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|
(kill(values),0);
0$
(saveratprint : ratprint, savefloat2bf : float2bf, ratprint : false, float2bf : true, 0);
0$
(lu_test(m) := block([mp],
mp : get_lu_factors(lu_factor(m,generalring)),
zeromatrixp(m - mp[1] . mp[2] . mp[3])),0);
0$
lu_test(matrix([1]));
true$
lu_test(matrix([0,1],[1,0]));
true$
lu_test(matrix([0,a],[b,0]));
true$
lu_test(matrix([a,b],[c,d]));
true$
lu_test(matrix([a,b],[b,d]));
true$
lu_test(matrix([1/2,b],[b,2/3]));
true$
lu_test(matrix([1/2 + %i, %i - 1],[9 - %i, 19 + %i]));
true$
lu_test(matrix([0,1,0],[0,0,1],[1,2,4]));
true$
lu_test(matrix([0,a,0],[b,0,0],[0,0,c]));
true$
lu_test(matrix([a,b,c],[d,e,f],[g,h,i]));
true$
lu_test(matrix([0,0,1],[1,0,0],[0,1,0]));
true$
lu_test(matrix([0,0,1],[1,0,0],[0,1,x]));
true$
lu_test(hilbert_matrix(3));
true$
lu_test(hilbert_matrix(4));
true$
lu_test(hilbert_matrix(5));
true$
lu_test(vandermonde_matrix([1,2,%i]));
true$
lu_test(vandermonde_matrix([1 + %i,1 - %i, 8, 32]));
true$
(lu_test(m, tol) := block([mp],
mp : get_lu_factors(lu_factor(m,bigfloatfield)),
every(lambda([s], is(cabs(s) < tol)), m - mp[1] . mp[2] . mp[3])),0);
0$
(fpprec : 20,0);
0$
lu_test(vandermonde_matrix([1,1/2,1/3,1/4]), 1.0e-18);
true$
(fpprec : 40,0);
0$
lu_test(vandermonde_matrix([1,1/2,1/3,1/4]), 1.0e-38);
true$
lu_test(hilbert_matrix(13), 1.0e-38);
true$
lu_test(hilbert_matrix(4) + %i * vandermonde_matrix([1,2,3,4]), 1.0e-15);
true$
(lu_test(m, tol) := block([mp],
mp : get_lu_factors(lu_factor(m,complexfield)),
every(lambda([s], is(cabs(s) < tol)),m - mp[1] . mp[2] . mp[3])),0);
0$
lu_test(hilbert_matrix(7) + %i * vandermonde_matrix([1,2,3,4,5,6,7]), 1.0e-10);
true$
(m : matrix([1,2,3],[4,5,6],[7,8,10]),0);
0$
(b : m . matrix([x],[y],[z]),0);
0$
lu_backsub(lu_factor(m,crering), b);
''(rat(matrix([x],[y],[z])))$
(m : matrix([0,2,3],[0,5,6],[7,8,10]),0);
0$
(b : m . matrix([x],[y],[z]),0);
0$
lu_backsub(lu_factor(m, crering), b);
''(rat(matrix([x],[y],[z])))$
(m : matrix([0,2,3],[0,5,6],[7,8,10]),0);
0$
(b : m . matrix([x],[y],[z]),0);
0$
lu_backsub(lu_factor(m, crering), b);
''(rat(matrix([x],[y],[z])))$
(m : matrix([0,1,2],[1,0,1],[0,0,8]),0);
0$
(b : m . matrix([x],[y],[z]),0);
0$
lu_backsub(lu_factor(m, crering), b);
''(rat(matrix([x],[y],[z])))$
(m : matrix([matrix([0,1],[1,0]), matrix([1,0],[%i,0])],
[matrix([1,0],[0,1]), matrix([1,1],[-1,1])]),0);
0$
(m1 : get_lu_factors(lu_factor(m, noncommutingring)),0);
0$
(matrix_element_mult : ".",0);
0$
zeromatrixp(m1[1] . m1[2] . m1[3] - m);
true$
(m : matrix([matrix([matrix([8,4],[4,13]),matrix([2,4],[7,9])],[matrix([2,7],[4,9]),matrix([10,6],[6,15])]),matrix([matrix([4,4],[12,5]),matrix([0,6],[6,8])],[matrix([8,3],[13,3]),matrix([6,5],[5,6])])],[matrix([matrix([4,12],[4,5]),matrix([8,13],[3,3])],[matrix([0,6],[6,8]),matrix([6,5],[5,6])]),matrix([matrix([18,5],[5,4]),matrix([5,9],[2,6])],[matrix([5,2],[9,6]),matrix([6,3],[3,11])])]),0);
0$
(m1 : get_lu_factors(lu_factor(m,'noncommutingring)),0);
0$
zeromatrixp(m1[1] . m1[2] . m1[3]-m);
true$
(ratprint : saveratprint, float2bf : savefloat2bf, 0);
0$
(kill(values),0);
0$
(kill(lu_test),0);
0$
(matrix_element_mult : "*",0);
0$
|
