Loosen tolerance in a few expm() tests
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Change 1r-14 to 5e-14 in the following two examples. This is likely
required because expm() in scipy was rewritten in C.
Example 1:
File "src/sage/matrix/matrix_double_dense.pyx", line 3666, in
sage.matrix.matrix_double_dense.Matrix_double_dense.exp
Failed example:
A.exp() # tol 1e-14
Expected:
[51.968956198705044 74.73656456700327]
[112.10484685050491 164.07380304920997]
Got:
[51.968956198707595 74.736564567007]
[112.10484685051048 164.07380304921807]
Tolerance exceeded in 4 of 4:
51.968956198705044 vs 51.968956198707595, tolerance 5e-14 > 1e-14
74.73656456700327 vs 74.736564567007, tolerance 5e-14 > 1e-14
112.10484685050491 vs 112.10484685051048, tolerance 5e-14 > 1e-14
164.07380304920997 vs 164.07380304921807, tolerance 5e-14 > 1e-14
Example 2:
File "src/sage/matrix/matrix_double_dense.pyx", line 3679, in
sage.matrix.matrix_double_dense.Matrix_double_dense.exp
Failed example:
A.exp() # tol 1e-14
Expected:
[51.968956198705044 74.73656456700327]
[112.10484685050491 164.07380304920997]
Got:
[51.968956198707595 74.736564567007]
[112.10484685051048 164.07380304921807]
Tolerance exceeded in 4 of 4:
51.968956198705044 vs 51.968956198707595, tolerance 5e-14 > 1e-14
74.73656456700327 vs 74.736564567007, tolerance 5e-14 > 1e-14
112.10484685050491 vs 112.10484685051048, tolerance 5e-14 > 1e-14
164.07380304920997 vs 164.07380304921807, tolerance 5e-14 > 1e-14
Change 1e-14 to 6e-14 in the following example. This is likely
necessary because expm() in scipy was rewritten in C.
File "src/sage/matrix/matrix2.pyx", line 15903,
in sage.matrix.matrix2.Matrix.exp
Failed example:
a.change_ring(RDF).exp() # rel tol 1e-14
Expected:
[42748127.31532951 7368259.244159399]
[234538976.1381042 40426191.45156228]
Got:
[ 42748127.31533201 7368259.244159831]
[234538976.13811788 40426191.45156465]
Tolerance exceeded in 4 of 4:
42748127.31532951 vs 42748127.31533201, tolerance 6e-14 > 1e-14
7368259.244159399 vs 7368259.244159831, tolerance 6e-14 > 1e-14
234538976.1381042 vs 234538976.13811788, tolerance 6e-14 > 1e-14
40426191.45156228 vs 40426191.45156465, tolerance 6e-14 > 1e-14
In the following example, we now use 5e-14 instead of 1e-14. This is
likely due to scipy's expm() being rewritten in C:
File "src/sage/symbolic/constants_c_impl.pxi", line 162, in
sage.symbolic.constants_c_impl.pxi.E.__pow__
Failed example:
e^A # rel tol 1e-14
Expected:
[51.968956198705044 74.73656456700327]
[112.10484685050491 164.07380304920997]
Got:
[51.968956198707595 74.736564567007]
[112.10484685051048 164.07380304921807]
Tolerance exceeded in 4 of 4:
51.968956198705044 vs 51.968956198707595, tolerance 5e-14 > 1e-14
74.73656456700327 vs 74.736564567007, tolerance 5e-14 > 1e-14
112.10484685050491 vs 112.10484685051048, tolerance 5e-14 > 1e-14
164.07380304920997 vs 164.07380304921807, tolerance 5e-14 > 1e-14
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SciPy upstream just merged scipy/scipy#21553 which rewrites the matrix exponential in C. I merged this PR to work around some other bug, and in the process noticed that a few tolerances will need to be loosened in our test suite.