""" Numerical python functions written for compatability with MATLAB commands with the same names. MATLAB compatible functions ------------------------------- :func:cohere Coherence (normalized cross spectral density) :func:csd Cross spectral density uing Welch's average periodogram :func:detrend Remove the mean or best fit line from an array :func:find Return the indices where some condition is true; numpy.nonzero is similar but more general. :func:griddata interpolate irregularly distributed data to a regular grid. :func:prctile find the percentiles of a sequence :func:prepca Principal Component Analysis :func:psd Power spectral density uing Welch's average periodogram :func:rk4 A 4th order runge kutta integrator for 1D or ND systems :func:specgram Spectrogram (power spectral density over segments of time) Miscellaneous functions ------------------------- Functions that don't exist in MATLAB, but are useful anyway: :meth:cohere_pairs Coherence over all pairs. This is not a MATLAB function, but we compute coherence a lot in my lab, and we compute it for a lot of pairs. This function is optimized to do this efficiently by caching the direct FFTs. :meth:rk4 A 4th order Runge-Kutta ODE integrator in case you ever find yourself stranded without scipy (and the far superior scipy.integrate tools) :meth:contiguous_regions return the indices of the regions spanned by some logical mask :meth:cross_from_below return the indices where a 1D array crosses a threshold from below :meth:cross_from_above return the indices where a 1D array crosses a threshold from above record array helper functions ------------------------------- A collection of helper methods for numpyrecord arrays .. _htmlonly: See :ref:misc-examples-index :meth:rec2txt pretty print a record array :meth:rec2csv store record array in CSV file :meth:csv2rec import record array from CSV file with type inspection :meth:rec_append_fields adds field(s)/array(s) to record array :meth:rec_drop_fields drop fields from record array :meth:rec_join join two record arrays on sequence of fields :meth:recs_join a simple join of multiple recarrays using a single column as a key :meth:rec_groupby summarize data by groups (similar to SQL GROUP BY) :meth:rec_summarize helper code to filter rec array fields into new fields For the rec viewer functions(e rec2csv), there are a bunch of Format objects you can pass into the functions that will do things like color negative values red, set percent formatting and scaling, etc. Example usage:: r = csv2rec('somefile.csv', checkrows=0) formatd = dict( weight = FormatFloat(2), change = FormatPercent(2), cost = FormatThousands(2), ) rec2excel(r, 'test.xls', formatd=formatd) rec2csv(r, 'test.csv', formatd=formatd) scroll = rec2gtk(r, formatd=formatd) win = gtk.Window() win.set_size_request(600,800) win.add(scroll) win.show_all() gtk.main() Deprecated functions --------------------- The following are deprecated; please import directly from numpy (with care--function signatures may differ): :meth:load load ASCII file - use numpy.loadtxt :meth:save save ASCII file - use numpy.savetxt """ from __future__ import division, print_function import csv, warnings, copy, os, operator from itertools import izip import numpy as np ma = np.ma from matplotlib import verbose import matplotlib.cbook as cbook from matplotlib import docstring from matplotlib.path import Path def logspace(xmin,xmax,N): return np.exp(np.linspace(np.log(xmin), np.log(xmax), N)) def _norm(x): "return sqrt(x dot x)" return np.sqrt(np.dot(x,x)) def window_hanning(x): "return x times the hanning window of len(x)" return np.hanning(len(x))*x def window_none(x): "No window function; simply return x" return x def detrend(x, key=None): if key is None or key=='constant': return detrend_mean(x) elif key=='linear': return detrend_linear(x) def demean(x, axis=0): "Return x minus its mean along the specified axis" x = np.asarray(x) if axis == 0 or axis is None or x.ndim <= 1: return x - x.mean(axis) ind = [slice(None)] * x.ndim ind[axis] = np.newaxis return x - x.mean(axis)[ind] def detrend_mean(x): "Return x minus the mean(x)" return x - x.mean() def detrend_none(x): "Return x: no detrending" return x def detrend_linear(y): "Return y minus best fit line; 'linear' detrending " # This is faster than an algorithm based on linalg.lstsq. x = np.arange(len(y), dtype=np.float_) C = np.cov(x, y, bias=1) b = C[0,1]/C[0,0] a = y.mean() - b*x.mean() return y - (b*x + a) #This is a helper function that implements the commonality between the #psd, csd, and spectrogram. It is *NOT* meant to be used outside of mlab def _spectral_helper(x, y, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning, noverlap=0, pad_to=None, sides='default', scale_by_freq=None): #The checks for if y is x are so that we can use the same function to #implement the core of psd(), csd(), and spectrogram() without doing #extra calculations. We return the unaveraged Pxy, freqs, and t. same_data = y is x #Make sure we're dealing with a numpy array. If y and x were the same #object to start with, keep them that way x = np.asarray(x) if not same_data: y = np.asarray(y) else: y = x # zero pad x and y up to NFFT if they are shorter than NFFT if len(x)1: Pxy = Pxy.mean(axis=1) return Pxy, freqs @docstring.dedent_interpd def specgram(x, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning, noverlap=128, pad_to=None, sides='default', scale_by_freq=None): """ Compute a spectrogram of data in *x*. Data are split into *NFFT* length segments and the PSD of each section is computed. The windowing function *window* is applied to each segment, and the amount of overlap of each segment is specified with *noverlap*. If *x* is real (i.e. non-complex) only the spectrum of the positive frequencie is returned. If *x* is complex then the complete spectrum is returned. %(PSD)s *noverlap*: integer The number of points of overlap between blocks. The default value is 128. Returns a tuple (*Pxx*, *freqs*, *t*): - *Pxx*: 2-D array, columns are the periodograms of successive segments - *freqs*: 1-D array of frequencies corresponding to the rows in Pxx - *t*: 1-D array of times corresponding to midpoints of segments. .. seealso:: :func:psd :func:psd differs in the default overlap; in returning the mean of the segment periodograms; and in not returning times. """ assert(NFFT > noverlap) Pxx, freqs, t = _spectral_helper(x, x, NFFT, Fs, detrend, window, noverlap, pad_to, sides, scale_by_freq) Pxx = Pxx.real #Needed since helper implements generically return Pxx, freqs, t _coh_error = """Coherence is calculated by averaging over *NFFT* length segments. Your signal is too short for your choice of *NFFT*. """ @docstring.dedent_interpd def cohere(x, y, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning, noverlap=0, pad_to=None, sides='default', scale_by_freq=None): """ The coherence between *x* and *y*. Coherence is the normalized cross spectral density: .. math:: C_{xy} = \\frac{|P_{xy}|^2}{P_{xx}P_{yy}} *x*, *y* Array or sequence containing the data %(PSD)s *noverlap*: integer The number of points of overlap between blocks. The default value is 0 (no overlap). The return value is the tuple (*Cxy*, *f*), where *f* are the frequencies of the coherence vector. For cohere, scaling the individual densities by the sampling frequency has no effect, since the factors cancel out. .. seealso:: :func:psd and :func:csd For information about the methods used to compute :math:P_{xy}, :math:P_{xx} and :math:P_{yy}. """ if len(x)<2*NFFT: raise ValueError(_coh_error) Pxx, f = psd(x, NFFT, Fs, detrend, window, noverlap, pad_to, sides, scale_by_freq) Pyy, f = psd(y, NFFT, Fs, detrend, window, noverlap, pad_to, sides, scale_by_freq) Pxy, f = csd(x, y, NFFT, Fs, detrend, window, noverlap, pad_to, sides, scale_by_freq) Cxy = np.divide(np.absolute(Pxy)**2, Pxx*Pyy) Cxy.shape = (len(f),) return Cxy, f def donothing_callback(*args): pass def cohere_pairs( X, ij, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning, noverlap=0, preferSpeedOverMemory=True, progressCallback=donothing_callback, returnPxx=False): u""" Call signature:: Cxy, Phase, freqs = cohere_pairs( X, ij, ...) Compute the coherence and phase for all pairs *ij*, in *X*. *X* is a *numSamples* * *numCols* array *ij* is a list of tuples. Each tuple is a pair of indexes into the columns of X for which you want to compute coherence. For example, if *X* has 64 columns, and you want to compute all nonredundant pairs, define *ij* as:: ij = [] for i in range(64): for j in range(i+1,64): ij.append( (i,j) ) *preferSpeedOverMemory* is an optional bool. Defaults to true. If False, limits the caching by only making one, rather than two, complex cache arrays. This is useful if memory becomes critical. Even when *preferSpeedOverMemory* is False, :func:cohere_pairs will still give significant performace gains over calling :func:cohere for each pair, and will use subtantially less memory than if *preferSpeedOverMemory* is True. In my tests with a 43000,64 array over all nonredundant pairs, *preferSpeedOverMemory* = True delivered a 33% performance boost on a 1.7GHZ Athlon with 512MB RAM compared with *preferSpeedOverMemory* = False. But both solutions were more than 10x faster than naively crunching all possible pairs through :func:cohere. Returns:: (Cxy, Phase, freqs) where: - *Cxy*: dictionary of (*i*, *j*) tuples -> coherence vector for that pair. I.e., Cxy[(i,j) = cohere(X[:,i], X[:,j]). Number of dictionary keys is len(ij). - *Phase*: dictionary of phases of the cross spectral density at each frequency for each pair. Keys are (*i*, *j*). - *freqs*: vector of frequencies, equal in length to either the coherence or phase vectors for any (*i*, *j*) key. Eg., to make a coherence Bode plot:: subplot(211) plot( freqs, Cxy[(12,19)]) subplot(212) plot( freqs, Phase[(12,19)]) For a large number of pairs, :func:cohere_pairs can be much more efficient than just calling :func:cohere for each pair, because it caches most of the intensive computations. If :math:N is the number of pairs, this function is :math:O(N) for most of the heavy lifting, whereas calling cohere for each pair is :math:O(N^2). However, because of the caching, it is also more memory intensive, making 2 additional complex arrays with approximately the same number of elements as *X*. See :file:test/cohere_pairs_test.py in the src tree for an example script that shows that this :func:cohere_pairs and :func:cohere give the same results for a given pair. .. seealso:: :func:psd For information about the methods used to compute :math:P_{xy}, :math:P_{xx} and :math:P_{yy}. """ numRows, numCols = X.shape # zero pad if X is too short if numRows < NFFT: tmp = X X = np.zeros( (NFFT, numCols), X.dtype) X[:numRows,:] = tmp del tmp numRows, numCols = X.shape # get all the columns of X that we are interested in by checking # the ij tuples allColumns = set() for i,j in ij: allColumns.add(i); allColumns.add(j) Ncols = len(allColumns) # for real X, ignore the negative frequencies if np.iscomplexobj(X): numFreqs = NFFT else: numFreqs = NFFT//2+1 # cache the FFT of every windowed, detrended NFFT length segement # of every channel. If preferSpeedOverMemory, cache the conjugate # as well if cbook.iterable(window): assert(len(window) == NFFT) windowVals = window else: windowVals = window(np.ones(NFFT, X.dtype)) ind = range(0, numRows-NFFT+1, NFFT-noverlap) numSlices = len(ind) FFTSlices = {} FFTConjSlices = {} Pxx = {} slices = range(numSlices) normVal = np.linalg.norm(windowVals)**2 for iCol in allColumns: progressCallback(i/Ncols, 'Cacheing FFTs') Slices = np.zeros( (numSlices,numFreqs), dtype=np.complex_) for iSlice in slices: thisSlice = X[ind[iSlice]:ind[iSlice]+NFFT, iCol] thisSlice = windowVals*detrend(thisSlice) Slices[iSlice,:] = np.fft.fft(thisSlice)[:numFreqs] FFTSlices[iCol] = Slices if preferSpeedOverMemory: FFTConjSlices[iCol] = np.conjugate(Slices) Pxx[iCol] = np.divide(np.mean(abs(Slices)**2, axis=0), normVal) del Slices, ind, windowVals # compute the coherences and phases for all pairs using the # cached FFTs Cxy = {} Phase = {} count = 0 N = len(ij) for i,j in ij: count +=1 if count%10==0: progressCallback(count/N, 'Computing coherences') if preferSpeedOverMemory: Pxy = FFTSlices[i] * FFTConjSlices[j] else: Pxy = FFTSlices[i] * np.conjugate(FFTSlices[j]) if numSlices>1: Pxy = np.mean(Pxy, axis=0) #Pxy = np.divide(Pxy, normVal) Pxy /= normVal #Cxy[(i,j)] = np.divide(np.absolute(Pxy)**2, Pxx[i]*Pxx[j]) Cxy[i,j] = abs(Pxy)**2 / (Pxx[i]*Pxx[j]) Phase[i,j] = np.arctan2(Pxy.imag, Pxy.real) freqs = Fs/NFFT*np.arange(numFreqs) if returnPxx: return Cxy, Phase, freqs, Pxx else: return Cxy, Phase, freqs def entropy(y, bins): r""" Return the entropy of the data in *y*. .. math:: \sum p_i \log_2(p_i) where :math:p_i is the probability of observing *y* in the :math:i^{th} bin of *bins*. *bins* can be a number of bins or a range of bins; see :func:numpy.histogram. Compare *S* with analytic calculation for a Gaussian:: x = mu + sigma * randn(200000) Sanalytic = 0.5 * ( 1.0 + log(2*pi*sigma**2.0) ) """ n,bins = np.histogram(y, bins) n = n.astype(np.float_) n = np.take(n, np.nonzero(n)[0]) # get the positive p = np.divide(n, len(y)) delta = bins[1]-bins[0] S = -1.0*np.sum(p*log(p)) + log(delta) #S = -1.0*np.sum(p*log(p)) return S def normpdf(x, *args): "Return the normal pdf evaluated at *x*; args provides *mu*, *sigma*" mu, sigma = args return 1./(np.sqrt(2*np.pi)*sigma)*np.exp(-0.5 * (1./sigma*(x - mu))**2) def levypdf(x, gamma, alpha): "Returm the levy pdf evaluated at *x* for params *gamma*, *alpha*" N = len(x) if N%2 != 0: raise ValueError('x must be an event length array; try\n' + \ 'x = np.linspace(minx, maxx, N), where N is even') dx = x[1]-x[0] f = 1/(N*dx)*np.arange(-N/2, N/2, np.float_) ind = np.concatenate([np.arange(N/2, N, int), np.arange(0, N/2, int)]) df = f[1]-f[0] cfl = exp(-gamma*np.absolute(2*pi*f)**alpha) px = np.fft.fft(np.take(cfl,ind)*df).astype(np.float_) return np.take(px, ind) def find(condition): "Return the indices where ravel(condition) is true" res, = np.nonzero(np.ravel(condition)) return res def longest_contiguous_ones(x): """ Return the indices of the longest stretch of contiguous ones in *x*, assuming *x* is a vector of zeros and ones. If there are two equally long stretches, pick the first. """ x = np.ravel(x) if len(x)==0: return np.array([]) ind = (x==0).nonzero()[0] if len(ind)==0: return np.arange(len(x)) if len(ind)==len(x): return np.array([]) y = np.zeros( (len(x)+2,), x.dtype) y[1:-1] = x dif = np.diff(y) up = (dif == 1).nonzero()[0]; dn = (dif == -1).nonzero()[0]; i = (dn-up == max(dn - up)).nonzero()[0][0] ind = np.arange(up[i], dn[i]) return ind def longest_ones(x): '''alias for longest_contiguous_ones''' return longest_contiguous_ones(x) def prepca(P, frac=0): """ WARNING: this function is deprecated -- please see class PCA instead Compute the principal components of *P*. *P* is a (*numVars*, *numObs*) array. *frac* is the minimum fraction of variance that a component must contain to be included. Return value is a tuple of the form (*Pcomponents*, *Trans*, *fracVar*) where: - *Pcomponents* : a (numVars, numObs) array - *Trans* : the weights matrix, ie, *Pcomponents* = *Trans* * *P* - *fracVar* : the fraction of the variance accounted for by each component returned A similar function of the same name was in the MATLAB R13 Neural Network Toolbox but is not found in later versions; its successor seems to be called "processpcs". """ warnings.warn('This function is deprecated -- see class PCA instead') U,s,v = np.linalg.svd(P) varEach = s**2/P.shape[1] totVar = varEach.sum() fracVar = varEach/totVar ind = slice((fracVar>=frac).sum()) # select the components that are greater Trans = U[:,ind].transpose() # The transformed data Pcomponents = np.dot(Trans,P) return Pcomponents, Trans, fracVar[ind] class PCA: def __init__(self, a): """ compute the SVD of a and store data for PCA. Use project to project the data onto a reduced set of dimensions Inputs: *a*: a numobservations x numdims array Attrs: *a* a centered unit sigma version of input a *numrows*, *numcols*: the dimensions of a *mu* : a numdims array of means of a *sigma* : a numdims array of atandard deviation of a *fracs* : the proportion of variance of each of the principal components *Wt* : the weight vector for projecting a numdims point or array into PCA space *Y* : a projected into PCA space The factor loadings are in the Wt factor, ie the factor loadings for the 1st principal component are given by Wt[0] """ n, m = a.shape if nnumcols') self.numrows, self.numcols = n, m self.mu = a.mean(axis=0) self.sigma = a.std(axis=0) a = self.center(a) self.a = a U, s, Vh = np.linalg.svd(a, full_matrices=False) Y = np.dot(Vh, a.T).T vars = s**2/float(len(s)) self.fracs = vars/vars.sum() self.Wt = Vh self.Y = Y def project(self, x, minfrac=0.): 'project x onto the principle axes, dropping any axes where fraction of variance=minfrac if ndims==2: Yreduced = Y[:,mask] else: Yreduced = Y[mask] return Yreduced def center(self, x): 'center the data using the mean and sigma from training set a' return (x - self.mu)/self.sigma @staticmethod def _get_colinear(): c0 = np.array([ 0.19294738, 0.6202667 , 0.45962655, 0.07608613, 0.135818 , 0.83580842, 0.07218851, 0.48318321, 0.84472463, 0.18348462, 0.81585306, 0.96923926, 0.12835919, 0.35075355, 0.15807861, 0.837437 , 0.10824303, 0.1723387 , 0.43926494, 0.83705486]) c1 = np.array([ -1.17705601, -0.513883 , -0.26614584, 0.88067144, 1.00474954, -1.1616545 , 0.0266109 , 0.38227157, 1.80489433, 0.21472396, -1.41920399, -2.08158544, -0.10559009, 1.68999268, 0.34847107, -0.4685737 , 1.23980423, -0.14638744, -0.35907697, 0.22442616]) c2 = c0 + 2*c1 c3 = -3*c0 + 4*c1 a = np.array([c3, c0, c1, c2]).T return a def prctile(x, p = (0.0, 25.0, 50.0, 75.0, 100.0)): """ Return the percentiles of *x*. *p* can either be a sequence of percentile values or a scalar. If *p* is a sequence, the ith element of the return sequence is the *p*(i)-th percentile of *x*. If *p* is a scalar, the largest value of *x* less than or equal to the *p* percentage point in the sequence is returned. """ # This implementation derived from scipy.stats.scoreatpercentile def _interpolate(a, b, fraction): """Returns the point at the given fraction between a and b, where 'fraction' must be between 0 and 1. """ return a + (b - a)*fraction scalar = True if cbook.iterable(p): scalar = False per = np.array(p) values = np.array(x).ravel() # copy values.sort() idxs = per /100. * (values.shape[0] - 1) ai = idxs.astype(np.int) bi = ai + 1 frac = idxs % 1 # handle cases where attempting to interpolate past last index cond = bi >= len(values) if scalar: if cond: ai -= 1 bi -= 1 frac += 1 else: ai[cond] -= 1 bi[cond] -= 1 frac[cond] += 1 return _interpolate(values[ai],values[bi],frac) def prctile_rank(x, p): """ Return the rank for each element in *x*, return the rank 0..len(*p*). Eg if *p* = (25, 50, 75), the return value will be a len(*x*) array with values in [0,1,2,3] where 0 indicates the value is less than the 25th percentile, 1 indicates the value is >= the 25th and < 50th percentile, ... and 3 indicates the value is above the 75th percentile cutoff. *p* is either an array of percentiles in [0..100] or a scalar which indicates how many quantiles of data you want ranked. """ if not cbook.iterable(p): p = np.arange(100.0/p, 100.0, 100.0/p) else: p = np.asarray(p) if p.max()<=1 or p.min()<0 or p.max()>100: raise ValueError('percentiles should be in range 0..100, not 0..1') ptiles = prctile(x, p) return np.searchsorted(ptiles, x) def center_matrix(M, dim=0): """ Return the matrix *M* with each row having zero mean and unit std. If *dim* = 1 operate on columns instead of rows. (*dim* is opposite to the numpy axis kwarg.) """ M = np.asarray(M, np.float_) if dim: M = (M - M.mean(axis=0)) / M.std(axis=0) else: M = (M - M.mean(axis=1)[:,np.newaxis]) M = M / M.std(axis=1)[:,np.newaxis] return M def rk4(derivs, y0, t): """ Integrate 1D or ND system of ODEs using 4-th order Runge-Kutta. This is a toy implementation which may be useful if you find yourself stranded on a system w/o scipy. Otherwise use :func:scipy.integrate. *y0* initial state vector *t* sample times *derivs* returns the derivative of the system and has the signature dy = derivs(yi, ti) Example 1 :: ## 2D system def derivs6(x,t): d1 = x[0] + 2*x[1] d2 = -3*x[0] + 4*x[1] return (d1, d2) dt = 0.0005 t = arange(0.0, 2.0, dt) y0 = (1,2) yout = rk4(derivs6, y0, t) Example 2:: ## 1D system alpha = 2 def derivs(x,t): return -alpha*x + exp(-t) y0 = 1 yout = rk4(derivs, y0, t) If you have access to scipy, you should probably be using the scipy.integrate tools rather than this function. """ try: Ny = len(y0) except TypeError: yout = np.zeros( (len(t),), np.float_) else: yout = np.zeros( (len(t), Ny), np.float_) yout[0] = y0 i = 0 for i in np.arange(len(t)-1): thist = t[i] dt = t[i+1] - thist dt2 = dt/2.0 y0 = yout[i] k1 = np.asarray(derivs(y0, thist)) k2 = np.asarray(derivs(y0 + dt2*k1, thist+dt2)) k3 = np.asarray(derivs(y0 + dt2*k2, thist+dt2)) k4 = np.asarray(derivs(y0 + dt*k3, thist+dt)) yout[i+1] = y0 + dt/6.0*(k1 + 2*k2 + 2*k3 + k4) return yout def bivariate_normal(X, Y, sigmax=1.0, sigmay=1.0, mux=0.0, muy=0.0, sigmaxy=0.0): """ Bivariate Gaussian distribution for equal shape *X*, *Y*. See bivariate normal _ at mathworld. """ Xmu = X-mux Ymu = Y-muy rho = sigmaxy/(sigmax*sigmay) z = Xmu**2/sigmax**2 + Ymu**2/sigmay**2 - 2*rho*Xmu*Ymu/(sigmax*sigmay) denom = 2*np.pi*sigmax*sigmay*np.sqrt(1-rho**2) return np.exp( -z/(2*(1-rho**2))) / denom def get_xyz_where(Z, Cond): """ *Z* and *Cond* are *M* x *N* matrices. *Z* are data and *Cond* is a boolean matrix where some condition is satisfied. Return value is (*x*, *y*, *z*) where *x* and *y* are the indices into *Z* and *z* are the values of *Z* at those indices. *x*, *y*, and *z* are 1D arrays. """ X,Y = np.indices(Z.shape) return X[Cond], Y[Cond], Z[Cond] def get_sparse_matrix(M,N,frac=0.1): """ Return a *M* x *N* sparse matrix with *frac* elements randomly filled. """ data = np.zeros((M,N))*0. for i in range(int(M*N*frac)): x = np.random.randint(0,M-1) y = np.random.randint(0,N-1) data[x,y] = np.random.rand() return data def dist(x,y): """ Return the distance between two points. """ d = x-y return np.sqrt(np.dot(d,d)) def dist_point_to_segment(p, s0, s1): """ Get the distance of a point to a segment. *p*, *s0*, *s1* are *xy* sequences This algorithm from http://softsurfer.com/Archive/algorithm_0102/algorithm_0102.htm#Distance%20to%20Ray%20or%20Segment """ p = np.asarray(p, np.float_) s0 = np.asarray(s0, np.float_) s1 = np.asarray(s1, np.float_) v = s1 - s0 w = p - s0 c1 = np.dot(w,v); if ( c1 <= 0 ): return dist(p, s0); c2 = np.dot(v,v) if ( c2 <= c1 ): return dist(p, s1); b = c1 / c2 pb = s0 + b * v; return dist(p, pb) def segments_intersect(s1, s2): """ Return *True* if *s1* and *s2* intersect. *s1* and *s2* are defined as:: s1: (x1, y1), (x2, y2) s2: (x3, y3), (x4, y4) """ (x1, y1), (x2, y2) = s1 (x3, y3), (x4, y4) = s2 den = ((y4-y3) * (x2-x1)) - ((x4-x3)*(y2-y1)) n1 = ((x4-x3) * (y1-y3)) - ((y4-y3)*(x1-x3)) n2 = ((x2-x1) * (y1-y3)) - ((y2-y1)*(x1-x3)) if den == 0: # lines parallel return False u1 = n1/den u2 = n2/den return 0.0 <= u1 <= 1.0 and 0.0 <= u2 <= 1.0 def fftsurr(x, detrend=detrend_none, window=window_none): """ Compute an FFT phase randomized surrogate of *x*. """ if cbook.iterable(window): x=window*detrend(x) else: x = window(detrend(x)) z = np.fft.fft(x) a = 2.*np.pi*1j phase = a * np.random.rand(len(x)) z = z*np.exp(phase) return np.fft.ifft(z).real def liaupunov(x, fprime): """ *x* is a very long trajectory from a map, and *fprime* returns the derivative of *x*. This function will be removed from matplotlib. Returns : .. math:: \lambda = \\frac{1}{n}\\sum \\ln|f^'(x_i)| .. seealso:: Lyapunov Exponent Sec 10.5 Strogatz (1994) "Nonlinear Dynamics and Chaos". Wikipedia article on Lyapunov Exponent _. .. note:: What the function here calculates may not be what you really want; *caveat emptor*. It also seems that this function's name is badly misspelled. """ warnings.warn("This does not belong in matplotlib and will be removed", DeprecationWarning) # 2009/06/13 return np.mean(np.log(np.absolute(fprime(x)))) class FIFOBuffer: """ A FIFO queue to hold incoming *x*, *y* data in a rotating buffer using numpy arrays under the hood. It is assumed that you will call asarrays much less frequently than you add data to the queue -- otherwise another data structure will be faster. This can be used to support plots where data is added from a real time feed and the plot object wants to grab data from the buffer and plot it to screen less freqeuently than the incoming. If you set the *dataLim* attr to :class:~matplotlib.transforms.BBox (eg :attr:matplotlib.Axes.dataLim), the *dataLim* will be updated as new data come in. TODO: add a grow method that will extend nmax .. note:: mlab seems like the wrong place for this class. """ def __init__(self, nmax): """ Buffer up to *nmax* points. """ self._xa = np.zeros((nmax,), np.float_) self._ya = np.zeros((nmax,), np.float_) self._xs = np.zeros((nmax,), np.float_) self._ys = np.zeros((nmax,), np.float_) self._ind = 0 self._nmax = nmax self.dataLim = None self.callbackd = {} def register(self, func, N): """ Call *func* every time *N* events are passed; *func* signature is func(fifo). """ self.callbackd.setdefault(N, []).append(func) def add(self, x, y): """ Add scalar *x* and *y* to the queue. """ if self.dataLim is not None: xy = np.asarray([(x,y),]) self.dataLim.update_from_data_xy(xy, None) ind = self._ind % self._nmax #print 'adding to fifo:', ind, x, y self._xs[ind] = x self._ys[ind] = y for N,funcs in self.callbackd.iteritems(): if (self._ind%N)==0: for func in funcs: func(self) self._ind += 1 def last(self): """ Get the last *x*, *y* or *None*. *None* if no data set. """ if self._ind==0: return None, None ind = (self._ind-1) % self._nmax return self._xs[ind], self._ys[ind] def asarrays(self): """ Return *x* and *y* as arrays; their length will be the len of data added or *nmax*. """ if self._ind All rights reserved. This license was generated from the BSD license template as found in: http://www.opensource.org/licenses/bsd-license.php Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of the IPython project nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. """ import operator import math #***************************************************************************** # Globals #**************************************************************************** # function definitions exp_safe_MIN = math.log(2.2250738585072014e-308) exp_safe_MAX = 1.7976931348623157e+308 def exp_safe(x): """ Compute exponentials which safely underflow to zero. Slow, but convenient to use. Note that numpy provides proper floating point exception handling with access to the underlying hardware. """ if type(x) is np.ndarray: return exp(np.clip(x,exp_safe_MIN,exp_safe_MAX)) else: return math.exp(x) def amap(fn,*args): """ amap(function, sequence[, sequence, ...]) -> array. Works like :func:map, but it returns an array. This is just a convenient shorthand for numpy.array(map(...)). """ return np.array(map(fn,*args)) def rms_flat(a): """ Return the root mean square of all the elements of *a*, flattened out. """ return np.sqrt(np.mean(np.absolute(a)**2)) def l1norm(a): """ Return the *l1* norm of *a*, flattened out. Implemented as a separate function (not a call to :func:norm for speed). """ return np.sum(np.absolute(a)) def l2norm(a): """ Return the *l2* norm of *a*, flattened out. Implemented as a separate function (not a call to :func:norm for speed). """ return np.sqrt(np.sum(np.absolute(a)**2)) def norm_flat(a,p=2): """ norm(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 the string 'Infinity' to get the L-infinity norm. """ # This function was being masked by a more general norm later in # the file. We may want to simply delete it. if p=='Infinity': return np.amax(np.absolute(a)) else: return (np.sum(np.absolute(a)**p))**(1.0/p) def frange(xini,xfin=None,delta=None,**kw): """ frange([start,] stop[, step, keywords]) -> array of floats Return a numpy ndarray containing a progression of floats. Similar to :func:numpy.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 :func:range and :func:numpy.arange. This is deliberate, since :func: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 :func:range can be obtained by setting the keyword *closed* = 0, in this case, :func:frange basically becomes :func:numpy.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*. :func: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). :func:numpy.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]) or 1,3,5,7, depending on floating point vagueries >>> frange(1,6.5,npts=5) array([ 1. , 2.375, 3.75 , 5.125, 6.5 ]) """ #defaults kw.setdefault('closed',1) endpoint = kw['closed'] != 0 # funny logic to allow the *first* argument to be optional (like range()) # This was modified with a simpler version from a similar frange() found # at http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/66472 if xfin == None: xfin = xini + 0.0 xini = 0.0 if delta == None: delta = 1.0 # compute # of points, spacing and return final list try: npts=kw['npts'] delta=(xfin-xini)/float(npts-endpoint) except KeyError: npts = int(round((xfin-xini)/delta)) + endpoint #npts = int(floor((xfin-xini)/delta)*(1.0+1e-10)) + endpoint # round finds the nearest, so the endpoint can be up to # delta/2 larger than xfin. return np.arange(npts)*delta+xini # end frange() def identity(n, rank=2, dtype='l', typecode=None): """ Returns the identity matrix of shape (*n*, *n*, ..., *n*) (rank *r*). For ranks higher than 2, this object is simply a multi-index Kronecker delta:: / 1 if i0=i1=...=iR, id[i0,i1,...,iR] = -| \ 0 otherwise. Optionally a *dtype* (or typecode) may be given (it defaults to 'l'). Since rank defaults to 2, this function behaves in the default case (when only *n* is given) like numpy.identity(n) -- but surprisingly, it is much faster. """ if typecode is not None: dtype = typecode iden = np.zeros((n,)*rank, dtype) for i in range(n): idx = (i,)*rank iden[idx] = 1 return iden def base_repr (number, base = 2, padding = 0): """ Return the representation of a *number* in any given *base*. """ chars = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ' if number < base: \ return (padding - 1) * chars [0] + chars [int (number)] max_exponent = int (math.log (number)/math.log (base)) max_power = long (base) ** max_exponent lead_digit = int (number/max_power) return chars [lead_digit] + \ base_repr (number - max_power * lead_digit, base, \ max (padding - 1, max_exponent)) def binary_repr(number, max_length = 1025): """ Return the binary representation of the input *number* as a string. This is more efficient than using :func: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. """ #assert number < 2L << max_length shifts = map (operator.rshift, max_length * [number], \ range (max_length - 1, -1, -1)) digits = map (operator.mod, shifts, max_length * [2]) if not digits.count (1): return 0 digits = digits [digits.index (1):] return ''.join (map (repr, digits)).replace('L','') def log2(x,ln2 = math.log(2.0)): """ 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 integer exact power of 2. """ try: bin_n = binary_repr(x)[1:] except (AssertionError,TypeError): return math.log(x)/ln2 else: if '1' in bin_n: return math.log(x)/ln2 else: return len(bin_n) def ispower2(n): """ Returns 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. """ bin_n = binary_repr(n)[1:] if '1' in bin_n: return 0 else: return len(bin_n) def isvector(X): """ Like the MATLAB function with the same name, returns *True* if the supplied numpy array or matrix *X* looks like a vector, meaning it has a one non-singleton axis (i.e., it can have multiple axes, but all must have length 1, except for one of them). If you just want to see if the array has 1 axis, use X.ndim == 1. """ return np.prod(X.shape)==np.max(X.shape) ### end fperez numutils code #helpers for loading, saving, manipulating and viewing numpy record arrays def safe_isnan(x): ':func:numpy.isnan for arbitrary types' if cbook.is_string_like(x): return False try: b = np.isnan(x) except NotImplementedError: return False except TypeError: return False else: return b def safe_isinf(x): ':func:numpy.isinf for arbitrary types' if cbook.is_string_like(x): return False try: b = np.isinf(x) except NotImplementedError: return False except TypeError: return False else: return b def rec_append_fields(rec, names, arrs, dtypes=None): """ Return a new record array with field names populated with data from arrays in *arrs*. If appending a single field, then *names*, *arrs* and *dtypes* do not have to be lists. They can just be the values themselves. """ if (not cbook.is_string_like(names) and cbook.iterable(names) \ and len(names) and cbook.is_string_like(names[0])): if len(names) != len(arrs): raise ValueError("number of arrays do not match number of names") else: # we have only 1 name and 1 array names = [names] arrs = [arrs] arrs = map(np.asarray, arrs) if dtypes is None: dtypes = [a.dtype for a in arrs] elif not cbook.iterable(dtypes): dtypes = [dtypes] if len(arrs) != len(dtypes): if len(dtypes) == 1: dtypes = dtypes * len(arrs) else: raise ValueError("dtypes must be None, a single dtype or a list") newdtype = np.dtype(rec.dtype.descr + zip(names, dtypes)) newrec = np.recarray(rec.shape, dtype=newdtype) for field in rec.dtype.fields: newrec[field] = rec[field] for name, arr in zip(names, arrs): newrec[name] = arr return newrec def rec_drop_fields(rec, names): """ Return a new numpy record array with fields in *names* dropped. """ names = set(names) Nr = len(rec) newdtype = np.dtype([(name, rec.dtype[name]) for name in rec.dtype.names if name not in names]) newrec = np.recarray(rec.shape, dtype=newdtype) for field in newdtype.names: newrec[field] = rec[field] return newrec def rec_keep_fields(rec, names): """ Return a new numpy record array with only fields listed in names """ if cbook.is_string_like(names): names = names.split(',') arrays = [] for name in names: arrays.append(rec[name]) return np.rec.fromarrays(arrays, names=names) def rec_groupby(r, groupby, stats): """ *r* is a numpy record array *groupby* is a sequence of record array attribute names that together form the grouping key. eg ('date', 'productcode') *stats* is a sequence of (*attr*, *func*, *outname*) tuples which will call x = func(attr) and assign *x* to the record array output with attribute *outname*. For example:: stats = ( ('sales', len, 'numsales'), ('sales', np.mean, 'avgsale') ) Return record array has *dtype* names for each attribute name in the the *groupby* argument, with the associated group values, and for each outname name in the *stats* argument, with the associated stat summary output. """ # build a dictionary from groupby keys-> list of indices into r with # those keys rowd = dict() for i, row in enumerate(r): key = tuple([row[attr] for attr in groupby]) rowd.setdefault(key, []).append(i) # sort the output by groupby keys keys = rowd.keys() keys.sort() rows = [] for key in keys: row = list(key) # get the indices for this groupby key ind = rowd[key] thisr = r[ind] # call each stat function for this groupby slice row.extend([func(thisr[attr]) for attr, func, outname in stats]) rows.append(row) # build the output record array with groupby and outname attributes attrs, funcs, outnames = zip(*stats) names = list(groupby) names.extend(outnames) return np.rec.fromrecords(rows, names=names) def rec_summarize(r, summaryfuncs): """ *r* is a numpy record array *summaryfuncs* is a list of (*attr*, *func*, *outname*) tuples which will apply *func* to the the array *r*[attr] and assign the output to a new attribute name *outname*. The returned record array is identical to *r*, with extra arrays for each element in *summaryfuncs*. """ names = list(r.dtype.names) arrays = [r[name] for name in names] for attr, func, outname in summaryfuncs: names.append(outname) arrays.append(np.asarray(func(r[attr]))) return np.rec.fromarrays(arrays, names=names) def rec_join(key, r1, r2, jointype='inner', defaults=None, r1postfix='1', r2postfix='2'): """ Join record arrays *r1* and *r2* on *key*; *key* is a tuple of field names -- if *key* is a string it is assumed to be a single attribute name. If *r1* and *r2* have equal values on all the keys in the *key* tuple, then their fields will be merged into a new record array containing the intersection of the fields of *r1* and *r2*. *r1* (also *r2*) must not have any duplicate keys. The *jointype* keyword can be 'inner', 'outer', 'leftouter'. To do a rightouter join just reverse *r1* and *r2*. The *defaults* keyword is a dictionary filled with {column_name:default_value} pairs. The keywords *r1postfix* and *r2postfix* are postfixed to column names (other than keys) that are both in *r1* and *r2*. """ if cbook.is_string_like(key): key = (key, ) for name in key: if name not in r1.dtype.names: raise ValueError('r1 does not have key field %s'%name) if name not in r2.dtype.names: raise ValueError('r2 does not have key field %s'%name) def makekey(row): return tuple([row[name] for name in key]) r1d = dict([(makekey(row),i) for i,row in enumerate(r1)]) r2d = dict([(makekey(row),i) for i,row in enumerate(r2)]) r1keys = set(r1d.keys()) r2keys = set(r2d.keys()) common_keys = r1keys & r2keys r1ind = np.array([r1d[k] for k in common_keys]) r2ind = np.array([r2d[k] for k in common_keys]) common_len = len(common_keys) left_len = right_len = 0 if jointype == "outer" or jointype == "leftouter": left_keys = r1keys.difference(r2keys) left_ind = np.array([r1d[k] for k in left_keys]) left_len = len(left_ind) if jointype == "outer": right_keys = r2keys.difference(r1keys) right_ind = np.array([r2d[k] for k in right_keys]) right_len = len(right_ind) def key_desc(name): 'if name is a string key, use the larger size of r1 or r2 before merging' dt1 = r1.dtype[name] if dt1.type != np.string_: return (name, dt1.descr[0][1]) dt2 = r1.dtype[name] assert dt2==dt1 if dt1.num>dt2.num: return (name, dt1.descr[0][1]) else: return (name, dt2.descr[0][1]) keydesc = [key_desc(name) for name in key] def mapped_r1field(name): """ The column name in *newrec* that corresponds to the column in *r1*. """ if name in key or name not in r2.dtype.names: return name else: return name + r1postfix def mapped_r2field(name): """ The column name in *newrec* that corresponds to the column in *r2*. """ if name in key or name not in r1.dtype.names: return name else: return name + r2postfix r1desc = [(mapped_r1field(desc[0]), desc[1]) for desc in r1.dtype.descr if desc[0] not in key] r2desc = [(mapped_r2field(desc[0]), desc[1]) for desc in r2.dtype.descr if desc[0] not in key] newdtype = np.dtype(keydesc + r1desc + r2desc) newrec = np.recarray((common_len + left_len + right_len,), dtype=newdtype) if defaults is not None: for thiskey in defaults: if thiskey not in newdtype.names: warnings.warn('rec_join defaults key="%s" not in new dtype names "%s"'%( thiskey, newdtype.names)) for name in newdtype.names: dt = newdtype[name] if dt.kind in ('f', 'i'): newrec[name] = 0 if jointype != 'inner' and defaults is not None: # fill in the defaults enmasse newrec_fields = newrec.dtype.fields.keys() for k, v in defaults.iteritems(): if k in newrec_fields: newrec[k] = v for field in r1.dtype.names: newfield = mapped_r1field(field) if common_len: newrec[newfield][:common_len] = r1[field][r1ind] if (jointype == "outer" or jointype == "leftouter") and left_len: newrec[newfield][common_len:(common_len+left_len)] = r1[field][left_ind] for field in r2.dtype.names: newfield = mapped_r2field(field) if field not in key and common_len: newrec[newfield][:common_len] = r2[field][r2ind] if jointype == "outer" and right_len: newrec[newfield][-right_len:] = r2[field][right_ind] newrec.sort(order=key) return newrec def recs_join(key, name, recs, jointype='outer', missing=0., postfixes=None): """ Join a sequence of record arrays on single column key. This function only joins a single column of the multiple record arrays *key* is the column name that acts as a key *name* is the name of the column that we want to join *recs* is a list of record arrays to join *jointype* is a string 'inner' or 'outer' *missing* is what any missing field is replaced by *postfixes* if not None, a len recs sequence of postfixes returns a record array with columns [rowkey, name0, name1, ... namen-1]. or if postfixes [PF0, PF1, ..., PFN-1] are supplied, [rowkey, namePF0, namePF1, ... namePFN-1]. Example:: r = recs_join("date", "close", recs=[r0, r1], missing=0.) """ results = [] aligned_iters = cbook.align_iterators(operator.attrgetter(key), *[iter(r) for r in recs]) def extract(r): if r is None: return missing else: return r[name] if jointype == "outer": for rowkey, row in aligned_iters: results.append([rowkey] + map(extract, row)) elif jointype == "inner": for rowkey, row in aligned_iters: if None not in row: # throw out any Nones results.append([rowkey] + map(extract, row)) if postfixes is None: postfixes = ['%d'%i for i in range(len(recs))] names = ",".join([key] + ["%s%s" % (name, postfix) for postfix in postfixes]) return np.rec.fromrecords(results, names=names) def csv2rec(fname, comments='#', skiprows=0, checkrows=0, delimiter=',', converterd=None, names=None, missing='', missingd=None, use_mrecords=False): """ Load data from comma/space/tab delimited file in *fname* into a numpy record array and return the record array. If *names* is *None*, a header row is required to automatically assign the recarray names. The headers will be lower cased, spaces will be converted to underscores, and illegal attribute name characters removed. If *names* is not *None*, it is a sequence of names to use for the column names. In this case, it is assumed there is no header row. - *fname*: can be a filename or a file handle. Support for gzipped files is automatic, if the filename ends in '.gz' - *comments*: the character used to indicate the start of a comment in the file - *skiprows*: is the number of rows from the top to skip - *checkrows*: is the number of rows to check to validate the column data type. When set to zero all rows are validated. - *converterd*: if not *None*, is a dictionary mapping column number or munged column name to a converter function. - *names*: if not None, is a list of header names. In this case, no header will be read from the file - *missingd* is a dictionary mapping munged column names to field values which signify that the field does not contain actual data and should be masked, e.g. '0000-00-00' or 'unused' - *missing*: a string whose value signals a missing field regardless of the column it appears in - *use_mrecords*: if True, return an mrecords.fromrecords record array if any of the data are missing If no rows are found, *None* is returned -- see :file:examples/loadrec.py """ if converterd is None: converterd = dict() if missingd is None: missingd = {} import dateutil.parser import datetime parsedate = dateutil.parser.parse fh = cbook.to_filehandle(fname) class FH: """ For space-delimited files, we want different behavior than comma or tab. Generally, we want multiple spaces to be treated as a single separator, whereas with comma and tab we want multiple commas to return multiple (empty) fields. The join/strip trick below effects this. """ def __init__(self, fh): self.fh = fh def close(self): self.fh.close() def seek(self, arg): self.fh.seek(arg) def fix(self, s): return ' '.join(s.split()) def __next__(self): return self.fix(next(self.fh)) def __iter__(self): for line in self.fh: yield self.fix(line) if delimiter==' ': fh = FH(fh) reader = csv.reader(fh, delimiter=delimiter) def process_skiprows(reader): if skiprows: for i, row in enumerate(reader): if i>=(skiprows-1): break return fh, reader process_skiprows(reader) def ismissing(name, val): "Should the value val in column name be masked?" if val == missing or val == missingd.get(name) or val == '': return True else: return False def with_default_value(func, default): def newfunc(name, val): if ismissing(name, val): return default else: return func(val) return newfunc def mybool(x): if x=='True': return True elif x=='False': return False else: raise ValueError('invalid bool') dateparser = dateutil.parser.parse mydateparser = with_default_value(dateparser, datetime.date(1,1,1)) myfloat = with_default_value(float, np.nan) myint = with_default_value(int, -1) mystr = with_default_value(str, '') mybool = with_default_value(mybool, None) def mydate(x): # try and return a date object d = dateparser(x) if d.hour>0 or d.minute>0 or d.second>0: raise ValueError('not a date') return d.date() mydate = with_default_value(mydate, datetime.date(1,1,1)) def get_func(name, item, func): # promote functions in this order funcmap = {mybool:myint,myint:myfloat, myfloat:mydate, mydate:mydateparser, mydateparser:mystr} try: func(name, item) except: if func==mystr: raise ValueError('Could not find a working conversion function') else: return get_func(name, item, funcmap[func]) # recurse else: return func # map column names that clash with builtins -- TODO - extend this list itemd = { 'return' : 'return_', 'file' : 'file_', 'print' : 'print_', } def get_converters(reader): converters = None for i, row in enumerate(reader): if i==0: converters = [mybool]*len(row) if checkrows and i>checkrows: break #print i, len(names), len(row) #print 'converters', zip(converters, row) for j, (name, item) in enumerate(izip(names, row)): func = converterd.get(j) if func is None: func = converterd.get(name) if func is None: #if not item.strip(): continue func = converters[j] if len(item.strip()): func = get_func(name, item, func) else: # how should we handle custom converters and defaults? func = with_default_value(func, None) converters[j] = func return converters # Get header and remove invalid characters needheader = names is None if needheader: for row in reader: #print 'csv2rec', row if len(row) and row[0].startswith(comments): continue headers = row break # remove these chars delete = set("""~!@#\$%^&*()-=+~\|]}[{';: /?.>,<""") delete.add('"') names = [] seen = dict() for i, item in enumerate(headers): item = item.strip().lower().replace(' ', '_') item = ''.join([c for c in item if c not in delete]) if not len(item): item = 'column%d'%i item = itemd.get(item, item) cnt = seen.get(item, 0) if cnt>0: names.append(item + '_%d'%cnt) else: names.append(item) seen[item] = cnt+1 else: if cbook.is_string_like(names): names = [n.strip() for n in names.split(',')] # get the converter functions by inspecting checkrows converters = get_converters(reader) if converters is None: raise ValueError('Could not find any valid data in CSV file') # reset the reader and start over fh.seek(0) reader = csv.reader(fh, delimiter=delimiter) process_skiprows(reader) if needheader: while 1: # skip past any comments and consume one line of column header row = next(reader) if len(row) and row[0].startswith(comments): continue break # iterate over the remaining rows and convert the data to date # objects, ints, or floats as approriate rows = [] rowmasks = [] for i, row in enumerate(reader): if not len(row): continue if row[0].startswith(comments): continue # Ensure that the row returned always has the same nr of elements row.extend([''] * (len(converters) - len(row))) rows.append([func(name, val) for func, name, val in zip(converters, names, row)]) rowmasks.append([ismissing(name, val) for name, val in zip(names, row)]) fh.close() if not len(rows): return None if use_mrecords and np.any(rowmasks): try: from numpy.ma import mrecords except ImportError: raise RuntimeError('numpy 1.05 or later is required for masked array support') else: r = mrecords.fromrecords(rows, names=names, mask=rowmasks) else: r = np.rec.fromrecords(rows, names=names) return r # a series of classes for describing the format intentions of various rec views class FormatObj: def tostr(self, x): return self.toval(x) def toval(self, x): return str(x) def fromstr(self, s): return s def __hash__(self): """ override the hash function of any of the formatters, so that we don't create duplicate excel format styles """ return hash(self.__class__) class FormatString(FormatObj): def tostr(self, x): val = repr(x) return val[1:-1] #class FormatString(FormatObj): # def tostr(self, x): # return '"%r"'%self.toval(x) class FormatFormatStr(FormatObj): def __init__(self, fmt): self.fmt = fmt def tostr(self, x): if x is None: return 'None' return self.fmt%self.toval(x) class FormatFloat(FormatFormatStr): def __init__(self, precision=4, scale=1.): FormatFormatStr.__init__(self, '%%1.%df'%precision) self.precision = precision self.scale = scale def __hash__(self): return hash((self.__class__, self.precision, self.scale)) def toval(self, x): if x is not None: x = x * self.scale return x def fromstr(self, s): return float(s)/self.scale class FormatInt(FormatObj): def tostr(self, x): return '%d'%int(x) def toval(self, x): return int(x) def fromstr(self, s): return int(s) class FormatBool(FormatObj): def toval(self, x): return str(x) def fromstr(self, s): return bool(s) class FormatPercent(FormatFloat): def __init__(self, precision=4): FormatFloat.__init__(self, precision, scale=100.) class FormatThousands(FormatFloat): def __init__(self, precision=4): FormatFloat.__init__(self, precision, scale=1e-3) class FormatMillions(FormatFloat): def __init__(self, precision=4): FormatFloat.__init__(self, precision, scale=1e-6) class FormatDate(FormatObj): def __init__(self, fmt): self.fmt = fmt def __hash__(self): return hash((self.__class__, self.fmt)) def toval(self, x): if x is None: return 'None' return x.strftime(self.fmt) def fromstr(self, x): import dateutil.parser return dateutil.parser.parse(x).date() class FormatDatetime(FormatDate): def __init__(self, fmt='%Y-%m-%d %H:%M:%S'): FormatDate.__init__(self, fmt) def fromstr(self, x): import dateutil.parser return dateutil.parser.parse(x) defaultformatd = { np.bool_ : FormatBool(), np.int16 : FormatInt(), np.int32 : FormatInt(), np.int64 : FormatInt(), np.float32 : FormatFloat(), np.float64 : FormatFloat(), np.object_ : FormatObj(), np.string_ : FormatString(), } def get_formatd(r, formatd=None): 'build a formatd guaranteed to have a key for every dtype name' if formatd is None: formatd = dict() for i, name in enumerate(r.dtype.names): dt = r.dtype[name] format = formatd.get(name) if format is None: format = defaultformatd.get(dt.type, FormatObj()) formatd[name] = format return formatd def csvformat_factory(format): format = copy.deepcopy(format) if isinstance(format, FormatFloat): format.scale = 1. # override scaling for storage format.fmt = '%r' return format def rec2txt(r, header=None, padding=3, precision=3, fields=None): """ Returns a textual representation of a record array. *r*: numpy recarray *header*: list of column headers *padding*: space between each column *precision*: number of decimal places to use for floats. Set to an integer to apply to all floats. Set to a list of integers to apply precision individually. Precision for non-floats is simply ignored. *fields* : if not None, a list of field names to print. fields can be a list of strings like ['field1', 'field2'] or a single comma separated string like 'field1,field2' Example:: precision=[0,2,3] Output:: ID Price Return ABC 12.54 0.234 XYZ 6.32 -0.076 """ if fields is not None: r = rec_keep_fields(r, fields) if cbook.is_numlike(precision): precision = [precision]*len(r.dtype) def get_type(item,atype=int): tdict = {None:int, int:float, float:str} try: atype(str(item)) except: return get_type(item,tdict[atype]) return atype def get_justify(colname, column, precision): ntype = type(column[0]) if ntype==np.str or ntype==np.str_ or ntype==np.string0 or ntype==np.string_: length = max(len(colname),column.itemsize) return 0, length+padding, "%s" # left justify if ntype==np.int or ntype==np.int16 or ntype==np.int32 or ntype==np.int64 or ntype==np.int8 or ntype==np.int_: length = max(len(colname),np.max(map(len,map(str,column)))) return 1, length+padding, "%d" # right justify # JDH: my powerbook does not have np.float96 using np 1.3.0 """ In [2]: np.__version__ Out[2]: '1.3.0.dev5948' In [3]: !uname -a Darwin Macintosh-5.local 9.4.0 Darwin Kernel Version 9.4.0: Mon Jun 9 19:30:53 PDT 2008; root:xnu-1228.5.20~1/RELEASE_I386 i386 i386 In [4]: np.float96 --------------------------------------------------------------------------- AttributeError Traceback (most recent call la """ if ntype==np.float or ntype==np.float32 or ntype==np.float64 or (hasattr(np, 'float96') and (ntype==np.float96)) or ntype==np.float_: fmt = "%." + str(precision) + "f" length = max(len(colname),np.max(map(len,map(lambda x:fmt%x,column)))) return 1, length+padding, fmt # right justify return 0, max(len(colname),np.max(map(len,map(str,column))))+padding, "%s" if header is None: header = r.dtype.names justify_pad_prec = [get_justify(header[i],r.__getitem__(colname),precision[i]) for i, colname in enumerate(r.dtype.names)] justify_pad_prec_spacer = [] for i in range(len(justify_pad_prec)): just,pad,prec = justify_pad_prec[i] if i == 0: justify_pad_prec_spacer.append((just,pad,prec,0)) else: pjust,ppad,pprec = justify_pad_prec[i-1] if pjust == 0 and just == 1: justify_pad_prec_spacer.append((just,pad-padding,prec,0)) elif pjust == 1 and just == 0: justify_pad_prec_spacer.append((just,pad,prec,padding)) else: justify_pad_prec_spacer.append((just,pad,prec,0)) def format(item, just_pad_prec_spacer): just, pad, prec, spacer = just_pad_prec_spacer if just == 0: return spacer*' ' + str(item).ljust(pad) else: if get_type(item) == float: item = (prec%float(item)) elif get_type(item) == int: item = (prec%int(item)) return item.rjust(pad) textl = [] textl.append(''.join([format(colitem,justify_pad_prec_spacer[j]) for j, colitem in enumerate(header)])) for i, row in enumerate(r): textl.append(''.join([format(colitem,justify_pad_prec_spacer[j]) for j, colitem in enumerate(row)])) if i==0: textl[0] = textl[0].rstrip() text = os.linesep.join(textl) return text def rec2csv(r, fname, delimiter=',', formatd=None, missing='', missingd=None, withheader=True): """ Save the data from numpy recarray *r* into a comma-/space-/tab-delimited file. The record array dtype names will be used for column headers. *fname*: can be a filename or a file handle. Support for gzipped files is automatic, if the filename ends in '.gz' *withheader*: if withheader is False, do not write the attribute names in the first row for formatd type FormatFloat, we override the precision to store full precision floats in the CSV file .. seealso:: :func:csv2rec For information about *missing* and *missingd*, which can be used to fill in masked values into your CSV file. """ if missingd is None: missingd = dict() def with_mask(func): def newfunc(val, mask, mval): if mask: return mval else: return func(val) return newfunc if r.ndim != 1: raise ValueError('rec2csv only operates on 1 dimensional recarrays') formatd = get_formatd(r, formatd) funcs = [] for i, name in enumerate(r.dtype.names): funcs.append(with_mask(csvformat_factory(formatd[name]).tostr)) fh, opened = cbook.to_filehandle(fname, 'wb', return_opened=True) writer = csv.writer(fh, delimiter=delimiter) header = r.dtype.names if withheader: writer.writerow(header) # Our list of specials for missing values mvals = [] for name in header: mvals.append(missingd.get(name, missing)) ismasked = False if len(r): row = r[0] ismasked = hasattr(row, '_fieldmask') for row in r: if ismasked: row, rowmask = row.item(), row._fieldmask.item() else: rowmask = [False] * len(row) writer.writerow([func(val, mask, mval) for func, val, mask, mval in zip(funcs, row, rowmask, mvals)]) if opened: fh.close() def griddata(x,y,z,xi,yi,interp='nn'): """ zi = griddata(x,y,z,xi,yi) fits a surface of the form *z* = *f*(*x*, *y*) to the data in the (usually) nonuniformly spaced vectors (*x*, *y*, *z*). :func:griddata interpolates this surface at the points specified by (*xi*, *yi*) to produce *zi*. *xi* and *yi* must describe a regular grid, can be either 1D or 2D, but must be monotonically increasing. A masked array is returned if any grid points are outside convex hull defined by input data (no extrapolation is done). If interp keyword is set to 'nn' (default), uses natural neighbor interpolation based on Delaunay triangulation. By default, this algorithm is provided by the :mod:matplotlib.delaunay package, written by Robert Kern. The triangulation algorithm in this package is known to fail on some nearly pathological cases. For this reason, a separate toolkit (:mod:mpl_tookits.natgrid) has been created that provides a more robust algorithm fof triangulation and interpolation. This toolkit is based on the NCAR natgrid library, which contains code that is not redistributable under a BSD-compatible license. When installed, this function will use the :mod:mpl_toolkits.natgrid algorithm, otherwise it will use the built-in :mod:matplotlib.delaunay package. If the interp keyword is set to 'linear', then linear interpolation is used instead of natural neighbor. In this case, the output grid is assumed to be regular with a constant grid spacing in both the x and y directions. For regular grids with nonconstant grid spacing, you must use natural neighbor interpolation. Linear interpolation is only valid if :mod:matplotlib.delaunay package is used - :mod:mpl_tookits.natgrid only provides natural neighbor interpolation. The natgrid matplotlib toolkit can be downloaded from http://sourceforge.net/project/showfiles.php?group_id=80706&package_id=142792 """ try: from mpl_toolkits.natgrid import _natgrid, __version__ _use_natgrid = True except ImportError: import matplotlib.delaunay as delaunay from matplotlib.delaunay import __version__ _use_natgrid = False if not griddata._reported: if _use_natgrid: verbose.report('using natgrid version %s' % __version__) else: verbose.report('using delaunay version %s' % __version__) griddata._reported = True if xi.ndim != yi.ndim: raise TypeError("inputs xi and yi must have same number of dimensions (1 or 2)") if xi.ndim != 1 and xi.ndim != 2: raise TypeError("inputs xi and yi must be 1D or 2D.") if not len(x)==len(y)==len(z): raise TypeError("inputs x,y,z must all be 1D arrays of the same length") # remove masked points. if hasattr(z,'mask'): # make sure mask is not a scalar boolean array. if z.mask.ndim: x = x.compress(z.mask == False) y = y.compress(z.mask == False) z = z.compressed() if _use_natgrid: # use natgrid toolkit if available. if interp != 'nn': raise ValueError("only natural neighor interpolation" " allowed when using natgrid toolkit in griddata.") if xi.ndim == 2: xi = xi[0,:] yi = yi[:,0] # override default natgrid internal parameters. _natgrid.seti('ext',0) _natgrid.setr('nul',np.nan) # cast input arrays to doubles (this makes a copy) x = x.astype(np.float) y = y.astype(np.float) z = z.astype(np.float) xo = xi.astype(np.float) yo = yi.astype(np.float) if min(xo[1:]-xo[0:-1]) < 0 or min(yo[1:]-yo[0:-1]) < 0: raise ValueError('output grid defined by xi,yi must be monotone increasing') # allocate array for output (buffer will be overwritten by nagridd) zo = np.empty((yo.shape[0],xo.shape[0]), np.float) _natgrid.natgridd(x,y,z,xo,yo,zo) else: # use Robert Kern's delaunay package from scikits (default) if xi.ndim != yi.ndim: raise TypeError("inputs xi and yi must have same number of dimensions (1 or 2)") if xi.ndim != 1 and xi.ndim != 2: raise TypeError("inputs xi and yi must be 1D or 2D.") if xi.ndim == 1: xi,yi = np.meshgrid(xi,yi) # triangulate data tri = delaunay.Triangulation(x,y) # interpolate data if interp == 'nn': interp = tri.nn_interpolator(z) zo = interp(xi,yi) elif interp == 'linear': # make sure grid has constant dx, dy dx = xi[0,1:]-xi[0,0:-1] dy = yi[1:,0]-yi[0:-1,0] epsx = np.finfo(xi.dtype).resolution epsy = np.finfo(yi.dtype).resolution if dx.max()-dx.min() > epsx or dy.max()-dy.min() > epsy: raise ValueError("output grid must have constant spacing" " when using interp='linear'") interp = tri.linear_interpolator(z) zo = interp[yi.min():yi.max():complex(0,yi.shape[0]), xi.min():xi.max():complex(0,xi.shape[1])] else: raise ValueError("interp keyword must be one of" " 'linear' (for linear interpolation) or 'nn'" " (for natural neighbor interpolation). Default is 'nn'.") # mask points on grid outside convex hull of input data. if np.any(np.isnan(zo)): zo = np.ma.masked_where(np.isnan(zo),zo) return zo griddata._reported = False ################################################## # Linear interpolation algorithms ################################################## def less_simple_linear_interpolation( x, y, xi, extrap=False ): """ This function provides simple (but somewhat less so than :func:cbook.simple_linear_interpolation) linear interpolation. :func:simple_linear_interpolation will give a list of point between a start and an end, while this does true linear interpolation at an arbitrary set of points. This is very inefficient linear interpolation meant to be used only for a small number of points in relatively non-intensive use cases. For real linear interpolation, use scipy. """ if cbook.is_scalar(xi): xi = [xi] x = np.asarray(x) y = np.asarray(y) xi = np.asarray(xi) s = list(y.shape) s[0] = len(xi) yi = np.tile( np.nan, s ) for ii,xx in enumerate(xi): bb = x == xx if np.any(bb): jj, = np.nonzero(bb) yi[ii] = y[jj[0]] elif xxx[-1]: if extrap: yi[ii] = y[-1] else: jj, = np.nonzero(x x[-1], the routine tries an extrapolation. The relevance of the data obtained from this, of course, is questionable... Original implementation by Halldor Bjornsson, Icelandic Meteorolocial Office, March 2006 halldor at vedur.is Completely reworked and optimized for Python by Norbert Nemec, Institute of Theoretical Physics, University or Regensburg, April 2006 Norbert.Nemec at physik.uni-regensburg.de """ # Cast key variables as float. x=np.asarray(x, np.float_) y=np.asarray(y, np.float_) assert x.shape == y.shape N=len(y) if yp is None: yp = slopes(x,y) else: yp=np.asarray(yp, np.float_) xi=np.asarray(xi, np.float_) yi=np.zeros(xi.shape, np.float_) # calculate linear slopes dx = x[1:] - x[:-1] dy = y[1:] - y[:-1] s = dy/dx #note length of s is N-1 so last element is #N-2 # find the segment each xi is in # this line actually is the key to the efficiency of this implementation idx = np.searchsorted(x[1:-1], xi) # now we have generally: x[idx[j]] <= xi[j] <= x[idx[j]+1] # except at the boundaries, where it may be that xi[j] < x[0] or xi[j] > x[-1] # the y-values that would come out from a linear interpolation: sidx = s.take(idx) xidx = x.take(idx) yidx = y.take(idx) xidxp1 = x.take(idx+1) yo = yidx + sidx * (xi - xidx) # the difference that comes when using the slopes given in yp dy1 = (yp.take(idx)- sidx) * (xi - xidx) # using the yp slope of the left point dy2 = (yp.take(idx+1)-sidx) * (xi - xidxp1) # using the yp slope of the right point dy1dy2 = dy1*dy2 # The following is optimized for Python. The solution actually # does more calculations than necessary but exploiting the power # of numpy, this is far more efficient than coding a loop by hand # in Python yi = yo + dy1dy2 * np.choose(np.array(np.sign(dy1dy2), np.int32)+1, ((2*xi-xidx-xidxp1)/((dy1-dy2)*(xidxp1-xidx)), 0.0, 1/(dy1+dy2),)) return yi ################################################## # Code related to things in and around polygons ################################################## def inside_poly(points, verts): """ *points* is a sequence of *x*, *y* points. *verts* is a sequence of *x*, *y* vertices of a polygon. Return value is a sequence of indices into points for the points that are inside the polygon. """ # Make a closed polygon path poly = Path( verts ) # Check to see which points are contained withing the Path return [ idx for idx, p in enumerate(points) if poly.contains_point(p) ] def poly_below(xmin, xs, ys): """ Given a sequence of *xs* and *ys*, return the vertices of a polygon that has a horizontal base at *xmin* and an upper bound at the *ys*. *xmin* is a scalar. Intended for use with :meth:matplotlib.axes.Axes.fill, eg:: xv, yv = poly_below(0, x, y) ax.fill(xv, yv) """ if ma.isMaskedArray(xs) or ma.isMaskedArray(ys): numpy = ma else: numpy = np xs = numpy.asarray(xs) ys = numpy.asarray(ys) Nx = len(xs) Ny = len(ys) assert(Nx==Ny) x = xmin*numpy.ones(2*Nx) y = numpy.ones(2*Nx) x[:Nx] = xs y[:Nx] = ys y[Nx:] = ys[::-1] return x, y def poly_between(x, ylower, yupper): """ Given a sequence of *x*, *ylower* and *yupper*, return the polygon that fills the regions between them. *ylower* or *yupper* can be scalar or iterable. If they are iterable, they must be equal in length to *x*. Return value is *x*, *y* arrays for use with :meth:matplotlib.axes.Axes.fill. """ if ma.isMaskedArray(ylower) or ma.isMaskedArray(yupper) or ma.isMaskedArray(x): numpy = ma else: numpy = np Nx = len(x) if not cbook.iterable(ylower): ylower = ylower*numpy.ones(Nx) if not cbook.iterable(yupper): yupper = yupper*numpy.ones(Nx) x = numpy.concatenate( (x, x[::-1]) ) y = numpy.concatenate( (yupper, ylower[::-1]) ) return x,y def is_closed_polygon(X): """ Tests whether first and last object in a sequence are the same. These are presumably coordinates on a polygonal curve, in which case this function tests if that curve is closed. """ return np.all(X[0] == X[-1]) def contiguous_regions(mask): """ return a list of (ind0, ind1) such that mask[ind0:ind1].all() is True and we cover all such regions TODO: this is a pure python implementation which probably has a much faster numpy impl """ in_region = None boundaries = [] for i, val in enumerate(mask): if in_region is None and val: in_region = i elif in_region is not None and not val: boundaries.append((in_region, i)) in_region = None if in_region is not None: boundaries.append((in_region, i+1)) return boundaries def cross_from_below(x, threshold): """ return the indices into *x* where *x* crosses some threshold from below, eg the i's where:: x[i-1]=threshold Example code:: import matplotlib.pyplot as plt t = np.arange(0.0, 2.0, 0.1) s = np.sin(2*np.pi*t) fig = plt.figure() ax = fig.add_subplot(111) ax.plot(t, s, '-o') ax.axhline(0.5) ax.axhline(-0.5) ind = cross_from_below(s, 0.5) ax.vlines(t[ind], -1, 1) ind = cross_from_above(s, -0.5) ax.vlines(t[ind], -1, 1) plt.show() .. seealso:: :func:cross_from_above and :func:contiguous_regions """ x = np.asarray(x) threshold = threshold ind = np.nonzero( (x[:-1]=threshold))[0] if len(ind): return ind+1 else: return ind def cross_from_above(x, threshold): """ return the indices into *x* where *x* crosses some threshold from below, eg the i's where:: x[i-1]>threshold and x[i]<=threshold .. seealso:: :func:cross_from_below and :func:contiguous_regions` """ x = np.asarray(x) ind = np.nonzero( (x[:-1]>=threshold) & (x[1:]