A system of linear equations such that the backslash matlab and numpy.linalg.solve create different solutions
I have the following problem using numpy 1.3.0 and MATLAB 7.9.0: python code
import numpy as np Lu = [[1.01250000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[-0.00250000000000000,1.01250000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,-0.00250000000000000,1.01250000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,-0.00250000000000000,1.01250000000000,0,0,0,-0.00250000000000000,0,0,0,0,0,0,0,0,0,0,0,0],[-0.00250000000000000,0,0,0,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0,0,0,0,0,0,0],[0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0,0,0,0,0,0],[0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0,0,0,0,0],[0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,0,0,0,-0.00250000000000000,0,0,0,0,0,0,0,0],[0,0,0,0,-0.00250000000000000,0,0,0,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0,0,0],[0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0,0],[0,0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0],[0,0,0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,0,0,0,-0.00250000000000000,0,0,0,0],[0,0,0,0,0,0,0,0,-0.00250000000000000,0,0,0,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0],[0,0,0,0,0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0],[0,0,0,0,0,0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0],[0,0,0,0,0,0,0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,0,0,0,-0.00250000000000000],[0,0,0,0,0,0,0,0,0,0,0,0,-0.00250000000000000,0,0,0,1.01250000000000,-0.00250000000000000,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01250000000000,-0.00250000000000000,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01250000000000,-0.00250000000000000],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01250000000000]] rhs = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0.0050, 0.0050, 0.0050, 0.0050] Lu = np.array(Lu) rhs = np.array(rhs) ans = np.linalg.solve(Lu,rhs) print ans
outputs output
[ 1.87241716e-13 1.89545264e-13 1.89545264e-13 1.87241716e-13
7.56433496e-11 7.63890449e-11 7.63890449e-11 7.56433496e-11
3.04833369e-08 3.07089522e-08 3.07089522e-08 3.04833369e-08
1.22844835e-05 1.23451480e-05 1.23451480e-05 1.22844835e-05
4.95055571e-03 4.96277946e-03 4.96277946e-03 4.95055571e-03]
whereas the backslash in MATLAB produces the output
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0050 0.0050 0.0050 0.0050
I have not found any other linear algebraic equation system where numpy and matlab produce different solutions. I am currently out of town and therefore cannot check if another variant of numpy (on another computer) will give the correct result. Is np.linalg.solve the wrong function to use this system (Lu system matrix is sparse)? Is this a bug in my version of numpy? Are there any problems in my code?
Thank!
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Actually, they are probably the same solution. MATLAB rounds to 0.0000 (when printing at least), while python gives you much more verbose numbers (some problems can come from floating point rounding errors). The only numbers that appear as 0.0050
are those that are e-03
. All other numbers are less than 0.0005, so it can be rounded to the nearest 0.0000.
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