f \n", Z);
printf ("\n TOTAL VOLUME (m^3): %10.5e \n", printf ("\n TOTAL VOLUME (m^3): %10.5e \n", Vol * VolFac);
Vol * VolFac);
printf ("\n NUMBER OF PARTICLES (unitless): %i \n", N); printf ("\n NUMBER OF PARTICLES (unitless): %i \n", N);
fclose (tfp); fclose (tfp);
@ -495,50 +474,57 @@ Kinetic () { // Write Function here!
// printf(" Total Kinetic Energy is %f\n",N*mvs*m/2.); // printf(" Total Kinetic Energy is %f\n",N*mvs*m/2.);
return kin; return kin;
} }
double
getF (double dist) {}
double
getLocalPot (double dist) {}
// void
// transposeMatrix (double mat[MAXPART][3], double matT[3][MAXPART]) {
// for (int i = 0; i < 3; i++) {
// for (int j = 0; j < MAXPART; j++) {
// matT[i][j] = mat[j][i];
// }
// }
// }
double double
PotentialAndAcceleration () { PotentialAndAcceleration () {
double quot, rnorm, term1, term2, Pot;
int i, j, k;
double f, dist, tmp = 0.;
double distTmp = 0;
double posItoJ[3]; // position of i relative to j
double epsilon_8 = 8. * epsilon;
memset (a, 0, sizeof (a)); memset (a, 0, sizeof (a));
double Pot = 0.;
// double rT[3][MAXPART];
// transposeMatrix (r, rT);
Pot = 0.; for (int i = 0; i < N - 1; i++) {
for (int j = i + 1; j < N; j++) {
for (i = 0; i < N - 1; i++) { double quot, rnorm, term1, term2;
for (j = i + 1; j < N; j++) {
// CALCULATE POTENTIAL ENERGY // CALCULATE POTENTIAL ENERGY
dist = 0.; double dist = 0.;
distTmp = 0; double posItoJ[3]; // position of i relative to j
for (int k = 0; k < 3; k++) { for (int k = 0; k < 3; k++) {
// POT // POT
distTmp = r[i][k] - r[j][k]; double distTmp = r[i][k] - r[j][k];
dist += distTmp * distTmp; dist += distTmp * distTmp;
// ACCEL // ACCEL
posItoJ[k] = distTmp; posItoJ[k] = distTmp;
} }
quot = sigma / sqrt (dist); quot = sigma * sigma / dist;
term2 = quot * quot; term2 = quot * quot * quot;
term2 = term2 * term2 * term2; Pot += epsilon_8 * term2 * (term2 - 1);
term1 = term2 * term2;
Pot += 8 * epsilon * (term1 - term2);
// From derivative of Lennard-Jones with sigma and epsilon // From derivative of Lennard-Jones with sigma and epsilon
// set equal to 1 in natural units! // set equal to 1 in natural units!
double rSqd_inv7 double distSqd = dist * dist;
= 1.0 / (dist * dist * dist * dist * dist * dist * dist); double rSqd_inv4 = 1.0 / (distSqd * distSqd);
double rSqd_inv4 = rSqd_inv7 * dist * dist * dist; double rSqd_inv7 = rSqd_inv4 / (distSqd * dist);
f = 24 * (2 * rSqd_inv7 - rSqd_inv4); double f = 24.0 * (2.0 * rSqd_inv7 - rSqd_inv4);
// from F = ma, where m = 1 in natural units! // from F = ma, where m = 1 in natural units!
for (k = 0; k < 3; k++) { for (int k = 0; k < 3; k++) {
tmp = posItoJ[k] * f; double tmp = posItoJ[k] * f;
a[i][k] += tmp; a[i][k] += tmp;
a[j][k] -= tmp; a[j][k] -= tmp;
} }
@ -599,8 +585,7 @@ computeAccelerations () {
} }
// From derivative of Lennard-Jones with sigma and epsilon // From derivative of Lennard-Jones with sigma and epsilon
// set equal to 1 in natural units! // set equal to 1 in natural units!
double rSqd_inv7 double rSqd_inv7 = 1.0 / (rSqd * rSqd * rSqd * rSqd * rSqd * rSqd * rSqd);
= 1.0 / (rSqd * rSqd * rSqd * rSqd * rSqd * rSqd * rSqd);
double rSqd_inv4 = rSqd_inv7 * rSqd * rSqd * rSqd; double rSqd_inv4 = rSqd_inv7 * rSqd * rSqd * rSqd;
f = 24 * (2 * rSqd_inv7 - rSqd_inv4); f = 24 * (2 * rSqd_inv7 - rSqd_inv4);
@ -649,14 +634,12 @@ VelocityVerlet (double dt, int iter, double *PE, FILE *fp) {
for (j = 0; j < 3; j++) { for (j = 0; j < 3; j++) {
if (r[i][j] < 0.) { if (r[i][j] < 0.) {
v[i][j] *= -1.; //- elastic walls v[i][j] *= -1.; //- elastic walls
psum psum += 2 * m * fabs (v[i][j]) / dt; // contribution to pressure
+= 2 * m * fabs (v[i][j]) / dt; // contribution to pressure
// from "left" walls // from "left" walls
} }
if (r[i][j] >= L) { if (r[i][j] >= L) {
v[i][j] *= -1.; //- elastic walls v[i][j] *= -1.; //- elastic walls
psum psum += 2 * m * fabs (v[i][j]) / dt; // contribution to pressure
+= 2 * m * fabs (v[i][j]) / dt; // contribution to pressure
// from "right" walls // from "right" walls
} }
} }