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

[Robert Kern]

I. Myself wrote:
> 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 ]))


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-- 
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