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array2d.txt
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array2d.txt
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-- FreeFem++ v4.6 (Thu Apr 2 15:47:38 CEST 2020 - git v4.6)
Load: lg_fem lg_mesh lg_mesh3 eigenvalue
1 : // array2d.edp
2 : //
3 : // Discussion:
4 : //
5 : // Demonstrate how 2D matrices can be defined and manipulated.
6 : //
7 : // Location:
8 : //
9 : // http://people.sc.fsu.edu/~jburkardt/freefem++/array2d/array2d.edp
10 : //
11 : // Modified:
12 : //
13 : // 02 July 2015
14 : //
15 : // Author:
16 : //
17 : // John Burkardt
18 : //
19 : load "lapack" Add lapack interface ...
20 :
21 : cout << "\n";
22 : cout << "ARRAY2D:\n";
23 : cout << " Demonstrate how 2D matrices can be defined and
... : manipulated.\n";
24 : //
25 : // Define a 3x3 matrix A
26 : //
27 : // [ 0 1 0 ]
28 : // [ 0 0 1 ]
29 : // [ 1 1 1 ]
30 : //
31 : real[int,int] A(3,3);
32 :
33 : A = 1.0;
34 : A(0,0) = 0.0;
35 : A(0,2) = 0.0;
36 : A(1,0) = 0.0;
37 : A(1,1) = 0.0;
38 : cout << "\n";
39 : cout << " Matrix A = " << A << endl;
40 : //
41 : // Define a 3x3 matrix B:
42 : //
43 : // [ 3 1 1 ]
44 : // [ 1 1 3 ]
45 : // [ 3 3 3 ]
46 : //
47 : real[int,int] B(3,3);
48 : //B = 3.0;
49 : //B(0,1) = 1.0;
50 : //B(0,2) = 1.0;
51 : //B(1,0) = 1.0;
52 : //B(1,0) = 1.0;
53 : B = [ [ 3.0, 1.0, 1.0 ], [ 1.0, 1.0, 3.0 ], [ 3.0, 3.0, 3.0 ] ];
54 : cout << "\n";
55 : cout << " Matrix B = " << B << endl;
56 : //
57 : // Compute A*B.
58 : // This operation requires the "load lapack" statement above.
59 : //
60 : real[int,int] AxB(3,3);
61 : AxB = A * B;
62 : cout << "\n";
63 : cout << " Matrix AxB = product A*B = " << AxB << endl;
64 : //
65 : // Compute A transpose.
66 : //
67 : real[int,int] AT(3,3);
68 : AT = A';
69 : cout << "\n";
70 : cout << " Matrix AT = A' = transpose A' " << AT << endl;
71 : //
72 : // Define a matrix C.
73 :
74 : //
75 : // C = 1 1 0 1
76 : // 1 1 1 1
77 : // 1 0 1 1
78 : //
79 : real[int,int] C(3,4);
80 : C = 1.0;
81 : C(2,1) = 0.0;
82 : C(0,2) = 0.0;
83 : cout << "\n";
84 : cout << " Matrix C = " << C << endl;
85 : cout << " First row of C = C(0,:) = " << C(0,:) << endl;
86 : //
87 : // Define a vector d, and copy row 0 of C into it.
88 : //
89 : real[int] d(4);
90 : d = C(0,:);
91 : cout << "\n";
92 : cout << " d = C(0,:)\n";
93 : cout << " Size of d = d.n = " << d.n << "\n";
94 : cout << " Entries of d = " << d << "\n";
95 : //
96 : // Define vectors e and f, and create a matrix G as their outer product.
97 : //
98 : real[int] e(3);
99 : e=[1,2,3];
100 : real[int] f(4);
101 : f=[4,5,6,7];
102 : real[int,int] G(3,4);
103 : G = e * f';
104 : cout << "\n";
105 : cout << " Vector e = " << e << "\n";
106 : cout << " Vector f = " << f << "\n";
107 : cout << " Matrix G = e * f' = " << G << "\n";
108 : //
109 : // Define vectors h and i, and use them to pre- and post-multiply
110 : // the 3x4 matrix C.
111 : //
112 : real[int] h(3);
113 : h = [ 1.0, 1.0, 1.0 ];
114 : real[int] i(4);
115 : i = [ 1.0, 1.0, 1.0, 1.0 ];
116 : real[int] j(4);
117 : j = h' * C;
118 : real[int] k(3);
119 : k = C * i;
120 : cout << "\n";
121 : cout << " Premultiply j = h' * C = " << j << "\n";
122 : cout << " Postmultiply k = C * i = " << k << "\n";
123 : //
124 : // (Rectangular) Matrix multiplication.
125 : //
126 : real[int,int] L(3,4);
127 : L = A * G;
128 : cout << "\n";
129 : cout << " L = A * G = " << L << endl;
130 : //
131 : // Matrix addition.
132 : //
133 : real[int,int] M(3,3);
134 : M = A + B;
135 : cout << "\n";
136 : cout << " M = A + B = " << M << endl;
137 : //
138 : // Scalar multiplication.
139 : //
140 : M = 2 * M;
141 : cout << " M = 2 * M = " << M << endl;
142 : //
143 : // Scalar addition.
144 : //
145 : //M = M .+ 10;
146 : //cout << " M = M + 10 = " << M << endl;
147 : //
148 : // Elementwise multiplication.
149 : //
150 : M = A .* B;
151 : cout << " M = A .* B = " << M << endl;
152 : //
153 : // Elementwise division
154 : //
155 : M = A ./ B;
156 : cout << " M = A ./ B = " << M << endl;
157 : //
158 : // Inverse.
159 : //
160 : M = A ^ -1;
161 : cout << " M = A ^ -1 = " << M << endl;
162 : //
163 : // Dimensions.
164 : //
165 : cout << " Dimensions of A = (A.m,A.n) = " << A.m << "," << A.n << "\n";
166 : //
167 : // Solution operator is multiplication by inverse:
168 : //
169 : real[int] x1(3);
170 : real[int] x2(3);
171 : real[int] y2(3);
172 : real[int,int] Ainv(3,3);
173 : x1 = [ 1, 2, 3];
174 : cout << "\n";
175 : cout << " Solution X1 = " << x1 << "\n";
176 : y2 = A * x1;
177 : cout << " Y2 = A * X1 = " << y2 << "\n";
178 : //x2 = ( A ^ -1 ) * y2;
179 : Ainv = ( A ^ - 1 );
180 : x2 = Ainv * y2;
181 : cout << " X2 = A^-1 * Y2 = " << x2 << "\n";
182 : //
183 : // Maximum, doesn't work!
184 : //
185 : //cout << " max ( M ) = " << max ( M ) << "\n";
186 : //
187 : // Norms? Doesn't work.
188 : //
189 : //cout << || M ||_1 << "\n";
190 : //
191 : // Terminate.
192 : //
193 : cout << "\n";
194 : cout << "ARRAY2D:\n";
195 : cout << " Normal end of execution.\n";
196 :
197 : exit ( 0 );
198 :
199 : sizestack + 1024 =2112 ( 1088 )
ARRAY2D:
Demonstrate how 2D matrices can be defined and manipulated.
Matrix A = 3 3
0 1 0
0 0 1
1 1 1
Matrix B = 3 3
3 1 1
1 1 3
3 3 3
Matrix AxB = product A*B = 3 3
1 1 3
3 3 3
7 5 7
Matrix AT = A' = transpose A' 3 3
0 0 1
1 0 1
0 1 1
Matrix C = 3 4
1 1 0 1
1 1 1 1
1 0 1 1
First row of C = C(0,:) = 4
1 1 0 1
d = C(0,:)
Size of d = d.n = 4
Entries of d = 4
1 1 0 1
Vector e = 3
1 2 3
Vector f = 4
4 5 6 7
Matrix G = e * f' = 3 4
4 5 6 7
8 10 12 14
12 15 18 21
Premultiply j = h' * C = 4
3 3 3 3
Postmultiply k = C * i = 3
3 4 3
L = A * G = 3 4
8 10 12 14
12 15 18 21
24 30 36 42
M = A + B = 3 3
3 2 1
1 1 4
4 4 4
M = 2 * M = 3 3
6 4 2
2 2 8
8 8 8
M = A .* B = 3 3
0 1 0
0 0 3
3 3 3
M = A ./ B = 3 3
0 1 0
0 0 0.3333333333
0.3333333333 0.3333333333 0.3333333333
M = A ^ -1 = 3 3
-1 -1 1
1 0 0
0 1 0
Dimensions of A = (A.m,A.n) = 3,3
Solution X1 = 3
1 2 3
Y2 = A * X1 = 3
2 3 6
X2 = A^-1 * Y2 = 3
1 2 3
ARRAY2D:
Normal end of execution.
current line = 197
exit(0)
err code 0 , mpirank 0
CodeAlloc : nb ptr 3926, size :485208 mpirank: 0
Ok: Normal End