Python Scipy lfilter中的小数精度？

Question

Does anybody has idea about decimal precision in python (lfilter). According to their documentation for Matlab filter() and SciPy lfilter(), it seems like they should be equivalent. I am doing the some calculations in matlab and in python ... unfortunately the results which I have obtained are differ and I don't have any idea why ?

As an input I am using the same sets of coefficients :

b1 = np.array([0.987968850910341,  -1.975937701820681,   0.987968850910341]) 
a1 = np.array([1.000000000000000,  -1.975859694926928,   0.976015708714434])

and following code for filter in python:

filtered = lfilter(b1, a1, signal_in, axis=0 )

and in matlab:

filtered = filter(b1, a1, signal_in)

but the results are differ ... and those from matlab are correct one. However there should be agreement on the fourth place after decimal.

I will be so grateful for any suggestion what is wrong here.

greetings

here is piece of my input data:

    108699371.346
108699354.081
108699336.818
108699319.553
108699302.288
108699285.023
108699267.757
108699250.494
108699233.231
108699215.969
108699198.707
108699181.443
108699164.18
108699146.917
108699129.654
108699112.393
108699095.133
108699077.872
108699060.611
108699043.351
108699026.091
108699008.832
108698991.572
108698974.312
108698957.053
108698939.794
108698922.536
108698905.274
108698888.014
108698870.754
108698853.494
108698836.234
108698818.976
108698801.719
108698784.462
108698767.205
108698749.95
108698732.693
108698715.436
108698698.179

Answer 1

At least on my system (scipy 0.16.0, Python 3.4.3, MATLAB r2014b, all 64bit), the results are identical. However, MATLAB and numpy display them differently. numpy displays the results to 8 decimal places by default, while MATLAB displays the results to only 4 decimal places by default. However, internally, both have many more places of precision (both use double precision floating point numbers, which have 15-17 decimal places of precision).

If I use sprintf to display the MATLAB results to 8 decimal places, the results are identical to the scipy results (using a character-by-character comparison). So it isn't that scipy is doing anything wrong, or even anything different numerically, numpy just has different defaults for how it displays floating-point numbers than MATLAB.

So what numpy prints by default:

array([  1.07391593e+08,   1.04799110e+08,   1.02252456e+08,
         9.97509288e+07,   9.72938364e+07,   9.48804965e+07,
         9.25102361e+07,   9.01823919e+07,   8.78963097e+07,
         8.56513445e+07,   8.34468604e+07,   8.12822305e+07,
         7.91568365e+07,   7.70700690e+07,   7.50213272e+07,
         7.30100186e+07,   7.10355593e+07,   6.90973734e+07,
         6.71948935e+07,   6.53275598e+07,   6.34948208e+07,
         6.16961327e+07,   5.99309594e+07,   5.81987724e+07,
         5.64990510e+07,   5.48312815e+07,   5.31949579e+07,
         5.15895811e+07,   5.00146595e+07,   4.84697083e+07,
         4.69542498e+07,   4.54678129e+07,   4.40099335e+07,
         4.25801542e+07,   4.11780240e+07,   3.98030987e+07,
         3.84549400e+07,   3.71331165e+07,   3.58372028e+07,
         3.45667795e+07])

What MATLAB prints by default:

filtered =

    1.0e+08 *

    Columns 1 through 14

        1.0739    1.0480    1.0225    0.9975    0.9729    0.9488    0.9251    0.9018    0.8790    0.8565    0.8345    0.8128    0.7916    0.7707

    Columns 15 through 28

        0.7502    0.7301    0.7104    0.6910    0.6719    0.6533    0.6349    0.6170    0.5993    0.5820    0.5650    0.5483    0.5319    0.5159

    Columns 29 through 40

        0.5001    0.4847    0.4695    0.4547    0.4401    0.4258    0.4118    0.3980    0.3845    0.3713    0.3584    0.3457

What MATLAB prints when I set it to use 8 decimal places of precision with sprintf('%0.8e, ',filtered) :

1.07391593e+08, 1.04799110e+08, 1.02252456e+08, 9.97509288e+07, 9.72938364e+07, 9.48804965e+07, 9.25102361e+07, 9.01823919e+07, 8.78963097e+07, 8.56513445e+07, 8.34468604e+07, 8.12822305e+07, 7.91568365e+07, 7.70700690e+07, 7.50213272e+07, 7.30100186e+07, 7.10355593e+07, 6.90973734e+07, 6.71948935e+07, 6.53275598e+07, 6.34948208e+07, 6.16961327e+07, 5.99309594e+07, 5.81987724e+07, 5.64990510e+07, 5.48312815e+07, 5.31949579e+07, 5.15895811e+07, 5.00146595e+07, 4.84697083e+07, 4.69542498e+07, 4.54678129e+07, 4.40099335e+07, 4.25801542e+07, 4.11780240e+07, 3.98030987e+07, 3.84549400e+07, 3.71331165e+07, 3.58372028e+07, 3.45667795e+07, 

The scipy and MATLAB results set to have the same format:

scipy:  1.07391593e+08 1.04799110e+08 1.02252456e+08 9.97509288e+07 9.72938364e+07 9.48804965e+07 9.25102361e+07 9.01823919e+07 8.78963097e+07 8.56513445e+07 8.34468604e+07 8.12822305e+07 7.91568365e+07 7.70700690e+07 7.50213272e+07 7.30100186e+07 7.10355593e+07 6.90973734e+07 6.71948935e+07 6.53275598e+07 6.34948208e+07 6.16961327e+07 5.99309594e+07 5.81987724e+07 5.64990510e+07 5.48312815e+07 5.31949579e+07 5.15895811e+07 5.00146595e+07 4.84697083e+07 4.69542498e+07 4.54678129e+07 4.40099335e+07 4.25801542e+07 4.11780240e+07 3.98030987e+07 3.84549400e+07 3.71331165e+07 3.58372028e+07 3.45667795e+07 
MATLAB: 1.07391593e+08 1.04799110e+08 1.02252456e+08 9.97509288e+07 9.72938364e+07 9.48804965e+07 9.25102361e+07 9.01823919e+07 8.78963097e+07 8.56513445e+07 8.34468604e+07 8.12822305e+07 7.91568365e+07 7.70700690e+07 7.50213272e+07 7.30100186e+07 7.10355593e+07 6.90973734e+07 6.71948935e+07 6.53275598e+07 6.34948208e+07 6.16961327e+07 5.99309594e+07 5.81987724e+07 5.64990510e+07 5.48312815e+07 5.31949579e+07 5.15895811e+07 5.00146595e+07 4.84697083e+07 4.69542498e+07 4.54678129e+07 4.40099335e+07 4.25801542e+07 4.11780240e+07 3.98030987e+07 3.84549400e+07 3.71331165e+07 3.58372028e+07 3.45667795e+07

Also, you don't need the axis argument for the scipy filter, at least if you use a vector (1D array).