;ò ÎÑAHc@sÅdZdklZdeidZeiZdddddd d d d d ddddddddddddddgZdkZdk Z dk Z dk Z dk Z dk Te dgƒdd ZZZe id!ƒZd"Zd#„Zd$„Zd d%„Zd d&„Zd'„Zd(„Zd)„Zd*„Zd+„Zd,„Zd-„Zd.d/„Ze e d0„Z!d1„Z"d.d2d3„Z#d.d d4„Z$d5d6„Z%e id7ƒd8„Z&d9„Z'd:„Z(dS(;sä A set of convenient utilities for numerical work. Most of this module requires Numerical Python or is meant to be used with it. See http://www.pfdubois.com/numpy for details. $Id: numutils.py 958 2005-12-27 23:17:51Z fperez $(sReleases%s <%s>sFernandossum_flats mean_flatsrms_flats base_reprs binary_reprsaminsamaxsamaps zeros_likes empty_likesfrangesdiagonal_matrixsidentitysfromfunction_kwslog2sispower2snormsl1normsl2normsexp_safesinfsinftysInfinitysNumericN(s*if0.0if2.2250738585072014e-308f1.7976931348623157e+308cCs>t|ƒtjott|ttƒƒSnti|ƒSdS(sÐCompute exponentials which safely underflow to zero. Slow but convenient to use. Note that NumArray will introduce proper floating point exception handling with access to the underlying hardware.N(stypesxs ArrayTypesexpsclips exp_safe_MINs exp_safe_MAXsmath(sx((sA/u/d/b/dbachman/=/lib/python2.3/site-packages/IPython/numutils.pysexp_safe4scGstt||ŒƒSdS(s¨amap(function, sequence[, sequence, ...]) -> array. Works like map(), but it returns an array. This is just a convenient shorthand for Numeric.array(map(...))N(sarraysmapsfnsargs(sfnsargs((sA/u/d/b/dbachman/=/lib/python2.3/site-packages/IPython/numutils.pysamap@scCstit|ƒ|ƒSdS(sBamin(m,axis=0) returns the minimum of m along dimension axis. N(sminimumsreducesasarraysmsaxis(smsaxis((sA/u/d/b/dbachman/=/lib/python2.3/site-packages/IPython/numutils.pysaminGscCstit|ƒ|ƒSdS(sBamax(m,axis=0) returns the maximum of m along dimension axis. N(smaximumsreducesasarraysmsaxis(smsaxis((sA/u/d/b/dbachman/=/lib/python2.3/site-packages/IPython/numutils.pysamaxLscCst|i|iƒƒSdS(sÈReturn an array of zeros of the shape and typecode of a. If you don't explicitly need the array to be zeroed, you should instead use empty_like(), which is faster as it only allocates memory.N(szerossasshapestypecode(sa((sA/u/d/b/dbachman/=/lib/python2.3/site-packages/IPython/numutils.pys zeros_likeQscCst|i|iƒƒSdS(sReturn an empty (uninitialized) array of the shape and typecode of a. Note that this does NOT initialize the returned array. If you require your array to be initialized, you should use zeros_like(). This requires Numeric.empty(), which appeared in Numeric 23.7.N(semptysasshapestypecode(sa((sA/u/d/b/dbachman/=/lib/python2.3/site-packages/IPython/numutils.pys empty_likeYscCs8|iƒoti|iƒSntit|ƒƒSdS(s„Return the sum of all the elements of a, flattened out. 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Ref: http://mathworld.wolfram.com/L2-Norm.htmliN(smathssqrtssum_flatsabsolutesa(sa((sA/u/d/b/dbachman/=/lib/python2.3/site-packages/IPython/numutils.pysl2norm€sicCsJ|ddfjott|ƒiƒSntt|ƒ|ƒd|SdS(sˆnorm(a,p=2) -> l-p norm of a.flat Return the l-p norm of a, considered as a flat array. This is NOT a true matrix norm, since arrays of arbitrary rank are always flattened. p can be a number or one of the strings ('inf','Infinity') to get the L-infinity norm. Ref: http://mathworld.wolfram.com/VectorNorm.html http://mathworld.wolfram.com/L-Infinity-Norm.htmlsinfsInfinityf1.0N(spsmaxsabsolutesasflatssum_flat(sasp((sA/u/d/b/dbachman/=/lib/python2.3/site-packages/IPython/numutils.pysnorm‰s cKsÈ|iddƒ|ddj}|tjo|d}d}n|tjo d}ny&|d}||t||ƒ}Wn1t j o%t t ||||ƒƒ}nXt |ƒ||SdS(s&frange([start,] stop[, step, keywords]) -> array of floats Return a Numeric array() containing a progression of floats. Similar to arange(), but defaults to a closed interval. frange(x0, x1) returns [x0, x0+1, x0+2, ..., x1]; start defaults to 0, and the endpoint *is included*. This behavior is different from that of range() and arange(). This is deliberate, since frange will probably be more useful for generating lists of points for function evaluation, and endpoints are often desired in this use. The usual behavior of range() can be obtained by setting the keyword 'closed=0', in this case frange() basically becomes arange(). When step is given, it specifies the increment (or decrement). All arguments can be floating point numbers. frange(x0,x1,d) returns [x0,x0+d,x0+2d,...,xfin] where xfin<=x1. frange can also be called with the keyword 'npts'. This sets the number of points the list should contain (and overrides the value 'step' might have been given). arange() doesn't offer this option. Examples: >>> frange(3) array([ 0., 1., 2., 3.]) >>> frange(3,closed=0) array([ 0., 1., 2.]) >>> frange(1,6,2) array([1, 3, 5]) >>> frange(1,6.5,npts=5) array([ 1. , 2.375, 3.75 , 5.125, 6.5 ]) sclosediif0.0f1.0snptsN( skws setdefaultsendpointsxfinsNonesxinisdeltasnptssfloatsKeyErrorsintsroundsarange(sxinisxfinsdeltaskwsendpointsnpts((sA/u/d/b/dbachman/=/lib/python2.3/site-packages/IPython/numutils.pysfrangešs       #cCs|tt|ƒƒSdS(sWReturn square diagonal matrix whose non-zero elements are given by the input array.N(sdiagsidentityslen(sdiag((sA/u/d/b/dbachman/=/lib/python2.3/site-packages/IPython/numutils.pysdiagonal_matrixÔsslcCsOt|f|d|ƒ}x+t|ƒD]}|f|}d||jpt‚tti||gt|dddƒƒ}tti||dgƒ}|i dƒ odSn||i dƒ}di tt |ƒƒiddƒSdS( s7Return the binary representation of the input number as a string. This is more efficient than using base_repr with base 2. Increase the value of max_length for very large numbers. Note that on 32-bit machines, 2**1023 is the largest integer power of 2 which can be converted to a Python float.liiÿÿÿÿiissLN(snumbers max_lengthsAssertionErrorsmapsoperatorsrshiftsrangesshiftssmodsdigitsscountsindexsjoinsreprsreplace(snumbers max_lengthsdigitssshifts((sA/u/d/b/dbachman/=/lib/python2.3/site-packages/IPython/numutils.pys binary_reprúsf2.0cCsqyt|ƒd}Wn*ttfj oti|ƒ|Sn.Xd|joti|ƒ|Sn t|ƒSdS(s«Return the log(x) in base 2. This is a _slow_ function but which is guaranteed to return the correct integer value if the input is an ineger exact power of 2.is1N( s binary_reprsxsbin_nsAssertionErrors TypeErrorsmathslogsln2slen(sxsln2sbin_n((sA/u/d/b/dbachman/=/lib/python2.3/site-packages/IPython/numutils.pyslog2 s cCs3t|ƒd}d|jodSn t|ƒSdS(sŒReturns the log base 2 of n if n is a power of 2, zero otherwise. Note the potential ambiguity if n==1: 2**0==1, interpret accordingly.is1iN(s binary_reprsnsbin_nslen(snsbin_n((sA/u/d/b/dbachman/=/lib/python2.3/site-packages/IPython/numutils.pysispower2s  cKs|tt|ƒƒ|SdS(sGDrop-in replacement for fromfunction() from Numerical Python. Allows passing keyword arguments to the desired function. Call it as (keywords are optional): fromfunction_kw(MyFunction, dimensions, keywords) The function MyFunction() is responsible for handling the dictionary of keywords it will recieve.N(sfunctionstuplesindicess dimensionsskwargs(sfunctions dimensionsskwargs((sA/u/d/b/dbachman/=/lib/python2.3/site-packages/IPython/numutils.pysfromfunction_kw&s ()s__doc__sIPythonsReleasesauthorss __author__slicenses __license__s__all__s__main__smathsoperatorssyssNumericsarraysinfsinftysInfinityslogs exp_safe_MINs exp_safe_MAXsexp_safesamapsaminsamaxs zeros_likes empty_likessum_flats mean_flatsrms_flatsl1normsl2normsnormsNonesfrangesdiagonal_matrixsidentitys base_reprs binary_reprslog2sispower2sfromfunction_kw("sexp_safes exp_safe_MINs__main__soperatorsinfsrms_flats binary_reprsfromfunction_kwsfrangesInfinitys__all__s empty_likesispower2smathsinftyslog2s mean_flats __license__s zeros_likes __author__ssyssl2normsamapsReleasessum_flatsdiagonal_matrixsamaxsidentitysamins exp_safe_MAXsNumerics base_reprsnormsl1norm((sA/u/d/b/dbachman/=/lib/python2.3/site-packages/IPython/numutils.pys?sB  N            :