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@ -21,6 +21,8 @@ from dispersion_relation import w2k #, k2w
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from wafo.wafodata import WafoData, now
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from wafo.misc import sub_dict_select, nextpow2, discretize, JITImport, findpeaks #, tranproc
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from wafo.graphutil import cltext
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from wafo.kdetools import qlevels
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from wafo import wafodata
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try:
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from wafo.gaussian import Rind
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except ImportError:
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@ -1154,7 +1156,9 @@ class SpecData1D(WafoData):
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>>> w = np.linspace(0,4,256)
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>>> S1 = Sj.tospecdata(w) #Make spectrum object from numerical values
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>>> S = sm.SpecData1D(Sj(w),w) # Alternatively do it manually
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S.to_mm_pdf()
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mm = S.to_mm_pdf()
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mm.plot()
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mm.plot(plotflag=1)
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'''
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S = self.copy()
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@ -1163,11 +1167,11 @@ class SpecData1D(WafoData):
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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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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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paramu = [-5 * sqrt(m[0]), 5 * 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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@ -1184,13 +1188,13 @@ class SpecData1D(WafoData):
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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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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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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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@ -1201,19 +1205,23 @@ class SpecData1D(WafoData):
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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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uvdens = np.rot90(uvdens, -2)
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dh = h[1]-h[0]
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uvdens *= dh*dh
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uvdens = np.rot90(uvdens,-2)
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dh = h[1] - h[0]
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uvdens *= dh * dh
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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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mmpdf = WafoData(uvdens, args=(h, h), xlab='max [m]', ylab='min [m]',
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title='Joint density of maximum and minimum')
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try:
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pl = [10, 30, 50, 70, 90, 95, 99, 99.9]
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mmpdf.cl = qlevels(uvdens, pl, h, h)
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mmpdf.pl = pl
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except:
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pass
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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, kind='Tc', paramt=None, **options):
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'''
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Density of crest/trough- period or length, version 2.
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@ -1221,7 +1229,7 @@ class SpecData1D(WafoData):
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----------
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u : real scalar
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reference level (default the most frequently crossed level).
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pdef : string, 'Tc', Tt', 'Lc' or 'Lt'
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kind : string, 'Tc', Tt', 'Lc' or 'Lt'
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'Tc', gives half wave period, Tc (default).
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'Tt', gives half wave period, Tt
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'Lc' and 'Lt' ditto for wave length.
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@ -1267,23 +1275,23 @@ class SpecData1D(WafoData):
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opts = dict(speed=9)
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opts.update(options)
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if pdef[0] in ('l', 'L'):
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if kind[0] in ('l', 'L'):
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if self.type != 'k1d':
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raise ValueError('Must be spectrum of type: k1d')
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elif pdef[0] in ('t', 'T'):
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elif kind[0] in ('t', 'T'):
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if self.type != 'freq':
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raise ValueError('Must be spectrum of type: freq')
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else:
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raise ValueError('pdef must be Tc,Tt or Lc, Lt')
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# if strncmpi('l',def,1)
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# if strncmpi('l',kind,1)
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# spec=spec2spec(spec,'k1d')
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# elseif strncmpi('t',def,1)
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# elseif strncmpi('t',kind,1)
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# spec=spec2spec(spec,'freq')
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# else
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# error('Unknown def')
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# error('Unknown kind')
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# end
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pdef2defnr = dict(tc=1, lc=1, tt= -1, lt= -1)
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defnr = pdef2defnr[pdef.lower()]
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kind2defnr = dict(tc=1, lc=1, tt= -1, lt= -1)
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defnr = kind2defnr[kind.lower()]
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S = self.copy()
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S.normalize()
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@ -1363,9 +1371,9 @@ class SpecData1D(WafoData):
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titledict = dict(tc='Density of Tc', tt='Density of Tt', lc='Density of Lc', lt='Density of Lt')
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Htxt = titledict.get(pdef.lower())
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Htxt = titledict.get(kind.lower())
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if pdef[0].lower() == 'l':
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if kind[0].lower() == 'l':
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xtxt = 'wave length [m]'
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else:
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xtxt = 'period [s]'
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@ -1441,6 +1449,347 @@ class SpecData1D(WafoData):
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hstack((Scd, Scc))))
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return big
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def to_mmt_pdf(self, paramt=None,paramu=None,utc=None,kind='mm',verbose=False,**options):
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''' Returns joint density of Maximum, minimum and period.
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Parameters
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----------
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u = reference level (default the most frequently crossed level).
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kind : string
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defining density returned
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'Mm' : maximum and the following minimum. (M,m) (default)
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'rfc' : maximum and the rainflow minimum height.
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'AcAt' : (crest,trough) heights.
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'vMm' : level v separated Maximum and minimum (M,m)_v
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'MmTMm' : maximum, minimum and period between (M,m,TMm)
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'vMmTMm': level v separated Maximum, minimum and period
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between (M,m,TMm)_v
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'MmTMd' : level v separated Maximum, minimum and the period
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from Max to level v-down-crossing (M,m,TMd)_v.
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'MmTdm' : level v separated Maximum, minimum and the period from
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level v-down-crossing to min. (M,m,Tdm)_v
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NB! All 'T' above can be replaced by 'L' to get wave length
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instead.
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paramt : [0 tn Nt]
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defines discretization of half period: tn is the longest period
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considered while Nt is the number of points, i.e. (Nt-1)/tn is the
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sampling frequnecy. paramt= [0 10 51] implies that the halfperiods
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are considered at 51 linearly spaced points in the interval [0,10],
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i.e. sampling frequency is 5 Hz.
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paramu : [u v N]
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defines discretization of maxima and minima ranges: u is the lowest
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minimum considered, v the highest maximum and N is the number of
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levels (u,v) included.
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options :
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rind-options structure containing optional parameters controlling
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the performance of the integration. See rindoptset for details.
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[] = default values are used.
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Returns
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-------
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f = pdf (density structure) of crests (trough) heights
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TO_MMT_PDF calculates densities of wave characteristics in a
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stationary Gaussian transform process X(t) where
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Y(t) = g(X(t)) (Y zero-mean Gaussian with spectrum given in input spec).
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The tr. g can be estimated using lc2tr, dat2tr, hermitetr or ochitr.
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Examples
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--------
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The joint density of zero separated Max2min cycles in time (a);
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in space (b); AcAt in time for nonlinear sea model (c):
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Hm0=7;Tp=11;
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S = jonswap(4*pi/Tp,[Hm0 Tp]);
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Sk = spec2spec(S,'k1d');
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L0 = spec2mom(S,1);
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paramu = [sqrt(L0)*[-4 4] 41];
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ft = spec2mmtpdf(S,0,'vmm',[],paramu); pdfplot(ft) % a)
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fs = spec2mmtpdf(Sk,0,'vmm'); figure, pdfplot(fs) % b)
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[sk, ku, me]=spec2skew(S);
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g = hermitetr([],[sqrt(L0) sk ku me]);
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Snorm=S; Snorm.S=S.S/L0; Snorm.tr=g;
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ftg=spec2mmtpdf(Snorm,0,'AcAt',[],paramu); pdfplot(ftg) % c)
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See also
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--------
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rindoptset, dat2tr, datastructures, wavedef, perioddef
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References
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---------
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Podgorski et al. (2000)
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"Exact distributions for apparent waves in irregular seas"
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Ocean Engineering, Vol 27, no 1, pp979-1016.
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P. A. Brodtkorb (2004),
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Numerical evaluation of multinormal expectations
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In Lund university report series
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and in the Dr.Ing thesis:
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The probability of Occurrence of dangerous Wave Situations at Sea.
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Dr.Ing thesis, Norwegian University of Science and Technolgy, NTNU,
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Trondheim, Norway.
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Per A. Brodtkorb (2006)
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"Evaluating Nearly Singular Multinormal Expectations with Application to
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Wave Distributions",
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Methodology And Computing In Applied Probability, Volume 8, Number 1, pp. 65-91(27)
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'''
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opts = dict(speed=4, nit=2, method=0)
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opts.update(**options)
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ftype = self.freqtype
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kind2defnr = dict( ac=-2,at=-2,
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rfc=-1,
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mm=0,
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mmtmm=1, mmlmm=1,
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vmm=2,
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vmmtmm=3, vmmlmm=3,
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mmtmd=4, vmmtmd=4, mmlmd=4,vmmlmd=4,
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mmtdm=5, vmmtdm=5, mmldm=5, vmmldm=5)
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defnr = kind2defnr.get(kind, 0)
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in_space = (ftype=='k') # distribution in space or time
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if defnr>=3 or defnr==1:
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in_space = (kind[-2].upper()=='L')
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if in_space:
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#spec = spec2spec(spec,'k1d') ;
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ptxt = 'space';
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else:
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#spec = spec2spec(spec,'freq');
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ptxt='time';
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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 = [-5 * sqrt(m[0]), 5 * 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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t0, tn, Nt = paramt
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t = linspace(0, tn / A, Nt) # normalized times
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Nstart = 1 + round(t0/tn*(Nt-1)) # the starting point to evaluate
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Nx = paramu[2]
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if (defnr>1):
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paramu[0] = max(0,paramu[0])
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if (paramu[1]<0):
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raise ValueError('Discretization levels must be larger than zero')
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#Transform amplitudes to Gaussian levels:
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#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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h = linspace(*paramu)
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if defnr>1: # level v separated Max2min densities
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hg = np.hstack((utc+h,utc-h))
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hg, der = g.dat2gauss(utc+h, ones(Nx))
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hg1, der1 = g.dat2gauss(utc-h, ones(Nx))
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der, der1 = np.abs(der), np.abs(der1)
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hg = np.hstack((hg,hg1))
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else: # Max2min densities
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hg, der = np.abs(g.dat2gauss(h, ones(Nx)))
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der = der1 = np.abs(der)
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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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#NB!!! the spec2XXpdf.exe programmes is very sensitive to how you interpolate
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# the covariances, especially where the process is very dependent
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# and the covariance matrix is nearly singular. (i.e. for small t
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# and high levels of u if Tc and low levels of u if Tt)
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# The best is to interpolate the spectrum linearly so that S.S>=0
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# This makes sure that the covariance matrix is positive
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# semi-definitt, since the circulant spectrum are the eigenvalues of
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# the circulant covariance matrix.
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callFortran = 0; # %options.method<0;
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#if callFortran, % call fortran
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#ftmp = cov2mmtpdfexe(R,dt,u,defnr,Nstart,hg,options);
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#err = repmat(nan,size(ftmp));
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#else
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[ftmp,err,terr,options] = cov2mmtpdf(R,dt,u,defnr,Nstart,hg,options)
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#end
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note = ''
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if hasattr(self,'note'):
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note = note + self.note
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tmp = 'L' if in_space else 'T'
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if Nx>2:
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titledict = {'-2':'Joint density of (Ac,At) in %s' % ptxt,
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'-1':'Joint density of (M,m_{rfc}) in %s' % ptxt,
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'0':'Joint density of (M,m) in %s' % ptxt,
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'1':'Joint density of (M,m,%sMm) in %s' % (tmp, ptxt),
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'2':'Joint density of (M,m)_{v=%2.5g} in %s' % (utc, ptxt),
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'3':'Joint density of (M,m,%sMm)_{v=%2.5g} in %s' % (tmp,utc, ptxt),
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'4':'Joint density of (M,m,%sMd)_{v=%2.5g} in %s' % (tmp,utc, ptxt),
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'5':'Joint density of (M,m,%sdm)_{v=%2.5g} in %s' % (tmp,utc, ptxt)}
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title = titledict[defnr]
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labx = 'Max [m]'
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laby = 'min [m]';
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args = (h,h)
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else:
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note = note + 'Density is not scaled to unity'
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if defnr in (-2,-1,0,1):
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title = 'Density of (%sMm, M = %2.5g, m = %2.5g)' % (tmp,h[1],h[0])
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elif defnr in (2,3):
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title = 'Density of (%sMm, M = %2.5g, m = %2.5g)_{v=%2.5g}' % (tmp,h[1],-h[1],utc)
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elif defnr==4:
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title = 'Density of (%sMd, %sMm, M = %2.5g, m = %2.5g)_{v=%2.5g}' % (tmp,tmp,h[1],-h[1],utc)
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elif defnr==5:
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title = 'Density of (%sdm, %sMm, M = %2.5g, m = %2.5g)_{v=%2.5g}' % (tmp,tmp,h[1],-h[1],utc)
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f = wafodata();
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# f.options = options;
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# if defnr>1 or defnr==-2:
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# f.u = utc # save level u
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#
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# if Nx>2 % amplitude distributions wanted
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# f.x{2} = h;
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# f.labx{2} = 'min [m]';
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#
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#
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# if defnr>2 || defnr==1
|
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# der0 = der1[:,None] * der[None,:]
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# ftmp = np.reshape(ftmp,Nx,Nx,Nt) * der0[:,:, None] / A
|
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# err = np.reshape(err,Nx,Nx,Nt) * der0[:,:, None] / A
|
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#
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# f.x{3} = t(:)*A
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# labz = 'wave length [m]' if in_space else 'period [sec]'
|
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#
|
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# else
|
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|
# der0 = der[:,None] * der[None,:]
|
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|
|
# ftmp = np.reshape(ftmp,Nx,Nx) * der0
|
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|
# err = np.reshape(err,Nx,Nx) * der0
|
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|
#
|
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|
|
# if (defnr==-1):
|
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|
|
# ftmp0 = fliplr(mctp2rfc(fliplr(ftmp)));
|
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|
|
|
# err = abs(ftmp0-fliplr(mctp2rfc(fliplr(ftmp+err))));
|
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|
|
# ftmp = ftmp0;
|
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|
|
|
# elif (defnr==-2):
|
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|
|
|
# ftmp0=fliplr(mctp2tc(fliplr(ftmp),utc,paramu))*sqrt(L4*L0)/L2;
|
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|
|
# err =abs(ftmp0-fliplr(mctp2tc(fliplr(ftmp+err),utc,paramu))*sqrt(L4*L0)/L2);
|
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|
|
# index1=find(f.x{1}>0);
|
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|
|
# index2=find(f.x{2}<0);
|
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|
|
# ftmp=flipud(ftmp0(index2,index1));
|
|
|
|
|
# err =flipud(err(index2,index1));
|
|
|
|
|
# f.x{1} = f.x{1}(index1);
|
|
|
|
|
# f.x{2} = abs(flipud(f.x{2}(index2)));
|
|
|
|
|
# end
|
|
|
|
|
# end
|
|
|
|
|
# f.f = ftmp;
|
|
|
|
|
# f.err = err;
|
|
|
|
|
# else % Only time or wave length distributions wanted
|
|
|
|
|
# f.f = ftmp/A;
|
|
|
|
|
# f.err = err/A;
|
|
|
|
|
# f.x{1}=A*t';
|
|
|
|
|
# if strcmpi(def(1),'t')
|
|
|
|
|
# f.labx{1} = 'period [sec]';
|
|
|
|
|
# else
|
|
|
|
|
# f.labx{1} = 'wave length [m]';
|
|
|
|
|
# end
|
|
|
|
|
# if defnr>3,
|
|
|
|
|
# f.f = reshape(f.f,[Nt, Nt]);
|
|
|
|
|
# f.err = reshape(f.err,[Nt, Nt]);
|
|
|
|
|
# f.x{2}= A*t';
|
|
|
|
|
# if strcmpi(def(1),'t')
|
|
|
|
|
# f.labx{2} = 'period [sec]';
|
|
|
|
|
# else
|
|
|
|
|
# f.labx{2} = 'wave length [m]';
|
|
|
|
|
# end
|
|
|
|
|
# end
|
|
|
|
|
# end
|
|
|
|
|
#
|
|
|
|
|
#
|
|
|
|
|
# try
|
|
|
|
|
# [f.cl,f.pl]=qlevels(f.f,[10 30 50 70 90 95 99 99.9],f.x{1},f.x{2});
|
|
|
|
|
# catch
|
|
|
|
|
# warning('WAFO:SPEC2MMTPDF','Singularity likely in pdf')
|
|
|
|
|
# end
|
|
|
|
|
# %pdfplot(f)
|
|
|
|
|
#
|
|
|
|
|
# %Test of spec2mmtpdf
|
|
|
|
|
# % cd f:\matlab\matlab\wafo\source\sp2thpdfalan
|
|
|
|
|
# % addpath f:\matlab\matlab\wafo ,initwafo, addpath f:\matlab\matlab\graphutil
|
|
|
|
|
# % Hm0=7;Tp=11; S = jonswap(4*pi/Tp,[Hm0 Tp]);
|
|
|
|
|
# % ft = spec2mmtpdf(S,0,'vMmTMm',[0.3,.4,11],[0 .00005 2]);
|
|
|
|
|
|
|
|
|
|
return f #% main
|
|
|
|
|
|
|
|
|
|
# function dens = cov2mmtpdfexe(R,dt,u,defnr,Nstart,hg,options)
|
|
|
|
|
# % Write parameters to file
|
|
|
|
|
# %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
|
|
|
|
# Nx = max(1,length(hg));
|
|
|
|
|
# if (defnr>1)
|
|
|
|
|
# Nx = Nx/2; %level v separated max2min densities wanted
|
|
|
|
|
# end
|
|
|
|
|
# Ntime = size(R,1);
|
|
|
|
|
#
|
|
|
|
|
# filenames = {'h.in','reflev.in'};
|
|
|
|
|
# cleanup(filenames{:})
|
|
|
|
|
#
|
|
|
|
|
# fid = fopen('h.in','wt');
|
|
|
|
|
# fprintf(fid,'%12.10f\n',hg);
|
|
|
|
|
# fclose(fid);
|
|
|
|
|
#
|
|
|
|
|
# %XSPLT = options.xsplit;
|
|
|
|
|
# nit = options.nit;
|
|
|
|
|
# speed = options.speed;
|
|
|
|
|
# seed = options.seed;
|
|
|
|
|
# SCIS = abs(options.method); % method<=0
|
|
|
|
|
#
|
|
|
|
|
# disp('writing data')
|
|
|
|
|
# fid=fopen('reflev.in','wt');
|
|
|
|
|
# fprintf(fid,'%2.0f \n',Ntime);
|
|
|
|
|
# fprintf(fid,'%2.0f \n',Nstart);
|
|
|
|
|
# fprintf(fid,'%2.0f \n',nit);
|
|
|
|
|
# fprintf(fid,'%2.0f \n',speed);
|
|
|
|
|
# fprintf(fid,'%2.0f \n',SCIS);
|
|
|
|
|
# fprintf(fid,'%2.0f \n',seed); % select a random seed for rind
|
|
|
|
|
# fprintf(fid,'%2.0f \n',Nx);
|
|
|
|
|
# fprintf(fid,'%12.10E \n',dt);
|
|
|
|
|
# fprintf(fid,'%12.10E \n',u);
|
|
|
|
|
# fprintf(fid,'%2.0f \n',defnr); % def
|
|
|
|
|
# fclose(fid);
|
|
|
|
|
#
|
|
|
|
|
# filenames2 = writecov(R);
|
|
|
|
|
#
|
|
|
|
|
# disp(' Starting Fortran executable.')
|
|
|
|
|
#
|
|
|
|
|
# dos([ wafoexepath 'cov2mmtpdf.exe']); %compiled cov2mmtpdf.f with rind70.f
|
|
|
|
|
#
|
|
|
|
|
# dens = load('dens.out');
|
|
|
|
|
#
|
|
|
|
|
# cleanup(filenames{:},filenames2{:})
|
|
|
|
|
#
|
|
|
|
|
# %% Clean up
|
|
|
|
|
#
|
|
|
|
|
# return
|
|
|
|
|
def to_specnorm(self):
|
|
|
|
|
S = self.copy()
|
|
|
|
|
S.normalize()
|
|
|
|
|
@ -3277,9 +3626,9 @@ def test_mm_pdf():
|
|
|
|
|
import numpy as np
|
|
|
|
|
import wafo.spectrum.models as sm
|
|
|
|
|
Sj = sm.Jonswap(Hm0=7, Tp=11)
|
|
|
|
|
w = np.linspace(0,4,256)
|
|
|
|
|
w = np.linspace(0, 4, 256)
|
|
|
|
|
S1 = Sj.tospecdata(w) #Make spectrum object from numerical values
|
|
|
|
|
S = sm.SpecData1D(Sj(w),w) # Alternatively do it manually
|
|
|
|
|
S = sm.SpecData1D(Sj(w), w) # Alternatively do it manually
|
|
|
|
|
mm = S.to_mm_pdf()
|
|
|
|
|
|
|
|
|
|
if __name__ == '__main__':
|
|
|
|
|
|
Per.Andreas.Brodtkorb
14 years ago