SciPy - I need an example of use of linalg.lstsq()

[I. Myself]

And it has to run on Windows, so it can't use xplt.

I would prefer that it use the simplest multi-dimensional model, z = k +
a*x1 + b*x2 + c*x3 + d*x4

Anyone have such a thing?

Thanks,

Mitchell Timin

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or articles, or do testing or research for ANNEvolve, let me know.

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[Robert Kern]

And it has to run on Windows, so it can't use xplt.

Huh?

A. xplt runs on Windows, too.
B. xplt has nothing to do with linalg.lstsq().
C. xplt has been removed from scipy.

I would prefer that it use the simplest multi-dimensional model, z = k +
a*x1 + b*x2 + c*x3 + d*x4

In [1]: import numpy as np

In [2]: np.linalg.lstsq?
Type: function
Base Class: <type 'function'>
String Form: <function lstsq at 0x6d3f30>
Namespace: Interactive
File:
/Library/Frameworks/Python.framework/Versions/2.4/lib/python2.4/site-packages/numpy-0.9.7.2476-py2.4-macosx-10.4-ppc.egg/numpy/linalg/linalg.py
Definition: np.linalg.lstsq(a, b, rcond=1e-10)
Docstring:
returns x,resids,rank,s
where x minimizes 2-norm(|b - Ax|)
resids is the sum square residuals
rank is the rank of A
s is the rank of the singular values of A in descending order

If b is a matrix then x is also a matrix with corresponding columns.
If the rank of A is less than the number of columns of A or greater than
the number of rows, then residuals will be returned as an empty array
otherwise resids = sum((b-dot(A,x)**2).
Singular values less than s[0]*rcond are treated as zero.


In [3]: z = np.rand(10)

In [4]: x1 = np.rand(10)

In [5]: x2 = np.rand(10)

In [6]: x3 = np.rand(10)

In [7]: x4 = np.rand(10)

In [8]: A = np.column_stack([x1, x2, x3, x4, np.ones(10, float)])

In [9]: A
Out[9]:
array([[ 0.07257264, 0.36544251, 0.68467294, 0.33813333, 1. ],
[ 0.09520828, 0.27102091, 0.04673061, 0.12905473, 1. ],
[ 0.839834 , 0.46010114, 0.3949568 , 0.38983012, 1. ],
[ 0.49776387, 0.70666191, 0.85005579, 0.47738743, 1. ],
[ 0.25457977, 0.93335912, 0.88441593, 0.05255062, 1. ],
[ 0.85982216, 0.97920853, 0.27991214, 0.94230651, 1. ],
[ 0.03224487, 0.1275237 , 0.66943552, 0.320765 , 1. ],
[ 0.86807363, 0.63800103, 0.67153924, 0.69125023, 1. ],
[ 0.26571213, 0.68845408, 0.06478114, 0.03657494, 1. ],
[ 0.46615143, 0.99464106, 0.9303421 , 0.61363703, 1. ]])

In [10]: np.linalg.lstsq(A, z)
Out[10]:
(array([-0.32421087, -0.23330787, 0.13369118, -0.28334431, 0.84010014]),
array([ 0.22958042]),
5,
array([ 4.59505886, 1.1181838 , 0.85704672, 0.70211311, 0.4420187 ]))


If you have more scipy questions, you will probably want to ask on the
scipy-user list:

http://www.scipy.org/Mailing_Lists

--
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
that is made terrible by our own mad attempt to interpret it as though it had
an underlying truth."
-- Umberto Eco

 

[I. Myself]

Huh?

A. xplt runs on Windows, too.
B. xplt has nothing to do with linalg.lstsq().
C. xplt has been removed from scipy.

Thank you. I have been misled by the Scipy Tutorial by Travis
Oliphant. It has an example which uses xplt; it also mentions that xplt
is only for x-windows.

Your example below seems like just what I'm looking for. I will try it out.

Thanks again.

Mitchell Timin

I would prefer that it use the simplest multi-dimensional model, z = k +
a*x1 + b*x2 + c*x3 + d*x4

In [1]: import numpy as np

In [2]: np.linalg.lstsq?
Type: function
Base Class: <type 'function'>
String Form: <function lstsq at 0x6d3f30>
Namespace: Interactive
File:
/Library/Frameworks/Python.framework/Versions/2.4/lib/python2.4/site-packages/numpy-0.9.7.2476-py2.4-macosx-10.4-ppc.egg/numpy/linalg/linalg.py
Definition: np.linalg.lstsq(a, b, rcond=1e-10)
Docstring:
returns x,resids,rank,s
where x minimizes 2-norm(|b - Ax|)
resids is the sum square residuals
rank is the rank of A
s is the rank of the singular values of A in descending order

If b is a matrix then x is also a matrix with corresponding columns.
If the rank of A is less than the number of columns of A or greater than
the number of rows, then residuals will be returned as an empty array
otherwise resids = sum((b-dot(A,x)**2).
Singular values less than s[0]*rcond are treated as zero.


In [3]: z = np.rand(10)

In [4]: x1 = np.rand(10)

In [5]: x2 = np.rand(10)

In [6]: x3 = np.rand(10)

In [7]: x4 = np.rand(10)

In [8]: A = np.column_stack([x1, x2, x3, x4, np.ones(10, float)])

In [9]: A
Out[9]:
array([[ 0.07257264, 0.36544251, 0.68467294, 0.33813333, 1. ],
[ 0.09520828, 0.27102091, 0.04673061, 0.12905473, 1. ],
[ 0.839834 , 0.46010114, 0.3949568 , 0.38983012, 1. ],
[ 0.49776387, 0.70666191, 0.85005579, 0.47738743, 1. ],
[ 0.25457977, 0.93335912, 0.88441593, 0.05255062, 1. ],
[ 0.85982216, 0.97920853, 0.27991214, 0.94230651, 1. ],
[ 0.03224487, 0.1275237 , 0.66943552, 0.320765 , 1. ],
[ 0.86807363, 0.63800103, 0.67153924, 0.69125023, 1. ],
[ 0.26571213, 0.68845408, 0.06478114, 0.03657494, 1. ],
[ 0.46615143, 0.99464106, 0.9303421 , 0.61363703, 1. ]])

In [10]: np.linalg.lstsq(A, z)
Out[10]:
(array([-0.32421087, -0.23330787, 0.13369118, -0.28334431, 0.84010014]),
array([ 0.22958042]),
5,
array([ 4.59505886, 1.1181838 , 0.85704672, 0.70211311, 0.4420187 ]))


If you have more scipy questions, you will probably want to ask on the
scipy-user list:

http://www.scipy.org/Mailing_Lists

--
I'm proud of http://ANNEvolve.sourceforge.net. If you want to write software,
or articles, or do testing or research for ANNEvolve, let me know.

Humans may know that my email address is: (but remove the 3 digit number)
zenguy at shaw666 dot ca