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@ -30,6 +30,12 @@ try:
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except ImportError:
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except ImportError:
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warnings.warn('Compile the c_library.pyd again!')
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warnings.warn('Compile the c_library.pyd again!')
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c_library = None
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c_library = None
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try:
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from wafo import cov2mod
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except ImportError:
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warnings.warn('Compile the cov2mod.pyd again!')
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cov2mod = None
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#from wafo.transform import TrData
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#from wafo.transform import TrData
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from wafo.transform.models import TrLinear
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from wafo.transform.models import TrLinear
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@ -255,7 +261,7 @@ def plotspec(specdata, linetype='b-', flag=1):
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spectype = specdata.type.lower()
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spectype = specdata.type.lower()
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stype = spectype[-3::]
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stype = spectype[-3::]
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if stype in ('enc','req','k1d') : #1D plot
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if stype in ('enc', 'req', 'k1d') : #1D plot
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Fn = freq[-1] # Nyquist frequency
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Fn = freq[-1] # Nyquist frequency
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indm = findpeaks(data, n=4)
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indm = findpeaks(data, n=4)
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maxS = data.max()
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maxS = data.max()
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@ -266,19 +272,19 @@ def plotspec(specdata, linetype='b-', flag=1):
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Fp = freq[indm]# %peak frequency/wave number
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Fp = freq[indm]# %peak frequency/wave number
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if len(indm)==1:
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if len(indm) == 1:
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txt = [('fp = %0.2g' % Fp) + funit]
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txt = [('fp = %0.2g' % Fp) + funit]
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else:
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else:
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txt = []
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txt = []
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for i,fp in enumerate(Fp.tolist()):
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for i, fp in enumerate(Fp.tolist()):
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txt.append(('fp%d = %0.2g' % (i,fp)) + funit)
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txt.append(('fp%d = %0.2g' % (i, fp)) + funit)
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if (flag == 3):
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if (flag == 3):
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plotbackend.subplot(2,1,1)
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plotbackend.subplot(2, 1, 1)
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if (flag == 1) or (flag ==3):#% Plot in normal scale
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if (flag == 1) or (flag == 3):#% Plot in normal scale
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plotbackend.plot(np.vstack([Fp, Fp]),np.vstack([zeros(len(indm)), data.take(indm)]),':',
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plotbackend.plot(np.vstack([Fp, Fp]), np.vstack([zeros(len(indm)), data.take(indm)]), ':',
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freq,data,linetype)
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freq, data, linetype)
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# if isfield(S,'CI'),
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# if isfield(S,'CI'),
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# plot(freq,S.S*S.CI(1), 'r:' )
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# plot(freq,S.S*S.CI(1), 'r:' )
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@ -287,29 +293,29 @@ def plotspec(specdata, linetype='b-', flag=1):
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a = plotbackend.axis()
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a = plotbackend.axis()
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a1 = Fn
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a1 = Fn
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if (Fp>0):
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if (Fp > 0):
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a1 = max(min(Fn,10*max(Fp)),a[1]);
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a1 = max(min(Fn, 10 * max(Fp)), a[1]);
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plotbackend.axis([0, a1 ,0, max(1.01*maxS,a[3])])
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plotbackend.axis([0, a1 , 0, max(1.01 * maxS, a[3])])
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plotbackend.title('Spectral density')
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plotbackend.title('Spectral density')
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plotbackend.xlabel(xlbl_txt)
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plotbackend.xlabel(xlbl_txt)
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plotbackend.ylabel(ylbl1_txt )
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plotbackend.ylabel(ylbl1_txt)
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if (flag==3):
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if (flag == 3):
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plotbackend.subplot(2,1,2)
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plotbackend.subplot(2, 1, 2)
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if (flag == 2) or (flag ==3) : # Plot in logaritmic scale
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if (flag == 2) or (flag == 3) : # Plot in logaritmic scale
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ind = np.flatnonzero(data>0)
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ind = np.flatnonzero(data > 0)
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plotbackend.plot(np.vstack([Fp,Fp]),np.vstack((min(10*log10(data.take(ind)/maxS)).repeat(len(Fp)),
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plotbackend.plot(np.vstack([Fp, Fp]), np.vstack((min(10 * log10(data.take(ind) / maxS)).repeat(len(Fp)),
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10*log10(data.take(indm)/maxS))),':')
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10 * log10(data.take(indm) / maxS))), ':')
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# hold on
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# hold on
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# if isfield(S,'CI'),
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# if isfield(S,'CI'),
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# plot(freq(ind),10*log10(S.S(ind)*S.CI(1)/maxS), 'r:' )
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# plot(freq(ind),10*log10(S.S(ind)*S.CI(1)/maxS), 'r:' )
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# plot(freq(ind),10*log10(S.S(ind)*S.CI(2)/maxS), 'r:' )
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# plot(freq(ind),10*log10(S.S(ind)*S.CI(2)/maxS), 'r:' )
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# end
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# end
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plotbackend.plot(freq[ind],10*log10(data[ind]/maxS),linetype)
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plotbackend.plot(freq[ind], 10 * log10(data[ind] / maxS), linetype)
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# if ih, a=axis; else a=[0 0 0 0]; end
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# if ih, a=axis; else a=[0 0 0 0]; end
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# axis([0 max(min(Fn,max(10*Fp)),a(2)) -20 max(1.01*10*log10(1),a(4))]) % log10(maxS)
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# axis([0 max(min(Fn,max(10*Fp)),a(2)) -20 max(1.01*10*log10(1),a(4))]) % log10(maxS)
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@ -650,14 +656,14 @@ class SpecData1D(WafoData):
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def __init__(self, *args, **kwds):
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def __init__(self, *args, **kwds):
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self.name_ = kwds.pop('name', 'WAFO Spectrum Object')
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self.name_ = kwds.pop('name', 'WAFO Spectrum Object')
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self.type = kwds.pop('type','freq')
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self.type = kwds.pop('type', 'freq')
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self.freqtype = kwds.pop('freqtype','w')
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self.freqtype = kwds.pop('freqtype', 'w')
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self.angletype = ''
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self.angletype = ''
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self.h = kwds.pop('h',inf)
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self.h = kwds.pop('h', inf)
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self.tr = kwds.pop('tr',None) #TrLinear()
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self.tr = kwds.pop('tr', None) #TrLinear()
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self.phi = kwds.pop('phi',0.0)
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self.phi = kwds.pop('phi', 0.0)
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self.v = kwds.pop('v',0.0)
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self.v = kwds.pop('v', 0.0)
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self.norm = kwds.pop('norm',False)
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self.norm = kwds.pop('norm', False)
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super(SpecData1D, self).__init__(*args, **kwds)
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super(SpecData1D, self).__init__(*args, **kwds)
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self.setlabels()
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self.setlabels()
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@ -1113,6 +1119,113 @@ class SpecData1D(WafoData):
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return SL, SN
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return SL, SN
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def to_mm_pdf(self, paramt=None, paramu=None, utc=None, nit=2, EPS=5e-5,
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EPSS=1e-6, C=4.5, EPS0=1e-5, IAC=1, ISQ=0, verbose=False):
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'''
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nit = order of numerical integration: 0,1,2,3,4,5.
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paramu = parameter vector defining discretization of min/max values.
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t = grid of time points between maximum and minimum (to
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integrate out). interval between maximum and the following
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minimum,
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The variable ISQ marks which type of conditioning will be used ISQ=0
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means random time where the probability is minimum, ISQ=1 is the time
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where the variance of the residual process is minimal(ISQ=1 is faster).
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NIT, IAC are described in CROSSPACK paper, EPS0 is the accuracy constant
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used in choosing the number of nodes in numerical integrations
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(XX1, H1 vectors). The nodes and weights and other parameters are
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read in the subroutine INITINTEG from files Z.DAT, H.DAT and ACCUR.DAT.
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NIT=0, IAC=1 then one uses RIND0 - subroutine, all other cases
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goes through RIND1, ...,RIND5. NIT=0, here means explicite formula
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approximation for XIND=E[Y^+1{ HH<BU(I)<0 for all I, I=1,...,N}], where
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BU(I) is deterministic function.
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NIT=1, leads tp call RIND1, IAC=0 is also explicit form approximation,
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while IAC=1 leads to maximum one dimensional integral.
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.......
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NIT=5, leads tp call RIND5, IAC is maximally 4-dimensional integral,
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while IAC=1 leads to maximum 5 dimensional integral.
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'''
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S = self.copy()
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S.normalize()
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m, unused_mtxt = self.moment(nr=4, even=True)
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A = sqrt(m[0] / m[1])
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if paramt is None:
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distanceBetweenExtremes = 5*pi*sqrt(m[1]/m[2]) #(2.5 * mean distance between extremes)
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paramt = [0, distanceBetweenExtremes, 43]
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if paramu is None:
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paramu = [-4*sqrt(m[0]), 4*sqrt(m[0]), 41]
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if self.tr is None:
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g = TrLinear(var=m[0])
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else:
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g = self.tr
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if utc is None:
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utc = g.gauss2dat(0) # most frequent crossed level
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# transform reference level into Gaussian level
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u = g.dat2gauss(utc)
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if verbose:
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print('The level u for Gaussian process = %g' % u)
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unused_t0, tn, Nt = paramt
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t = linspace(0, tn/A, Nt) # normalized times
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#Transform amplitudes to Gaussian levels:
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h = linspace(*paramu);
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dt = t[1] - t[0]
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nr = 4
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R = S.tocov_matrix(nr, Nt-1, dt)
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#ulev = linspace(*paramu)
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#vlev = linspace(*paramu)
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trdata = g.trdata()
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Tg = trdata.args
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Xg = trdata.data
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cov2mod.initinteg(EPS, EPSS, EPS0, C, IAC, ISQ)
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uvdens = cov2mod.cov2mmpdfreg(t, R, h, h, Tg, Xg, nit)
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dh = h[1]-h[0]
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uvdens *= dh*dh
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# if (defnr==0)
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# f.f =fliplr(mctp2rfc(fliplr(ftmp)));%* sqrt(-R(1,6)/R(1,4))/2/pi;
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# f.title ='Joint density of maximum and rainflow minimum';
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# f.labx{1}='max [m]';
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# f.labx{2}='rainflow min [m]';
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# elseif (defnr==-1)
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# %CC= normalizing constant= 1/ expected number of u-up-crossings of X
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# %CC = 2*pi*sqrt(L0/L2)*exp(0.5D0*u*u/L0);
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# % CC = normalizing constant = 1/ expected number of zero-up-crossings of X'
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# %CC = 2*pi*sqrt(L2/L4);
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# fact = sqrt(L0/L4);
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#
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# f.f = fliplr(mctp2tc(fliplr(ftmp*fact),utc,paramu));
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# index1 = find(f.x{1}>0);
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# index2 = find(f.x{2}<0);
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# f.f = flipud(f.f(index2,index1));
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# f.x{1} = f.x{1}(index1);
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# f.x{2} = abs(flipud(f.x{2}(index2)));
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# f.title ='Joint density of crest and trough';
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# f.labx{1}='Crest [m]';
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# f.labx{2}='Trough [m]';
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# else %(defnr==1)
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mmpdf = WafoData(uvdens,args=(h,h), title='Joint density of maximum and minimum',
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xlab='max [m]',ylab='min [m]')
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return mmpdf
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#[f.cl,f.pl] = qlevels(f.f,[10, 30, 50, 70, 90, 95, 99, 99.9],f.x{1},f.x{2})
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def to_t_pdf(self, u=None, pdef='Tc', paramt=None, **options):
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def to_t_pdf(self, u=None, pdef='Tc', paramt=None, **options):
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'''
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'''
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@ -1254,7 +1367,7 @@ class SpecData1D(WafoData):
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indI[3] = Ntd - 1
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indI[3] = Ntd - 1
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#% positive wave period
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#% positive wave period
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BIG = self._covinput(pt, R)
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BIG = self._covinput_t_pdf(pt, R)
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tmp = rind(BIG, ex[:Ntdc], B_lo, B_up, indI, xc, Nt)
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tmp = rind(BIG, ex[:Ntdc], B_lo, B_up, indI, xc, Nt)
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f[pt], err[pt] = tmp[:2]
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f[pt], err[pt] = tmp[:2]
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@ -1279,7 +1392,7 @@ class SpecData1D(WafoData):
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return pdf
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return pdf
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def _covinput(self, pt, R):
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def _covinput_t_pdf(self, pt, R):
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"""
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"""
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Return covariance matrix for Tc or Tt period problems
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Return covariance matrix for Tc or Tt period problems
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@ -1813,7 +1926,7 @@ class SpecData1D(WafoData):
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svec = rvec + 1J * ivec
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svec = rvec + 1J * ivec
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else:
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else:
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amp = amp.T
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amp = amp.T
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svec=[]
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svec = []
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for i in range(cases):
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for i in range(cases):
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rvec, ivec = c_library.disufq(amp[i].real, amp[i].imag, w, kw, water_depth,
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rvec, ivec = c_library.disufq(amp[i].real, amp[i].imag, w, kw, water_depth,
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g, nmin, nmax, 1, ns)
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g, nmin, nmax, 1, ns)
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@ -2329,7 +2442,7 @@ class SpecData1D(WafoData):
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#%wnc = min(wnNew,wnOld-1e-5)
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#%wnc = min(wnNew,wnOld-1e-5)
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wnc = wnNew
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wnc = wnNew
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#specfun = lambda xi : stineman_interp(xi, w, S1)
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#specfun = lambda xi : stineman_interp(xi, w, S1)
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specfun = interpolate.interp1d(w,S1, kind='cubic')
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specfun = interpolate.interp1d(w, S1, kind='cubic')
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x, unused_y = discretize(specfun, 0, wnc)
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x, unused_y = discretize(specfun, 0, wnc)
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dwMin = minimum(min(diff(x)), dwMin)
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dwMin = minimum(min(diff(x)), dwMin)
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@ -2437,9 +2550,9 @@ class SpecData1D(WafoData):
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'''
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'''
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m, unused_mtxt = self.moment(nr=4, even=False)
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m, unused_mtxt = self.moment(nr=4, even=False)
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fact_dict=dict(alpha=0,eps2=1,eps4=3,qp=3,Qp=3)
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fact_dict = dict(alpha=0, eps2=1, eps4=3, qp=3, Qp=3)
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fun = lambda fact: fact_dict.get(fact,fact)
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fun = lambda fact: fact_dict.get(fact, fact)
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fact = atleast_1d(map(fun,list(factors)))
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fact = atleast_1d(map(fun, list(factors)))
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#fact = atleast_1d(fact)
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|
#fact = atleast_1d(fact)
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|
|
alpha = m[2] / sqrt(m[0] * m[4])
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alpha = m[2] / sqrt(m[0] * m[4])
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|
@ -2793,13 +2906,13 @@ class SpecData2D(WafoData):
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def toacf(self):
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|
def toacf(self):
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|
pass
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pass
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|
|
def tospecdata(self,type=None):
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|
def tospecdata(self, type=None):
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|
pass
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|
pass
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|
def sim(self):
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|
|
def sim(self):
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|
pass
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|
pass
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|
|
def sim_nl(self):
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|
|
def sim_nl(self):
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|
pass
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|
pass
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|
|
def rotate(self, phi=0,rotateGrid=False,method='linear'):
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|
def rotate(self, phi=0, rotateGrid=False, method='linear'):
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|
|
'''
|
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|
|
'''
|
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|
|
Rotate spectrum clockwise around the origin.
|
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|
|
Rotate spectrum clockwise around the origin.
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|
|
@ -2837,58 +2950,58 @@ class SpecData2D(WafoData):
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|
|
#Snew=S;
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#Snew=S;
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|
|
self.phi = mod(self.phi+phi+pi,2*pi)-pi
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|
|
self.phi = mod(self.phi + phi + pi, 2 * pi) - pi
|
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|
|
stype = self.type.lower()[-3::]
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|
stype = self.type.lower()[-3::]
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|
|
if stype=='dir':
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|
|
if stype == 'dir':
|
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|
|
#% any of the directinal types
|
|
|
|
#% any of the directinal types
|
|
|
|
#% Make sure theta is from -pi to pi
|
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|
|
#% Make sure theta is from -pi to pi
|
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|
|
theta = self.args[0]
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|
|
theta = self.args[0]
|
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|
|
phi0 = theta[0]+pi;
|
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|
|
phi0 = theta[0] + pi;
|
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|
|
self.args[0] = theta-phi0
|
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|
|
self.args[0] = theta - phi0
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|
|
|
# make sure -pi<phi<pi
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|
|
# make sure -pi<phi<pi
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|
|
self.phi = mod(self.phi+phi0+pi,2*pi)-pi
|
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|
|
self.phi = mod(self.phi + phi0 + pi, 2 * pi) - pi
|
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|
|
if (rotateGrid and (self.phi!=0)):
|
|
|
|
if (rotateGrid and (self.phi != 0)):
|
|
|
|
# Do a physical rotation of spectrum
|
|
|
|
# Do a physical rotation of spectrum
|
|
|
|
#theta = Snew.args[0]
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|
|
|
#theta = Snew.args[0]
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|
|
|
ntOld = len(theta);
|
|
|
|
ntOld = len(theta);
|
|
|
|
if (mod(theta[0]-theta[-1],2*pi)==0):
|
|
|
|
if (mod(theta[0] - theta[-1], 2 * pi) == 0):
|
|
|
|
nt = ntOld-1
|
|
|
|
nt = ntOld - 1
|
|
|
|
else:
|
|
|
|
else:
|
|
|
|
nt = ntOld
|
|
|
|
nt = ntOld
|
|
|
|
|
|
|
|
|
|
|
|
theta[0:nt] = mod(theta[0:nt]-self.phi+pi,2*pi)-pi
|
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|
|
theta[0:nt] = mod(theta[0:nt] - self.phi + pi, 2 * pi) - pi
|
|
|
|
self.phi = 0
|
|
|
|
self.phi = 0
|
|
|
|
ind = theta.argsort()
|
|
|
|
ind = theta.argsort()
|
|
|
|
self.data = self.data[ind,:]
|
|
|
|
self.data = self.data[ind, :]
|
|
|
|
self.args[0] = theta[ind]
|
|
|
|
self.args[0] = theta[ind]
|
|
|
|
if (nt<ntOld):
|
|
|
|
if (nt < ntOld):
|
|
|
|
if (self.args[0][0]==-pi):
|
|
|
|
if (self.args[0][0] == -pi):
|
|
|
|
self.data[ntOld,:] = self.data[0,:]
|
|
|
|
self.data[ntOld, :] = self.data[0, :]
|
|
|
|
else:
|
|
|
|
else:
|
|
|
|
#ftype = self.freqtype
|
|
|
|
#ftype = self.freqtype
|
|
|
|
freq = self.args[1]
|
|
|
|
freq = self.args[1]
|
|
|
|
theta = linspace(-pi,pi,ntOld)
|
|
|
|
theta = linspace(-pi, pi, ntOld)
|
|
|
|
[F,T] = meshgrid(freq,theta)
|
|
|
|
[F, T] = meshgrid(freq, theta)
|
|
|
|
|
|
|
|
|
|
|
|
dtheta = self.theta[1]-self.theta[0]
|
|
|
|
dtheta = self.theta[1] - self.theta[0]
|
|
|
|
self.theta[nt] = self.theta[nt-1]+dtheta;
|
|
|
|
self.theta[nt] = self.theta[nt - 1] + dtheta;
|
|
|
|
self.data[nt,:] = self.data[0,:]
|
|
|
|
self.data[nt, :] = self.data[0, :]
|
|
|
|
self.data = interp2(freq,np.vstack([self.theta[0]-dtheta,self.theta]),
|
|
|
|
self.data = interp2(freq, np.vstack([self.theta[0] - dtheta, self.theta]),
|
|
|
|
np.vstack([self.data[nt,:],self.data]),F,T,method)
|
|
|
|
np.vstack([self.data[nt, :], self.data]), F, T, method)
|
|
|
|
self.args[0] = theta
|
|
|
|
self.args[0] = theta
|
|
|
|
|
|
|
|
|
|
|
|
elif stype=='k2d':
|
|
|
|
elif stype == 'k2d':
|
|
|
|
#any of the 2D wave number types
|
|
|
|
#any of the 2D wave number types
|
|
|
|
#Snew.phi = mod(Snew.phi+phi+pi,2*pi)-pi;
|
|
|
|
#Snew.phi = mod(Snew.phi+phi+pi,2*pi)-pi;
|
|
|
|
if (rotateGrid and (self.phi!=0)):
|
|
|
|
if (rotateGrid and (self.phi != 0)):
|
|
|
|
# Do a physical rotation of spectrum
|
|
|
|
# Do a physical rotation of spectrum
|
|
|
|
|
|
|
|
|
|
|
|
[k,k2] = meshgrid(*self.args)
|
|
|
|
[k, k2] = meshgrid(*self.args)
|
|
|
|
[th,r] = cart2pol(k,k2)
|
|
|
|
[th, r] = cart2pol(k, k2)
|
|
|
|
[k,k2] = pol2cart(th+self.phi,r)
|
|
|
|
[k, k2] = pol2cart(th + self.phi, r)
|
|
|
|
ki1, ki2 = self.args
|
|
|
|
ki1, ki2 = self.args
|
|
|
|
Sn = interp2(ki1,ki2,self.data,k,k2,method)
|
|
|
|
Sn = interp2(ki1, ki2, self.data, k, k2, method)
|
|
|
|
self.data = np.where(np.isnan(Sn), 0, Sn)
|
|
|
|
self.data = np.where(np.isnan(Sn), 0, Sn)
|
|
|
|
|
|
|
|
|
|
|
|
self.phi = 0;
|
|
|
|
self.phi = 0;
|
|
|
|
@ -2958,107 +3071,107 @@ class SpecData2D(WafoData):
|
|
|
|
if self.type not in two_dim_spectra:
|
|
|
|
if self.type not in two_dim_spectra:
|
|
|
|
raise ValueError('Unknown 2D spectrum type!')
|
|
|
|
raise ValueError('Unknown 2D spectrum type!')
|
|
|
|
|
|
|
|
|
|
|
|
if vari==None and nr<=1:
|
|
|
|
if vari == None and nr <= 1:
|
|
|
|
vari='x'
|
|
|
|
vari = 'x'
|
|
|
|
elif vari==None:
|
|
|
|
elif vari == None:
|
|
|
|
vari='xt'
|
|
|
|
vari = 'xt'
|
|
|
|
else: #% secure the mutual order ('xyt')
|
|
|
|
else: #% secure the mutual order ('xyt')
|
|
|
|
vari=''.join(sorted(vari.lower()))
|
|
|
|
vari = ''.join(sorted(vari.lower()))
|
|
|
|
Nv=len(vari)
|
|
|
|
Nv = len(vari)
|
|
|
|
|
|
|
|
|
|
|
|
if vari[0]=='t' and Nv>1:
|
|
|
|
if vari[0] == 't' and Nv > 1:
|
|
|
|
vari = vari[1::]+ vari[0]
|
|
|
|
vari = vari[1::] + vari[0]
|
|
|
|
|
|
|
|
|
|
|
|
Nv = len(vari)
|
|
|
|
Nv = len(vari)
|
|
|
|
|
|
|
|
|
|
|
|
if not self.type.endswith('dir'):
|
|
|
|
if not self.type.endswith('dir'):
|
|
|
|
S1 = self.tospecdata(self.type[:-2]+'dir')
|
|
|
|
S1 = self.tospecdata(self.type[:-2] + 'dir')
|
|
|
|
else:
|
|
|
|
else:
|
|
|
|
S1 = self
|
|
|
|
S1 = self
|
|
|
|
w = ravel(S1.args[0])
|
|
|
|
w = ravel(S1.args[0])
|
|
|
|
theta = S1.args[1]-S1.phi
|
|
|
|
theta = S1.args[1] - S1.phi
|
|
|
|
S = S1.data
|
|
|
|
S = S1.data
|
|
|
|
Sw = simps(S,x=theta,axis=0)
|
|
|
|
Sw = simps(S, x=theta, axis=0)
|
|
|
|
m = [simps(Sw,x=w)]
|
|
|
|
m = [simps(Sw, x=w)]
|
|
|
|
mtext=['m0']
|
|
|
|
mtext = ['m0']
|
|
|
|
|
|
|
|
|
|
|
|
if nr>0:
|
|
|
|
if nr > 0:
|
|
|
|
vec = []
|
|
|
|
vec = []
|
|
|
|
g = np.atleast_1d(S1.__dict__.get('g', gravity()))
|
|
|
|
g = np.atleast_1d(S1.__dict__.get('g', gravity()))
|
|
|
|
kx=w**2/g[0] # maybe different normalization in x and y => diff. g
|
|
|
|
kx = w ** 2 / g[0] # maybe different normalization in x and y => diff. g
|
|
|
|
ky=w**2/g[-1]
|
|
|
|
ky = w ** 2 / g[-1]
|
|
|
|
|
|
|
|
|
|
|
|
nw=w.size
|
|
|
|
nw = w.size
|
|
|
|
|
|
|
|
|
|
|
|
if 'x' in vari:
|
|
|
|
if 'x' in vari:
|
|
|
|
ct = np.cos(theta[:,None])
|
|
|
|
ct = np.cos(theta[:, None])
|
|
|
|
Sc = simps(S*ct,x=theta, axis=0)
|
|
|
|
Sc = simps(S * ct, x=theta, axis=0)
|
|
|
|
vec.append(kx*Sc)
|
|
|
|
vec.append(kx * Sc)
|
|
|
|
mtext.append('mx')
|
|
|
|
mtext.append('mx')
|
|
|
|
if 'y' in vari:
|
|
|
|
if 'y' in vari:
|
|
|
|
st = np.sin(theta[:,None])
|
|
|
|
st = np.sin(theta[:, None])
|
|
|
|
Ss = simps(S*st,x=theta, axis=0)
|
|
|
|
Ss = simps(S * st, x=theta, axis=0)
|
|
|
|
vec.append(ky*Ss)
|
|
|
|
vec.append(ky * Ss)
|
|
|
|
mtext.append('my')
|
|
|
|
mtext.append('my')
|
|
|
|
if 't' in vari:
|
|
|
|
if 't' in vari:
|
|
|
|
vec.append(w*Sw)
|
|
|
|
vec.append(w * Sw)
|
|
|
|
mtext.append('mt')
|
|
|
|
mtext.append('mt')
|
|
|
|
|
|
|
|
|
|
|
|
if nr>1:
|
|
|
|
if nr > 1:
|
|
|
|
if 'x' in vari:
|
|
|
|
if 'x' in vari:
|
|
|
|
Sc2 = simps(S*ct**2,x=theta, axis=0)
|
|
|
|
Sc2 = simps(S * ct ** 2, x=theta, axis=0)
|
|
|
|
vec.append(kx**2*Sc2)
|
|
|
|
vec.append(kx ** 2 * Sc2)
|
|
|
|
mtext.append('mxx')
|
|
|
|
mtext.append('mxx')
|
|
|
|
if 'y' in vari:
|
|
|
|
if 'y' in vari:
|
|
|
|
Ss2 = simps(S*st**2,x=theta, axis=0)
|
|
|
|
Ss2 = simps(S * st ** 2, x=theta, axis=0)
|
|
|
|
vec.append(ky**2*Ss2)
|
|
|
|
vec.append(ky ** 2 * Ss2)
|
|
|
|
mtext.append('myy')
|
|
|
|
mtext.append('myy')
|
|
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if 't' in vari:
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if 't' in vari:
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vec.append(w**2*Sw)
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vec.append(w ** 2 * Sw)
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mtext.append('mtt')
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mtext.append('mtt')
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if 'x' in vari and 'y' in vari:
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if 'x' in vari and 'y' in vari:
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Scs = simps(S*ct*st,x=theta, axis=0)
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Scs = simps(S * ct * st, x=theta, axis=0)
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vec.append(kx*ky*Scs)
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vec.append(kx * ky * Scs)
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mtext.append('mxy')
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mtext.append('mxy')
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if 'x' in vari and 't' in vari:
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if 'x' in vari and 't' in vari:
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vec.append(kx*w*Sc)
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vec.append(kx * w * Sc)
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mtext.append('mxt')
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mtext.append('mxt')
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if 'y' in vari and 't' in vari:
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if 'y' in vari and 't' in vari:
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vec.append(ky*w*Sc)
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vec.append(ky * w * Sc)
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mtext.append('myt')
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mtext.append('myt')
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if nr>3:
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if nr > 3:
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if 'x' in vari:
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if 'x' in vari:
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Sc3 = simps(S*ct**3,x=theta, axis=0)
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Sc3 = simps(S * ct ** 3, x=theta, axis=0)
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Sc4 = simps(S*ct**4,x=theta, axis=0)
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Sc4 = simps(S * ct ** 4, x=theta, axis=0)
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vec.append(kx**4*Sc4)
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vec.append(kx ** 4 * Sc4)
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mtext.append('mxxxx')
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mtext.append('mxxxx')
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if 'y' in vari:
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if 'y' in vari:
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Ss3 = simps(S*st**3,x=theta, axis=0)
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Ss3 = simps(S * st ** 3, x=theta, axis=0)
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Ss4 = simps(S*st**4,x=theta, axis=0)
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Ss4 = simps(S * st ** 4, x=theta, axis=0)
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vec.append(ky**4*Ss4)
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vec.append(ky ** 4 * Ss4)
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mtext.append('myyyy')
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mtext.append('myyyy')
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if 't' in vari:
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if 't' in vari:
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vec.append(w**4*Sw)
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vec.append(w ** 4 * Sw)
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mtext.append('mtttt')
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mtext.append('mtttt')
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if 'x' in vari and 'y' in vari:
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if 'x' in vari and 'y' in vari:
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Sc2s = simps(S*ct**2*st,x=theta, axis=0)
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Sc2s = simps(S * ct ** 2 * st, x=theta, axis=0)
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Sc3s = simps(S*ct**3*st,x=theta, axis=0)
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Sc3s = simps(S * ct ** 3 * st, x=theta, axis=0)
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Scs2 = simps(S*ct*st**2,x=theta, axis=0)
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Scs2 = simps(S * ct * st ** 2, x=theta, axis=0)
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Scs3 = simps(S*ct*st**3,x=theta, axis=0)
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Scs3 = simps(S * ct * st ** 3, x=theta, axis=0)
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Sc2s2 = simps(S*ct**2*st**2,x=theta, axis=0)
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Sc2s2 = simps(S * ct ** 2 * st ** 2, x=theta, axis=0)
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vec.extend((kx**3*ky*Sc3s,kx**2*ky**2*Sc2s2, kx*ky**3*Scs3))
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vec.extend((kx ** 3 * ky * Sc3s, kx ** 2 * ky ** 2 * Sc2s2, kx * ky ** 3 * Scs3))
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mtext.extend(('mxxxy','mxxyy','mxyyy'))
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mtext.extend(('mxxxy', 'mxxyy', 'mxyyy'))
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if 'x' in vari and 't' in vari:
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if 'x' in vari and 't' in vari:
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vec.extend((kx**3*w*Sc3, kx**2*w**2*Sc2, kx*w**3*Sc))
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vec.extend((kx ** 3 * w * Sc3, kx ** 2 * w ** 2 * Sc2, kx * w ** 3 * Sc))
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mtext.extend(('mxxxt','mxxtt','mxttt'))
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mtext.extend(('mxxxt', 'mxxtt', 'mxttt'))
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if 'y' in vari and 't' in vari:
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if 'y' in vari and 't' in vari:
|
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vec.extend((ky**3*w*Ss3, ky**2*w**2*Ss2, ky*w**3*Ss))
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vec.extend((ky ** 3 * w * Ss3, ky ** 2 * w ** 2 * Ss2, ky * w ** 3 * Ss))
|
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mtext.extend(('myyyt','myytt','myttt'))
|
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mtext.extend(('myyyt', 'myytt', 'myttt'))
|
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if 'x' in vari and 'y' in vari and 't' in vari:
|
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if 'x' in vari and 'y' in vari and 't' in vari:
|
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vec.extend((kx**2*ky*w*Sc2s, kx*ky**2*w*Scs2, kx*ky*w**2*Scs))
|
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vec.extend((kx ** 2 * ky * w * Sc2s, kx * ky ** 2 * w * Scs2, kx * ky * w ** 2 * Scs))
|
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mtext.extend(('mxxyt','mxyyt','mxytt'))
|
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|
mtext.extend(('mxxyt', 'mxyyt', 'mxytt'))
|
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#end % if nr>1
|
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|
#end % if nr>1
|
|
|
|
m.extend([simps(vals, x=w) for vals in vec])
|
|
|
|
m.extend([simps(vals, x=w) for vals in vec])
|
|
|
|
return np.asarray(m), mtext
|
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|
return np.asarray(m), mtext
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Per.Andreas.Brodtkorb
14 years ago