Output from imldet1.sas |
Source
0 Graphs |
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NOTE: Capture of log output started.
NOTE: %INCLUDE (level 1) file n:\psy6140\examples\iml\imldet1.sas is file n:\psy6140\examples\iml\imldet1.sas.
265 +title 'Properties of determinants'; 266 +proc iml;
IML Ready
266 + reset print log; 267 + /*----------------------------------------* 268 + | IMLDET1: Properties of determinants | 269 + *----------------------------------------*/ 270 + A = {3 1, 2 4};
A 2 rows 2 cols (numeric) 3 1 2 4
271 + r = det(A);
R 1 row 1 col (numeric) 10
272 + 273 + *-- 1. Interchange rows or cols -> -1 # det(A); 274 + r = det(A[{2 1},]);
R 1 row 1 col (numeric) -10
275 + r = det(A[,{2 1}]);
R 1 row 1 col (numeric) -10
276 + 277 + *-- 2. transpose -> det a unchanged; 278 + r = det( A`);
R 1 row 1 col (numeric) 10
279 + 280 + *-- 3. multiply row # k -> k # det a; 281 + r = diag({3 1}) * A;
R 2 rows 2 cols (numeric) 9 3 2 4
282 + r = det( diag({3 1}) * A);
R 1 row 1 col (numeric) 30
283 + 284 + *-- 4. multiply matrix # k -> k**2 # det(a); 285 + r = det(3 # A);
R 1 row 1 col (numeric) 90
286 + 287 + *-- 5. det (a * b) -> det(a) # det(b); 288 + B={ 4 2, 3 5};
B 2 rows 2 cols (numeric) 4 2 3 5
289 + r = det(B);
R 1 row 1 col (numeric) 14
290 + r = det(A * B);
R 1 row 1 col (numeric) 140
291 + r = det(A) # det(B);
R 1 row 1 col (numeric) 140
292 + 293 + *-- 6. proportional rows -> det = 0; 294 + C={1 5, 2 6, 4 4};
C 3 rows 2 cols (numeric) 1 5 2 6 4 4
295 + C=C || C[,1];
C 3 rows 3 cols (numeric) 1 5 1 2 6 2 4 4 4
296 + r = det(C);
R 1 row 1 col (numeric) 0
297 + 298 + *-- 7. Add multiple of one row to another -> det unchanged; 299 + A[2,] = A[2,] - 2#A[1,];
A 2 rows 2 cols (numeric) 3 1 -4 2
300 + r = det(A);
R 1 row 1 col (numeric) 10
301 +quit;
Exiting IML.
NOTE: The PROCEDURE IML used 0.17 seconds.
302 +
NOTE: %INCLUDE (level 1) ending.