def add_bootstrap_plot_full(aeps,
aep_qs,
skew,
mu,
sigma,
nbs=1,
nsamples=50,
color="brown",
s=25):
"""
Analyitcal Bootstrap with Empirical Plotting
"""
f, a = plot_aep_full(aeps, aep_qs, skew, mu, sigma)
for i in range(0, nbs):
rvs = pearson3.rvs(skew, loc=mu, scale=sigma, size=nsamples)
lp3_data = LP3(rvs)
log_peaks = lp3_data.log
skew_new = lp3_data.weighted_skew(rskew, rskew_mse)
mu_new = lp3_data.log.mean()
sigma_new = lp3_data.log.std()
x = np.linspace(
pearson3.ppf(0.0001, skew_new, loc=mu_new, scale=sigma_new),
pearson3.ppf(0.9999, skew, loc=mu, scale=sigma), 100)
fax2.plot(pearson3.pdf(x, skew_new, loc=mu_new, scale=sigma_new),
10**x,
"black",
lw=2,
alpha=1,
label="pearson3 pdf")
a.set_title(f"{nbs} Bootstraps", fontsize=20)
return f, a
def moment_plot(self):
"""
# 绘制矩法估计参数理论概率曲线
"""
x = np.linspace(self.prob_lim_left, self.prob_lim_right, 1000)
theo_y = (pearson3.ppf(1 - x / 100, self.coeff_of_skew) *
self.coeff_of_var + 1) * self.expectation
self.ax.plot(x, theo_y, "--", lw=1, label="矩法估计参数概率曲线")
def fitted_plot(self):
"""
# 绘制适线后的概率曲线
"""
x = np.linspace(self.prob_lim_left, self.prob_lim_right, 1000)
theoY = (pearson3.ppf(1 - x / 100, self.fit_CS) * self.fit_CV +
1) * self.fit_EX
self.ax.plot(x, theoY, lw=2, label="适线后概率曲线")
def prob_to_value(self, prob):
"""
# 由设计频率转换设计值
## 输入参数
+ `prob`：设计频率，单位百分数
## 输出参数
+ `value`：设计值
"""
value = (pearson3.ppf(1 - prob / 100, self.fit_CS) * self.fit_CV +
1) * self.fit_EX
print("%.4f%% 的设计频率对应的设计值为 %.2f" % (prob, value))
return value
def p3ProbPlot(Ex, Cv, Cs, show=False):
"""
该函数用于绘制P3曲线
Ex 曲线的数学期望
Cv 曲线的变差系数
Cs 曲线的偏态系数
show=False 是否显示图像，默认不显示
"""
# 获取理论曲线的控制点
x = np.linspace(0.1, 99.9, 1000)
theoryY = (pearson3.ppf(1 - x / 100, Cs) * Cv + 1) * Ex
# 绘制理论曲线
plt.plot(x, theoryY, 'r-', lw=2, label='理论频率曲线')
plt.legend()
if show == True:
plt.show()
def add_bootstrap_plot_from_sample_pop_full(aeps,
aep_qs,
skew,
mu,
sigma,
rskew,
rskew_mse,
nbs=1,
nsamples=10,
color="brown",
nx=200,
s=25):
"""
Bootstrap with Empirical Plotting
"""
f, a = plot_aep_full(aeps, aep_qs, skew, mu, sigma)
xs = np.linspace(0.9999, 0.0001, nx)
for i in range(0, nbs):
rvs = np.random.choice(aep_qs, size=nsamples)
lp3_data = LP3(rvs)
log_peaks = lp3_data.log
skew_new = lp3_data.weighted_skew(rskew, rskew_mse)
mu_new = lp3_data.log.mean()
sigma_new = lp3_data.log.std()
ys = []
for x in xs:
ys.append(10**pearson3.ppf(1 - x,
skew_new,
loc=mu_new,
scale=sigma_new))
# Some Unusual Behavior results in negative skew?
# Reversing here for plotting, need to debug this.
if skew_new > 0:
a.scatter(x=xs, y=ys, color=color, s=s)
a.set_title(f"{nsamples}: Samples -- {nbs} Bootstraps", fontsize=20)
return f, a
from scipy.stats import pearson3 import matplotlib.pyplot as plt fig, ax = plt.subplots(1, 1) # Calculate a few first moments: skew = 0.1 mean, var, skew, kurt = pearson3.stats(skew, moments='mvsk') # Display the probability density function (``pdf``): x = np.linspace(pearson3.ppf(0.01, skew), pearson3.ppf(0.99, skew), 100) ax.plot(x, pearson3.pdf(x, skew), 'r-', lw=5, alpha=0.6, label='pearson3 pdf') # Alternatively, the distribution object can be called (as a function) # to fix the shape, location and scale parameters. This returns a "frozen" # RV object holding the given parameters fixed. # Freeze the distribution and display the frozen ``pdf``: rv = pearson3(skew) ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') # Check accuracy of ``cdf`` and ``ppf``: vals = pearson3.ppf([0.001, 0.5, 0.999], skew) np.allclose([0.001, 0.5, 0.999], pearson3.cdf(vals, skew)) # True # Generate random numbers:
def plot_aep_full(aeps, aep_qs, skew, mu, sigma, color="Brown", ci=95):
# PDF
fig, ax = plt.subplots(figsize=(30, 8))
ax.xaxis.set_visible(False)
ax.yaxis.set_visible(False)
gs = gridspec.GridSpec(ncols=6, nrows=1, figure=fig)
fax1 = fig.add_subplot(gs[0:5])
fax2 = fig.add_subplot(gs[5], sharey=fax1)
fax2.axes.yaxis.set_visible(False)
fax2.axes.xaxis.set_visible(False)
x = np.linspace(pearson3.ppf(0.0001, skew, loc=mu, scale=sigma),
pearson3.ppf(0.9999, skew, loc=mu, scale=sigma), 100)
fax2.plot(pearson3.pdf(x, skew, loc=mu, scale=sigma),
10**x,
"black",
lw=2,
alpha=1,
label="pearson3 pdf")
density_range = pearson3.pdf(x, skew, loc=mu, scale=sigma)
# -----------------------------------------------------------------------------------------------------------------------------------------------------
# fax2.fill_between(, 0, 100, color='black', alpha = 0.2)
# fax2.fill_between(density_range, q90lower, q90upper, color='gray', alpha = 0.2)
# fax2.fill_between(density_range, q90lower, pdfmin, color='lightgray', alpha = 0.2)
fax2.set_xlim([0, np.max(density_range)])
fax1.set_ylim([20000, 1200000])
fax2.set_yscale("log")
pdfmin = 10**x[0]
pdfmax = 10**x[-1]
# adjust the line for to match the extent of peakfq plots
fax1.plot(aeps[1:-10], aep_qs[1:-10], "black", linewidth=2, alpha=0.8)
# Plot Formatting
# fax1.invert_xaxis()
fax1.set_xscale("logit")
# fax1.xaxis.set_major_formatter(ticker.FuncFormatter(myLogitFormat))
fax1.set_yscale("log")
fax1.set_xlim([0.990, 0.002])
fax1.set_ylim([20000, 1200000])
# fax1.set_xlabel('Annual exceedance probability, [%]');fax1.set_ylabel('Discharge, [cfs]')
fax1.set_title("Flow Frequency Curve")
fax1.grid(True, which="both")
fax1.xaxis.set_minor_formatter(ticker.FuncFormatter(logit_plot_format))
fax1.yaxis.set_major_formatter(ticker.FuncFormatter(log_plot_format))
fax1.set_xlabel("Annual Exceendence Probability")
fax1.set_ylabel("Flow (cfs)")
# fax1.axhline(pdfmax, 0, 1e9, color='purple');
upper_ci, lower_ci = ci * 0.01, (100 - ci) * 0.01
qupper = int(10**pearson3.ppf(upper_ci, skew, loc=mu, scale=sigma))
qlower = int(10**pearson3.ppf(lower_ci, skew, loc=mu, scale=sigma))
fax1.fill_between(np.arange(0.990, 0.002, -0.001),
pdfmax,
qupper,
color="gray",
alpha=0.2)
fax1.fill_between(np.arange(0.990, 0.002, -0.001),
qlower,
qupper,
color="black",
alpha=0.2)
fax1.fill_between(np.arange(0.990, 0.002, -0.001),
qlower,
pdfmin,
color="gray",
alpha=0.2)
fax2.grid()
fig.tight_layout(pad=1.00, h_pad=0, w_pad=-1, rect=None)
return fig, fax1
def plot_fitting(self, sv_ratio=0, ex_fitting=True, output=True):
"""
# 优化适线
## 输入参数
+ `sv_ratio`：倍比系数，即偏态系数 `Cs` 与 变差系数 `Cv` 之比。
默认为 0，即关闭倍比系数功能。
- 当 `sv_ratio` ≠ 0 时，Cs 不参与适线运算中，且 `Cs` = `sv_ratio` × `Cv`；
- 当 `sv_ratio` = 0 时，Cs 正常参与适线运算。
+ `ex_fitting`：适线时是否调整 EX，默认为 True
+ `output`：是否在控制台输出参数，默认为 True
"""
if sv_ratio == 0:
if ex_fitting:
p3 = lambda prob, ex, cv, cs: (pearson3.ppf(
1 - prob / 100, cs) * cv + 1) * ex
[self.fit_EX, self.fit_CV, self.fit_CS], pcov = curve_fit(
p3, self.empi_prob, self.arr,
[self.expectation, self.coeff_of_var, self.coeff_of_skew])
else:
p3 = lambda prob, cv, cs: (pearson3.ppf(1 - prob / 100, cs) *
cv + 1) * self.expectation
[self.fit_CV, self.fit_CS
], pcov = curve_fit(p3, self.empi_prob, self.arr,
[self.coeff_of_var, self.coeff_of_skew])
self.fit_EX = self.expectation
else:
if ex_fitting:
p3 = lambda prob, ex, cv: (pearson3.ppf(
1 - prob / 100, cv * sv_ratio) * cv + 1) * ex
[self.fit_EX, self.fit_CV
], pcov = curve_fit(p3, self.empi_prob, self.arr,
[self.expectation, self.coeff_of_var])
else:
p3 = lambda prob, cv: (pearson3.ppf(
1 - prob / 100, cv * sv_ratio) * cv + 1) * self.expectation
[self.fit_CV], pcov = curve_fit(p3, self.empi_prob, self.arr,
[self.coeff_of_var])
self.fit_EX = self.expectation
self.fit_CS = self.fit_CV * sv_ratio
if output:
print("适线后")
print("期望 EX 为 %.2f" % self.fit_EX)
print("变差系数 Cv 为 %.4f" % self.fit_CV)
print("偏态系数 Cs 为 %.4f" % self.fit_CS)