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This will hopefully become a complete set of the basic functions available in
matlab. The syntax is kept as close to the matlab syntax as possible. One
fundamental change is that the first index in matlab varies the fastest (as in
FORTRAN). That means that it will usually perform reductions over columns,
whereas with this object the most natural reductions are over rows. It's perfectly
possible to make this work the way it does in matlab if that's desired.
( t *Nc G s
t i | ƒ S( sœ rand(d1,...,dn) returns a matrix of the given dimensions
which is initialized to random numbers from a uniform distribution
in the range [0,1).
N( t RandomArrayt randomt args( R ( ( t2 /usr/lib64/python2.4/site-packages/Numeric/MLab.pyt rand s c G sD t i | ƒ } t i | ƒ } t d t | ƒ ƒ t d t | ƒ S( sx u = randn(d0,d1,...,dn) returns zero-mean, unit-variance Gaussian
random numbers in an array of size (d0,d1,...,dn).iþÿÿÿi N( R R R t x1t x2t sqrtt logt cost pi( R R R ( ( R t randn s i c C sx | d j o
| } n t | ƒ t d ƒ j o | } | } n t t i t | ƒ t | ƒ ƒ | ƒ } t | d | ƒS( s„ eye(N, M=N, k=0, typecode=None) returns a N-by-M matrix where the
k-th diagonal is all ones, and everything else is zeros.
t dt typecodeN( t Mt Nonet Nt typeR t equalt subtractt outert aranget kt mt asarray( R R R R R ( ( R t eye$ s
(c C su | d j o
| } n t | ƒ t d ƒ j o | } | } n t t i t | ƒ t | ƒ ƒ | ƒ } | i | ƒ S( s• tri(N, M=N, k=0, typecode=None) returns a N-by-M matrix where all
the diagonals starting from lower left corner up to the k-th are all ones.
R
N( R R R R R t
greater_equalR R R R R t astype( R R R R R ( ( R t tri0 s
(c C s= t | ƒ } | i } t | ƒ d j o‘ | d t | ƒ } | d j o% t t | | i
ƒ ƒ | f ƒ } n4 | d j o& t | t | | i
ƒ ƒ f ƒ } n t | d | ƒ| Sn t | ƒ d j od t i
t | d | d d | ƒ| ƒ } | d j o | | Sq9| d j o | | Sq9| Sn
t d ‚ d S( s diag(v,k=0) returns the k-th diagonal if v is a matrix or
returns a matrix with v as the k-th diagonal if v is a vector.
i i R i s Input must be 1- or 2-D.N( R t vt shapet st lent absR t nt concatenatet zerosR R t addt reducet
ValueError( R R R# R ( ( R t diag= s$
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&*
c C sL t | ƒ } t | i ƒ d j o
t d ‚ n | d d … d d d … f S( s“ fliplr(m) returns a 2-D matrix m with the rows preserved and
columns flipped in the left/right direction. Only works with 2-D
arrays.
i s Input must be 2-D.Niÿÿÿÿ( R R R! R R( ( R ( ( R t fliplrS s
c C s@ t | ƒ } t | i ƒ d j o
t d ‚ n | d d d … S( sŠ flipud(m) returns a 2-D matrix with the columns preserved and
rows flipped in the up/down direction. Only works with 2-D arrays.
i s Input must be 2-D.Niÿÿÿÿ( R R R! R R( ( R ( ( R t flipud] s
i c C sµ t | ƒ } t | i ƒ d j o
t d ‚ n | d } | d j o | Snd | d j o t t | ƒ ƒ SnC | d j o t t | ƒ ƒ Sn" | d j o t t | ƒ ƒ Sn d S( so rot90(m,k=1) returns the matrix found by rotating m by k*90 degrees
in the counterclockwise direction.
i s Input must be 2-D.i i i i N( R R R! R R( R t transposeR* R+ ( R R ( ( R t rot90h s
c C sb | i ƒ } t | d d ƒ} t | i d | i d d | d | i ƒ ƒ| } | i | ƒ | S( s¢ tril(m,k=0) returns the elements on and below the k-th diagonal of
m. k=0 is the main diagonal, k > 0 is above and k < 0 is below the main
diagonal.
t savespacei i R R N(
R t
spacesavert svspR R R R R t outR. ( R R R0 R1 ( ( R t trilu s 3
c C sd | i ƒ } t | d d ƒ} d t | i d | i d | d | i ƒ ƒ | } | i | ƒ | S( s¢ triu(m,k=0) returns the elements on and above the k-th diagonal of
m. k=0 is the main diagonal, k > 0 is above and k < 0 is below the main
diagonal.
R. i i N(
R R/ R0 R R R R R R1 R. ( R R R0 R1 ( ( R t triu€ s 5
c C s t | ƒ } t i | | ƒ S( sA max(m,axis=0) returns the maximum of m along dimension axis.
N( R R t maximumR' t axis( R R5 ( ( R t maxŽ s c C s t | ƒ } t i | | ƒ S( sA min(m,axis=0) returns the minimum of m along dimension axis.
N( R R t minimumR' R5 ( R R5 ( ( R t min” s c C s& t | ƒ } t | | ƒ t | | ƒ S( sN ptp(m,axis=0) returns the maximum - minimum along the the given dimension
N( R R R6 R5 R8 ( R R5 ( ( R t ptpœ s c C s- t | ƒ } t i | | ƒ t | i | ƒ S( s… mean(m,axis=0) returns the mean of m along the given dimension.
If m is of integer type, returns a floating point answer.
N( R R R& R' R5 t floatR ( R R5 ( ( R t mean¢ s c C s" t | ƒ } t t t | ƒ ƒ ƒ S( sI msort(m) returns a sort along the first dimension of m as in MATLAB.
N( R R R, t sort( R ( ( R t msortª s c C sz t | ƒ } | i d d d j o | t | i d d ƒ Sn6 t | ƒ } | i d d } | | d | | d Sd S( sD median(m) returns a median of m along the first dimension of m.
i i i f2.0N( R= R t sortedR t intt index( R R> R@ ( ( R t median° s c C s£ t | ƒ } t | i | ƒ } t t | | ƒ ƒ } | d j o t | i ƒ | } n | i | d | i | | _ | | } t
t i | | | ƒ | d ƒ S( sÁ std(m,axis=0) returns the standard deviation along the given
dimension of m. The result is unbiased with division by N-1.
If m is of integer type returns a floating point answer.
i i f1.0N( i (
R R t xR: R R5 R# R; t mxR! R R& R' ( R R5 R# RB RC ( ( R t std» s
c C s t | ƒ } t i | | ƒ S( sd cumsum(m,axis=0) returns the cumulative sum of the elements along the
given dimension of m.
N( R R R& t
accumulateR5 ( R R5 ( ( R t cumsumÉ s c C s t | ƒ } t i | | ƒ S( s[ prod(m,axis=0) returns the product of the elements along the given
dimension of m.
N( R R t multiplyR' R5 ( R R5 ( ( R t prodÐ s c C s t | ƒ } t i | | ƒ S( sa cumprod(m) returns the cumulative product of the elments along the
given dimension of m.
N( R R RG RE R5 ( R R5 ( ( R t cumprod× s iÿÿÿÿc C sÀ t | ƒ } | d j o
d } n t | d | ƒ} t | ƒ } t | i ƒ } t
d ƒ g | } t
d ƒ g | } t
d d ƒ | | <t
d d ƒ | | <t
i | | | | | d | ƒ S( su trapz(y,x=None,axis=-1) integrates y along the given dimension of
the data array using the trapezoidal rule.
f1.0R5 i iÿÿÿÿf2.0N( R t yRB R R
t diffR5 R! R t ndt slicet slice1t slice2R& R' ( RJ RB R5 RO R
RN RL ( ( R t trapzÞ s
c C sï t | ƒ } t | i ƒ } | d j o
d } n | d j o
t d ‚ n | d j o | Sn‹ | d j o` t d ƒ g | } t d ƒ g | } t d d ƒ | | <t d d ƒ | | <| | | | Sn t t | d | ƒ | d ƒ Sd S( sÎ diff(x,n=1,axis=-1) calculates the n'th difference along the axis specified.
Note that the result is one shorter in the axis'th dimension.
Returns x if n == 0. Raises ValueError if n < 0.
i i s# MLab.diff, order argument negative.iÿÿÿÿN(
R RB R! R RL R# R( RM R RN RO R5 RK ( RB R# R5 RN RO RL ( ( R RK ï s
c C s* | d j o
| } n | } | o t | ƒ } t | ƒ } n | i d d j o t | ƒ } n | i d d j o t | ƒ } n | i d } | i d | j o
t d ‚ n | t | d d ƒ} | t | d d ƒ} | o | d } n | d } t t t | ƒ t
| ƒ ƒ | ƒ } | S( s Estimate the covariance matrix.
If m is a vector, return the variance. For matrices where each row
is an observation, and each column a variable, return the covariance
matrix. Note that in this case diag(cov(m)) is a vector of
variances for each column.
cov(m) is the same as cov(m, m)
Normalization is by (N-1) where N is the number of observations
(unbiased estimate). If bias is 1 then normalization is by N.
If rowvar is zero, then each row is a variable with
observations in the columns.
i i s2 x and y must have the same number of observations.R5 f1.0N( RJ R R t rowvarR, R R R( R; t biast factt squeezet dott conjugatet val( R RJ RQ RR RW R RS ( ( R t cov s*
%c C s5 t | | ƒ } t | ƒ } | t t i | | ƒ ƒ S( s! The correlation coefficients
N( RX RB RJ t cR) R
R RG R ( RB RJ RY R
( ( R t corrcoef- s c C s@ t | ƒ } t | i ƒ } t | t t t | d ƒ | ƒ ƒ ƒ S( s> squeeze(a) returns a with any ones from the shape of a removedi N( R t aR t bt reshapet tuplet compresst not_equal( R[ R\ ( ( R RT 7 s c C sZ d k } t d | ƒ } | d d } | i | t d | | | d ƒ ƒ | i | ƒ S( sœ kaiser(M, beta) returns a Kaiser window of length M with shape parameter
beta. It depends on the cephes module for the modified bessel function i0.
Ni i f2.0( t cephesR R R# t alphat i0t betaR ( R Rd R# Rb Ra ( ( R t kaiser> s
c C sO t d | ƒ } d d t d t | | d ƒ d t d t | | d ƒ S( s5 blackman(M) returns the M-point Blackman window.
i f0.41999999999999998f0.5f2.0i f0.080000000000000002f4.0N( R R R# R
R ( R R# ( ( R t blackmanG s c C sL t d | ƒ } t t | | d d ƒ d | | d d d | | d ƒ S( s5 bartlett(M) returns the M-point Bartlett window.
i i f2.0N( R R R# t wheret
less_equal( R R# ( ( R t bartlettN s c C s1 t d | ƒ } d d t d t | | d ƒ S( s3 hanning(M) returns the M-point Hanning window.
i f0.5f2.0i N( R R R# R
R ( R R# ( ( R t hanningT s c C s1 t d | ƒ } d d t d t | | d ƒ S( s3 hamming(M) returns the M-point Hamming window.
i f0.54000000000000004f0.46000000000000002f2.0i N( R R R# R
R ( R R# ( ( R t hammingZ s c C s* t t | d j d | ƒ } t | ƒ | S( s? sinc(x) returns sin(pi*x)/(pi*x) at all points of array x.
i f9.9999999999999995e-21N( R Rg RB RJ t sin( RB RJ ( ( R t sinc` s c C s
t i | ƒ S( sn [x,v] = eig(m) returns the eigenvalues of m in x and the corresponding
eigenvectors in the rows of v.
N( t
LinearAlgebrat eigenvectorsR ( R ( ( R t eigf s c C s
t i | ƒ S( sC [u,x,v] = svd(m) return the singular value decomposition of m.
N( Rn t singular_value_decompositionR ( R ( ( R t svdl s c C sT t | ƒ } | i ƒ d d g j o | i } | i } n
d } | } t | | ƒ S( s6 phi = angle(z) return the angle of complex argument z.t Dt Fi N( R t zR t imagt zimagt realt zrealt arctan2( Ru Rw Ry ( ( R t angler s
c C s÷ t | ƒ t i t i t i g j o t | g ƒ } n
t | ƒ } t | ƒ } t | i ƒ d j o
t
d ‚ n d } x | | d j o | d } q| Wt | | ƒ } t | ƒ } t
| d f d ƒ } t | ƒ } x$ | | d d j o | d } qÝ Wt | | ƒ } t | ƒ } | d j od t t | d f | i ƒ ƒ d ƒ } | d | d | d d d … f <t | ƒ d | | d *n | i ƒ d j o t | i d d d
ƒp, | i ƒ d j o& t | i d d d ƒo
| i } n | S( sò return the roots of the polynomial coefficients in p.
The values in the rank-1 array p are coefficients of a polynomial.
If the length of p is n+1 then the polynomial is
p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
i s Input must be a rank-1 array.i Rs i iÿÿÿÿNRt t rtolf9.9999999999999995e-08f1e-14( R t pt typest IntTypet FloatTypet ComplexTypeR R! R# R R( t indR R% t rootR) t onesR t ARp t allcloseRv Rx ( R} R… Rƒ R# R‚ R ( ( R t roots~ s6 %
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(( t __doc__t NumericR R R R R R R) R* R+ R- R2 R3 R6 R8 R9 R; R= RA RD RF RH RI RP RK RX RZ Rn RT Re Rf Ri Rj Rk Rm Rp Rr R{ R‡ (% R R2 RP Rj R3 RK R{ RF R‡ R9 Re R R8 R) R= Rn R RH RD Rp R+ R6 Rf RZ Ri R- RT Rm R R RX Rr RI RA R* Rk R; ( ( R t ? sL
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