1034 lines
41 KiB
Mathematica
1034 lines
41 KiB
Mathematica
(* Content-type: application/vnd.wolfram.mathematica *)
|
|
|
|
(*** Wolfram Notebook File ***)
|
|
(* http://www.wolfram.com/nb *)
|
|
|
|
(* CreatedBy='Mathematica 13.1' *)
|
|
|
|
(*CacheID: 234*)
|
|
(* Internal cache information:
|
|
NotebookFileLineBreakTest
|
|
NotebookFileLineBreakTest
|
|
NotebookDataPosition[ 158, 7]
|
|
NotebookDataLength[ 40948, 1025]
|
|
NotebookOptionsPosition[ 38625, 984]
|
|
NotebookOutlinePosition[ 39072, 1002]
|
|
CellTagsIndexPosition[ 39029, 999]
|
|
WindowFrame->Normal*)
|
|
|
|
(* Beginning of Notebook Content *)
|
|
Notebook[{
|
|
|
|
Cell[CellGroupData[{
|
|
Cell["\:4ee3\:7801", "Subsection",
|
|
CellChangeTimes->{{3.924555227023057*^9,
|
|
3.9245552380596447`*^9}},ExpressionUUID->"0af2c2ea-193f-4649-a13d-\
|
|
0c6d54e22272"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"(*", "\:5b9a\:4e49\:6709\:6548\:6570\:5b57\:51fd\:6570", "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"EffectiveDigits", "[",
|
|
RowBox[{"a_", ",", "b_"}], "]"}], ":=",
|
|
RowBox[{"Module", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
"m", ",", "n", ",", "scientificA", ",", "base", ",", "exponent"}],
|
|
"}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]",
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
"\:5c06a\:8f6c\:6362\:4e3a\:79d1\:5b66\:8bb0\:6570\:6cd5\:5f62\:5f0f\
|
|
", " ", "0.", "xyz"}], "..."}], "\[Times]",
|
|
RowBox[{"10", "^", "m"}]}], "*)"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"scientificA", "=",
|
|
RowBox[{"MantissaExponent", "[",
|
|
RowBox[{"RealAbs", "[", "a", "]"}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"base", "=",
|
|
RowBox[{"scientificA", "[",
|
|
RowBox[{"[", "1", "]"}], "]"}]}], ";", "\[IndentingNewLine]",
|
|
RowBox[{"exponent", "=",
|
|
RowBox[{"scientificA", "[",
|
|
RowBox[{"[", "2", "]"}], "]"}]}], ";", "\[IndentingNewLine]",
|
|
RowBox[{"m", "=", "exponent"}], ";", "\[IndentingNewLine]",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{
|
|
"(*", "\:627e\:5230\:6ee1\:8db3\:4e0d\:7b49\:5f0f\:7684\:6700\:5927\
|
|
\:7684n", "*)"}], "\[IndentingNewLine]",
|
|
RowBox[{"n", "=",
|
|
RowBox[{"Max", "[",
|
|
RowBox[{"0", ",",
|
|
RowBox[{"Floor", "[",
|
|
RowBox[{"m", "-",
|
|
RowBox[{"Log10", "[",
|
|
RowBox[{"2", " ",
|
|
RowBox[{"Abs", "[",
|
|
RowBox[{"a", "-", "b"}], "]"}]}], "]"}]}], "]"}]}], "]"}]}],
|
|
";", "\[IndentingNewLine]", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
"(*", "\:8fd4\:56de\:6709\:6548\:6570\:5b57\:4f4d\:6570", "*)"}],
|
|
"\[IndentingNewLine]", "n"}]}], "\[IndentingNewLine]", "]"}]}],
|
|
";"}]}]], "Input",
|
|
CellChangeTimes->{{3.9251073293545046`*^9, 3.9251073526776114`*^9}, {
|
|
3.925107410625913*^9, 3.9251074145765753`*^9}, 3.92510744585256*^9, {
|
|
3.9251075602171364`*^9, 3.9251075689329004`*^9}, {3.9251076054553037`*^9,
|
|
3.9251076310428567`*^9}, {3.925107679326515*^9, 3.925107685315797*^9}, {
|
|
3.9251077959428487`*^9,
|
|
3.925107810713959*^9}},ExpressionUUID->"8c29b7ad-df78-4904-86b4-\
|
|
d30b6a44c46b"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"GaussN", "[", "n_", "]"}], ":=",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"n", "^", "3"}], "+",
|
|
RowBox[{"3",
|
|
RowBox[{"n", "^", "2"}]}], "-", "n"}], ")"}], "/", "3"}]}],
|
|
";"}]], "Input",
|
|
CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
|
|
3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9,
|
|
3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
|
|
3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9,
|
|
3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
|
|
3.9245640966207247`*^9, 3.9245641010009136`*^9}, 3.925107325009946*^9},
|
|
CellLabel->"In[1]:=",ExpressionUUID->"d383ac27-2b85-4a1c-8f34-a880413b2a3f"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"PrincipalMinors", "[", "M_", "]"}], ":=",
|
|
RowBox[{"Module", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"n", "=",
|
|
RowBox[{"Length", "[", "M", "]"}]}], ",", "minors"}], "}"}], ",",
|
|
RowBox[{
|
|
RowBox[{"minors", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{"Det", "[",
|
|
RowBox[{"M", "[",
|
|
RowBox[{"[",
|
|
RowBox[{
|
|
RowBox[{"1", ";;", "k"}], ",",
|
|
RowBox[{"1", ";;", "k"}]}], "]"}], "]"}], "]"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"k", ",", "1", ",", "n"}], "}"}]}], "]"}]}], ";",
|
|
"minors"}]}], "]"}]}], ";"}]], "Input",
|
|
CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
|
|
3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9,
|
|
3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
|
|
3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9,
|
|
3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
|
|
3.9245640966207247`*^9, 3.924564112173971*^9}},
|
|
CellLabel->"In[2]:=",ExpressionUUID->"d5cfeb24-8247-4e06-ac4e-99584add822b"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"LUDe", "[", "matrix_", "]"}], ":=",
|
|
RowBox[{"Module", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"lu", ",", "perm", ",", "l", ",", "u", ",", "n"}], "}"}], ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"lu", ",", "perm"}], "}"}], "=",
|
|
RowBox[{
|
|
RowBox[{"LUDecomposition", "[", "matrix", "]"}], "[",
|
|
RowBox[{"[",
|
|
RowBox[{"1", ";;", "2"}], "]"}], "]"}]}], ";",
|
|
RowBox[{
|
|
"(*", "\:83b7\:53d6LU\:5206\:89e3\:7684LU\:77e9\:9635\:548c\:8f74\:5411\
|
|
\:91cf", "*)"}], "\[IndentingNewLine]",
|
|
RowBox[{"n", "=",
|
|
RowBox[{"Length", "[", "lu", "]"}]}], ";",
|
|
RowBox[{"(*", "\:77e9\:9635\:7684\:5927\:5c0f", "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"l", "=",
|
|
RowBox[{
|
|
RowBox[{"LowerTriangularize", "[",
|
|
RowBox[{"lu", ",",
|
|
RowBox[{"-", "1"}]}], "]"}], "+",
|
|
RowBox[{"IdentityMatrix", "[", "n", "]"}]}]}], ";",
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
"\:83b7\:53d6L\:77e9\:9635", "\:ff1a",
|
|
"LU\:77e9\:9635\:7684\:4e0b\:4e09\:89d2\:90e8\:5206\:52a0\:4e0a\:5355\
|
|
\:4f4d\:77e9\:9635\:7684\:5bf9\:89d2\:7ebf"}], "*)"}], "\[IndentingNewLine]",
|
|
RowBox[{"u", "=",
|
|
RowBox[{"UpperTriangularize", "[", "lu", "]"}]}], ";",
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
"\:83b7\:53d6U\:77e9\:9635", "\:ff1a",
|
|
"LU\:77e9\:9635\:7684\:4e0a\:4e09\:89d2\:90e8\:5206"}], "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"Map", "[",
|
|
RowBox[{"MatrixForm", ",",
|
|
RowBox[{"{",
|
|
RowBox[{"l", ",", "u"}], "}"}]}], "]"}]}]}],
|
|
RowBox[{
|
|
"(*", "\:8fd4\:56de\:5305\:542bL\:548cU\:7684\:5217\:8868", "*)"}],
|
|
"]"}]}], ";"}]], "Input",
|
|
CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
|
|
3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9,
|
|
3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
|
|
3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9,
|
|
3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
|
|
3.9245640966207247`*^9, 3.9245641245795727`*^9}},
|
|
CellLabel->"In[3]:=",ExpressionUUID->"09cbb4b3-a43f-4430-aff6-bc0592dba7aa"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"ChDe", "[", "A_", "]"}], ":=",
|
|
RowBox[{
|
|
RowBox[{"Transpose", "[",
|
|
RowBox[{"CholeskyDecomposition", "[", "A", "]"}], "]"}], "//",
|
|
"MatrixForm"}]}], ";"}]], "Input",
|
|
CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
|
|
3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9,
|
|
3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
|
|
3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9,
|
|
3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
|
|
3.9245640966207247`*^9, 3.9245641294390497`*^9}},
|
|
CellLabel->"In[4]:=",ExpressionUUID->"55d18b28-5e77-464d-841c-e533675bb9e2"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"PrincipalMinors", "[", "M_", "]"}], ":=",
|
|
RowBox[{"Module", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"n", "=",
|
|
RowBox[{"Length", "[", "M", "]"}]}], ",", "minors"}], "}"}], ",",
|
|
RowBox[{
|
|
RowBox[{"minors", "=",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{"Det", "[",
|
|
RowBox[{"M", "[",
|
|
RowBox[{"[",
|
|
RowBox[{
|
|
RowBox[{"1", ";;", "k"}], ",",
|
|
RowBox[{"1", ";;", "k"}]}], "]"}], "]"}], "]"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"k", ",", "1", ",", "n"}], "}"}]}], "]"}]}], ";",
|
|
"minors"}]}], "]"}]}], ";"}],
|
|
RowBox[{
|
|
"(*", "\:8fd4\:56deM\:7684\:5404\:9636\:987a\:5e8f\:4e3b\:5b50\:5f0f",
|
|
"*)"}]}]], "Input",
|
|
CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
|
|
3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9,
|
|
3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
|
|
3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9,
|
|
3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
|
|
3.9245640966207247`*^9, 3.924564135113705*^9}},
|
|
CellLabel->"In[5]:=",ExpressionUUID->"cad63f8b-e1a7-4ea9-8cbc-d8ef3fddddb2"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
"(*", "\:9002\:7528\:4e8e\:4e09\:5bf9\:89d2\:77e9\:9635\:7684Crout\:5206\
|
|
\:89e3", "*)"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"CroutDe", "[", "matrix_", "]"}], ":=",
|
|
RowBox[{"Module", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"n", "=",
|
|
RowBox[{"Length", "[", "matrix", "]"}]}], ",", "l", ",", "u"}],
|
|
"}"}], ",",
|
|
RowBox[{
|
|
RowBox[{"l", "=",
|
|
RowBox[{"LowerTriangularize", "[", "matrix", "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"u", "=",
|
|
RowBox[{"UpperTriangularize", "[",
|
|
RowBox[{"IdentityMatrix", "[", "n", "]"}], "]"}]}], ";",
|
|
RowBox[{"(*", "\:5355\:4f4d\:4e0a\:4e09\:89d2\:77e9\:9635", "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
"\:586b\:5145", " ", "L", " ", "\:548c", " ", "U", " ",
|
|
"\:7684\:5143\:7d20"}], "*)"}],
|
|
RowBox[{"Do", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"l", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"i", ",", "i"}], "]"}], "]"}], "=",
|
|
RowBox[{
|
|
RowBox[{"matrix", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"i", ",", "i"}], "]"}], "]"}], "-",
|
|
RowBox[{"Sum", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"l", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"i", ",", "k"}], "]"}], "]"}],
|
|
RowBox[{"u", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"k", ",", "i"}], "]"}], "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"k", ",", "1", ",",
|
|
RowBox[{"i", "-", "1"}]}], "}"}]}], "]"}]}]}], ",",
|
|
RowBox[{"If", "[",
|
|
RowBox[{
|
|
RowBox[{"i", "<", "n"}], ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"u", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"i", ",",
|
|
RowBox[{"i", "+", "1"}]}], "]"}], "]"}], "=",
|
|
RowBox[{
|
|
RowBox[{"matrix", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"i", ",",
|
|
RowBox[{"i", "+", "1"}]}], "]"}], "]"}], "/",
|
|
RowBox[{"l", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"i", ",", "i"}], "]"}], "]"}]}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"l", "[",
|
|
RowBox[{"[",
|
|
RowBox[{
|
|
RowBox[{"i", "+", "1"}], ",", "i"}], "]"}], "]"}], "=",
|
|
RowBox[{
|
|
RowBox[{"matrix", "[",
|
|
RowBox[{"[",
|
|
RowBox[{
|
|
RowBox[{"i", "+", "1"}], ",", "i"}], "]"}], "]"}], "-",
|
|
RowBox[{"Sum", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"l", "[",
|
|
RowBox[{"[",
|
|
RowBox[{
|
|
RowBox[{"i", "+", "1"}], ",", "k"}], "]"}], "]"}], " ",
|
|
RowBox[{"u", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"k", ",", "i"}], "]"}], "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"k", ",", "1", ",",
|
|
RowBox[{"i", "-", "1"}]}], "}"}]}], "]"}]}]}]}]}],
|
|
"]"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"MatrixForm", "/@",
|
|
RowBox[{"{",
|
|
RowBox[{"l", ",", "u"}], "}"}]}]}]}], "]"}]}], ";"}]}]], "Input",
|
|
CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
|
|
3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9,
|
|
3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
|
|
3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9,
|
|
3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
|
|
3.9245640966207247`*^9, 3.9245641505664206`*^9}},
|
|
CellLabel->"In[6]:=",ExpressionUUID->"05acbbc3-479c-4e50-a4dc-aaf84550f6e8"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
"(*", "\:9002\:7528\:4e8e\:4e00\:822c\:77e9\:9635\:7684Crout\:5206\:89e3",
|
|
"*)"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"CroutDeCo", "[", "matrix_", "]"}], ":=",
|
|
RowBox[{"Module", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"n", "=",
|
|
RowBox[{"Length", "[", "matrix", "]"}]}], ",", "l", ",", "u", ",",
|
|
"sum"}], "}"}], ",",
|
|
RowBox[{
|
|
RowBox[{"l", "=",
|
|
RowBox[{"ConstantArray", "[",
|
|
RowBox[{"0", ",",
|
|
RowBox[{"{",
|
|
RowBox[{"n", ",", "n"}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"u", "=",
|
|
RowBox[{"IdentityMatrix", "[", "n", "]"}]}], ";",
|
|
RowBox[{"(*", "\:5355\:4f4d\:4e0a\:4e09\:89d2\:77e9\:9635", "*)"}],
|
|
RowBox[{"Do", "[",
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
"\:8ba1\:7b97", " ", "l", " ", "\:7684\:7b2c", " ", "i", " ",
|
|
"\:884c\:548c", " ", "u", " ", "\:7684\:7b2c", " ", "i", " ",
|
|
"\:5217"}], "*)"}],
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"Do", "[",
|
|
RowBox[{"(*",
|
|
RowBox[{"\:8ba1\:7b97", " ", "l", " ", "\:7684\:5143\:7d20"}],
|
|
"*)"}],
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"sum", "=",
|
|
RowBox[{"Sum", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"l", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"i", ",", "k"}], "]"}], "]"}], " ",
|
|
RowBox[{"u", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"k", ",", "j"}], "]"}], "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"k", ",", "1", ",",
|
|
RowBox[{
|
|
RowBox[{"Min", "[",
|
|
RowBox[{"i", ",", "j"}], "]"}], "-", "1"}]}], "}"}]}],
|
|
"]"}]}], ";", "\[IndentingNewLine]",
|
|
RowBox[{"If", "[",
|
|
RowBox[{
|
|
RowBox[{"i", ">=", "j"}], ",",
|
|
RowBox[{
|
|
RowBox[{"l", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"i", ",", "j"}], "]"}], "]"}], "=",
|
|
RowBox[{
|
|
RowBox[{"matrix", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"i", ",", "j"}], "]"}], "]"}], "-", "sum"}]}]}],
|
|
"]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"j", ",", "1", ",", "n"}], "}"}]}], "]"}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"Do", "[",
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
RowBox[{"\:8ba1\:7b97", " ", "u", " ", "\:7684\:5143\:7d20"}],
|
|
"\:ff0c",
|
|
"\:53ea\:8ba1\:7b97\:975e\:5bf9\:89d2\:7ebf\:5143\:7d20",
|
|
"\:ff0c", "\:5bf9\:89d2\:7ebf\:5143\:7d20\:5df2\:8bbe\:4e3a1"}],
|
|
"*)"}],
|
|
RowBox[{
|
|
RowBox[{"If", "[",
|
|
RowBox[{
|
|
RowBox[{"j", ">", "i"}], ",",
|
|
RowBox[{
|
|
RowBox[{"sum", "=",
|
|
RowBox[{"Sum", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"l", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"i", ",", "k"}], "]"}], "]"}], " ",
|
|
RowBox[{"u", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"k", ",", "j"}], "]"}], "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"k", ",", "1", ",",
|
|
RowBox[{"i", "-", "1"}]}], "}"}]}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"u", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"i", ",", "j"}], "]"}], "]"}], "=",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"matrix", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"i", ",", "j"}], "]"}], "]"}], "-", "sum"}],
|
|
")"}], "/",
|
|
RowBox[{"l", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"i", ",", "i"}], "]"}], "]"}]}]}]}]}], "]"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"j", ",", "1", ",", "n"}], "}"}]}], "]"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"MatrixForm", "/@",
|
|
RowBox[{"{",
|
|
RowBox[{"l", ",", "u"}], "}"}]}]}]}], "]"}]}], ";"}]}]], "Input",
|
|
CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
|
|
3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9,
|
|
3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
|
|
3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9,
|
|
3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
|
|
3.9245640966207247`*^9, 3.92456415596951*^9}},
|
|
CellLabel->"In[7]:=",ExpressionUUID->"cf7097dc-67d2-4f27-a92e-0d3cdf2673ba"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"PBJ", "[", "A_", "]"}], ":=",
|
|
RowBox[{"Max", "[",
|
|
RowBox[{"Abs", "[",
|
|
RowBox[{"Eigenvalues", "[", "A", "]"}], "]"}], "]"}]}],
|
|
RowBox[{"(*", "\:8c31\:534a\:5f84", "*)"}], ";"}]], "Input",
|
|
CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
|
|
3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9,
|
|
3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
|
|
3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9,
|
|
3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
|
|
3.9245640966207247`*^9, 3.924564160023576*^9}},
|
|
CellLabel->"In[8]:=",ExpressionUUID->"61610133-11de-4935-a818-8eab399e0a08"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"Cond", "[",
|
|
RowBox[{"A_", ",", "p_"}], "]"}], ":=",
|
|
RowBox[{"Module", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"normA", ",", "normInvA"}], "}"}], ",",
|
|
RowBox[{
|
|
RowBox[{"normA", "=",
|
|
RowBox[{"Norm", "[",
|
|
RowBox[{"A", ",", "p"}], "]"}]}], ";",
|
|
RowBox[{"(*", "\:8ba1\:7b97\:77e9\:9635A\:7684p\:8303\:6570", "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"normInvA", "=",
|
|
RowBox[{"Norm", "[",
|
|
RowBox[{
|
|
RowBox[{"Inverse", "[", "A", "]"}], ",", "p"}], "]"}]}], ";",
|
|
RowBox[{
|
|
"(*", "\:8ba1\:7b97\:77e9\:9635A\:9006\:7684p\:8303\:6570", "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"normA", "*", "normInvA"}]}]}], " ",
|
|
RowBox[{"(*", "\:8fd4\:56de\:6761\:4ef6\:6570", "*)"}], "]"}]}],
|
|
";"}]], "Input",
|
|
CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
|
|
3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9,
|
|
3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
|
|
3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9,
|
|
3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
|
|
3.9245640966207247`*^9, 3.924564163686198*^9}},
|
|
CellLabel->"In[9]:=",ExpressionUUID->"8330e8f6-05cf-4d38-982e-97240a3d449f"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"Jacobi", "[", "A_", "]"}], ":=",
|
|
RowBox[{"Module", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"DD", ",", "L", ",", "U", ",", "n"}], "}"}], ",",
|
|
RowBox[{
|
|
RowBox[{"n", "=",
|
|
RowBox[{"Length", "[", "A", "]"}]}], ";",
|
|
RowBox[{"(*", "\:83b7\:53d6\:77e9\:9635\:7684\:5927\:5c0f", "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"DD", "=",
|
|
RowBox[{"DiagonalMatrix", "[",
|
|
RowBox[{"Diagonal", "[", "A", "]"}], "]"}]}], ";",
|
|
RowBox[{"(*",
|
|
RowBox[{"\:6784\:9020\:5bf9\:89d2\:77e9\:9635", " ", "DD"}], "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"L", "=",
|
|
RowBox[{"-",
|
|
RowBox[{"LowerTriangularize", "[",
|
|
RowBox[{"A", ",",
|
|
RowBox[{"-", "1"}]}], "]"}]}]}], ";",
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
"\:83b7\:53d6\:4e0b\:4e09\:89d2\:90e8\:5206", "\:ff0c",
|
|
"\:5e76\:53d6\:8d1f\:6570", "\:ff0c",
|
|
"\:5bf9\:89d2\:7ebf\:53ca\:4ee5\:4e0a\:5143\:7d20\:4e3a0"}], "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"U", "=",
|
|
RowBox[{"-",
|
|
RowBox[{"UpperTriangularize", "[",
|
|
RowBox[{"A", ",", "1"}], "]"}]}]}], ";",
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
"\:83b7\:53d6\:4e0a\:4e09\:89d2\:90e8\:5206", "\:ff0c",
|
|
"\:5e76\:53d6\:8d1f\:6570", "\:ff0c",
|
|
"\:5bf9\:89d2\:7ebf\:53ca\:4ee5\:4e0b\:5143\:7d20\:4e3a0"}], "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"Inverse", "[", "DD", "]"}], ".",
|
|
RowBox[{"(",
|
|
RowBox[{"L", "+", "U"}], ")"}]}], "//", "MatrixForm"}]}]}], " ",
|
|
RowBox[{
|
|
"(*", "\:8ba1\:7b97\:8fed\:4ee3\:77e9\:9635\:5e76\:8fd4\:56de", "*)"}],
|
|
"]"}]}], ";"}]], "Input",
|
|
CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
|
|
3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9,
|
|
3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
|
|
3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9,
|
|
3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
|
|
3.9245640966207247`*^9, 3.9245641683775*^9}},
|
|
CellLabel->"In[10]:=",ExpressionUUID->"31fd9b80-da51-4399-8d6d-7a7a95dedde9"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"GS", "[", "A_", "]"}], ":=",
|
|
RowBox[{"Module", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"DD", ",", "L", ",", "U", ",", "n"}], "}"}], ",",
|
|
RowBox[{
|
|
RowBox[{"n", "=",
|
|
RowBox[{"Length", "[", "A", "]"}]}], ";",
|
|
RowBox[{"(*", "\:83b7\:53d6\:77e9\:9635\:7684\:5927\:5c0f", "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"DD", "=",
|
|
RowBox[{"DiagonalMatrix", "[",
|
|
RowBox[{"Diagonal", "[", "A", "]"}], "]"}]}], ";",
|
|
RowBox[{"(*",
|
|
RowBox[{"\:6784\:9020\:5bf9\:89d2\:77e9\:9635", " ", "DD"}], "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"L", "=",
|
|
RowBox[{"-",
|
|
RowBox[{"LowerTriangularize", "[",
|
|
RowBox[{"A", ",",
|
|
RowBox[{"-", "1"}]}], "]"}]}]}], ";",
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
"\:83b7\:53d6\:4e0b\:4e09\:89d2\:90e8\:5206", "\:ff0c",
|
|
"\:5e76\:53d6\:8d1f\:6570", "\:ff0c",
|
|
"\:5bf9\:89d2\:7ebf\:53ca\:4ee5\:4e0a\:5143\:7d20\:4e3a0"}], "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"U", "=",
|
|
RowBox[{"-",
|
|
RowBox[{"UpperTriangularize", "[",
|
|
RowBox[{"A", ",", "1"}], "]"}]}]}], ";",
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
"\:83b7\:53d6\:4e0a\:4e09\:89d2\:90e8\:5206", "\:ff0c",
|
|
"\:5e76\:53d6\:8d1f\:6570", "\:ff0c",
|
|
"\:5bf9\:89d2\:7ebf\:53ca\:4ee5\:4e0b\:5143\:7d20\:4e3a0"}], "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"Inverse", "[",
|
|
RowBox[{"DD", "-", "L"}], "]"}], ".", "U"}], "//",
|
|
"MatrixForm"}]}]}],
|
|
RowBox[{
|
|
"(*", "\:8ba1\:7b97\:8fed\:4ee3\:77e9\:9635\:5e76\:8fd4\:56de", "*)"}],
|
|
"]"}]}], ";"}]], "Input",
|
|
CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
|
|
3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9,
|
|
3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
|
|
3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9,
|
|
3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
|
|
3.9245640966207247`*^9, 3.924564175395494*^9}},
|
|
CellLabel->"In[11]:=",ExpressionUUID->"9427686b-95f7-4bb3-8dd3-6608b56a43f5"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"IsStrictlyDiagonallyDominant", "[", "matrix_", "]"}], ":=",
|
|
RowBox[{"Module", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"n", "=",
|
|
RowBox[{"Length", "[", "matrix", "]"}]}], ",", "rowSum", ",",
|
|
"diagElem"}], "}"}], ",",
|
|
RowBox[{"And", "@@",
|
|
RowBox[{"Table", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"diagElem", "=",
|
|
RowBox[{"Abs", "[",
|
|
RowBox[{"matrix", "[",
|
|
RowBox[{"[",
|
|
RowBox[{"i", ",", "i"}], "]"}], "]"}], "]"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"rowSum", "=",
|
|
RowBox[{
|
|
RowBox[{"Total", "[",
|
|
RowBox[{"Abs", "[",
|
|
RowBox[{"matrix", "[",
|
|
RowBox[{"[", "i", "]"}], "]"}], "]"}], "]"}], "-",
|
|
"diagElem"}]}], ";", "\[IndentingNewLine]",
|
|
RowBox[{"diagElem", ">", "rowSum"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}]}]}], "]"}]}],
|
|
";"}]], "Input",
|
|
CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
|
|
3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9,
|
|
3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
|
|
3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9,
|
|
3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
|
|
3.9245640966207247`*^9, 3.924564178263303*^9}},
|
|
CellLabel->"In[12]:=",ExpressionUUID->"80e75e01-3f0c-4715-9e1d-a52d41219a4a"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"SOR", "[",
|
|
RowBox[{"M_", ",", "w_"}], "]"}], ":=",
|
|
RowBox[{"Module", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"DD", ",", "L", ",", "U", ",", "n"}], "}"}], ",",
|
|
RowBox[{
|
|
RowBox[{"n", "=",
|
|
RowBox[{"Length", "[", "M", "]"}]}], ";",
|
|
RowBox[{"(*", "\:83b7\:53d6\:77e9\:9635\:7684\:5927\:5c0f", "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"DD", "=",
|
|
RowBox[{"DiagonalMatrix", "[",
|
|
RowBox[{"Diagonal", "[", "M", "]"}], "]"}]}], ";",
|
|
RowBox[{"(*",
|
|
RowBox[{"\:6784\:9020\:5bf9\:89d2\:77e9\:9635", " ", "DD"}], "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"L", "=",
|
|
RowBox[{"-",
|
|
RowBox[{"LowerTriangularize", "[",
|
|
RowBox[{"M", ",",
|
|
RowBox[{"-", "1"}]}], "]"}]}]}], ";",
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
"\:83b7\:53d6\:4e0b\:4e09\:89d2\:90e8\:5206", "\:ff0c",
|
|
"\:5e76\:53d6\:8d1f\:6570", "\:ff0c",
|
|
"\:5bf9\:89d2\:7ebf\:53ca\:4ee5\:4e0a\:5143\:7d20\:4e3a0"}], "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"U", "=",
|
|
RowBox[{"-",
|
|
RowBox[{"UpperTriangularize", "[",
|
|
RowBox[{"M", ",", "1"}], "]"}]}]}], ";",
|
|
RowBox[{"(*",
|
|
RowBox[{
|
|
"\:83b7\:53d6\:4e0a\:4e09\:89d2\:90e8\:5206", "\:ff0c",
|
|
"\:5e76\:53d6\:8d1f\:6570", "\:ff0c",
|
|
"\:5bf9\:89d2\:7ebf\:53ca\:4ee5\:4e0b\:5143\:7d20\:4e3a0"}], "*)"}],
|
|
"\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"Inverse", "[",
|
|
RowBox[{"DD", "-",
|
|
RowBox[{"w", " ", "L"}]}], "]"}], ".",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"1", "-", "w"}], ")"}], " ", "DD"}], "+",
|
|
RowBox[{"w", " ", "U"}]}], ")"}]}], "//", "MatrixForm"}]}]}], " ",
|
|
RowBox[{
|
|
"(*", "\:8ba1\:7b97SOR\:8fed\:4ee3\:77e9\:9635\:5e76\:8fd4\:56de", "*)"}],
|
|
"]"}]}], ";"}]], "Input",
|
|
CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
|
|
3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9,
|
|
3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
|
|
3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9,
|
|
3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
|
|
3.9245640966207247`*^9, 3.9245641818996167`*^9}},
|
|
CellLabel->"In[13]:=",ExpressionUUID->"cae67269-c439-4e79-a488-ef1787d38305"],
|
|
|
|
Cell[BoxData["\[IndentingNewLine]"], "Input",
|
|
CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
|
|
3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9,
|
|
3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
|
|
3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9,
|
|
3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
|
|
3.9245640966207247`*^9, 3.9245641818996167`*^9}},
|
|
CellLabel->"In[14]:=",ExpressionUUID->"35a98b0b-7f78-42ba-bedd-e7f6867bf3df"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell["\:51fd\:6570\:6587\:6863", "Subsection",
|
|
CellChangeTimes->{
|
|
3.924555241757887*^9},ExpressionUUID->"8c053a0e-ae75-4d2b-a257-\
|
|
96c36d9e4df0"],
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{"\:6c42\:7528\:8fd1\:4f3c\:503ca\:6765\:8fd1\:4f3c\:7cbe\:786e\:503c\
|
|
b\:7684\:6709\:6548\:6570\:5b57\:4f4d\:6570", "\:ff1a",
|
|
StyleBox[
|
|
RowBox[{"EffectiveDigits", "[",
|
|
RowBox[{"a", ",", "b"}], "]"}],
|
|
FontWeight->"Bold"]}], "\[IndentingNewLine]",
|
|
RowBox[{"\:7edf\:8ba1\:987a\:5e8fGauss\:6d88\:53bb\:6cd5\:7684\:4e58\:9664\
|
|
\:6cd5\:8ba1\:7b97\:6b21\:6570", "\:ff1a",
|
|
StyleBox[
|
|
RowBox[{"GaussN", "[", "n", "]"}],
|
|
FontWeight->"Bold"], "\:ff0c",
|
|
"n\:4e3a\:7ebf\:6027\:65b9\:7a0b\:7ec4\:7684\:672a\:77e5\:6570\:4e2a\:6570"}\
|
|
], "\n",
|
|
RowBox[{"LU\:5206\:89e3", "\:ff1a",
|
|
StyleBox[
|
|
RowBox[{"LUDe", "[", "M", "]"}],
|
|
FontWeight->"Bold"], "\:ff0c",
|
|
RowBox[{"\:8fd4\:56de",
|
|
RowBox[{"{",
|
|
RowBox[{"L", ",", "U"}], "}"}]}], "\:ff0c",
|
|
"L\:4e3a\:5355\:4f4d\:4e0b\:4e09\:89d2\:77e9\:9635", "\:ff0c",
|
|
"U\:4e3a\:4e0a\:4e09\:89d2\:77e9\:9635"}], "\n",
|
|
RowBox[{"Cholesky\:5206\:89e3", "\:ff1a",
|
|
StyleBox[
|
|
RowBox[{"ChDe", "[", "M", "]"}],
|
|
FontWeight->"Bold"], "\:ff0c", "\:63a5\:6536\:4e00\:4e2a\:77e9\:9635M",
|
|
"\:ff0c",
|
|
RowBox[{
|
|
"\:628aM\:5206\:89e3\:4e3a\:4e00\:4e2a\:4e0b\:4e09\:89d2\:77e9\:9635G\:548c\
|
|
\:5176\:8f6c\:7f6e",
|
|
FormBox[
|
|
SuperscriptBox["G", "T"],
|
|
TraditionalForm], "\:7684\:4e58\:79ef"}], "\:ff0c",
|
|
RowBox[{"\:5373",
|
|
FormBox[
|
|
RowBox[{"M", "=",
|
|
SuperscriptBox["GG", "T"]}],
|
|
TraditionalForm]}], "\:ff0c", "\:8fd4\:56deG"}], "\n",
|
|
RowBox[{"\:5224\:5b9a\:662f\:5426\:4e3a\:6b63\:5b9a\:77e9\:9635", "\:ff1a",
|
|
StyleBox[
|
|
RowBox[{"PositiveDefiniteMatrixQ", "[", "A", "]"}],
|
|
FontWeight->"Bold"]}], "\n",
|
|
RowBox[{"\:6c42\:5404\:9636\:987a\:5e8f\:4e3b\:5b50\:5f0f", "\:ff1a",
|
|
StyleBox[
|
|
RowBox[{"PrincipalMinors", "[", "A", "]"}],
|
|
FontWeight->"Bold"]}], "\n",
|
|
RowBox[{
|
|
RowBox[{"\:4e09\:5bf9\:89d2\:77e9\:9635\:7684Crout\:5206\:89e3",
|
|
RowBox[{"\:ff08",
|
|
RowBox[{
|
|
"\:6548\:7387\:66f4\:5feb", "\:ff0c",
|
|
"\:53ea\:80fd\:7528\:4e8e\:4e09\:5bf9\:89d2\:77e9\:9635"}], "\:ff09"}]}],
|
|
"\:ff1a",
|
|
StyleBox[
|
|
RowBox[{"CroutDe", "[", "A", "]"}],
|
|
FontWeight->"Bold"], "\:ff0c",
|
|
"\:8fd4\:56de\:4e00\:4e2a\:4e0b\:4e09\:89d2\:77e9\:9635\:548c\:4e00\:4e2a\
|
|
\:5355\:4f4d\:4e0a\:4e09\:89d2\:77e9\:9635"}], "\[IndentingNewLine]",
|
|
RowBox[{"\:666e\:901a\:77e9\:9635\:7684Crout\:5206\:89e3", "\:ff1a",
|
|
StyleBox[
|
|
RowBox[{"CroutDeCo", "[", "A", "]"}],
|
|
FontWeight->"Bold"], "\:ff0c",
|
|
"\:8fd4\:56de\:4e00\:4e2a\:4e0b\:4e09\:89d2\:77e9\:9635\:548c\:4e00\:4e2a\
|
|
\:5355\:4f4d\:4e0a\:4e09\:89d2\:77e9\:9635"}], "\n",
|
|
RowBox[{"\:5411\:91cf\:6216\:77e9\:9635\:7684\:8303\:6570", "\:ff1a",
|
|
StyleBox[
|
|
RowBox[{"Norm", "[",
|
|
RowBox[{"A", ",", "p"}], "]"}],
|
|
FontWeight->"Bold"], "\:ff0c", "p\:53ef\:4ee5\:4e3a1", ",", "2", ",",
|
|
"Infinity", ",",
|
|
RowBox[{"\"\<Frobenius\>\"",
|
|
RowBox[{"\:ff08",
|
|
RowBox[{"F", "-", "\:8303\:6570"}], "\:ff09"}]}]}], "\n",
|
|
RowBox[{"\:6c42\:77e9\:9635\:7684\:8c31\:534a\:5f84", "\:ff1a",
|
|
StyleBox[
|
|
RowBox[{"PBJ", "[", "A", "]"}],
|
|
FontWeight->"Bold"]}], "\n",
|
|
RowBox[{"\:6c42\:77e9\:9635\:7684p\:6761\:4ef6\:6570", "\:ff1a",
|
|
StyleBox[
|
|
RowBox[{"Cond", "[",
|
|
RowBox[{"A", ",", "p"}], "]"}],
|
|
FontWeight->"Bold"]}], "\n",
|
|
RowBox[{"\:6c42Jacobi\:8fed\:4ee3\:6cd5\:7684\:8fed\:4ee3\:77e9\:9635",
|
|
"\:ff1a",
|
|
StyleBox[
|
|
RowBox[{"Jacobi", "[", "A", "]"}],
|
|
FontWeight->"Bold"]}], "\n",
|
|
RowBox[{"\:6c42GS\:8fed\:4ee3\:6cd5\:7684\:8fed\:4ee3\:77e9\:9635", "\:ff1a",
|
|
StyleBox[
|
|
RowBox[{"GS", "[", "A", "]"}],
|
|
FontWeight->"Bold"]}], "\n",
|
|
RowBox[{"\:5224\:5b9a\:77e9\:9635\:662f\:5426\:4e25\:683c\:5bf9\:89d2\:5360\
|
|
\:4f18", "\:ff1a",
|
|
StyleBox[
|
|
RowBox[{"IsStrictlyDiagonallyDominant", "[", "A", "]"}],
|
|
FontWeight->"Bold"]}], "\n",
|
|
RowBox[{"\:6c42SOR\:65b9\:6cd5\:7684\:8fed\:4ee3\:77e9\:9635", "\:ff1a",
|
|
StyleBox[
|
|
RowBox[{"SOR", "[",
|
|
RowBox[{"A", ",", "w"}], "]"}],
|
|
FontWeight->"Bold"], "\:ff0c",
|
|
"w\:4e3a\:677e\:5f1b\:56e0\:5b50"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"QR\:5206\:89e3", "\:ff1a",
|
|
StyleBox[
|
|
RowBox[{"QRDecomposition", "[", "M", "]"}],
|
|
FontWeight->"Bold"], "\:ff0c",
|
|
"\:8fd4\:56de\:4e00\:4e2a\:6b63\:4ea4\:77e9\:9635\:548c\:4e00\:4e2a\:4e0a\
|
|
\:4e09\:89d2\:77e9\:9635"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
StyleBox[
|
|
RowBox[{"\:8bf7\:5148",
|
|
StyleBox["\:8ba1\:7b97\:7b14\:8bb0\:672c",
|
|
FontWeight->"Bold",
|
|
FontColor->RGBColor[1., 0., 0.]]}]], "\:ff0c",
|
|
"\:7136\:540e\:5728\:4e0b\:9762\:7684\:4ee3\:7801\:533a\:57df\:4f7f\:7528\
|
|
\:4e0a\:8ff0\:51fd\:6570", "\:ff1a"}]}], "Text",
|
|
CellChangeTimes->{{3.9245552533653126`*^9, 3.924555320850746*^9}, {
|
|
3.924564662669675*^9, 3.9245646830186796`*^9}, {3.924564758396234*^9,
|
|
3.924564795234249*^9}, {3.9245665699632225`*^9, 3.9245665984255333`*^9}, {
|
|
3.9250935894417396`*^9, 3.9250936431895814`*^9}, {3.9250937757510953`*^9,
|
|
3.9250937803540096`*^9}, {3.925107746562063*^9, 3.9251077733268404`*^9},
|
|
3.9251078250537634`*^9},ExpressionUUID->"b16b1ea4-cce2-4a2b-92e1-\
|
|
4cba1822d789"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"MatrixForm", "/@",
|
|
RowBox[{"QRDecomposition", "[",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"1", ",", "3", ",", "2"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"3", ",", "7", ",", "5"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"4", ",", "3", ",", "6"}], "}"}]}], "}"}], "]"}]}]], "Input",
|
|
CellChangeTimes->{{3.9250936030389614`*^9, 3.9250936139902987`*^9}, {
|
|
3.925093647590356*^9, 3.9250936484560027`*^9}, {3.92509886150305*^9,
|
|
3.925098878633748*^9}, {3.9250993167303553`*^9, 3.92509931843845*^9}, {
|
|
3.9250994233264294`*^9, 3.925099427631544*^9}, {3.9251073673601284`*^9,
|
|
3.925107374212509*^9}, {3.925107691377334*^9, 3.925107738600565*^9},
|
|
3.925107836400502*^9, {3.9251081795700912`*^9, 3.925108203832847*^9}},
|
|
CellLabel->"In[43]:=",ExpressionUUID->"6602253a-4119-44c0-bc64-e5d9454a8813"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
TagBox[
|
|
RowBox[{"(", "\[NoBreak]", GridBox[{
|
|
{
|
|
FractionBox["1",
|
|
SqrtBox["26"]],
|
|
FractionBox["3",
|
|
SqrtBox["26"]],
|
|
RowBox[{"2", " ",
|
|
SqrtBox[
|
|
FractionBox["2", "13"]]}]},
|
|
{
|
|
FractionBox["21",
|
|
SqrtBox["2899"]],
|
|
FractionBox["37",
|
|
SqrtBox["2899"]],
|
|
RowBox[{"-",
|
|
FractionBox["33",
|
|
SqrtBox["2899"]]}]},
|
|
{
|
|
FractionBox["19",
|
|
SqrtBox["446"]],
|
|
RowBox[{"-",
|
|
FractionBox["9",
|
|
SqrtBox["446"]]}],
|
|
SqrtBox[
|
|
FractionBox["2", "223"]]}
|
|
},
|
|
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
|
|
GridBoxSpacings->{"Columns" -> {
|
|
Offset[0.27999999999999997`], {
|
|
Offset[0.7]},
|
|
Offset[0.27999999999999997`]}, "Rows" -> {
|
|
Offset[0.2], {
|
|
Offset[0.4]},
|
|
Offset[0.2]}}], "\[NoBreak]", ")"}],
|
|
Function[BoxForm`e$,
|
|
MatrixForm[BoxForm`e$]]], ",",
|
|
TagBox[
|
|
RowBox[{"(", "\[NoBreak]", GridBox[{
|
|
{
|
|
SqrtBox["26"],
|
|
RowBox[{"18", " ",
|
|
SqrtBox[
|
|
FractionBox["2", "13"]]}],
|
|
FractionBox["41",
|
|
SqrtBox["26"]]},
|
|
{"0",
|
|
SqrtBox[
|
|
FractionBox["223", "13"]],
|
|
FractionBox["29",
|
|
SqrtBox["2899"]]},
|
|
{"0", "0",
|
|
FractionBox["5",
|
|
SqrtBox["446"]]}
|
|
},
|
|
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
|
|
GridBoxSpacings->{"Columns" -> {
|
|
Offset[0.27999999999999997`], {
|
|
Offset[0.7]},
|
|
Offset[0.27999999999999997`]}, "Rows" -> {
|
|
Offset[0.2], {
|
|
Offset[0.4]},
|
|
Offset[0.2]}}], "\[NoBreak]", ")"}],
|
|
Function[BoxForm`e$,
|
|
MatrixForm[BoxForm`e$]]]}], "}"}]], "Output",
|
|
CellChangeTimes->{
|
|
3.925098879682623*^9, 3.9250993188961515`*^9, 3.925099427889161*^9,
|
|
3.9251073756964054`*^9, {3.925107418691803*^9, 3.9251074280846853`*^9},
|
|
3.9251075733334427`*^9, 3.925107634871909*^9, {3.9251076889143767`*^9,
|
|
3.925107738830758*^9}, 3.9251077759632983`*^9, {3.92510781526136*^9,
|
|
3.925107836598177*^9}, 3.9251082041653175`*^9},
|
|
CellLabel->"Out[43]=",ExpressionUUID->"c0bd8b3a-1571-42b1-853e-65e1b315a5d8"]
|
|
}, Open ]]
|
|
}, Open ]]
|
|
},
|
|
WindowSize->{935.25, 556.875},
|
|
WindowMargins->{{0, Automatic}, {Automatic, 0}},
|
|
Magnification:>0.9 Inherited,
|
|
FrontEndVersion->"13.1 for Microsoft Windows (64-bit) (2022\:5e746\:670816\
|
|
\:65e5)",
|
|
StyleDefinitions->"Default.nb",
|
|
ExpressionUUID->"a745022f-71b2-45f5-8169-27c3ff4d45e9"
|
|
]
|
|
(* End of Notebook Content *)
|
|
|
|
(* Internal cache information *)
|
|
(*CellTagsOutline
|
|
CellTagsIndex->{}
|
|
*)
|
|
(*CellTagsIndex
|
|
CellTagsIndex->{}
|
|
*)
|
|
(*NotebookFileOutline
|
|
Notebook[{
|
|
Cell[CellGroupData[{
|
|
Cell[580, 22, 162, 3, 48, "Subsection",ExpressionUUID->"0af2c2ea-193f-4649-a13d-0c6d54e22272"],
|
|
Cell[745, 27, 2390, 57, 315, "Input",ExpressionUUID->"8c29b7ad-df78-4904-86b4-d30b6a44c46b"],
|
|
Cell[3138, 86, 800, 17, 26, "Input",ExpressionUUID->"d383ac27-2b85-4a1c-8f34-a880413b2a3f"],
|
|
Cell[3941, 105, 1214, 29, 39, "Input",ExpressionUUID->"d5cfeb24-8247-4e06-ac4e-99584add822b"],
|
|
Cell[5158, 136, 2279, 54, 170, "Input",ExpressionUUID->"09cbb4b3-a43f-4430-aff6-bc0592dba7aa"],
|
|
Cell[7440, 192, 734, 14, 39, "Input",ExpressionUUID->"55d18b28-5e77-464d-841c-e533675bb9e2"],
|
|
Cell[8177, 208, 1345, 33, 75, "Input",ExpressionUUID->"cad63f8b-e1a7-4ea9-8cbc-d8ef3fddddb2"],
|
|
Cell[9525, 243, 4218, 106, 205, "Input",ExpressionUUID->"05acbbc3-479c-4e50-a4dc-aaf84550f6e8"],
|
|
Cell[13746, 351, 5043, 125, 246, "Input",ExpressionUUID->"cf7097dc-67d2-4f27-a92e-0d3cdf2673ba"],
|
|
Cell[18792, 478, 754, 14, 39, "Input",ExpressionUUID->"61610133-11de-4935-a818-8eab399e0a08"],
|
|
Cell[19549, 494, 1359, 31, 94, "Input",ExpressionUUID->"8330e8f6-05cf-4d38-982e-97240a3d449f"],
|
|
Cell[20911, 527, 2272, 54, 170, "Input",ExpressionUUID->"31fd9b80-da51-4399-8d6d-7a7a95dedde9"],
|
|
Cell[23186, 583, 2244, 54, 170, "Input",ExpressionUUID->"9427686b-95f7-4bb3-8dd3-6608b56a43f5"],
|
|
Cell[25433, 639, 1579, 38, 90, "Input",ExpressionUUID->"80e75e01-3f0c-4715-9e1d-a52d41219a4a"],
|
|
Cell[27015, 679, 2491, 61, 170, "Input",ExpressionUUID->"cae67269-c439-4e79-a488-ef1787d38305"],
|
|
Cell[29509, 742, 551, 7, 43, "Input",ExpressionUUID->"35a98b0b-7f78-42ba-bedd-e7f6867bf3df"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[30097, 754, 148, 3, 48, "Subsection",ExpressionUUID->"8c053a0e-ae75-4d2b-a257-96c36d9e4df0"],
|
|
Cell[30248, 759, 5085, 124, 366, "Text",ExpressionUUID->"b16b1ea4-cce2-4a2b-92e1-4cba1822d789"],
|
|
Cell[CellGroupData[{
|
|
Cell[35358, 887, 870, 17, 39, "Input",ExpressionUUID->"6602253a-4119-44c0-bc64-e5d9454a8813"],
|
|
Cell[36231, 906, 2366, 74, 99, "Output",ExpressionUUID->"c0bd8b3a-1571-42b1-853e-65e1b315a5d8"]
|
|
}, Open ]]
|
|
}, Open ]]
|
|
}
|
|
]
|
|
*)
|
|
|