I have a script which uses no randomisation that gives me different answers when I run it. I expect the answer to be the same, every time I run the script. The problem appears to only happen for certain (ill-conditioned) input data.
The snippet comes from an algorithm to compute a specific type of controller for a linear system, and it mostly consists of doing linear algebra (matrix inversions, Riccati equation, eigenvalues).
Obviously, this is a major worry for me, as I now cannot trust my code to give me the right results. I know the result can be wrong for poorly conditioned data, but I expect consistently wrong. Why is the answer not always the same on my Windows machine? Why do the Linux & Windows machine not give the same results?
I'm using Python 2.7.9 (default, Dec 10 2014, 12:24:55) [MSC v.1500 32 bit (Intel)] on win 32, with Numpy version 1.8.2 and Scipy 0.14.0. (Windows 8, 64bit).
The code is below. I've also tried running the code on two Linux machines, and there the script always gives the same answer (but the machines gave differing answers). One was running Python 2.7.8, with Numpy 1.8.2 and Scipy 0.14.0. The second was running Python 2.7.3 with Numpy 1.6.1 and Scipy 0.12.0.
I solve the Riccati equation three times, and then print the answers. I expect the same answer every time, instead I get the sequence '1.75305103767e-09; 3.25501787302e-07; 3.25501787302e-07'.
import numpy as np
import scipy.linalg
matrix = np.matrix
A = matrix([[ 0.00000000e+00, 2.96156260e+01, 0.00000000e+00,
-1.00000000e+00],
[ -2.96156260e+01, -6.77626358e-21, 1.00000000e+00,
-2.11758237e-22],
[ 0.00000000e+00, 0.00000000e+00, 2.06196064e+00,
5.59422224e+01],
[ 0.00000000e+00, 0.00000000e+00, 2.12407340e+01,
-2.06195974e+00]])
B = matrix([[ 0. , 0. , 0. ],
[ 0. , 0. , 0. ],
[ -342.35401351, -14204.86532216, 31.22469724],
[ 1390.44997337, 342.33745324, -126.81720597]])
Q = matrix([[ 5.00000001, 0. , 0. , 0. ],
[ 0. , 5.00000001, 0. , 0. ],
[ 0. , 0. , 0. , 0. ],
[ 0. , 0. , 0. , 0. ]])
R = matrix([[ -3.75632852e+04, -0.00000000e+00, 0.00000000e+00],
[ -0.00000000e+00, -3.75632852e+04, 0.00000000e+00],
[ 0.00000000e+00, 0.00000000e+00, 4.00000000e+00]])
counter = 0
while counter < 3:
counter +=1
X = scipy.linalg.solve_continuous_are(A, B, Q, R)
print(-3449.15531628 - X[0,0])
My numpy config is as below print np.show_config()
lapack_opt_info:
libraries = ['mkl_blas95', 'mkl_lapack95', 'mkl_intel_c', 'mkl_intel_thread', 'mkl_core', 'libiomp5md', 'mkl_blas95', 'mkl_lapack95', 'mkl_intel_c', 'mkl_intel_thread', 'mkl_core', 'libiomp5md']
library_dirs = ['c:/Program Files (x86)/Intel/Composer XE 2013 SP1/mkl/lib/ia32', 'C:/Program Files (x86)/Intel/Composer XE 2013 SP1/compiler/lib/ia32']
define_macros = [('SCIPY_MKL_H', None)]
include_dirs = ['c:/Program Files (x86)/Intel/Composer XE 2013 SP1/mkl/include']
blas_opt_info:
libraries = ['mkl_blas95', 'mkl_lapack95', 'mkl_intel_c', 'mkl_intel_thread', 'mkl_core', 'libiomp5md']
library_dirs = ['c:/Program Files (x86)/Intel/Composer XE 2013 SP1/mkl/lib/ia32', 'C:/Program Files (x86)/Intel/Composer XE 2013 SP1/compiler/lib/ia32']
define_macros = [('SCIPY_MKL_H', None)]
include_dirs = ['c:/Program Files (x86)/Intel/Composer XE 2013 SP1/mkl/include']
openblas_info:
NOT AVAILABLE
lapack_mkl_info:
libraries = ['mkl_blas95', 'mkl_lapack95', 'mkl_intel_c', 'mkl_intel_thread', 'mkl_core', 'libiomp5md', 'mkl_blas95', 'mkl_lapack95', 'mkl_intel_c', 'mkl_intel_thread', 'mkl_core', 'libiomp5md']
library_dirs = ['c:/Program Files (x86)/Intel/Composer XE 2013 SP1/mkl/lib/ia32', 'C:/Program Files (x86)/Intel/Composer XE 2013 SP1/compiler/lib/ia32']
define_macros = [('SCIPY_MKL_H', None)]
include_dirs = ['c:/Program Files (x86)/Intel/Composer XE 2013 SP1/mkl/include']
blas_mkl_info:
libraries = ['mkl_blas95', 'mkl_lapack95', 'mkl_intel_c', 'mkl_intel_thread', 'mkl_core', 'libiomp5md']
library_dirs = ['c:/Program Files (x86)/Intel/Composer XE 2013 SP1/mkl/lib/ia32', 'C:/Program Files (x86)/Intel/Composer XE 2013 SP1/compiler/lib/ia32']
define_macros = [('SCIPY_MKL_H', None)]
include_dirs = ['c:/Program Files (x86)/Intel/Composer XE 2013 SP1/mkl/include']
mkl_info:
libraries = ['mkl_blas95', 'mkl_lapack95', 'mkl_intel_c', 'mkl_intel_thread', 'mkl_core', 'libiomp5md']
library_dirs = ['c:/Program Files (x86)/Intel/Composer XE 2013 SP1/mkl/lib/ia32', 'C:/Program Files (x86)/Intel/Composer XE 2013 SP1/compiler/lib/ia32']
define_macros = [('SCIPY_MKL_H', None)]
include_dirs = ['c:/Program Files (x86)/Intel/Composer XE 2013 SP1/mkl/include']
None
(edits to trim the question down)
