""" Class objects for data, spectrum, covariance function and time series in WAFO To represent data, spectra, covariance functions and time series in WAFO, the classes WafoData, SpecData1D, CovData1D and TimeSeries is used. Here follows a list of their attributes: WafoData ---------- data : array_like args : vector for 1D, list of vectors for 2D, 3D, ... date : Date and time of creation or change. labels : AxisLabels children : list of WafoData objects SpecData1D ------------ data : One sided Spectrum values args : freguency values of freqtype type :String: 'freq', 'dir', 'k2d', k1d', 'encdir' or 'enc'. freqtype :'w' OR 'f' OR 'k' Frequency/wave number lag, length nf. tr : Transformation function (default [] (none)). h : Water depth (default inf). norm : Normalization flag, Logical 1 if S is normalized, 0 if not date :Date and time of creation or change. v : Ship speed, if .type = 'enc' or 'encdir'. phi angle of rotation of the coordinate system (counter-clocwise) e.g. azymuth of a ship. CovData1D ---------- data : Covariance function values. Size [ny nx nt], all singleton dim. removed. args : Lag of first space dimension, length nx. .h Water depth. .tr Transformation function. .type 'enc', 'rot' or 'none'. .v Ship speed, if .type='enc' .phi Rotation of coordinate system, e.g. direction of ship .norm Normalization flag, Logical 1 if autocorrelation, 0 if covariance. .Rx ... .Rtttt Obvious derivatives of .R. .note Memorandum string. .date Date and time of creation or change. """ #------------------------------------------------------------------------------- # Name: module1 # Purpose: # # Author: pab # # Created: 16.09.2008 # Copyright: (c) pab 2008 # Licence: #------------------------------------------------------------------------------- #!/usr/bin/env python from __future__ import division import warnings import numpy import numpy as np from time import gmtime, strftime from wafo.misc import nextpow2, discretize, findextrema, findrfc, sub_dict_select #import wafo.spectrum.dispersion_relation as disp_rel #from scipy import fft from scipy.integrate import simps, trapz from pylab import stineman_interp import scipy.interpolate as interpolate import warnings try: import diffsumfunq except: pass from plotbackend import plotbackend __all__ = ['SpecData1D','SpecData2D','WafoData', 'AxisLabels','CovData1D', 'TimeSeries','sensortypeid','sensortype'] def empty_copy(obj): class Empty(obj.__class__): def __init__(self): pass newcopy = Empty() newcopy.__class__ = obj.__class__ return newcopy def _set_seed(iseed): if iseed != None: try: np.random.set_state(iseed) except: np.random.seed(iseed) class WafoData(object): '''Container class for data objects in WAFO Member variables ---------------- data : array_like args : vector for 1D, list of vectors for 2D, 3D, ... labels : AxisLabels children : list of WafoData objects Member methods -------------- plot : copy : Example ------- >>> import numpy as np >>> x = np.arange(-2,2,0.2) # Plot 2 objects in one call >>> d2 = WafoData(np.sin(x),x,xlab='x',ylab='sin',title='sinus') >>> d2.plot() % Plot with confidence interval d3 = wdata(sin(x),x); d3 = set(d3,'dataCI',[sin(x(:))*0.9 sin(x(:))*1.2]); plot(d3) See also -------- wdata/plot, specdata, covdata ''' def __init__(self,data=None,args=None,**kwds): self.data = data self.args = args self.date = strftime("%a, %d %b %Y %H:%M:%S", gmtime()) self.plotter = None self.children = None self.labels = AxisLabels(**kwds) self.setplotter() def plot(self,*args,**kwds): if self.children!=None: plotbackend.hold('on') for child in self.children: tmp = child.plot(*args,**kwds) tmp2 = self.plotter.plot(self,*args,**kwds) return tmp2 def copy(self): newcopy = empty_copy(self) newcopy.__dict__.update(self.__dict__) return newcopy def setplotter(self): ''' Set plotter based on the data type data_1d, data_2d, data_3d or data_nd ''' if isinstance(self.args,(list,tuple)): # Multidimensional data ndim = len(self.args) if ndim<2: warnings.warn('Unable to determine plotter-type, because len(self.args)<2.') print('If the data is 1D, then self.args should be a vector!') print('If the data is 2D, then length(self.args) should be 2.') print('If the data is 3D, then length(self.args) should be 3.') print('Unless you fix this, the plot methods will not work!') elif ndim==2: self.plotter = Plotter_2d() else: warnings.warn('Plotter method not implemented for ndim>2') else: #One dimensional data self.plotter = Plotter_1d() class AxisLabels: def __init__(self,title='',xlab='',ylab='',zlab='',**kwds): self.title = title self.xlab = xlab self.ylab = ylab self.zlab = zlab def copy(self): lbkwds = self.labels.__dict__.copy() labels = AxisLabels(**lbkwds) return labels def labelfig(self): try: plotbackend.title(self.title) plotbackend.xlabel(self.xlab) plotbackend.ylabel(self.ylab) plotbackend.zlabel(self.zlab) except: pass class Plotter_1d(object): """ class comment bar barh loglog semilogx semilogy plot stem scatter """ def __init__(self,plotmethod='plot'): self.plotfun = None self.plotbackend = plotbackend try: self.plotfun = plotbackend.__dict__[plotmethod] except: pass def show(self): plotbackend.show() def plot(self,wdata,*args,**kwds): if isinstance(wdata.args,(list,tuple)): args1 = tuple((wdata.args))+(wdata.data,)+args else: args1 = tuple((wdata.args,))+(wdata.data,)+args self.plotfun(*args1,**kwds) wdata.labels.labelfig() class Plotter_2d(Plotter_1d): """ class comment contour mesh surf """ def __init__(self,plotmethod='contour'): super(Plotter_2d,self).__init__(plotmethod) #self.plotfun = plotbackend.__dict__[plotmethod] class TrGauss(WafoData): def __init__(self,*args,**kwds): super(TrGauss, self).__init__(*args,**kwds) class CycleCount(object): def __init__(self,M,m): self.M = M self.m = m def amplitudes(self): return (self.M-self.m)/2. class SpecData1D(WafoData): """ Container class for 1D spectrum data objects in WAFO Member variables ---------------- data : array_like args : vector for 1D, list of vectors for 2D, 3D, ... type : string spectrum type, one of 'freq', 'k1d', 'enc' (default 'freq') freqtype : letter frequency type, one of: 'f', 'w' or 'k' (default 'w') Examples -------- >>> import numpy as np >>> import wafo.spectrum.models as sm >>> Sj = sm.Jonswap(Hm0=3) >>> w = np.linspace(0,4,256) >>> S1 = Sj.toSpecData(w) #Make spectrum object from numerical values >>> S = SpecData1D(Sj(w),w) # Alternatively do it manually See also -------- WafoData CovData """ def __init__(self,*args,**kwds): super(SpecData1D, self).__init__(*args,**kwds) self.name='WAFO Spectrum Object' self.type='freq' self.freqtype='w' self.angletype='' self.h=np.inf self.tr=None self.phi=0. self.v=0. self.norm=0 somekeys = ['angletype', 'phi', 'name', 'h', 'tr', 'freqtype', 'v', 'type', 'norm'] self.__dict__.update(sub_dict_select(kwds,somekeys)) self.setlabels() ## def copy(self): ## newcopy = empty_copy(self) ## newcopy.update(self.__dict__) ## #kwds = self.__dict__.copy() ## #wdata = SpecData1D(**kwds) ## #wdata.labels = sel.labels.copy() ## return newcopy def toacf_matrix(self,nr=0,Nt=None,dt=None): ''' Computes covariance function and its derivatives, alternative version Parameters ---------- Nr = number of derivatives in output, Nr<=4 (default 0) Nt = number in time grid, i.e., number of time-lags. (default rate*(n-1)) where rate = round(1/(2*f(end)*dt)) or rate = round(pi/(w(n)*dt)) depending on S. dt = time spacing for R Returns ------- R = [R0, R1,...Rnr] matrix with autocovariance and its derivatives, i.e., Ri (i=1:nr) are column vectors with the 1'st to nr'th derivatives of R0. size Nt+1 x Nr+1 NB! This routine requires that the spectrum grid is equidistant starting from zero frequency. Example: -------- S = jonswap; dt = 0.1; R = spec2cov2(S,3,256,dt); See also -------- spec2cov, specinterp, datastructures ''' ftype = self.freqtype #; %options are 'f' and 'w' and 'k' freq = self.args n = length(freq) dTold = self.sampling_period() if dt is None: dt = dTold rate = 1 else: rate = np.maximum(np.round(dTold*1./dt),1.) if Nt is None: Nt = rate*(n-1) else: #%check if Nt is ok Nt = np.minimum(Nt,rate*(n-1)); checkdt = 1.2*min(np.diff(freq))/2./np.pi; if ftype in 'k': lagtype = 'x' else: lagtype = 't' if ftype in 'f': checkdt = checkdt*2*np.pi msg1 = 'The step dt = %g in computation of the density is too small.' % dt msg2 = 'The step dt = %g step is small, may cause numerical inaccuracies.' % dt if (checkdt < 2.**-16/dt): np.disp(msg1) np.disp('The computed covariance (by FFT(2^K)) may differ from the theoretical.') np.disp('Solution:') raise ValueError('use larger dt or sparser grid for spectrum.') #% Calculating covariances #%~~~~~~~~~~~~~~~~~~~~~~~~ S2 = self.copy() S2.resample(dt) R2 = S2.toacf(nr,Nt,rate=1) R = np.zeros((Nt+1,nr+1)) R[:,0] = R2.data[0:Nt+1] fieldname = 'R' + lagtype*nr for ix in range(1,nr+1): fn = fieldname[1:ix]; R[:,0:Nt+1] = gettattr(R2,fn)[0:Nt+1]; EPS0 = 0.0001 cc = R[0,0]-R[1,0]*(R[1,0]/R[0,0]); if Nt+1>=5: #%cc1=R(1,1)-R(3,1)*(R(3,1)/R(1,1))+R(3,2)*(R(3,2)/R(1,3)); #%cc3=R(1,1)-R(5,1)*(R(5,1)/R(1,1))+R(5,2)*(R(5,2)/R(1,3)); cc2 = R(0,0)-R(4,0)*(R(4,0)/R(0,0)); if (cc2R(x,t); Nt and Ny set =>R(y,t) 4) Any type, Nt, Nx and Ny set => R(x,y,t) 5) Any type, Nt not set, Nx and/or Ny set => Nt set to default, goto 3) or 4) NB! This routine requires that the spectrum grid is equidistant starting from zero frequency. NB! If you are using a model spectrum, S, with sharp edges to calculate covariances then you should probably round off the sharp edges like this: Example: >>> import wafo.spectrum.models as sm >>> Sj = sm.Jonswap() >>> S = Sj.toSpecData() >>> S.data[0:40] = 0.0 >>> S.data[100:-1] = 0.0 >>> Nt = len(S.data)-1; >>> R = S.toacf(nr=0,Nt=Nt) R = spec2cov(S,0,Nt); win = parzen(2*Nt+1); R.R = R.R.*win(Nt+1:end); S1 = cov2spec(R); R2 = spec2cov(S1); figure(1) plotspec(S),hold on, plotspec(S1,'r') figure(2) covplot(R), hold on, covplot(R2,[],[],'r') figure(3) semilogy(abs(R2.R-R.R)), hold on, semilogy(abs(S1.S-S.S)+1e-7,'r') See also cov2spec, datastructures ''' freq = self.args n = freq.size if freq[0]>0: raise ValueError('Spectrum does not start at zero frequency/wave number.\n Correct it with resample, for example.') dw = np.abs(np.diff(freq,n=2,axis=0)) if np.any(dw>1.0e-8): raise ValueError('Not equidistant frequencies/wave numbers in spectrum.\n Correct it with resample, for example.') if rate is None: rate=1 #; %interpolation rate elif rate>16: rate=16 else: # make sure rate is a power of 2 rate=2**nextpow2(rate) if Nt is None: Nt = rate*(n-1) else: #check if Nt is ok Nt = np.minimum(Nt,rate*(n-1)) S = self.copy() if self.freqtype in 'k': lagtype = 'x' else: lagtype = 't' dT = S.sampling_period() #normalize spec so that sum(specn)/(n-1)=R(0)=var(X) specn = S.data*freq[-1] if S.freqtype in 'f': w = freq*2*np.pi else: w = freq nfft = rate*2**nextpow2(2*n-2); Rper = np.r_[specn, np.zeros(nfft-(2*n)+2) , np.conj(specn[n-1:0:-1])] #; % periodogram t = np.r_[0:Nt+1]*dT*(2*n-2)/nfft fft = np.fft.fft r = fft(Rper,nfft).real/(2*n-2) R = CovData1D(r[0:Nt+1],t,lagtype=lagtype) R.tr = S.tr; R.h = S.h; R.norm = S.norm; if nr>0: w = np.r_[w , np.zeros(nfft-2*n+2) ,-w[n-1:0:-1] ] fieldname = 'R' + lagtype*nr ; for ix in range(1,nr+1): Rper = (-1j*w*Rper) r = fft(Rper,nfft).real/(2*n-2) setattr(R,fieldname[0:ix+1],r[0:Nt+1]) return R def sim(self,ns=None,cases=1,dt=None,iseed=None,method='random',derivative=False): ''' Simulates a Gaussian process and its derivative from spectrum Parameters ---------- ns : scalar number of simulated points. (default length(S)-1=n-1). If ns>n-1 it is assummed that R(k)=0 for all k>n-1 cases : scalar number of replicates (default=1) dt : scalar step in grid (default dt is defined by the Nyquist freq) iseed : int or state starting state/seed number for the random number generator (default none is set) method : string if 'exact' : simulation using cov2sdat if 'random' : random phase and amplitude simulation (default) derivative : bool if true : return derivative of simulated signal as well otherwise Returns ------- xs = a cases+1 column matrix ( t,X1(t) X2(t) ...). xsder = a cases+1 column matrix ( t,X1'(t) X2'(t) ...). Details ------- Performs a fast and exact simulation of stationary zero mean Gaussian process through circulant embedding of the covariance matrix or by summation of sinus functions with random amplitudes and random phase angle. If the spectrum has a non-empty field .tr, then the transformation is applied to the simulated data, the result is a simulation of a transformed Gaussian process. Note: The method 'exact' simulation may give high frequency ripple when used with a small dt. In this case the method 'random' works better. Example: >>> import wafo.spectrum.models as sm >>> Sj = sm.Jonswap();S = Sj.toSpecData(); >>> np =100; dt = .2; >>> x1 = S.sim(np,dt=dt); waveplot(x1,'r',x2,'g',1,1) See also -------- cov2sdat, gaus2dat Reference ----------- C.R Dietrich and G. N. Newsam (1997) "Fast and exact simulation of stationary Gaussian process through circulant embedding of the Covariance matrix" SIAM J. SCI. COMPT. Vol 18, No 4, pp. 1088-1107 Hudspeth, R.T. and Borgman, L.E. (1979) "Efficient FFT simulation of Digital Time sequences" Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM2, ''' fft = np.fft.fft S = self.copy() if dt is not None: S.resample(dt) ftype = S.freqtype freq = S.args dT = S.sampling_period() Nt = freq.size if ns is None: ns=Nt-1 if method in 'exact': #nr=0,Nt=None,dt=None R = S.toacf(nr=0); T = Nt*dT ix = np.flatnonzero(R.args>T); # Trick to avoid adding high frequency noise to the spectrum if ix.size>0: R.data[ix[0]::]=0.0 return R.sim(ns=ns,cases=cases,iseed=iseed,derivative=derivative) _set_seed(iseed) ns = ns+np.mod(ns,2) # make sure it is even fi = freq[1:-1] Si = S.data[1:-1] if ftype in ('w','k'): fact = 2.*np.pi Si = Si*fact; fi = fi/fact; zeros = np.zeros x = zeros((ns,cases+1)); df = 1/(ns*dT) # interpolate for freq. [1:(N/2)-1]*df and create 2-sided, uncentered spectra # ---------------------------------------------------------------------------- f = np.arange(1,ns/2.)*df Fs = np.hstack((0., fi, df*ns/2.)) Su = np.hstack((0., np.abs(Si)/2., 0.)); Si = np.interp(f,Fs,Su) Su=np.hstack((0., Si,0, Si[(ns/2)-2::-1])) del(Si, Fs) # Generate standard normal random numbers for the simulations # ----------------------------------------------------------- randn = np.random.randn Zr = randn((ns/2)+1,cases) Zi = np.vstack((zeros((1,cases)), randn((ns/2)-1,cases), zeros((1,cases)))); A = zeros((ns,cases),dtype=complex) A[0:(ns/2+1),:] = Zr - 1j*Zi; del(Zr, Zi) A[(ns/2+1):ns,:] = A[ns/2-1:0:-1,:].conj(); A[0,:] = A[0,:]*np.sqrt(2.); A[(ns/2),:] = A[(ns/2),:]*np.sqrt(2.); # Make simulated time series # -------------------------- T = (ns-1)*dT Ssqr = np.sqrt(Su*df/2.) # stochastic amplitude A = A*Ssqr[:,np.newaxis]; # Deterministic amplitude #A = sqrt[1]*Ssqr(:,ones(1,cases)).*exp(sqrt(-1)*atan2(imag(A),real(A))); del( Su, Ssqr) x[:,1::] = fft(A,axis=0).real x[:,0] = np.linspace(0,T,ns) #'; %(0:dT:(np-1)*dT).'; if derivative: xder=np.zeros(ns,cases+1) w = 2.*np.pi*np.hstack((0, f, 0.,-f[-1::-1])) A = -1j*A*w[:,newaxis] xder[:,1:(cases+1)] = fft(A,axis=0).real; xder[:,0] = x[:,0] if S.tr is not None: np.disp(' Transforming data.') g=S.tr; G=np.fliplr(g); #% the invers of g if derivative: for ix in range(cases): tmp=tranproc(np.hstack((x[:,ix+1], xder[:,ix+1])),G); x[:,ix+1]=tmp[:,0]; xder[:,ix+1]=tmp[:,1]; else: for ix in range(cases): x[:,ix+1]=tranproc(x[:,ix+1],G); if derivative: return x,xder else: return x # function [x2,x,svec,dvec,A]=spec2nlsdat(S,np,dt,iseed,method,truncationLimit) def sim_nl(self,ns=None,cases=1,dt=None,iseed=None,method='random', fnlimit=1.4142,reltol=1e-3,g=9.81): """ Simulates a Randomized 2nd order non-linear wave X(t) Parameters ---------- ns : scalar number of simulated points. (default length(S)-1=n-1). If ns>n-1 it is assummed that R(k)=0 for all k>n-1 cases : scalar number of replicates (default=1) dt : scalar step in grid (default dt is defined by the Nyquist freq) iseed : int or state starting state/seed number for the random number generator (default none is set) method : string 'apStochastic' : Random amplitude and phase (default) 'aDeterministic' : Deterministic amplitude and random phase 'apDeterministic' : Deterministic amplitude and phase fnLimit : scalar normalized upper frequency limit of spectrum for 2'nd order components. The frequency is normalized with sqrt(gravity*tanh(kbar*waterDepth)/Amax)/(2*pi) (default sqrt(2), i.e., Convergence criterion [1]_). Other possible values are: sqrt(1/2) : No bump in trough criterion sqrt(pi/7) : Wave steepness criterion reltol : scalar relative tolerance defining where to truncate spectrum for the for sum and difference frequency effects Returns ------- xs2 = a cases+1 column matrix ( t,X1(t) X2(t) ...). xs1 = a cases+1 column matrix ( t,X1'(t) X2'(t) ...). Details ------- Performs a Fast simulation of Randomized 2nd order non-linear waves by summation of sinus functions with random amplitudes and phase angles. The extent to which the simulated result are applicable to real seastates are dependent on the validity of the assumptions: 1. Seastate is unidirectional 2. Surface elevation is adequately represented by 2nd order random wave theory 3. The first order component of the surface elevation is a Gaussian random process. If the spectrum does not decay rapidly enough towards zero, the contribution from the 2nd order wave components at the upper tail can be very large and unphysical. To ensure convergence of the perturbation series, the upper tail of the spectrum is truncated at FNLIMIT in the calculation of the 2nd order wave components, i.e., in the calculation of sum and difference frequency effects. This may also be combined with the elimination of second order effects from the spectrum, i.e., extract the linear components from the spectrum. One way to do this is to use SPEC2LINSPEC. Example -------- np =100; dt = .2; [x1, x2] = spec2nlsdat(jonswap,np,dt); waveplot(x1,'r',x2,'g',1,1) See also -------- spec2linspec, spec2sdat, cov2sdat References ---------- .. [1] Nestegaard, A and Stokka T (1995) A Third Order Random Wave model. In proc.ISOPE conf., Vol III, pp 136-142. .. [2] R. S Langley (1987) A statistical analysis of non-linear random waves. Ocean Engng, Vol 14, pp 389-407 .. [3] Marthinsen, T. and Winterstein, S.R (1992) 'On the skewness of random surface waves' In proc. ISOPE Conf., San Francisco, 14-19 june. """ # TODO % Check the methods: 'apdeterministic' and 'adeterministic' from wafo.spectrum import dispersion_relation as sm Hm0 = self.characteristic('Hm0')[0] Tm02 = self.characteristic('Tm02')[0] #Hm0 = spec2char(S,'Hm0'); #Tm02 = spec2char(S,'Tm02'); _set_seed(iseed) fft = np.fft.fft S = self.copy() if dt is not None: S.resample(dt) ftype = S.freqtype freq = S.args dT = S.sampling_period() Nt = freq.size if ns is None: ns = Nt-1 ns = ns+np.mod(ns,2) # make sure it is even fi = freq[1:-1] Si = S.data[1:-1] if ftype in ('w','k'): fact = 2.*np.pi Si = Si*fact; fi = fi/fact; Smax = max(Si) waterDepth = min(abs(S.h),10.**30); zeros = np.zeros x = zeros((ns,cases+1)); df = 1/(ns*dT) # interpolate for freq. [1:(N/2)-1]*df and create 2-sided, uncentered spectra # ---------------------------------------------------------------------------- f = np.arange(1,ns/2.)*df Fs = np.hstack((0., fi, df*ns/2.)) w = 2.*np.pi*Fs kw = sm.w2k(w ,0.,waterDepth,g)[0] Su = np.hstack((0., np.abs(Si)/2., 0.)); Si = np.interp(f,Fs,Su) nmin = (Si>Smax*reltol).argmax() nmax = np.flatnonzero(Si>0).max() Su = np.hstack((0., Si,0, Si[(ns/2)-2::-1])) del(Si, Fs) # Generate standard normal random numbers for the simulations # ----------------------------------------------------------- randn = np.random.randn Zr = randn((ns/2)+1,cases) Zi = np.vstack((zeros((1,cases)), randn((ns/2)-1,cases), zeros((1,cases)))); A = zeros((ns,cases),dtype=complex) A[0:(ns/2+1),:] = Zr - 1j*Zi; del(Zr, Zi) A[(ns/2+1):ns,:] = A[ns/2-1:0:-1,:].conj(); A[0,:] = A[0,:]*np.sqrt(2.); A[(ns/2),:] = A[(ns/2),:]*np.sqrt(2.); # Make simulated time series # -------------------------- T = (ns-1)*dT Ssqr = np.sqrt(Su*df/2.) if method.startswith('apd') : # apdeterministic # Deterministic amplitude and phase A[1:(ns/2),:] = A[1,0]; A[(ns/2+1):ns,:] = A[1,0].conj(); A = sqrt(2)*Ssqr[:,np.newaxis]*exp(1J*atan2(A.imag,A.real)) elif method.startswith('ade'): # adeterministic # Deterministic amplitude and random phase A = sqrt(2)*Ssqr[:,np.newaxis]*exp(1J*atan2(A.imag,A.real)); else: # stochastic amplitude A = A*Ssqr[:,np.newaxis]; # Deterministic amplitude #A = sqrt(2)*Ssqr(:,ones(1,cases)).*exp(sqrt(-1)*atan2(imag(A),real(A))); del( Su, Ssqr) x[:,1::] = fft(A,axis=0).real x[:,0] = np.linspace(0,T,ns) #'; %(0:dT:(np-1)*dT).'; x2 = x.copy() # If the spectrum does not decay rapidly enough towards zero, the # contribution from the wave components at the upper tail can be very # large and unphysical. # To ensure convergence of the perturbation series, the upper tail of the # spectrum is truncated in the calculation of sum and difference # frequency effects. # Find the critical wave frequency to ensure convergence. sqrt = np.sqrt log = np.log pi = np.pi tanh = np.tanh numWaves = 1000. # Typical number of waves in 3 hour seastate kbar = sm.w2k(2.*np.pi/Tm02,0.,waterDepth)[0]; Amax = sqrt(2*log(numWaves))*Hm0/4; #% Expected maximum amplitude for 1000 waves seastate fLimitUp = fnlimit*sqrt(g*tanh(kbar*waterDepth)/Amax)/(2*pi); fLimitLo = sqrt(g*tanh(kbar*waterDepth)*Amax/waterDepth)/(2*pi*waterDepth); nmax = min(np.flatnonzero(f<=fLimitUp).max(),nmax)+1; nmin = max(np.flatnonzero(fLimitLo<=f).min(),nmin)+1; #if isempty(nmax),nmax = np/2;end #if isempty(nmin),nmin = 2;end % Must always be greater than 1 fLimitUp = df*nmax; fLimitLo = df*nmin; print('2nd order frequency Limits = %g,%g'% (fLimitLo, fLimitUp)) ## if nargout>3, ## %compute the sum and frequency effects separately ## [svec, dvec] = disufq((A.'),w,kw,min(h,10^30),g,nmin,nmax); ## svec = svec.'; ## dvec = dvec.'; ## ## x2s = fft(svec); % 2'nd order sum frequency component ## x2d = fft(dvec); % 2'nd order difference frequency component ## ## % 1'st order + 2'nd order component. ## x2(:,2:end) =x(:,2:end)+ real(x2s(1:np,:))+real(x2d(1:np,:)); ## else rvec,ivec = diffsumfunq.disufq(A.real,A.imag,w,kw,waterDepth,g,nmin,nmax) svec = rvec + 1J*ivec x2o = fft(svec) # 2'nd order component # 1'st order + 2'nd order component. x2[:,1::] = x[:,1::]+ x2o[0:ns,:].real(); return x2, x def moment(self,nr=2,even=True,j=0): ''' Calculates spectral moments from spectrum Parameters ---------- nr : int order of moments (recomended maximum 4) even : bool False for all moments, True for only even orders j : int 0 or 1 Returns ------- m : list of moments mtext : list of strings describing the elements of m, see below Details ------- Calculates spectral moments of up to order NR by use of Simpson-integration. / / mj_t^i = | w^i S(w)^(j+1) dw, or mj_x^i = | k^i S(k)^(j+1) dk / / where k=w^2/gravity, i=0,1,...,NR The strings in output mtext have the same position in the list as the corresponding numerical value has in output m Notation in mtext: 'm0' is the variance, 'm0x' is the first-order moment in x, 'm0xx' is the second-order moment in x, 'm0t' is the first-order moment in t, etc. For the calculation of moments see Baxevani et al. Example: >>> import numpy as np >>> import wafo.spectrum.models as sm >>> Sj = sm.Jonswap(Hm0=3) >>> w = np.linspace(0,4,256) >>> S = SpecData1D(Sj(w),w) #Make spectrum object from numerical values >>> S.moment() ([0.56220770033914191, 0.35433180985851975], ['m0', 'm0tt']) References ---------- Baxevani A. et al. (2001) Velocities for Random Surfaces ''' pi= np.pi one_dim_spectra = ['freq','enc','k1d'] if self.type not in one_dim_spectra: raise ValueError('Unknown spectrum type!') f = np.ravel(self.args) S = np.ravel(self.data) if self.freqtype in ['f','w']: vari = 't' if self.freqtype=='f': f = 2.*pi*f S = S/(2.*pi) else: vari = 'x' S1=np.abs(S)**(j+1.) m = [simps(S1,x=f)] mtxt = 'm%d' % j mtext = [mtxt] step = np.mod(even,2)+1 df = f**step for i in range(step,nr+1,step): S1 = S1*df m.append(simps(S1,x=f)) mtext.append(mtxt+vari*i) return m, mtext def sampling_period(self): ''' Returns sampling interval from Nyquist frequency of spectrum Returns --------- dT : scalar sampling interval, unit: [m] if wave number spectrum, [s] otherwise Let wm be maximum frequency/wave number in spectrum, then dT=pi/wm if angular frequency, dT=1/(2*wm) if natural frequency (Hz) Example ------- S = jonswap; dt = spec2dt(S) See also ''' if self.freqtype in 'f': wmdt = 0.5 # Nyquist to sampling interval factor else: # ftype == w og ftype == k wmdt = np.pi; wm = self.args[-1] #Nyquist frequency dt = wmdt/wm; #sampling interval = 1/Fs return dt def resample(self,dt=None,Nmin=0,Nmax=2**13+1,method='stineman'): ''' Interpolate and zero-padd spectrum to change Nyquist freq. Parameters ---------- dt : scalar wanted sampling interval (default as given by S, see spec2dt) unit: [s] if frequency-spectrum, [m] if wave number spectrum Nmin : scalar minimum number of frequencies. Nmax : scalar minimum number of frequencies method : string interpolation method (options are 'linear', 'cubic' or 'stineman') To be used before simulation (e.g. spec2sdat) or evaluation of covariance function (spec2cov) to directly get wanted sampling interval. The input spectrum is interpolated and padded with zeros to reach the right max-frequency, w(end)=pi/dt, f(end)=1/(2*dt), or k(end)=pi/dt. The objective is that output frequency grid should be at least as dense as the input grid, have equidistant spacing and length equal to 2^k+1 (>=Nmin). If the max frequency is changed, the number of points in the spectrum is maximized to 2^13+1. Note: Also zero-padding down to zero freq, if S does not start there. If empty input dt, this is the only effect. See also -------- spec2cov, spec2sdat, covinterp, spec2dt ''' ftype = self.freqtype w = self.args.ravel() n = w.size #%doInterpolate = 0; if ftype=='f': Cnf2dt = 0.5; # Nyquist to sampling interval factor else: #% ftype == w og ftype == k Cnf2dt = np.pi wnOld = w[-1] # Old Nyquist frequency dTold = Cnf2dt/wnOld; # sampling interval=1/Fs if dt is None: dt=dTold # Find how many points that is needed nfft = 2**nextpow2(max(n-1,Nmin-1)) dttest = dTold*(n-1)/nfft while (dttest>dt) and (nfft0 or w[1]>0 or (nfft!=n) or dt!=dTold or any(abs(np.diff(w,axis=0))>1.0e-8); if doInterpolate>0: S1 = self.data dw = min(np.diff(w)); if dWn>0: #% add a zero just above old max-freq, and a zero at new max-freq #% to get correct interpolation there Nz = 1 + (dWn>dw) #; % Number of zeros to add if Nz==2: w = np.hstack((w, wnOld+dw, wnNew)) else: w = np.hstack((w, wnNew)) S1 = np.hstack((S1, np.zeros(Nz))) if w[0]>0: #% add a zero at freq 0, and, if there is space, a zero just below min-freq Nz = 1 + (w[0]>dw); #% Number of zeros to add if Nz==2: w=np.hstack((0, w[0]-dw, w)) else: w=np.hstack((0, w)) S1 = np.hstack((zeros(Nz), S1)) #% Do a final check on spacing in order to check that the gridding is #% sufficiently dense: #np1 = S1.size dwMin = np.finfo(float).max #%wnc = min(wnNew,wnOld-1e-5); wnc = wnNew; specfun = lambda xi : stineman_interp(xi,w,S1) x,y = discretize(specfun,0,wnc) dwMin = np.minimum(min(np.diff(x)),dwMin) newNfft = 2**nextpow2(np.ceil(wnNew/dwMin))+1 if newNfft>nfft: if (nfft<=2**15+1) and (newNfft>2**15+1): warnings.warn('Spectrum matrix is very large (>33k). Memory problems may occur.') nfft = newNfft; self.args = np.linspace(0,wnNew,nfft) if method=='stineman': self.data = stineman_interp(self.args,w,S1) else: intfun = interpolate.interp1d(w,S1,kind=method) self.data = intfun(self.args) self.data = self.data.clip(0) # clip negative values to 0 def normalize(self): pass def bandwidth(self,factors=0): ''' Return some spectral bandwidth and irregularity factors Returns -------- bw : arraylike vector of bandwidth factors Parameters ----------- factors : array-like Input vector 'factors' correspondence: 0 alpha=m2/sqrt(m0*m4) (irregularity factor) 1 eps2 = sqrt(m0*m2/m1^2-1) (narrowness factor) 2 eps4 = sqrt(1-m2^2/(m0*m4))=sqrt(1-alpha^2) (broadness factor) 3 Qp=(2/m0^2)int_0^inf f*S(f)^2 df (peakedness factor) Order of output is the same as order in 'factors' Example: >>> import numpy as np >>> import wafo.spectrum.models as sm >>> Sj = sm.Jonswap(Hm0=3) >>> w = np.linspace(0,4,256) >>> S = SpecData1D(Sj(w),w) #Make spectrum object from numerical values >>> S.bandwidth([0,1,2,3]) array([ 0.65354446, 0.3975428 , 0.75688813, 2.00207912]) ''' if self.freqtype in 'k': vari = 'k'; else: vari = 'w'; m,mtxt = self.moment(nr=4,even=False) sqrt = np.sqrt fact = np.atleast_1d(factors) alpha = m[2]/sqrt(m[0]*m[4]) eps2 = sqrt(m[0]*m[2]/m[1]**2.-1.) eps4 = sqrt(1.-m[2]**2./m[0]/m[4]); f = self.args S = self.data Qp = 2/m[0]**2.*simps(f*S**2,x=f); bw = np.array([alpha,eps2,eps4,Qp]) return bw[fact] def characteristic(self,fact='Hm0',T=1200,g=9.81): """Returns spectral characteristics and their covariance Parameters ---------- fact = vector with factor integers or a string or a cellarray of strings, see below.(default [1]) T : scalar recording time (sec) (default 1200 sec = 20 min) g : scalar acceleration of gravity [m/s^2] Returns ------- ch = vector of spectral characteristics R = matrix of the corresponding covariances given T chtext = a list of strings describing the elements of ch, see example. Description ------------ If input spectrum is of wave number type, output are factors for corresponding 'k1D', else output are factors for 'freq'. Input vector 'factors' correspondence: 1 Hm0 = 4*sqrt(m0) Significant wave height 2 Tm01 = 2*pi*m0/m1 Mean wave period 3 Tm02 = 2*pi*sqrt(m0/m2) Mean zero-crossing period 4 Tm24 = 2*pi*sqrt(m2/m4) Mean period between maxima 5 Tm_10 = 2*pi*m_1/m0 Energy period 6 Tp = 2*pi/{w | max(S(w))} Peak period 7 Ss = 2*pi*Hm0/(g*Tm02^2) Significant wave steepness 8 Sp = 2*pi*Hm0/(g*Tp^2) Average wave steepness 9 Ka = abs(int S(w)*exp(i*w*Tm02) dw ) /m0 Groupiness parameter 10 Rs = (S(0.092)+S(0.12)+S(0.15)/(3*max(S(w))) Quality control parameter 11 Tp1 = 2*pi*int S(w)^4 dw Peak Period (robust estimate for Tp) ------------------ int w*S(w)^4 dw 12 alpha = m2/sqrt(m0*m4) Irregularity factor 13 eps2 = sqrt(m0*m2/m1^2-1) Narrowness factor 14 eps4 = sqrt(1-m2^2/(m0*m4))=sqrt(1-alpha^2) Broadness factor 15 Qp = (2/m0^2)int_0^inf w*S(w)^2 dw Peakedness factor Order of output is same as order in 'factors' The covariances are computed with a Taylor expansion technique and is currently only available for factors 1, 2, and 3. Variances are also available for factors 4,5,7,12,13,14 and 15 Quality control: ---------------- Critical value for quality control parameter Rs is Rscrit = 0.02 for surface displacement records and Rscrit=0.0001 for records of surface acceleration or slope. If Rs > Rscrit then probably there are something wrong with the lower frequency part of S. Ss may be used as an indicator of major malfunction, by checking that it is in the range of 1/20 to 1/16 which is the usual range for locally generated wind seas. Examples: --------- >>> import numpy as np >>> import wafo.spectrum.models as sm >>> Sj = sm.Jonswap(Hm0=5) >>> S = Sj.toSpecData() #Make spectrum ob >>> S.characteristic(1) (array([ 8.59007646]), array([[ 0.03040216]]), ['Tm01']) >>> [ch, R, txt] = S.characteristic([1,2,3]) # fact a vector of integers >>> S.characteristic('Ss') # fact a string (array([ 0.04963112]), array([[ 2.63624782e-06]]), ['Ss']) >>> S.characteristic(['Hm0','Tm02']) # fact a list of strings (array([ 4.99833578, 8.03139757]), array([[ 0.05292989, 0.02511371], [ 0.02511371, 0.0274645 ]]), ['Hm0', 'Tm02']) See also --------- bandwidth, moment References ---------- Krogstad, H.E., Wolf, J., Thompson, S.P., and Wyatt, L.R. (1999) 'Methods for intercomparison of wave measurements' Coastal Enginering, Vol. 37, pp. 235--257 Krogstad, H.E. (1982) 'On the covariance of the periodogram' Journal of time series analysis, Vol. 3, No. 3, pp. 195--207 Tucker, M.J. (1993) 'Recommended standard for wave data sampling and near-real-time processing' Ocean Engineering, Vol.20, No.5, pp. 459--474 Young, I.R. (1999) "Wind generated ocean waves" Elsevier Ocean Engineering Book Series, Vol. 2, pp 239 """ #% TODO % Need more checking on computing the variances for Tm24,alpha, eps2 and eps4 #% TODO % Covariances between Tm24,alpha, eps2 and eps4 variables are also needed NaN = np.nan tfact = dict(Hm0=0,Tm01=1,Tm02=2,Tm24=3, Tm_10=4,Tp=5,Ss=6, Sp=7, Ka=8, Rs=9, Tp1=10,Alpha=11,Eps2=12,Eps4=13,Qp=14) tfact1 = ('Hm0','Tm01','Tm02','Tm24', 'Tm_10','Tp','Ss', 'Sp', 'Ka', 'Rs', 'Tp1','Alpha','Eps2','Eps4','Qp') if isinstance(fact,str): fact = list((fact,)) if isinstance(fact,(list,tuple)): nfact = [] for k in fact: if isinstance(k,str): nfact.append(tfact.get(k.capitalize(),15)) else: nfact.append(k) else: nfact = fact; nfact = np.atleast_1d(nfact) if np.any((nfact>14) | (nfact<0)): raise ValueError('Factor outside range (0,...,14)') vari = self.freqtype f = self.args.ravel() S1 = self.data.ravel() m,mtxt = self.moment(nr=4,even=False) #% moments corresponding to freq in Hz for k in range(1,5): m[k] = m[k]/(2*np.pi)**k pi = np.pi ind = np.flatnonzero(f>0) m.append(simps(S1[ind]/f[ind],f[ind])*2.*np.pi) #; % = m_1 m_10 = simps(S1[ind]**2/f[ind],f[ind])*(2*pi)**2/T # % = COV(m_1,m0|T=t0) m_11 = simps(S1[ind]**2./f[ind]**2,f[ind])*(2*pi)**3/T #% = COV(m_1,m_1|T=t0) sqrt = np.sqrt #% Hm0 Tm01 Tm02 Tm24 Tm_10 Hm0 = 4.*sqrt(m[0]); Tm01 = m[0]/m[1]; Tm02 = sqrt(m[0]/m[2]); Tm24 = sqrt(m[2]/m[4]); Tm_10= m[5]/m[0]; Tm12 = m[1]/m[2] ind = S1.argmax() maxS = S1[ind] #[maxS ind] = max(S1); Tp = 2.*pi/f[ind] # % peak period /length Ss = 2.*pi*Hm0/g/Tm02**2 # % Significant wave steepness Sp = 2.*pi*Hm0/g/Tp**2 #; % Average wave steepness Ka = abs(simps(S1*np.exp(1J*f*Tm02),f))/m[0]; #% groupiness factor #% Quality control parameter #% critical value is approximately 0.02 for surface displacement records #% If Rs>0.02 then there are something wrong with the lower frequency part #% of S. Rs = np.sum(np.interp(np.r_[0.0146, 0.0195, 0.0244]*2*pi,f,S1))/3./maxS; Tp2 = 2*pi*simps(S1**4,f)/simps(f*S1**4,f); alpha1 = Tm24/Tm02 #; % m(3)/sqrt(m(1)*m(5)); eps2 = sqrt(Tm01/Tm12-1.)# % sqrt(m(1)*m(3)/m(2)^2-1); eps4 = sqrt(1.-alpha1**2) #; % sqrt(1-m(3)^2/m(1)/m(5)); Qp = 2./m[0]**2*simps(f*S1**2,f); ch = np.r_[Hm0, Tm01, Tm02, Tm24, Tm_10, Tp, Ss, Sp, Ka, Rs, Tp2, alpha1, eps2, eps4, Qp] #% Select the appropriate values ch = ch[nfact] chtxt = [tfact1[i] for i in nfact] #if nargout>1, #% covariance between the moments: #%COV(mi,mj |T=t0) = int f^(i+j)*S(f)^2 df/T mij,mijtxt = self.moment(nr=8,even=False,j=1) for ix,tmp in enumerate(mij): mij[ix] = tmp/T/((2.*pi)**(ix-1.0)) #% and the corresponding variances for #%{'hm0', 'tm01', 'tm02', 'tm24', 'tm_10','tp','ss', 'sp', 'ka', 'rs', 'tp1','alpha','eps2','eps4','qp'} R = np.r_[4*mij[0]/m[0], mij[0]/m[1]**2.-2.*m[0]*mij[1]/m[1]**3.+m[0]**2.*mij[2]/m[1]**4., 0.25*(mij[0]/(m[0]*m[2])-2.*mij[2]/m[2]**2+m[0]*mij[4]/m[2]**3), 0.25*(mij[4]/(m[2]*m[4])-2*mij[6]/m[4]**2+m[2]*mij[8]/m[4]**3) , m_11/m[0]**2+(m[5]/m[0]**2)**2*mij[0]-2*m[5]/m[0]**3*m_10, NaN, (8*pi/g)**2*(m[2]**2/(4*m[0]**3)*mij[0]+mij[4]/m[0]-m[2]/m[0]**2*mij[2]), NaN*np.ones(4), m[2]**2*mij[0]/(4*m[0]**3*m[4])+mij[4]/(m[0]*m[4])+mij[8]*m[2]**2/(4*m[0]*m[4]**3)- m[2]*mij[2]/(m[0]**2*m[4])+m[2]**2*mij[4]/(2*m[0]**2*m[4]**2)-m[2]*mij[6]/m[0]/m[4]**2, (m[2]**2*mij[0]/4+(m[0]*m[2]/m[1])**2*mij[2]+m[0]**2*mij[4]/4-m[2]**2*m[0]*mij[1]/m[1]+ m[0]*m[2]*mij[2]/2-m[0]**2*m[2]/m[1]*mij[3])/eps2**2/m[1]**4, (m[2]**2*mij[0]/(4*m[0]**2)+mij[4]+m[2]**2*mij[8]/(4*m[4]**2)-m[2]*mij[2]/m[0]+ m[2]**2*mij[4]/(2*m[0]*m[4])-m[2]*mij[6]/m[4])*m[2]**2/(m[0]*m[4]*eps4)**2, NaN]; #% and covariances by a taylor expansion technique: #% Cov(Hm0,Tm01) Cov(Hm0,Tm02) Cov(Tm01,Tm02) S0 = np.r_[ 2./(sqrt(m[0])*m[1])*(mij[0]-m[0]*mij[1]/m[1]), 1./sqrt(m[2])*(mij[0]/m[0]-mij[2]/m[2]), 1./(2*m[1])*sqrt(m[0]/m[2])*(mij[0]/m[0]-mij[2]/m[2]-mij[1]/m[1]+m[0]*mij[3]/(m[1]*m[2]))] R1 = np.ones((15,15)); R1[:,:] = NaN for ix,Ri in enumerate(R): R1[ix,ix] = Ri R1[0,2:4] = S0[:2]; R1[1,2] = S0[2]; for ix in [0,1]: #%make lower triangular equal to upper triangular part R1[ix+1:,ix] = R1[ix,ix+1:] R = R[nfact] R1= R1[nfact,:][:,nfact] #% Needs further checking: #% Var(Tm24)= 0.25*(mij[4]/(m[2]*m[4])-2*mij[6]/m[4]**2+m[2]*mij[8]/m[4]**3) ... return ch, R1, chtxt def setlabels(self): ''' Set automatic title, x-,y- and z- labels on SPECDATA object based on type, angletype, freqtype ''' N = len(self.type); if N==0: raise ValueError('Object does not appear to be initialized, it is empty!') labels = ['','',''] if self.type.endswith('dir'): title = 'Directional Spectrum' if self.freqtype.startswith('w'): labels[0] = 'Frequency [rad/s]' labels[2] = 'S(w,\theta) [m^2 s / rad^2]' else: labels[0] = 'Frequency [Hz]' labels[2] = 'S(f,\theta) [m^2 s / rad]' if self.angletype.startswith('r'): labels[1] = 'Wave directions [rad]' elif self.angletype.startswith('d'): labels[1] = 'Wave directions [deg]' elif self.type.endswith('freq'): title = 'Spectral density' if self.freqtype.startswith('w'): labels[0] = 'Frequency [rad/s]' labels[1] = 'S(w) [m^2 s/ rad]' else: labels[0] = 'Frequency [Hz]' labels[1] = 'S(f) [m^2 s]' else: title = 'Wave Number Spectrum' labels[0] = 'Wave number [rad/m]' if self.type.endswith('k1d'): labels[1] = 'S(k) [m^3/ rad]' elif self.type.endswith('k2d'): labels[1] = labels[0] labels[2] = 'S(k1,k2) [m^4/ rad^2]' else: raise ValueError('Object does not appear to be initialized, it is empty!') if self.norm!=0: title = 'Normalized ' + title labels[0] = 'Normalized ' + labels[0].split('[')[0] if not self.type.endswith('dir'): labels[1] = labels[1].split('[')[0] labels[2] = labels[2].split('[')[0] self.labels.title = title self.labels.xlab = labels[0] self.labels.ylab = labels[1] self.labels.zlab = labels[2] class SpecData2D(WafoData): """ Container class for 2D spectrum data objects in WAFO Member variables ---------------- data : array_like args : vector for 1D, list of vectors for 2D, 3D, ... type : string spectrum type (default 'freq') freqtype : letter frequency type (default 'w') angletype : string angle type of directional spectrum (default 'radians') Examples -------- >>> import numpy as np >>> import wafo.spectrum.models as sm >>> Sj = sm.Jonswap(Hm0=3) >>> w = np.linspace(0,4,256) >>> S = SpecData1D(Sj(w),w) #Make spectrum object from numerical values See also -------- WafoData CovData """ def __init__(self,*args,**kwds): super(SpecData2D, self).__init__(*args,**kwds) self.name='WAFO Spectrum Object' self.type='freq' self.freqtype='w' self.angletype='' self.h=np.inf self.tr=None self.phi=0. self.v=0. self.norm=0 somekeys = ['angletype', 'phi', 'name', 'h', 'tr', 'freqtype', 'v', 'type', 'norm'] self.__dict__.update(sub_dict_select(kwds,somekeys)) if self.type.endswith('dir') and self.angletype=='': self.angletype = 'radians' self.setlabels() def toacf(self): pass def sim(self): pass def sim_nl(self): pass def rotate(self): pass def moment(self,nr=2,vari='xt',even=True): ''' Calculates spectral moments from spectrum Parameters ---------- nr : int order of moments (maximum 4) vari : string variables in model, optional when two-dim.spectrum, string with 'x' and/or 'y' and/or 't' even : bool False for all moments, True for only even orders Returns ------- m : list of moments mtext : list of strings describing the elements of m, see below Details ------- Calculates spectral moments of up to order four by use of Simpson-integration. // m_jkl=|| k1^j*k2^k*w^l S(w,th) dw dth // where k1=w^2/gravity*cos(th-phi), k2=w^2/gravity*sin(th-phi) and phi is the angle of the rotation in S.phi. If the spectrum has field .g, gravity is replaced by S.g. The strings in output mtext have the same position in the cell array as the corresponding numerical value has in output m Notation in mtext: 'm0' is the variance, 'mx' is the first-order moment in x, 'mxx' is the second-order moment in x, 'mxt' is the second-order cross moment between x and t, 'myyyy' is the fourth-order moment in y etc. For the calculation of moments see Baxevani et al. Example: S=demospec('dir') [m,mtext]=spec2mom(S,2,'xyt') References ---------- Baxevani A. et al. (2001) Velocities for Random Surfaces ''' ##% Tested on: Matlab 6.0 ##% Tested on: Matlab 5.3 ##% History: ##% Revised by I.R. 04.04.2001: Introducing the rotation angle phi. ##% Revised by A.B. 23.05.2001: Correcting 'mxxyy' and introducing ##% 'mxxyt','mxyyt' and 'mxytt'. ##% Revised by A.B. 21.10.2001: Correcting 'mxxyt'. ##% Revised by A.B. 21.10.2001: Adding odd-order moments. ##% By es 27.08.1999 pi= np.pi two_dim_spectra = ['dir','encdir','k2d'] if self.type not in two_dim_spectra: raise ValueError('Unknown 2D spectrum type!') ## if (vari==None and nr<=1: ## vari='x' ## elif vari==None: ## vari='xt' ## else #% secure the mutual order ('xyt') ## vari=''.join(sorted(vari.lower())) ## Nv=len(vari) ## ## if vari[0]=='t' and Nv>1: ## vari = vari[1::]+ vari[0] ## ## Nv = len(vari) ## ## if not self.type.endswith('dir'): ## S1 = self.tospec(self.type[:-2]+'dir') ## else: ## S1 = self; ## w = np.ravel(S1.args[0]) ## theta = S1.args[1]-S1.phi ## S = S1.data ## Sw = simps(S,x=theta) ## m = [simps(Sw,x=w)] ## mtext=['m0'] ## ## if nr>0: ## ## nw=w.size ## if strcmpi(vari(1),'x') ## Sc=simpson(th,S1.S.*(cos(th)*ones(1,nw))).'; ## % integral S*cos(th) dth ## end ## if strcmpi(vari(1),'y') ## Ss=simpson(th,S1.S.*(sin(th)*ones(1,nw))).'; ## % integral S*sin(th) dth ## if strcmpi(vari(1),'x') ## Sc=simpson(th,S1.S.*(cos(th)*ones(1,nw))).'; ## end ## end ## if ~isfield(S1,'g') ## S1.g=gravity; ## end ## kx=w.^2/S1.g(1); % maybe different normalization in x and y => diff. g ## ky=w.^2/S1.g(end); ## ## if Nv>=1 ## switch vari ## case 'x' ## vec = kx.*Sc; ## mtext(end+1)={'mx'}; ## case 'y' ## vec = ky.*Ss; ## mtext(end+1)={'my'}; ## case 't' ## vec = w.*Sw; ## mtext(end+1)={'mt'}; ## end ## else ## vec = [kx.*Sc ky.*Ss w*Sw]; ## mtext(end+(1:3))={'mx', 'my', 'mt'}; ## end ## if nr>1 ## if strcmpi(vari(1),'x') ## Sc=simpson(th,S1.S.*(cos(th)*ones(1,nw))).'; ## % integral S*cos(th) dth ## Sc2=simpson(th,S1.S.*(cos(th).^2*ones(1,nw))).'; ## % integral S*cos(th)^2 dth ## end ## if strcmpi(vari(1),'y')||strcmpi(vari(2),'y') ## Ss=simpson(th,S1.S.*(sin(th)*ones(1,nw))).'; ## % integral S*sin(th) dth ## Ss2=simpson(th,S1.S.*(sin(th).^2*ones(1,nw))).'; ## % integral S*sin(th)^2 dth ## if strcmpi(vari(1),'x') ## Scs=simpson(th,S1.S.*((cos(th).*sin(th))*ones(1,nw))).'; ## % integral S*cos(th)*sin(th) dth ## end ## end ## if ~isfield(S1,'g') ## S1.g=gravity; ## end ## ## if Nv==2 ## switch vari ## case 'xy' ## vec=[kx.*Sc ky.*Ss kx.^2.*Sc2 ky.^2.*Ss2 kx.*ky.*Scs]; ## mtext(end+(1:5))={'mx','my','mxx', 'myy', 'mxy'}; ## case 'xt' ## vec=[kx.*Sc w.*Sw kx.^2.*Sc2 w.^2.*Sw kx.*w.*Sc]; ## mtext(end+(1:5))={'mx','mt','mxx', 'mtt', 'mxt'}; ## case 'yt' ## vec=[ky.*Ss w.*Sw ky.^2.*Ss2 w.^2.*Sw ky.*w.*Ss]; ## mtext(end+(1:5))={'my','mt','myy', 'mtt', 'myt'}; ## end ## else ## vec=[kx.*Sc ky.*Ss w.*Sw kx.^2.*Sc2 ky.^2.*Ss2 w.^2.*Sw kx.*ky.*Scs kx.*w.*Sc ky.*w.*Ss]; ## mtext(end+(1:9))={'mx','my','mt','mxx', 'myy', 'mtt', 'mxy', 'mxt', 'myt'}; ## end ## if nr>3 ## if strcmpi(vari(1),'x') ## Sc3=simpson(th,S1.S.*(cos(th).^3*ones(1,nw))).'; ## % integral S*cos(th)^3 dth ## Sc4=simpson(th,S1.S.*(cos(th).^4*ones(1,nw))).'; ## % integral S*cos(th)^4 dth ## end ## if strcmpi(vari(1),'y')||strcmpi(vari(2),'y') ## Ss3=simpson(th,S1.S.*(sin(th).^3*ones(1,nw))).'; ## % integral S*sin(th)^3 dth ## Ss4=simpson(th,S1.S.*(sin(th).^4*ones(1,nw))).'; ## % integral S*sin(th)^4 dth ## if strcmpi(vari(1),'x') %both x and y ## Sc2s=simpson(th,S1.S.*((cos(th).^2.*sin(th))*ones(1,nw))).'; ## % integral S*cos(th)^2*sin(th) dth ## Sc3s=simpson(th,S1.S.*((cos(th).^3.*sin(th))*ones(1,nw))).'; ## % integral S*cos(th)^3*sin(th) dth ## Scs2=simpson(th,S1.S.*((cos(th).*sin(th).^2)*ones(1,nw))).'; ## % integral S*cos(th)*sin(th)^2 dth ## Scs3=simpson(th,S1.S.*((cos(th).*sin(th).^3)*ones(1,nw))).'; ## % integral S*cos(th)*sin(th)^3 dth ## Sc2s2=simpson(th,S1.S.*((cos(th).^2.*sin(th).^2)*ones(1,nw))).'; ## % integral S*cos(th)^2*sin(th)^2 dth ## end ## end ## if Nv==2 ## switch vari ## case 'xy' ## vec=[vec kx.^4.*Sc4 ky.^4.*Ss4 kx.^3.*ky.*Sc3s ... ## kx.^2.*ky.^2.*Sc2s2 kx.*ky.^3.*Scs3]; ## mtext(end+(1:5))={'mxxxx','myyyy','mxxxy','mxxyy','mxyyy'}; ## case 'xt' ## vec=[vec kx.^4.*Sc4 w.^4.*Sw kx.^3.*w.*Sc3 ... ## kx.^2.*w.^2.*Sc2 kx.*w.^3.*Sc]; ## mtext(end+(1:5))={'mxxxx','mtttt','mxxxt','mxxtt','mxttt'}; ## case 'yt' ## vec=[vec ky.^4.*Ss4 w.^4.*Sw ky.^3.*w.*Ss3 ... ## ky.^2.*w.^2.*Ss2 ky.*w.^3.*Ss]; ## mtext(end+(1:5))={'myyyy','mtttt','myyyt','myytt','myttt'}; ## end ## else ## vec=[vec kx.^4.*Sc4 ky.^4.*Ss4 w.^4.*Sw kx.^3.*ky.*Sc3s ... ## kx.^2.*ky.^2.*Sc2s2 kx.*ky.^3.*Scs3 kx.^3.*w.*Sc3 ... ## kx.^2.*w.^2.*Sc2 kx.*w.^3.*Sc ky.^3.*w.*Ss3 ... ## ky.^2.*w.^2.*Ss2 ky.*w.^3.*Ss kx.^2.*ky.*w.*Sc2s ... ## kx.*ky.^2.*w.*Scs2 kx.*ky.*w.^2.*Scs]; ## mtext(end+(1:15))={'mxxxx','myyyy','mtttt','mxxxy','mxxyy',... ## 'mxyyy','mxxxt','mxxtt','mxttt','myyyt','myytt','myttt','mxxyt','mxyyt','mxytt'}; ## ## end % if Nv==2 ... else ... ## end % if nr>3 ## end % if nr>1 ## m=[m simpson(w,vec)]; ## end % if nr>0 ## % end; %%if Nv==1... else... to be removed ## end % ... else two-dim spectrum def interp(self): pass def normalize(self): pass def bandwidth(self): pass def setlabels(self): ''' Set automatic title, x-,y- and z- labels on SPECDATA object based on type, angletype, freqtype ''' N = len(self.type); if N==0: raise ValueError('Object does not appear to be initialized, it is empty!') labels = ['','',''] if self.type.endswith('dir'): title = 'Directional Spectrum' if self.freqtype.startswith('w'): labels[0] = 'Frequency [rad/s]' labels[2] = 'S(w,\theta) [m**2 s / rad**2]' else: labels[0] = 'Frequency [Hz]' labels[2] = 'S(f,\theta) [m**2 s / rad]' if self.angletype.startswith('r'): labels[1] = 'Wave directions [rad]' elif self.angletype.startswith('d'): labels[1] = 'Wave directions [deg]' elif self.type.endswith('freq'): title = 'Spectral density' if self.freqtype.startswith('w'): labels[0] = 'Frequency [rad/s]' labels[1] = 'S(w) [m**2 s/ rad]' else: labels[0] = 'Frequency [Hz]' labels[1] = 'S(f) [m**2 s]' else: title = 'Wave Number Spectrum' labels[0] = 'Wave number [rad/m]' if self.type.endswith('k1d'): labels[1] = 'S(k) [m**3/ rad]' elif self.type.endswith('k2d'): labels[1] = labels[0] labels[2] = 'S(k1,k2) [m**4/ rad**2]' else: raise ValueError('Object does not appear to be initialized, it is empty!') if self.norm!=0: title = 'Normalized ' + title labels[0] = 'Normalized ' + labels[0].split('[')[0] if not self.type.endswith('dir'): labels[1] = labels[1].split('[')[0] labels[2] = labels[2].split('[')[0] self.labels.title = title self.labels.xlab = labels[0] self.labels.ylab = labels[1] self.labels.zlab = labels[2] class CovData1D(WafoData): """ Container class for 1D covariance data objects in WAFO Member variables ---------------- data : array_like args : vector for 1D, list of vectors for 2D, 3D, ... type : string spectrum type, one of 'freq', 'k1d', 'enc' (default 'freq') lagtype : letter lag type, one of: 'x', 'y' or 't' (default 't') Examples -------- >>> import numpy as np >>> import wafo.spectrum.models as sm >>> Sj = sm.Jonswap(Hm0=3) >>> w = np.linspace(0,4,256) >>> S = SpecData1D(Sj(w),w) #Make spectrum object from numerical values See also -------- WafoData CovData """ def __init__(self,*args,**kwds): super(CovData1D, self).__init__(*args,**kwds) self.name='WAFO Covariance Object' self.type='time' self.lagtype='t' self.h=np.inf self.tr=None self.phi=0. self.v=0. self.norm=0 somekeys = ['phi', 'name', 'h', 'tr', 'lagtype', 'v', 'type', 'norm'] self.__dict__.update(sub_dict_select(kwds,somekeys)) #self.setlabels() def copy(self): kwds = self.__dict__.copy() wdata = CovData1D(**kwds) return wdata def tospec(self,rate=None,method='linear',nugget=0.0,trunc=1e-5,fast=True): '''Computes spectral density from the auto covariance function Parameters ---------- rate = scalar, int 1,2,4,8...2^r, interpolation rate for f (default 1) method: string interpolation method 'stineman', 'linear', 'cubic' nugget = scalar, real nugget effect to ensure that round off errors do not result in negative spectral estimates. Good choice might be 10^-12. trunc : scalar, real truncates all spectral values where S/max(S) < trunc 0 <= trunc <1 This is to ensure that high frequency noise is not added to the spectrum. (default 1e-5) fast : bool if True : zero-pad to obtain power of 2 length ACF (default) otherwise no zero-padding of ACF, slower but more accurate. Returns -------- S = SpecData1D object spectral density NB! This routine requires that the covariance is evenly spaced starting from zero lag. Currently only capable of 1D matrices. Example: >>> import wafo.spectrum.models as sm >>> import numpy as np >>> import scipy.signal.signaltools as st >>> L = 129 >>> t = np.linspace(0,75,L) >>> R = np.zeros(L) >>> win = st.parzen(41) >>> R[0:20] = win[20:41] >>> R0 = CovData1D(R,t) >>> S0 = R0.tospec() >>> Sj = sm.Jonswap() >>> S = Sj.toSpecData() >>> R2 = S.toacf() >>> S1 = R2.tospec() >>> assert(all(abs(S1.data-S.data)<1e-4) ,'COV2SPEC') See also -------- spec2cov datastructures ''' dT = self.sampling_period() # dT = time-step between data points.(default = T(2)-T1)). ACF, ti = np.atleast_1d(self.data,self.args) if self.lagtype in 't': spectype = 'freq' ftype = 'w' else: spectype = 'k1d' ftype = 'k' if rate is None: rate = 1 #;%interpolation rate else: rate = 2**nextpow2(rate) #;%make sure rate is a power of 2 #% add a nugget effect to ensure that round off errors #% do not result in negative spectral estimates ACF[0] = ACF[0] +nugget n = ACF.size # embedding a circulant vector and Fourier transform if fast: nfft = 2**nextpow2(2*n-2) else: nfft = 2*n-2 nf = nfft/2 #;% number of frequencies fft = np.fft.fft ACF = np.r_[ACF,np.zeros(nfft-2*n+2),ACF[n-1:0:-1]] Rper = (fft(ACF,nfft).real).clip(0) #% periodogram RperMax = Rper.max() Rper = np.where(Rper1: So.args = np.linspace(0,pi/dT,nf*rate); if method=='stineman': So.data = stineman_interp(So.args,w,S) else: intfun = interpolate.interp1d(w,S,kind=method) So.data = intfun(So.args) So.data = So.data.clip(0) # clip negative values to 0 return So def sampling_period(self): ''' Returns sampling interval Returns --------- dT : scalar sampling interval, unit: [s] if lagtype=='t' [m] otherwise See also ''' dt1 = self.args[1]-self.args[0] N = np.size(self.args)-1 T = self.args[-1]-self.args[0] dt = T/N return dt def sim(self,ns=None,cases=1,dt=None,iseed=None,derivative=False): ''' Simulates a Gaussian process and its derivative from ACF Parameters ---------- ns : scalar number of simulated points. (default length(S)-1=n-1). If ns>n-1 it is assummed that R(k)=0 for all k>n-1 cases : scalar number of replicates (default=1) dt : scalar step in grid (default dt is defined by the Nyquist freq) iseed : int or state starting state/seed number for the random number generator (default none is set) derivative : bool if true : return derivative of simulated signal as well otherwise Returns ------- xs = a cases+1 column matrix ( t,X1(t) X2(t) ...). xsder = a cases+1 column matrix ( t,X1'(t) X2'(t) ...). Details ------- Performs a fast and exact simulation of stationary zero mean Gaussian process through circulant embedding of the covariance matrix. If the ACF has a non-empty field .tr, then the transformation is applied to the simulated data, the result is a simulation of a transformed Gaussian process. Note: The simulation may give high frequency ripple when used with a small dt. Example: >>> import wafo.spectrum.models as sm >>> Sj = sm.Jonswap() >>> S = Sj.toSpecData() #Make spec >>> R = S.toacf() >>> x = R.sim(ns=1000,dt=0.2) See also -------- spec2sdat, gaus2dat Reference ----------- C.R Dietrich and G. N. Newsam (1997) "Fast and exact simulation of stationary Gaussian process through circulant embedding of the Covariance matrix" SIAM J. SCI. COMPT. Vol 18, No 4, pp. 1088-1107 ''' # TODO fix it, it does not work #% add a nugget effect to ensure that round off errors #% do not result in negative spectral estimates nugget=0 #;%10^-12; _set_seed(iseed) ACF = self.data.ravel() n = ACF.size I = ACF.argmax() if I!=0: raise ValueError('ACF does not have a maximum at zero lag') ACF.shape = (n,1) dT = self.sampling_period() fft = np.fft.fft x=np.zeros((ns,cases+1)) if derivative: xder=x.copy() #% add a nugget effect to ensure that round off errors #% do not result in negative spectral estimates ACF[0]=ACF[0]+nugget; #% Fast and exact simulation of simulation of stationary #% Gaussian process throug circulant embedding of the #% Covariance matrix floatinfo = numpy.finfo(float) if (abs(ACF[-1])>floatinfo.eps): #% assuming ACF(n+1)==0 m2=2*n-1; nfft=2**nextpow2(max(m2,2*ns)); ACF=np.r_[ACF,np.zeros((nfft-m2,1)),ACF[-1:0:-1,:]] #disp('Warning: I am now assuming that ACF(k)=0 ') #disp('for k>MAXLAG.') else: # % ACF(n)==0 m2=2*n-2; nfft=2**nextpow2(max(m2,2*ns)) ACF=np.r_[ACF,np.zeros((nfft-m2,1)),ACF[n-1:1:-1,:]] #%m2=2*n-2; S=fft(ACF,nfft,axis=0).real #;% periodogram I=S.argmax() k=np.flatnonzero(S<0); if k.size>0: #disp('Warning: Not able to construct a nonnegative circulant ') #disp('vector from the ACF. Apply the parzen windowfunction ') #disp('to the ACF in order to avoid this.') #disp('The returned result is now only an approximation.') # truncating negative values to zero to ensure that # that this noise is not added to the simulated timeseries S[k] = 0. ix = np.flatnonzero(k>2*I) if ix.size>0: ## % truncating all oscillating values above 2 times the peak ## % frequency to zero to ensure that ## % that high frequency noise is not added to ## % the simulated timeseries. ix0 = k[ix[0]] S[ix0:-ix0] =0.0 sqrt = np.sqrt trunc = 1e-5; maxS = S[I] k=np.flatnonzero(S[I:-I]0: S[k+I]=0. #% truncating small values to zero to ensure that #% that high frequency noise is not added to #% the simulated timeseries cases1 = np.floor(cases/2); cases2 = np.ceil(cases/2); #% Generate standard normal random numbers for the simulations #% ----------------------------------------------------------- randn = np.random.randn epsi = randn(nfft,cases2)+1j*randn(nfft,cases2); Ssqr=sqrt(S/(nfft)) #; %sqrt(S(wn)*dw ) ephat=epsi*Ssqr[:,np.newaxis] y=fft(ephat,nfft); x[:,1:cases+1]=np.hstack((y[2:ns+2,0:cases2].real, y[2:ns+2,0:cases1].imag)) x[:,0]=np.linspace(0,(ns-1)*dT,ns) #%(0:dT:(dT*(np-1)))'; if derivative: Ssqr = Ssqr*np.r_[0:(nfft/2+1),-(nfft/2-1):0]*2*np.pi/nfft/dT ephat = epsi*Ssqr[:,np.newaxis] y = fft(ephat,nfft); xder[:,1:(cases+1)]= np.hstack((y[2:ns+2,0:cases2].imag -y[2:ns+2,0:cases1].real)) xder[:,0]=x[:,0] if self.tr is not None: np.disp(' Transforming data.') g=self.tr; G=np.fliplr(g); #% the invers of g if derivative: for ix in range(cases): tmp=tranproc(np.hstack((x[:,ix+1], xder[:,ix+1])),G); x[:,ix+1]=tmp[:,0]; xder[:,ix+1]=tmp[:,1]; else: for ix in range(cases): x[:,ix+1]=tranproc(x[:,ix+1],G); if derivative: return x,xder else: return x class TimeSeries(WafoData): ''' Container class for 1D TimeSeries data objects in WAFO Member variables ---------------- data : array_like args : vector for 1D, list of vectors for 2D, 3D, ... type : integer or string sensor type for time series (default 'n' : Surface elevation) see sensortype for more options position : vector of size 3 instrument position relative to the coordinate system ''' def __init__(self,*args,**kwds): super(TimeSeries, self).__init__(*args,**kwds) self.name='WAFO TimeSeries Object' self.type='n' self.position = np.zeros(3) somekeys = ['type', 'position'] self.__dict__.update(sub_dict_select(kwds,somekeys)) #self.setlabels() if not any(self.args): n = len(self.data) self.args = xrange(0,n) def sampling_period(self): ''' Returns sampling interval Returns --------- dT : scalar sampling interval, unit: [s] if lagtype=='t' [m] otherwise See also ''' dt1 = self.args[1]-self.args[0] N = np.size(self.args)-1 T = self.args[-1]-self.args[0] dt = T/N return dt def acf(self,lag=None,flag='biased',norm=False,dt = None): ''' Return auto covariance function from data. R = ACF vector length L+1 t = time lags length L+1 stdev = estimated large lag standard deviation of the estimate assuming x is a Gaussian process: if R(k)=0 for all lags k>q then an approximation of the variance for large samples due to Bartlett var(R(k))=1/N*(R(0)^2+2*R(1)^2+2*R(2)^2+ ..+2*R(q)^2) for k>q and where N=length(x). Special case is white noise where it equals R(0)^2/N for k>0 norm = 0 indicating that R is not normalized x = a column data vector or two column data matrix with sampled times and values. L = the maximum time-lag for which the ACF is estimated. (Default L=n-1) plotflag = 1 then the ACF is plotted vs lag 2 then the ACF is plotted vs lag in seconds 3 then the ACF is plotted vs lag and vs lag (sec dT = time-step between data points (default xn(2,1)-xn(1,1) or 1 Hz). flag = 'biased' : scales the raw cross-correlation by 1/n. (default) 'unbiased': scales the raw correlation by 1/(n-abs(k)), where k is the index into the result. - x may contain NaN's (i.e. missing values). Example: x = load('sea.dat'); rf = dat2cov(x,150,2) ''' n = len(self.data) if not lag: lag = n-1 x = self.data.copy() indnan = numpy.isnan(x) if any(indnan): x = x - numpy.mean(x[1-indnan]) # remove the mean pab 09.10.2000 #indnan = find(indnan); Ncens = n - sum(indnan) x[indnan] = 0. # pab 09.10.2000 much faster for censored samples else: indnan = None Ncens = n x = x - numpy.mean(x) fft = numpy.fft.fft nfft = 2**nextpow2(n) Rper = abs(fft(x,nfft))**2/Ncens # Raw periodogram R = numpy.real(fft(Rper))/nfft # %ifft=fft/nfft since Rper is real! lags = np.arange(0,lag+1) if flag.startswith('unbiased'): # unbiased result, i.e. divide by n-abs(lag) R=R[lags]*Ncens/ np.arange(Ncens,Ncens-lag,-1) #else % biased result, i.e. divide by n # r=r(1:L+1)*Ncens/Ncens; #c0 = R[0] dT = self.sampling_period() t = numpy.linspace(0,lag*dT,lag+1) cumsum = numpy.cumsum acf = CovData1D(R[lags],t) acf.stdev=numpy.sqrt(numpy.r_[ 0, 1 ,1+2*cumsum(R[1:]**2)]/Ncens) acf.children = [WafoData(-2.*acf.stdev[lags],t),WafoData(2.*acf.stdev[lags],t)] return acf def spec(self): pass def turning_points(self,h=0,wavetype=None,output='tp'): ''' Return turning points (tp) from data, optionally rainflowfiltered. Parameters ---------- h : scalar a threshold; if h<0, then tp=x; if h=0, then tp is a sequence of turning points (default); if h>0, then all rainflow cycles with height smaller than h are removed. wavetype : string defines the type of wave. Possible options are 'mw' 'Mw' or 'none'. If None all rainflow filtered min and max will be returned, otherwise only the rainflow filtered min and max, which define a wave according to the wave definition, will be returned. output : string 'tp' if only returning tp 'all' if tp and ind Returns ------- tp : TimeSeries object with times and turning points. ind : arraylike indices to the turning points in the original sequence. Example: x = load('sea.dat'); x1 = x(1:200,:); tp = dat2tp(x1,0,'Mw'); tph = dat2tp(x1,0.3,'Mw'); plot(x1(:,1),x1(:,2),tp(:,1),tp(:,2),'ro',tph(:,1),tph(:,2),'k*') See also --------- findcross, findrfc ''' if h<0: tp = self.copy() ind = np.arange(tp.args.size) if output.startswith('tp'): return tp else: return tp, ind x2 = self.data n = len(x2) ind = findextrema(x2) if ind.size<2: tp = None ind = None return tp #% In order to get the exact up-crossing intensity from rfc by #% mm2lc(tp2mm(rfc)) we have to add the indices #% to the last value (and also the first if the #% sequence of turning points does not start with a minimum). if x2[ind[0]]>x2[ind[1]]: #% adds indices to first and last value ind = np.r_[0, ind ,n] else: # adds index to the last value ind = np.r_[ind, n] if h>0: ind1 = findrfc(x2[ind],h) ind = ind[ind1] Nm =ind.size #% number of min and Max if wavetype in ('mw','Mw'): xor = lambda a,b : a^b #% make sure that the first is a Max if wdef == 'Mw' #% or make sure that the first is a min if wdef == 'mw' removeFirst = xor((x2[ind[0]]>x2[ind[1]]),wavetype.startswith('Mw')) if removeFirst: ind = ind[1::] Nm = Nm-1; #% make sure the number of minima and Maxima are according to the wavedef. #% i.e., make sure Nm=length(ind) is odd if (mod(Nm,2))!=1: ind = ind[:-1] Nm = Nm-1 try: t = self.args except: t = ind tp = TimeSeries(self.data[ind],t) return tp def lc_spectrum(self): pass def cycles(self): pass def trough_crest(self): pass def wave_period(self): pass def reconstruct(self): pass def plot_wave_idx(self): ''' spwaveplot ''' pass def findoutliers(self): pass def sensortypeid(*sensortypes): ''' Return ID for sensortype name Parameter --------- sensortypes : list of strings defining the sensortype Returns ------- sensorids : list of integers defining the sensortype Valid senor-ids and -types for time series are as follows: 0, 'n' : Surface elevation (n=Eta) 1, 'n_t' : Vertical surface velocity 2, 'n_tt' : Vertical surface acceleration 3, 'n_x' : Surface slope in x-direction 4, 'n_y' : Surface slope in y-direction 5, 'n_xx' : Surface curvature in x-direction 6, 'n_yy' : Surface curvature in y-direction 7, 'n_xy' : Surface curvature in xy-direction 8, 'P' : Pressure fluctuation about static MWL pressure 9, 'U' : Water particle velocity in x-direction 10, 'V' : Water particle velocity in y-direction 11, 'W' : Water particle velocity in z-direction 12, 'U_t' : Water particle acceleration in x-direction 13, 'V_t' : Water particle acceleration in y-direction 14, 'W_t' : Water particle acceleration in z-direction 15, 'X_p' : Water particle displacement in x-direction from its mean position 16, 'Y_p' : Water particle displacement in y-direction from its mean position 17, 'Z_p' : Water particle displacement in z-direction from its mean position Example: >>> sensortypeid('W','v') [11, 10] >>> sensortypeid('rubbish') [-1.#IND] See also sensortype, id ''' sensorid_table = dict(n=0,n_t=1,n_tt=2,n_x=3,n_y=4,n_xx=5, n_yy=6,n_xy=7,p=8,u=9,v=10,w=11,u_t=12, v_t=13,w_t=14,x_p=15,y_p=16,z_p=17) try: return [sensorid_table.get(name.lower(),np.NAN) for name in sensortypes] except: raise ValueError('Input must be a string!') def sensortype(*sensorids): ''' Return sensortype name Parameter --------- sensorids : vector or list of integers defining the sensortype Returns ------- sensornames : list of strings defining the sensortype Valid senor-ids and -types for time series are as follows: 0, 'n' : Surface elevation (n=Eta) 1, 'n_t' : Vertical surface velocity 2, 'n_tt' : Vertical surface acceleration 3, 'n_x' : Surface slope in x-direction 4, 'n_y' : Surface slope in y-direction 5, 'n_xx' : Surface curvature in x-direction 6, 'n_yy' : Surface curvature in y-direction 7, 'n_xy' : Surface curvature in xy-direction 8, 'P' : Pressure fluctuation about static MWL pressure 9, 'U' : Water particle velocity in x-direction 10, 'V' : Water particle velocity in y-direction 11, 'W' : Water particle velocity in z-direction 12, 'U_t' : Water particle acceleration in x-direction 13, 'V_t' : Water particle acceleration in y-direction 14, 'W_t' : Water particle acceleration in z-direction 15, 'X_p' : Water particle displacement in x-direction from its mean position 16, 'Y_p' : Water particle displacement in y-direction from its mean position 17, 'Z_p' : Water particle displacement in z-direction from its mean position Example: >>> sensortype(range(3)) ['n', 'n_t', 'n_tt'] See also sensortypeid, tran ''' validNames = ('n','n_t','n_tt','n_x','n_y','n_xx', 'n_yy','n_xy','p','u','v','w','u_t', 'v_t','w_t','x_p','y_p','z_p',np.NAN) ids = np.atleast_1d(*sensorids) if isinstance(ids,list): ids = np.hstack(ids) N = len(validNames)-1 try: return [validNames[id] for id in ids.clip(0,N)] except: raise ValueError('Input must be an integer!') def main(): from wafo.spectrum import models as sm sensortype(range(21)) w = np.linspace(0,3,100) Sj = sm.Jonswap() S = Sj.toSpecData() #S = SpecData1D(Sj(w),w) R = S.toacf(nr=1) S1 = S.copy() Si = R.tospec() ns =5000; dt = .2; x1 = S.sim_nl(ns= ns,dt=dt); x2 = TimeSeries(x1[:,1],x1[:,0]) R = x2.acf(lag=100) R.plot() S.plot('ro') t = S.moment() t1 = S.bandwidth([0,1,2,3]) S1 = S.copy() S1.resample(dt=0.3,method='cubic') S1.plot('k+') x = S1.sim(ns=100) import pylab pylab.clf() pylab.plot(x[:,0],x[:,1]) pylab.show() pylab.close('all') np.disp('done') if __name__ == '__main__': if False: #True: # import doctest doctest.testmod() else: #main() import wafo.spectrum.models as sm Sj = sm.Jonswap(); S = Sj.toSpecData(); R = S.toacf() x = R.sim(ns=1000,dt=0.2) S.characteristic(['hm0','tm02']) ns =1000; dt = .2; x1 = S.sim_nl(ns,dt=dt); x = np.arange(-2,2,0.2) # Plot 2 objects in one call d2 = WafoData(np.sin(x),x,xlab='x',ylab='sin',title='sinus') d0 = d2.copy() d0.data = d0.data*0.9 d1 = d2.copy() d1.data = d1.data*1.2 d1.children = [d0] d2.children = [d1] d2.plot() print 'Done'