You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
616 lines
16 KiB
Python
616 lines
16 KiB
Python
from wafo.plotbackend import plotbackend as plt
|
|
import numpy as np
|
|
|
|
#! CHAPTER3 Demonstrates distributions of wave characteristics
|
|
#!=============================================================
|
|
#!
|
|
#! Chapter3 contains the commands used in Chapter3 in the tutorial.
|
|
#!
|
|
#! Some of the commands are edited for fast computation.
|
|
#!
|
|
#! Section 3.2 Estimation of wave characteristics from data
|
|
#!----------------------------------------------------------
|
|
#! Example 1
|
|
#!~~~~~~~~~~
|
|
|
|
speed = 'fast'
|
|
#speed = 'slow'
|
|
import scipy.signal as ss
|
|
import wafo.data as wd
|
|
import wafo.misc as wm
|
|
import wafo.objects as wo
|
|
import wafo.stats as ws
|
|
import wafo.spectrum.models as wsm
|
|
xx = wd.sea()
|
|
xx[:, 1] = ss.detrend(xx[:, 1])
|
|
ts = wo.mat2timeseries(xx)
|
|
Tcrcr, ix = ts.wave_periods(vh=0, pdef='c2c', wdef='tw', rate=8)
|
|
Tc, ixc = ts.wave_periods(vh=0, pdef='u2d', wdef='tw', rate=8)
|
|
|
|
#! Histogram of crestperiod compared to the kernel density estimate
|
|
#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
|
import wafo.kdetools as wk
|
|
plt.clf()
|
|
print(Tc.mean())
|
|
print(Tc.max())
|
|
|
|
t = np.linspace(0.01,8,200);
|
|
ftc = wk.TKDE(Tc, L2=0, inc=128)
|
|
|
|
plt.plot(t,ftc.eval_grid(t), t, ftc.eval_grid_fast(t),'-.')
|
|
wm.plot_histgrm(Tc, normed=True)
|
|
plt.title('Kernel Density Estimates')
|
|
plt.xlabel('Tc [s]')
|
|
plt.axis([0, 8, 0, 0.5])
|
|
plt.show()
|
|
|
|
#! Extreme waves - model check: the highest and steepest wave
|
|
#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
|
plt.clf()
|
|
S, H = ts.wave_height_steepness(kind=0)
|
|
indS = S.argmax()
|
|
indH = H.argmax()
|
|
ts.plot_sp_wave([indH, indS],'k.')
|
|
plt.show()
|
|
|
|
#! Does the highest wave contradict a transformed Gaussian model?
|
|
#!----------------------------------------------------------------
|
|
|
|
# TODO: Fix this
|
|
|
|
#clf
|
|
#inds1 = (5965:5974)'; #! points to remove
|
|
#Nsim = 10;
|
|
#[y1, grec1, g2, test, tobs, mu1o, mu1oStd] = ...
|
|
# reconstruct(xx,inds1,Nsim);
|
|
#spwaveplot(y1,indA-10)
|
|
#hold on
|
|
#plot(xx(inds1,1),xx(inds1,2),'+')
|
|
#lamb = 2.;
|
|
#muLstd = tranproc(mu1o-lamb*mu1oStd,fliplr(grec1));
|
|
#muUstd = tranproc(mu1o+lamb*mu1oStd,fliplr(grec1));
|
|
#plot (y1(inds1,1), [muLstd muUstd],'b-')
|
|
#axis([1482 1498 -1 3]),
|
|
#wafostamp([],'(ER)')
|
|
#disp('Block = 6'),
|
|
#pause(pstate)
|
|
#
|
|
##!#! Expected value (solid) compared to data removed
|
|
#clf
|
|
#plot(xx(inds1,1),xx(inds1,2),'+'), hold on
|
|
#mu = tranproc(mu1o,fliplr(grec1));
|
|
#plot(y1(inds1,1), mu), hold off
|
|
#disp('Block = 7'), pause(pstate)
|
|
|
|
#! Crest height PDF
|
|
#!------------------
|
|
#! Transform data so that kde works better
|
|
plt.clf()
|
|
wave_data = ts.wave_parameters()
|
|
Ac = wave_data['Ac']
|
|
L2 = 0.6
|
|
|
|
ws.probplot(Ac**L2, dist='norm', plot=plt)
|
|
plt.show()
|
|
|
|
#!#!
|
|
plt.clf()#
|
|
fac = wk.TKDE(Ac,L2=L2)(np.linspace(0.01,3,200), output='plot')
|
|
fac.plot()
|
|
# wafostamp([],'(ER)')
|
|
print(fac.integrate(a=0.01, b=3))
|
|
print(fac.integrate())
|
|
print('Block = 8'),
|
|
# pause(pstate)
|
|
|
|
#!#! Empirical crest height CDF
|
|
plt.clf()
|
|
Fac = fac.to_cdf()
|
|
Femp = ws.edf(Ac)
|
|
Fac.plot()
|
|
Femp.plot()
|
|
plt.axis([0, 2, 0, 1])
|
|
|
|
#wafostamp([],'(ER)')
|
|
#disp('Block = 9'), pause(pstate)
|
|
|
|
#!#! Empirical crest height CDF compared to a Transformed Rayleigh approximation
|
|
|
|
# facr = trraylpdf(fac.x{1},'Ac',grec1);
|
|
# Facr = cumtrapz(facr.x{1},facr.f);
|
|
# hold on
|
|
# plot(facr.x{1},Facr,'.')
|
|
# axis([1.25 2.25 0.95 1])
|
|
# wafostamp([],'(ER)')
|
|
# disp('Block = 10'), pause(pstate)
|
|
|
|
#!#! Joint pdf of crest period and crest amplitude
|
|
plt.clf()
|
|
Tcf = wave_data['Tcf']
|
|
Tcb = wave_data['Tcb']
|
|
Tc = Tcf + Tcb
|
|
fTcAc = wk.TKDE([Tc, Ac],L2=0.5, inc=256).eval_grid_fast(output='plot')
|
|
fTcAc.labels.labx = 'Tc [s]'
|
|
fTcAc.labels.laby = 'Ac [m]'
|
|
fTcAc.plot()
|
|
plt.hold(True)
|
|
plt.plot(Tc, Ac,'k.')
|
|
plt.hold(False)
|
|
plt.show()
|
|
#wafostamp([],'(ER)')
|
|
#disp('Block = 11'), pause(pstate)
|
|
|
|
#!#! Example 4: Simple wave characteristics obtained from Jonswap spectrum
|
|
plt.clf()
|
|
S = wsm.Jonswap(Hm0=5, Tp=10).tospecdata()
|
|
m, mt = S.moment(nr=4, even=False)
|
|
print(m)
|
|
print(mt)
|
|
# disp('Block = 12'), pause(pstate)
|
|
|
|
plt.clf()
|
|
S.bandwidth(['alpha'])
|
|
ch, Sa2, chtxt = S.characteristic(['Hm0', 'Tm02'])
|
|
|
|
# disp('Block = 13'), pause(pstate)
|
|
|
|
#!#! Section 3.3.2 Explicit form approximations of wave characteristic densities
|
|
#!#! Longuett-Higgins model for Tc and Ac
|
|
# plt.clf()
|
|
# t = np.linspace(0,15,100)
|
|
# h = np.linspace(0,6,100)
|
|
# flh = lh83pdf(t, h, [m[0],m[1], m[2])
|
|
# #disp('Block = 14'), pause(pstate)
|
|
#
|
|
# #!#! Transformed Longuett-Higgins model for Tc and Ac
|
|
# clf
|
|
# [sk, ku ]=spec2skew(S);
|
|
# sa = sqrt(m(1));
|
|
# gh = hermitetr([],[sa sk ku 0]);
|
|
# flhg = lh83pdf(t,h,[m(1),m(2),m(3)],gh);
|
|
# disp('Block = 15'), pause(pstate)
|
|
|
|
#!#! Cavanie model for Tc and Ac
|
|
# clf
|
|
# t = np.linspace(0,10,100);
|
|
# h = np.linspace(0,7,100);
|
|
# fcav = cav76pdf(t,h,[m(1) m(2) m(3) m(5)],[]);
|
|
# disp('Block = 16'), pause(pstate)
|
|
#
|
|
# #!#! Example 5 Transformed Rayleigh approximation of crest- vs trough- amplitude
|
|
# clf
|
|
# xx = load('sea.dat');
|
|
# x = xx;
|
|
# x(:,2) = detrend(x(:,2));
|
|
# SS = dat2spec2(x);
|
|
# [sk, ku, me, si ] = spec2skew(SS);
|
|
# gh = hermitetr([],[si sk ku me]);
|
|
# Hs = 4*si;
|
|
# r = (0:0.05:1.1*Hs)';
|
|
# fac_h = trraylpdf(r,'Ac',gh);
|
|
# fat_h = trraylpdf(r,'At',gh);
|
|
# h = (0:0.05:1.7*Hs)';
|
|
# facat_h = trraylpdf(h,'AcAt',gh);
|
|
# pdfplot(fac_h)
|
|
# hold on
|
|
# pdfplot(fat_h,'--')
|
|
# hold off
|
|
# wafostamp([],'(ER)')
|
|
# disp('Block = 17'), pause(pstate)
|
|
#
|
|
# #!#!
|
|
# clf
|
|
# TC = dat2tc(xx, me);
|
|
# tc = tp2mm(TC);
|
|
# Ac = tc(:,2);
|
|
# At = -tc(:,1);
|
|
# AcAt = Ac+At;
|
|
# disp('Block = 18'), pause(pstate)
|
|
#
|
|
# #!#!
|
|
# clf
|
|
# Fac_h = [fac_h.x{1} cumtrapz(fac_h.x{1},fac_h.f)];
|
|
# subplot(3,1,1)
|
|
# Fac = plotedf(Ac,Fac_h);
|
|
# hold on
|
|
# plot(r,1-exp(-8*r.^2/Hs^2),'.')
|
|
# axis([1. 2. 0.9 1])
|
|
# title('Ac CDF')
|
|
#
|
|
# Fat_h = [fat_h.x{1} cumtrapz(fat_h.x{1},fat_h.f)];
|
|
# subplot(3,1,2)
|
|
# Fat = plotedf(At,Fat_h);
|
|
# hold on
|
|
# plot(r,1-exp(-8*r.^2/Hs^2),'.')
|
|
# axis([1. 2. 0.9 1])
|
|
# title('At CDF')
|
|
#
|
|
# Facat_h = [facat_h.x{1} cumtrapz(facat_h.x{1},facat_h.f)];
|
|
# subplot(3,1,3)
|
|
# Facat = plotedf(AcAt,Facat_h);
|
|
# hold on
|
|
# plot(r,1-exp(-2*r.^2/Hs^2),'.')
|
|
# axis([1.5 3.5 0.9 1])
|
|
# title('At+Ac CDF')
|
|
#
|
|
# wafostamp([],'(ER)')
|
|
# disp('Block = 19'), pause(pstate)
|
|
#
|
|
# #!#! Section 3.4 Exact wave distributions in transformed Gaussian Sea
|
|
# #!#! Section 3.4.1 Density of crest period, crest length or encountered crest period
|
|
# clf
|
|
# S1 = torsethaugen([],[6 8],1);
|
|
# D1 = spreading(101,'cos',pi/2,[15],[],0);
|
|
# D12 = spreading(101,'cos',0,[15],S1.w,1);
|
|
# SD1 = mkdspec(S1,D1);
|
|
# SD12 = mkdspec(S1,D12);
|
|
# disp('Block = 20'), pause(pstate)
|
|
#
|
|
# #!#! Crest period
|
|
# clf
|
|
# tic
|
|
# f_tc = spec2tpdf(S1,[],'Tc',[0 11 56],[],4);
|
|
# toc
|
|
# pdfplot(f_tc)
|
|
# wafostamp([],'(ER)')
|
|
# simpson(f_tc.x{1},f_tc.f)
|
|
# disp('Block = 21'), pause(pstate)
|
|
#
|
|
# #!#! Crest length
|
|
#
|
|
# if strncmpi(speed,'slow',1)
|
|
# opt1 = rindoptset('speed',5,'method',3);
|
|
# opt2 = rindoptset('speed',5,'nit',2,'method',0);
|
|
# else
|
|
# #! fast
|
|
# opt1 = rindoptset('speed',7,'method',3);
|
|
# opt2 = rindoptset('speed',7,'nit',2,'method',0);
|
|
# end
|
|
#
|
|
#
|
|
# clf
|
|
# if strncmpi(speed,'slow',1)
|
|
# NITa = 5;
|
|
# else
|
|
# disp('NIT=5 may take time, running with NIT=3 in the following')
|
|
# NITa = 3;
|
|
# end
|
|
# #!f_Lc = spec2tpdf2(S1,[],'Lc',[0 200 81],opt1); #! Faster and more accurate
|
|
# f_Lc = spec2tpdf(S1,[],'Lc',[0 200 81],[],NITa);
|
|
# pdfplot(f_Lc,'-.')
|
|
# wafostamp([],'(ER)')
|
|
# disp('Block = 22'), pause(pstate)
|
|
#
|
|
#
|
|
# f_Lc_1 = spec2tpdf(S1,[],'Lc',[0 200 81],1.5,NITa);
|
|
# #!f_Lc_1 = spec2tpdf2(S1,[],'Lc',[0 200 81],1.5,opt1);
|
|
#
|
|
# hold on
|
|
# pdfplot(f_Lc_1)
|
|
# wafostamp([],'(ER)')
|
|
#
|
|
# disp('Block = 23'), pause(pstate)
|
|
# #!#!
|
|
# clf
|
|
# simpson(f_Lc.x{1},f_Lc.f)
|
|
# simpson(f_Lc_1.x{1},f_Lc_1.f)
|
|
#
|
|
# disp('Block = 24'), pause(pstate)
|
|
# #!#!
|
|
# clf
|
|
# tic
|
|
#
|
|
# f_Lc_d1 = spec2tpdf(rotspec(SD1,pi/2),[],'Lc',[0 300 121],[],NITa);
|
|
# f_Lc_d12 = spec2tpdf(SD12,[],'Lc',[0 200 81],[],NITa);
|
|
# #! f_Lc_d1 = spec2tpdf2(rotspec(SD1,pi/2),[],'Lc',[0 300 121],opt1);
|
|
# #! f_Lc_d12 = spec2tpdf2(SD12,[],'Lc',[0 200 81],opt1);
|
|
# toc
|
|
# pdfplot(f_Lc_d1,'-.'), hold on
|
|
# pdfplot(f_Lc_d12), hold off
|
|
# wafostamp([],'(ER)')
|
|
#
|
|
# disp('Block = 25'), pause(pstate)
|
|
#
|
|
# #!#!
|
|
#
|
|
#
|
|
# clf
|
|
# opt1 = rindoptset('speed',5,'method',3);
|
|
# SD1r = rotspec(SD1,pi/2);
|
|
# if strncmpi(speed,'slow',1)
|
|
# f_Lc_d1_5 = spec2tpdf(SD1r,[], 'Lc',[0 300 121],[],5);
|
|
# pdfplot(f_Lc_d1_5), hold on
|
|
# else
|
|
# #! fast
|
|
# disp('Run the following example only if you want a check on computing time')
|
|
# disp('Edit the command file and remove #!')
|
|
# end
|
|
# f_Lc_d1_3 = spec2tpdf(SD1r,[],'Lc',[0 300 121],[],3);
|
|
# f_Lc_d1_2 = spec2tpdf(SD1r,[],'Lc',[0 300 121],[],2);
|
|
# f_Lc_d1_0 = spec2tpdf(SD1r,[],'Lc',[0 300 121],[],0);
|
|
# #!f_Lc_d1_n4 = spec2tpdf2(SD1r,[],'Lc',[0 400 161],opt1);
|
|
#
|
|
# pdfplot(f_Lc_d1_3), hold on
|
|
# pdfplot(f_Lc_d1_2)
|
|
# pdfplot(f_Lc_d1_0)
|
|
# #!pdfplot(f_Lc_d1_n4)
|
|
#
|
|
# #!simpson(f_Lc_d1_n4.x{1},f_Lc_d1_n4.f)
|
|
#
|
|
# disp('Block = 26'), pause(pstate)
|
|
#
|
|
# #!#! Section 3.4.2 Density of wave period, wave length or encountered wave period
|
|
# #!#! Example 7: Crest period and high crest waves
|
|
# clf
|
|
# tic
|
|
# xx = load('sea.dat');
|
|
# x = xx;
|
|
# x(:,2) = detrend(x(:,2));
|
|
# SS = dat2spec(x);
|
|
# si = sqrt(spec2mom(SS,1));
|
|
# SS.tr = dat2tr(x);
|
|
# Hs = 4*si
|
|
# method = 0;
|
|
# rate = 2;
|
|
# [S, H, Ac, At, Tcf, Tcb, z_ind, yn] = dat2steep(x,rate,method);
|
|
# Tc = Tcf+Tcb;
|
|
# t = linspace(0.01,8,200);
|
|
# ftc1 = kde(Tc,{'L2',0},t);
|
|
# pdfplot(ftc1)
|
|
# hold on
|
|
# #! f_t = spec2tpdf(SS,[],'Tc',[0 8 81],0,4);
|
|
# f_t = spec2tpdf(SS,[],'Tc',[0 8 81],0,2);
|
|
# simpson(f_t.x{1},f_t.f)
|
|
# pdfplot(f_t,'-.')
|
|
# hold off
|
|
# wafostamp([],'(ER)')
|
|
# toc
|
|
# disp('Block = 27'), pause(pstate)
|
|
#
|
|
# #!#!
|
|
# clf
|
|
# tic
|
|
#
|
|
# if strncmpi(speed,'slow',1)
|
|
# NIT = 4;
|
|
# else
|
|
# NIT = 2;
|
|
# end
|
|
# #! f_t2 = spec2tpdf(SS,[],'Tc',[0 8 81],[Hs/2],4);
|
|
# tic
|
|
# f_t2 = spec2tpdf(SS,[],'Tc',[0 8 81],Hs/2,NIT);
|
|
# toc
|
|
#
|
|
# Pemp = sum(Ac>Hs/2)/sum(Ac>0)
|
|
# simpson(f_t2.x{1},f_t2.f)
|
|
# index = find(Ac>Hs/2);
|
|
# ftc1 = kde(Tc(index),{'L2',0},t);
|
|
# ftc1.f = Pemp*ftc1.f;
|
|
# pdfplot(ftc1)
|
|
# hold on
|
|
# pdfplot(f_t2,'-.')
|
|
# hold off
|
|
# wafostamp([],'(ER)')
|
|
# toc
|
|
# disp('Block = 28'), pause(pstate)
|
|
#
|
|
# #!#! Example 8: Wave period for high crest waves
|
|
# #! clf
|
|
# tic
|
|
# f_tcc2 = spec2tccpdf(SS,[],'t>',[0 12 61],[Hs/2],[0],-1);
|
|
# toc
|
|
# simpson(f_tcc2.x{1},f_tcc2.f)
|
|
# f_tcc3 = spec2tccpdf(SS,[],'t>',[0 12 61],[Hs/2],[0],3,5);
|
|
# #! f_tcc3 = spec2tccpdf(SS,[],'t>',[0 12 61],[Hs/2],[0],1,5);
|
|
# simpson(f_tcc3.x{1},f_tcc3.f)
|
|
# pdfplot(f_tcc2,'-.')
|
|
# hold on
|
|
# pdfplot(f_tcc3)
|
|
# hold off
|
|
# toc
|
|
# disp('Block = 29'), pause(pstate)
|
|
#
|
|
# #!#!
|
|
# clf
|
|
# [TC tc_ind v_ind] = dat2tc(yn,[],'dw');
|
|
# N = length(tc_ind);
|
|
# t_ind = tc_ind(1:2:N);
|
|
# c_ind = tc_ind(2:2:N);
|
|
# Pemp = sum(yn(t_ind,2)<-Hs/2 & yn(c_ind,2)>Hs/2)/length(t_ind)
|
|
# ind = find(yn(t_ind,2)<-Hs/2 & yn(c_ind,2)>Hs/2);
|
|
# spwaveplot(yn,ind(2:4))
|
|
# wafostamp([],'(ER)')
|
|
# disp('Block = 30'), pause(pstate)
|
|
#
|
|
# #!#!
|
|
# clf
|
|
# Tcc = yn(v_ind(1+2*ind),1)-yn(v_ind(1+2*(ind-1)),1);
|
|
# t = linspace(0.01,14,200);
|
|
# ftcc1 = kde(Tcc,{'kernel' 'epan','L2',0},t);
|
|
# ftcc1.f = Pemp*ftcc1.f;
|
|
# pdfplot(ftcc1,'-.')
|
|
# wafostamp([],'(ER)')
|
|
# disp('Block = 31'), pause(pstate)
|
|
#
|
|
# tic
|
|
# f_tcc22_1 = spec2tccpdf(SS,[],'t>',[0 12 61],[Hs/2],[Hs/2],-1);
|
|
# toc
|
|
# simpson(f_tcc22_1.x{1},f_tcc22_1.f)
|
|
# hold on
|
|
# pdfplot(f_tcc22_1)
|
|
# hold off
|
|
# wafostamp([],'(ER)')
|
|
# disp('Block = 32'), pause(pstate)
|
|
#
|
|
# disp('The rest of this chapter deals with joint densities.')
|
|
# disp('Some calculations may take some time.')
|
|
# disp('You could experiment with other NIT.')
|
|
# #!return
|
|
#
|
|
# #!#! Section 3.4.3 Joint density of crest period and crest height
|
|
# #!#! Example 9. Some preliminary analysis of the data
|
|
# clf
|
|
# tic
|
|
# yy = load('gfaksr89.dat');
|
|
# SS = dat2spec(yy);
|
|
# si = sqrt(spec2mom(SS,1));
|
|
# SS.tr = dat2tr(yy);
|
|
# Hs = 4*si
|
|
# v = gaus2dat([0 0],SS.tr);
|
|
# v = v(2)
|
|
# toc
|
|
# disp('Block = 33'), pause(pstate)
|
|
#
|
|
# #!#!
|
|
# clf
|
|
# tic
|
|
# [TC, tc_ind, v_ind] = dat2tc(yy,v,'dw');
|
|
# N = length(tc_ind);
|
|
# t_ind = tc_ind(1:2:N);
|
|
# c_ind = tc_ind(2:2:N);
|
|
# v_ind_d = v_ind(1:2:N+1);
|
|
# v_ind_u = v_ind(2:2:N+1);
|
|
# T_d = ecross(yy(:,1),yy(:,2),v_ind_d,v);
|
|
# T_u = ecross(yy(:,1),yy(:,2),v_ind_u,v);
|
|
#
|
|
# Tc = T_d(2:end)-T_u(1:end);
|
|
# Tt = T_u(1:end)-T_d(1:end-1);
|
|
# Tcf = yy(c_ind,1)-T_u;
|
|
# Ac = yy(c_ind,2)-v;
|
|
# At = v-yy(t_ind,2);
|
|
# toc
|
|
# disp('Block = 34'), pause(pstate)
|
|
#
|
|
# #!#!
|
|
# clf
|
|
# tic
|
|
# t = linspace(0.01,15,200);
|
|
# kopt3 = kdeoptset('hs',0.25,'L2',0);
|
|
# ftc1 = kde(Tc,kopt3,t);
|
|
# ftt1 = kde(Tt,kopt3,t);
|
|
# pdfplot(ftt1,'k')
|
|
# hold on
|
|
# pdfplot(ftc1,'k-.')
|
|
# f_tc4 = spec2tpdf(SS,[],'Tc',[0 12 81],0,4,5);
|
|
# f_tc2 = spec2tpdf(SS,[],'Tc',[0 12 81],0,2,5);
|
|
# f_tc = spec2tpdf(SS,[],'Tc',[0 12 81],0,-1);
|
|
# pdfplot(f_tc,'b')
|
|
# hold off
|
|
# legend('kde(Tt)','kde(Tc)','f_{tc}')
|
|
# wafostamp([],'(ER)')
|
|
# toc
|
|
# disp('Block = 35'), pause(pstate)
|
|
#
|
|
# #!#! Example 10: Joint characteristics of a half wave:
|
|
# #!#! position and height of a crest for a wave with given period
|
|
# clf
|
|
# tic
|
|
# ind = find(4.4<Tc & Tc<4.6);
|
|
# f_AcTcf = kde([Tcf(ind) Ac(ind)],{'L2',[1 .5]});
|
|
# pdfplot(f_AcTcf)
|
|
# hold on
|
|
# plot(Tcf(ind), Ac(ind),'.');
|
|
# wafostamp([],'(ER)')
|
|
# toc
|
|
# disp('Block = 36'), pause(pstate)
|
|
#
|
|
# #!#!
|
|
# clf
|
|
# tic
|
|
# opt1 = rindoptset('speed',5,'method',3);
|
|
# opt2 = rindoptset('speed',5,'nit',2,'method',0);
|
|
#
|
|
# f_tcfac1 = spec2thpdf(SS,[],'TcfAc',[4.5 4.5 46],[0:0.25:8],opt1);
|
|
# f_tcfac2 = spec2thpdf(SS,[],'TcfAc',[4.5 4.5 46],[0:0.25:8],opt2);
|
|
#
|
|
# pdfplot(f_tcfac1,'-.')
|
|
# hold on
|
|
# pdfplot(f_tcfac2)
|
|
# plot(Tcf(ind), Ac(ind),'.');
|
|
#
|
|
# simpson(f_tcfac1.x{1},simpson(f_tcfac1.x{2},f_tcfac1.f,1))
|
|
# simpson(f_tcfac2.x{1},simpson(f_tcfac2.x{2},f_tcfac2.f,1))
|
|
# f_tcf4=spec2tpdf(SS,[],'Tc',[4.5 4.5 46],[0:0.25:8],6);
|
|
# f_tcf4.f(46)
|
|
# toc
|
|
# wafostamp([],'(ER)')
|
|
# disp('Block = 37'), pause(pstate)
|
|
#
|
|
# #!#!
|
|
# clf
|
|
# f_tcac_s = spec2thpdf(SS,[],'TcAc',[0 12 81],[Hs/2:0.1:2*Hs],opt1);
|
|
# disp('Block = 38'), pause(pstate)
|
|
#
|
|
# clf
|
|
# tic
|
|
# mom = spec2mom(SS,4,[],0);
|
|
# t = f_tcac_s.x{1};
|
|
# h = f_tcac_s.x{2};
|
|
# flh_g = lh83pdf(t',h',[mom(1),mom(2),mom(3)],SS.tr);
|
|
# clf
|
|
# ind=find(Ac>Hs/2);
|
|
# plot(Tc(ind), Ac(ind),'.');
|
|
# hold on
|
|
# pdfplot(flh_g,'k-.')
|
|
# pdfplot(f_tcac_s)
|
|
# toc
|
|
# wafostamp([],'(ER)')
|
|
# disp('Block = 39'), pause(pstate)
|
|
#
|
|
# #!#!
|
|
# clf
|
|
# #! f_tcac = spec2thpdf(SS,[],'TcAc',[0 12 81],[0:0.2:8],opt1);
|
|
# #! pdfplot(f_tcac)
|
|
# disp('Block = 40'), pause(pstate)
|
|
#
|
|
# #!#! Section 3.4.4 Joint density of crest and trough height
|
|
# #!#! Section 3.4.5 Min-to-max distributions Markov method
|
|
# #!#! Example 11. (min-max problems with Gullfaks data)
|
|
# #!#! Joint density of maximum and the following minimum
|
|
# clf
|
|
# tic
|
|
# tp = dat2tp(yy);
|
|
# Mm = fliplr(tp2mm(tp));
|
|
# fmm = kde(Mm);
|
|
# f_mM = spec2mmtpdf(SS,[],'mm',[],[-7 7 51],opt2);
|
|
#
|
|
# pdfplot(f_mM,'-.')
|
|
# hold on
|
|
# pdfplot(fmm,'k-')
|
|
# hold off
|
|
# wafostamp([],'(ER)')
|
|
# toc
|
|
# disp('Block = 41'), pause(pstate)
|
|
#
|
|
# #!#! The joint density of still water separated maxima and minima.
|
|
# clf
|
|
# tic
|
|
# ind = find(Mm(:,1)>v & Mm(:,2)<v);
|
|
# Mmv = abs(Mm(ind,:)-v);
|
|
# fmmv = kde(Mmv);
|
|
# f_vmm = spec2mmtpdf(SS,[],'vmm',[],[-7 7 51],opt2);
|
|
# clf
|
|
# pdfplot(fmmv,'k-')
|
|
# hold on
|
|
# pdfplot(f_vmm,'-.')
|
|
# hold off
|
|
# wafostamp([],'(ER)')
|
|
# toc
|
|
# disp('Block = 42'), pause(pstate)
|
|
#
|
|
#
|
|
# #!#!
|
|
# clf
|
|
# tic
|
|
# facat = kde([Ac At]);
|
|
# f_acat = spec2mmtpdf(SS,[],'AcAt',[],[-7 7 51],opt2);
|
|
# clf
|
|
# pdfplot(f_acat,'-.')
|
|
# hold on
|
|
# pdfplot(facat,'k-')
|
|
# hold off
|
|
# wafostamp([],'(ER)')
|
|
# toc
|
|
# disp('Block = 43'), pause(pstate)
|
|
|