portelli/Grid
1
0
Fork 0
mirror of https://github.com/paboyle/Grid.git synced 2024-09-20 09:15:38 +01:00
Code Releases Activity

Gamma right multiply code fix (now passes consistency check)

Browse Source
This commit is contained in:
Antonin Portelli 2017-01-24 17:36:23 -08:00
parent 2c3ebc1e07
commit 0432e30256
2 changed files with 263 additions and 87 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

96
lib/qcd/spin/Dirac.h
View File

@ -208,10 +208,10 @@ inline void rmultMinusGammaTGamma5(iMatrix<vtype, Ns> &ret, const iMatrix<vtype,
{ {
for(unsigned int i = 0; i < Ns; ++i) for(unsigned int i = 0; i < Ns; ++i)
{ {
ret(i, 0) = rhs(i, 2); ret(i, 0) = -rhs(i, 2);
ret(i, 1) = rhs(i, 3); ret(i, 1) = -rhs(i, 3);
ret(i, 2) = -rhs(i, 0); ret(i, 2) = rhs(i, 0);
ret(i, 3) = -rhs(i, 1); ret(i, 3) = rhs(i, 1);
} }
}; };
@ -241,10 +241,10 @@ inline void rmultGammaTGamma5(iMatrix<vtype, Ns> &ret, const iMatrix<vtype, Ns>
{ {
for(unsigned int i = 0; i < Ns; ++i) for(unsigned int i = 0; i < Ns; ++i)
{ {
ret(i, 0) = -rhs(i, 2); ret(i, 0) = rhs(i, 2);
ret(i, 1) = -rhs(i, 3); ret(i, 1) = rhs(i, 3);
ret(i, 2) = rhs(i, 0); ret(i, 2) = -rhs(i, 0);
ret(i, 3) = rhs(i, 1); ret(i, 3) = -rhs(i, 1);
} }
}; };
@ -274,10 +274,10 @@ inline void rmultMinusGammaX(iMatrix<vtype, Ns> &ret, const iMatrix<vtype, Ns> &
{ {
for(unsigned int i = 0; i < Ns; ++i) for(unsigned int i = 0; i < Ns; ++i)
{ {
ret(i, 0) = timesMinusI(rhs(i, 3)); ret(i, 0) = timesI(rhs(i, 3));
ret(i, 1) = timesMinusI(rhs(i, 2)); ret(i, 1) = timesI(rhs(i, 2));
ret(i, 2) = timesI(rhs(i, 1)); ret(i, 2) = timesMinusI(rhs(i, 1));
ret(i, 3) = timesI(rhs(i, 0)); ret(i, 3) = timesMinusI(rhs(i, 0));
} }
}; };
@ -307,10 +307,10 @@ inline void rmultGammaX(iMatrix<vtype, Ns> &ret, const iMatrix<vtype, Ns> &rhs)
{ {
for(unsigned int i = 0; i < Ns; ++i) for(unsigned int i = 0; i < Ns; ++i)
{ {
ret(i, 0) = timesI(rhs(i, 3)); ret(i, 0) = timesMinusI(rhs(i, 3));
ret(i, 1) = timesI(rhs(i, 2)); ret(i, 1) = timesMinusI(rhs(i, 2));
ret(i, 2) = timesMinusI(rhs(i, 1)); ret(i, 2) = timesI(rhs(i, 1));
ret(i, 3) = timesMinusI(rhs(i, 0)); ret(i, 3) = timesI(rhs(i, 0));
} }
}; };
@ -472,10 +472,10 @@ inline void rmultMinusGammaYGamma5(iMatrix<vtype, Ns> &ret, const iMatrix<vtype,
{ {
for(unsigned int i = 0; i < Ns; ++i) for(unsigned int i = 0; i < Ns; ++i)
{ {
ret(i, 0) = -rhs(i, 3); ret(i, 0) = rhs(i, 3);
ret(i, 1) = rhs(i, 2); ret(i, 1) = -rhs(i, 2);
ret(i, 2) = -rhs(i, 1); ret(i, 2) = rhs(i, 1);
ret(i, 3) = rhs(i, 0); ret(i, 3) = -rhs(i, 0);
} }
}; };
@ -505,10 +505,10 @@ inline void rmultGammaYGamma5(iMatrix<vtype, Ns> &ret, const iMatrix<vtype, Ns>
{ {
for(unsigned int i = 0; i < Ns; ++i) for(unsigned int i = 0; i < Ns; ++i)
{ {
ret(i, 0) = rhs(i, 3); ret(i, 0) = -rhs(i, 3);
ret(i, 1) = -rhs(i, 2); ret(i, 1) = rhs(i, 2);
ret(i, 2) = rhs(i, 1); ret(i, 2) = -rhs(i, 1);
ret(i, 3) = -rhs(i, 0); ret(i, 3) = rhs(i, 0);
} }
}; };
@ -538,10 +538,10 @@ inline void rmultMinusGammaZ(iMatrix<vtype, Ns> &ret, const iMatrix<vtype, Ns> &
{ {
for(unsigned int i = 0; i < Ns; ++i) for(unsigned int i = 0; i < Ns; ++i)
{ {
ret(i, 0) = timesMinusI(rhs(i, 2)); ret(i, 0) = timesI(rhs(i, 2));
ret(i, 1) = timesI(rhs(i, 3)); ret(i, 1) = timesMinusI(rhs(i, 3));
ret(i, 2) = timesI(rhs(i, 0)); ret(i, 2) = timesMinusI(rhs(i, 0));
ret(i, 3) = timesMinusI(rhs(i, 1)); ret(i, 3) = timesI(rhs(i, 1));
} }
}; };
@ -571,10 +571,10 @@ inline void rmultGammaZ(iMatrix<vtype, Ns> &ret, const iMatrix<vtype, Ns> &rhs)
{ {
for(unsigned int i = 0; i < Ns; ++i) for(unsigned int i = 0; i < Ns; ++i)
{ {
ret(i, 0) = timesI(rhs(i, 2)); ret(i, 0) = timesMinusI(rhs(i, 2));
ret(i, 1) = timesMinusI(rhs(i, 3)); ret(i, 1) = timesI(rhs(i, 3));
ret(i, 2) = timesMinusI(rhs(i, 0)); ret(i, 2) = timesI(rhs(i, 0));
ret(i, 3) = timesI(rhs(i, 1)); ret(i, 3) = timesMinusI(rhs(i, 1));
} }
}; };
@ -868,10 +868,10 @@ inline void rmultMinusSigmaXZ(iMatrix<vtype, Ns> &ret, const iMatrix<vtype, Ns>
{ {
for(unsigned int i = 0; i < Ns; ++i) for(unsigned int i = 0; i < Ns; ++i)
{ {
ret(i, 0) = rhs(i, 1); ret(i, 0) = -rhs(i, 1);
ret(i, 1) = -rhs(i, 0); ret(i, 1) = rhs(i, 0);
ret(i, 2) = rhs(i, 3); ret(i, 2) = -rhs(i, 3);
ret(i, 3) = -rhs(i, 2); ret(i, 3) = rhs(i, 2);
} }
}; };
@ -901,10 +901,10 @@ inline void rmultSigmaXZ(iMatrix<vtype, Ns> &ret, const iMatrix<vtype, Ns> &rhs)
{ {
for(unsigned int i = 0; i < Ns; ++i) for(unsigned int i = 0; i < Ns; ++i)
{ {
ret(i, 0) = -rhs(i, 1); ret(i, 0) = rhs(i, 1);
ret(i, 1) = rhs(i, 0); ret(i, 1) = -rhs(i, 0);
ret(i, 2) = -rhs(i, 3); ret(i, 2) = rhs(i, 3);
ret(i, 3) = rhs(i, 2); ret(i, 3) = -rhs(i, 2);
} }
}; };
@ -934,10 +934,10 @@ inline void rmultMinusSigmaYT(iMatrix<vtype, Ns> &ret, const iMatrix<vtype, Ns>
{ {
for(unsigned int i = 0; i < Ns; ++i) for(unsigned int i = 0; i < Ns; ++i)
{ {
ret(i, 0) = rhs(i, 1); ret(i, 0) = -rhs(i, 1);
ret(i, 1) = -rhs(i, 0); ret(i, 1) = rhs(i, 0);
ret(i, 2) = -rhs(i, 3); ret(i, 2) = rhs(i, 3);
ret(i, 3) = rhs(i, 2); ret(i, 3) = -rhs(i, 2);
} }
}; };
@ -967,10 +967,10 @@ inline void rmultSigmaYT(iMatrix<vtype, Ns> &ret, const iMatrix<vtype, Ns> &rhs)
{ {
for(unsigned int i = 0; i < Ns; ++i) for(unsigned int i = 0; i < Ns; ++i)
{ {
ret(i, 0) = -rhs(i, 1); ret(i, 0) = rhs(i, 1);
ret(i, 1) = rhs(i, 0); ret(i, 1) = -rhs(i, 0);
ret(i, 2) = rhs(i, 3); ret(i, 2) = -rhs(i, 3);
ret(i, 3) = -rhs(i, 2); ret(i, 3) = rhs(i, 2);
} }
}; };

254
lib/qcd/spin/gamma-gen/gamma-gen.nb
View File

@ -10,10 +10,10 @@
NotebookFileLineBreakTest NotebookFileLineBreakTest
NotebookFileLineBreakTest NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7] NotebookDataPosition[ 158, 7]
NotebookDataLength[ 55210, 1449] NotebookDataLength[ 60858, 1625]
NotebookOptionsPosition[ 53631, 1395] NotebookOptionsPosition[ 58965, 1561]
NotebookOutlinePosition[ 53992, 1411] NotebookOutlinePosition[ 59326, 1577]
CellTagsIndexPosition[ 53949, 1408] CellTagsIndexPosition[ 59283, 1574]
WindowFrame->Normal*) WindowFrame->Normal*)
(* Beginning of Notebook Content *) (* Beginning of Notebook Content *)
@ -59,7 +59,8 @@ Cell[BoxData["\<\"/Users/antonin/Development/Grid/lib/qcd/spin/gamma-gen\"\>"]\
3.694212832251072*^9, 3.694212924703574*^9, 3.694213477890645*^9, 3.694212832251072*^9, 3.694212924703574*^9, 3.694213477890645*^9,
3.694214215876555*^9, 3.694214744582322*^9, 3.694214868607993*^9, { 3.694214215876555*^9, 3.694214744582322*^9, 3.694214868607993*^9, {
3.694214930774279*^9, 3.694214956189962*^9}, 3.69421520097348*^9, 3.694214930774279*^9, 3.694214956189962*^9}, 3.69421520097348*^9,
3.6942153028002653`*^9, 3.694215388363636*^9, 3.694215531793765*^9}] 3.6942153028002653`*^9, 3.694215388363636*^9, 3.694215531793765*^9,
3.694293467607703*^9}]
}, Open ]], }, Open ]],
Cell[CellGroupData[{ Cell[CellGroupData[{
@ -256,6 +257,168 @@ Cell[BoxData[{
3.694185780274218*^9, 3.6941858224264593`*^9, {3.694185941282981*^9, 3.694185780274218*^9, 3.6941858224264593`*^9, {3.694185941282981*^9,
3.694185950262871*^9}}], 3.694185950262871*^9}}],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{"mat", "[",
RowBox[{"-", "gt5"}], "]"}], "//", "MatrixForm"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"(",
RowBox[{"r", " ", "=", " ",
RowBox[{"RandomReal", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"-", "10"}], ",", "10"}], "}"}], ",",
RowBox[{"{",
RowBox[{"4", ",", "4"}], "}"}]}], "]"}]}], ")"}], "//",
"MatrixForm"}]}], "Input",
CellChangeTimes->{{3.694293480790983*^9, 3.69429352615298*^9}, {
3.694293583868273*^9, 3.694293627905012*^9}}],
Cell[BoxData[
TagBox[
RowBox[{"(", "\[NoBreak]", GridBox[{
{"0", "0", "1", "0"},
{"0", "0", "0", "1"},
{
RowBox[{"-", "1"}], "0", "0", "0"},
{"0",
RowBox[{"-", "1"}], "0", "0"}
},
GridBoxAlignment->{
"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
Function[BoxForm`e$,
MatrixForm[BoxForm`e$]]]], "Output",
CellChangeTimes->{{3.6942934848800297`*^9, 3.694293510379167*^9}, {
3.694293591310405*^9, 3.694293628362492*^9}}],
Cell[BoxData[
TagBox[
RowBox[{"(", "\[NoBreak]", GridBox[{
{
RowBox[{"-", "0.25452891888633644`"}], "3.9497832842151723`",
RowBox[{"-", "6.956210966956014`"}],
RowBox[{"-", "1.1605509642484506`"}]},
{
RowBox[{"-", "9.759118843088793`"}], "5.857502491851477`",
"2.261037884838345`", "7.119654104319878`"},
{
RowBox[{"-", "2.281513144390619`"}],
RowBox[{"-", "6.615660517890536`"}], "0.8161523737384115`",
"6.455639430863592`"},
{"7.570477003311133`", "7.839673906449725`",
RowBox[{"-", "0.1228536610401676`"}],
RowBox[{"-", "3.5575684207365654`"}]}
},
GridBoxAlignment->{
"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
Function[BoxForm`e$,
MatrixForm[BoxForm`e$]]]], "Output",
CellChangeTimes->{{3.6942934848800297`*^9, 3.694293510379167*^9}, {
3.694293591310405*^9, 3.694293628381173*^9}}]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{
RowBox[{"mat", "[",
RowBox[{"-", "gt"}], "]"}], ".", "rhsv"}], "//",
"MatrixForm"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"rhsv", ".",
RowBox[{"mat", "[",
RowBox[{"-", "gt"}], "]"}]}], "//", "MatrixForm"}]}], "Input",
CellChangeTimes->{{3.694293596046916*^9, 3.694293618686639*^9}, {
3.6942936668548403`*^9, 3.694293671450027*^9}, {3.6942939975199223`*^9,
3.694294027927437*^9}}],
Cell[BoxData[
TagBox[
RowBox[{"(", "\[NoBreak]",
TagBox[GridBox[{
{
RowBox[{"-",
RowBox[{"rhs", "[", "2", "]"}]}]},
{
RowBox[{"-",
RowBox[{"rhs", "[", "3", "]"}]}]},
{
RowBox[{"-",
RowBox[{"rhs", "[", "0", "]"}]}]},
{
RowBox[{"-",
RowBox[{"rhs", "[", "1", "]"}]}]}
},
GridBoxAlignment->{
"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.5599999999999999]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
Column], "\[NoBreak]", ")"}],
Function[BoxForm`e$,
MatrixForm[BoxForm`e$]]]], "Output",
CellChangeTimes->{{3.694293605879734*^9, 3.69429361931848*^9},
3.694293671734251*^9, {3.6942940079400787`*^9, 3.694294028852909*^9}}],
Cell[BoxData[
TagBox[
RowBox[{"(", "\[NoBreak]",
TagBox[GridBox[{
{
RowBox[{"-",
RowBox[{"rhs", "[", "2", "]"}]}]},
{
RowBox[{"-",
RowBox[{"rhs", "[", "3", "]"}]}]},
{
RowBox[{"-",
RowBox[{"rhs", "[", "0", "]"}]}]},
{
RowBox[{"-",
RowBox[{"rhs", "[", "1", "]"}]}]}
},
GridBoxAlignment->{
"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.5599999999999999]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
Column], "\[NoBreak]", ")"}],
Function[BoxForm`e$,
MatrixForm[BoxForm`e$]]]], "Output",
CellChangeTimes->{{3.694293605879734*^9, 3.69429361931848*^9},
3.694293671734251*^9, {3.6942940079400787`*^9, 3.6942940288814163`*^9}}]
}, Open ]],
Cell["Generation of the abstract algebra:", "Text", Cell["Generation of the abstract algebra:", "Text",
CellChangeTimes->{{3.6942090658330803`*^9, 3.694209076132119*^9}}], CellChangeTimes->{{3.6942090658330803`*^9, 3.694209076132119*^9}}],
@ -352,7 +515,8 @@ Cell[BoxData[
3.6942128326290417`*^9, 3.6942129251958523`*^9, 3.694213478493619*^9, 3.6942128326290417`*^9, 3.6942129251958523`*^9, 3.694213478493619*^9,
3.694214216283064*^9, 3.694214744924881*^9, 3.694214869005068*^9, { 3.694214216283064*^9, 3.694214744924881*^9, 3.694214869005068*^9, {
3.694214931160738*^9, 3.6942149565175247`*^9}, 3.69421520140513*^9, 3.694214931160738*^9, 3.6942149565175247`*^9}, 3.69421520140513*^9,
3.694215303184371*^9, 3.694215388782826*^9, 3.694215532274271*^9}] 3.694215303184371*^9, 3.694215388782826*^9, 3.694215532274271*^9,
3.694293468120837*^9}]
}, Open ]], }, Open ]],
Cell["Full multiplication table:", "Text", Cell["Full multiplication table:", "Text",
@ -534,7 +698,8 @@ Cell[BoxData[
3.694212832700527*^9, 3.69421292529856*^9, 3.694213478604137*^9, 3.694212832700527*^9, 3.69421292529856*^9, 3.694213478604137*^9,
3.694214216368701*^9, 3.694214744992138*^9, 3.694214869090289*^9, { 3.694214216368701*^9, 3.694214744992138*^9, 3.694214869090289*^9, {
3.694214931237383*^9, 3.6942149565897913`*^9}, 3.6942152015279818`*^9, 3.694214931237383*^9, 3.6942149565897913`*^9}, 3.6942152015279818`*^9,
3.694215303248364*^9, 3.694215388866436*^9, 3.694215532359406*^9}] 3.694215303248364*^9, 3.694215388866436*^9, 3.694215532359406*^9,
3.694293468220346*^9}]
}, Open ]] }, Open ]]
}, Open ]], }, Open ]],
@ -1014,9 +1179,9 @@ Cell[BoxData[{
RowBox[{"ir", "+", "1"}]}]}], ",", RowBox[{"ir", "+", "1"}]}]}], ",",
RowBox[{"{", RowBox[{"{",
RowBox[{"c", ",", RowBox[{"c", ",",
RowBox[{ RowBox[{"rhsv", ".",
RowBox[{"mat", "[", "g", "]"}], ".", "rhsv"}]}], "}"}]}], "]"}], RowBox[{"mat", "[", "g", "]"}]}]}], "}"}]}], "]"}], ";",
";", "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{"out", " ", "=", RowBox[{"out", " ", "=",
RowBox[{"out", "<>", "\"\< }\\n};\\n\>\""}]}], ";", RowBox[{"out", "<>", "\"\< }\\n};\\n\>\""}]}], ";",
"\[IndentingNewLine]", "\[IndentingNewLine]",
@ -1238,7 +1403,8 @@ iMatrix<vtype,N>>::type \n{\n iMatrix<vtype,N> ret;\n for(int i=0;i<N;i++){\
3.694208089863509*^9, 3.6942082975753603`*^9}, {3.694212881031795*^9, 3.694208089863509*^9, 3.6942082975753603`*^9}, {3.694212881031795*^9,
3.694212885985661*^9}, {3.694213330227892*^9, 3.694213417940996*^9}, { 3.694212885985661*^9}, {3.694213330227892*^9, 3.694213417940996*^9}, {
3.694214921431739*^9, 3.694214951876449*^9}, {3.6942151046483088`*^9, 3.694214921431739*^9, 3.694214951876449*^9}, {3.6942151046483088`*^9,
3.694215118335286*^9}, {3.6942151634191313`*^9, 3.694215188429871*^9}}], 3.694215118335286*^9}, {3.6942151634191313`*^9, 3.694215188429871*^9}, {
3.6942940839999113`*^9, 3.694294090686364*^9}}],
Cell["Header file generation:", "Text", Cell["Header file generation:", "Text",
CellFrame->{{0, 0}, {0, 0.5}}, CellFrame->{{0, 0}, {0, 0.5}},
@ -1394,7 +1560,7 @@ Cell[BoxData[
}, Open ]] }, Open ]]
}, },
WindowSize->{1246, 1005}, WindowSize->{1246, 1005},
WindowMargins->{{Automatic, 155}, {Automatic, 0}}, WindowMargins->{{213, Automatic}, {Automatic, 0}},
FrontEndVersion->"11.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (September \ FrontEndVersion->"11.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (September \
21, 2016)", 21, 2016)",
StyleDefinitions->"Default.nb" StyleDefinitions->"Default.nb"
@ -1413,43 +1579,53 @@ Notebook[{
Cell[558, 20, 1295, 18, 502, "Text"], Cell[558, 20, 1295, 18, 502, "Text"],
Cell[CellGroupData[{ Cell[CellGroupData[{
Cell[1878, 42, 393, 8, 75, "Input"], Cell[1878, 42, 393, 8, 75, "Input"],
Cell[2274, 52, 654, 9, 32, "Output"] Cell[2274, 52, 680, 10, 32, "Output"]
}, Open ]], }, Open ]],
Cell[CellGroupData[{ Cell[CellGroupData[{
Cell[2965, 66, 114, 1, 64, "Section"], Cell[2991, 67, 114, 1, 64, "Section"],
Cell[3082, 69, 475, 14, 54, "Input"], Cell[3108, 70, 475, 14, 54, "Input"],
Cell[3560, 85, 139, 1, 30, "Text"], Cell[3586, 86, 139, 1, 30, "Text"],
Cell[3702, 88, 5454, 168, 427, "Input"], Cell[3728, 89, 5454, 168, 427, "Input"],
Cell[9159, 258, 119, 1, 30, "Text"],
Cell[9281, 261, 1295, 41, 96, "Input"],
Cell[10579, 304, 133, 1, 30, "Text"],
Cell[CellGroupData[{ Cell[CellGroupData[{
Cell[10737, 309, 479, 15, 32, "Input"], Cell[9207, 261, 547, 16, 54, "Input"],
Cell[11219, 326, 1259, 28, 96, "Output"] Cell[9757, 279, 820, 23, 92, "Output"],
Cell[10580, 304, 1245, 31, 92, "Output"]
}, Open ]], }, Open ]],
Cell[12493, 357, 110, 1, 30, "Text"],
Cell[CellGroupData[{ Cell[CellGroupData[{
Cell[12628, 362, 476, 12, 32, "Input"], Cell[11862, 340, 448, 12, 54, "Input"],
Cell[13107, 376, 6313, 160, 312, "Output"] Cell[12313, 354, 1028, 31, 96, "Output"],
Cell[13344, 387, 1030, 31, 96, "Output"]
}, Open ]],
Cell[14389, 421, 119, 1, 30, "Text"],
Cell[14511, 424, 1295, 41, 96, "Input"],
Cell[15809, 467, 133, 1, 30, "Text"],
Cell[CellGroupData[{
Cell[15967, 472, 479, 15, 32, "Input"],
Cell[16449, 489, 1285, 29, 96, "Output"]
}, Open ]],
Cell[17749, 521, 110, 1, 30, "Text"],
Cell[CellGroupData[{
Cell[17884, 526, 476, 12, 32, "Input"],
Cell[18363, 540, 6339, 161, 312, "Output"]
}, Open ]] }, Open ]]
}, Open ]], }, Open ]],
Cell[CellGroupData[{ Cell[CellGroupData[{
Cell[19469, 542, 117, 1, 64, "Section"], Cell[24751, 707, 117, 1, 64, "Section"],
Cell[19589, 545, 128, 2, 38, "Text"], Cell[24871, 710, 128, 2, 38, "Text"],
Cell[19720, 549, 2518, 48, 747, "Input"], Cell[25002, 714, 2518, 48, 747, "Input"],
Cell[22241, 599, 164, 3, 38, "Text"], Cell[27523, 764, 164, 3, 38, "Text"],
Cell[22408, 604, 4876, 148, 684, "Input"], Cell[27690, 769, 4876, 148, 684, "Input"],
Cell[27287, 754, 2588, 55, 201, "Input"], Cell[32569, 919, 2588, 55, 201, "Input"],
Cell[29878, 811, 149, 2, 38, "Text"], Cell[35160, 976, 149, 2, 38, "Text"],
Cell[30030, 815, 17190, 425, 3456, "Input"], Cell[35312, 980, 17242, 426, 3456, "Input"],
Cell[47223, 1242, 137, 2, 38, "Text"], Cell[52557, 1408, 137, 2, 38, "Text"],
Cell[47363, 1246, 468, 11, 32, "Input"] Cell[52697, 1412, 468, 11, 32, "Input"]
}, Open ]], }, Open ]],
Cell[CellGroupData[{ Cell[CellGroupData[{
Cell[47868, 1262, 116, 1, 64, "Section"], Cell[53202, 1428, 116, 1, 64, "Section"],
Cell[47987, 1265, 3046, 66, 285, "Input"], Cell[53321, 1431, 3046, 66, 285, "Input"],
Cell[51036, 1333, 2179, 48, 432, "Input"], Cell[56370, 1499, 2179, 48, 432, "Input"],
Cell[53218, 1383, 397, 9, 32, "Input"] Cell[58552, 1549, 397, 9, 32, "Input"]
}, Open ]] }, Open ]]
} }
] ]