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tools.py
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tools.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
version 0.1, Apr 23 2018
@author: fabio (dot) oriani (at) protonmail (dot) com
"""
#%%
#import matplotlib.pyplot as plt
import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from scipy.stats import rankdata
#from scipy.stats import norm
from scipy.ndimage.measurements import label
#from scipy.interpolate import interp1d
from skimage.measure import regionprops
from itertools import product, permutations
#from PIL import Image
from scipy.ndimage import rotate
from shapefile import Reader
from datetime import datetime, timedelta
from scipy.signal import fftconvolve
from scipy.ndimage import distance_transform_edt
from scipy import interpolate
import matplotlib.path as mplp
#from pickle import dump,load
from osgeo import gdal
from osgeo import osr
import struct
from scipy.optimize import curve_fit
from scipy.stats import gaussian_kde
import shapefile
import cmasher as cmr
try:
import mkl_fft as fft
except ImportError:
try:
import pyfftw.interfaces.numpy_fft as fft
except ImportError:
import numpy.fft as fft
def plot_shp(fname,col="default",enc='utf-8'): # import and plot a shapefile (.shp) given the local/global file path. col = color (optional)
ch=Reader(fname,encoding=enc)
n=0
for shape in list(ch.iterShapes()): # iterate oavell all shapes
npoints=len(shape.points) # total points
nparts = len(shape.parts) # total parts
if nparts == 1:
x_lon = np.zeros((len(shape.points),1))
y_lat = np.zeros((len(shape.points),1))
for ip in range(len(shape.points)):
x_lon[ip] = shape.points[ip][0]
y_lat[ip] = shape.points[ip][1]
n=n+1
if n==1 and col=="default": # fetch color from first part
p=plt.plot(x_lon,y_lat)
col=p[0].get_color()
elif n==1:
p=plt.plot(x_lon,y_lat,color=col)
else:
plt.plot(x_lon,y_lat,color=col)
else: # loop over parts of each shape, plot separately
for ip in range(nparts): # loop over parts, plot separately
i0=shape.parts[ip]
if ip < nparts-1:
i1 = shape.parts[ip+1]-1
else:
i1 = npoints
seg=shape.points[i0:i1+1]
x_lon = np.zeros((len(seg),1))
y_lat = np.zeros((len(seg),1))
for ip in range(len(seg)):
x_lon[ip] = seg[ip][0]
y_lat[ip] = seg[ip][1]
n=n+1
if n==1 and col=="default":
p=plt.plot(x_lon,y_lat)
col=p[0].get_color()
elif n==1:
p=plt.plot(x_lon,y_lat,color=col)
else:
plt.plot(x_lon,y_lat,color=col)
def shp_to_line(fname,enc='utf-8'): # return a (list of) line array from a (multiple-shape) shapefile
ch=Reader(fname,encoding=enc)
line=[] # output list of lines arrays [N,(x,y)]
for shape in list(ch.iterShapes()): # iterate over all shapes
npoints=len(shape.points) # total points
nparts = len(shape.parts) # total parts
# loop over parts of each shape, plot separately
for ip in range(nparts): # loop over parts, plot separately
i0=shape.parts[ip]
if ip < nparts-1:
i1 = shape.parts[ip+1]-1
else:
i1 = npoints
seg=shape.points[i0:i1+1]
x_lon = np.zeros((len(seg),1))
y_lat = np.zeros((len(seg),1))
for ip in range(len(seg)):
x_lon[ip] = seg[ip][0]
y_lat[ip] = seg[ip][1]
line.append(np.hstack((x_lon,y_lat)))
return line
def shp_to_mask(fname,xv,yv): # return a mask from a shapefile over a given grid xv,xy (from meshgrid)
line=shp_to_line(fname)
mask=np.empty_like(xv)*0
for n in range(len(line)):
mpath = mplp.Path(line[n])
points = np.array((xv.flatten(), yv.flatten())).T
mask = mask+mpath.contains_points(points).reshape(xv.shape)
mask=mask>0
return mask
## to test the result
# plt.scatter(xv,yv,c=mask)
# ft.plot_shp('data/CNTR_RG_60M_2020_4326.shp',col="brown") # world boundaries
def write_point_shp(base_name,x,y,field_name,field_type,records,esri_code=None):
"""
WRITES A POINT SHAPEFILE (.shp .shx .dbf .prj)
base_name [str] the base name for the files (no extension)
x [num vector] vector of x / lon coordinates
y [num vector] vector of y / lat coordinates
field_name [str list] field names
field_type [str list] field types: 'L' boolean, 'N' numerical , 'C' custom
records [iterables list] list of iterables (vectors or lists) containing the records. len(list)=N for N fields, and len(list[i])=M for M records (points)
esri_code [int] ESRI code of the used crs, if not given the .prj file is not created (unreferenced shape file)
"""
# create shapefile object
w = shapefile.Writer(base_name + '.shp')
# write fields
for i in range(len(field_name)):
w.field(field_name[i],field_type[i]) # field
# record points
r=np.vstack(records) # array from records list
for i in range(len(records[0])):
w.point(x[i],y[i])
w.record(*r[:,i])
w.close()
# georeferenziation file
if esri_code!=None:
spatialRef = osr.SpatialReference()
spatialRef.ImportFromEPSG(esri_code)
spatialRef.MorphToESRI()
file = open(base_name + '.prj', 'w')
file.write(spatialRef.ExportToWkt())
file.close()
def read_geotiff(fname):
# import geotiff image with georef class R, usage: im,R=read_geotiff(filename)
dataset = gdal.Open(fname, gdal.GA_ReadOnly)
nb=dataset.RasterCount # number of bands
xs=dataset.RasterXSize # raster x size
ys=dataset.RasterYSize # raster y size
im=np.empty([ys,xs,nb])*np.nan
for i in range(nb):
band = dataset.GetRasterBand(i+1)
raster = band.ReadRaster(xoff=0, yoff=0, # origin
xsize=xs, ysize=ys, # extension
buf_xsize=xs, buf_ysize=ys, # buffer = extension for full resolution
buf_type=gdal.GDT_Float32)
raster_float = struct.unpack('f'*xs*ys, raster)
im[:,:,i]=np.reshape(raster_float,[ys,xs])
im=np.squeeze(im)
geotr = dataset.GetGeoTransform()
dataset=None
band=None
class make_R:
def __init__(self,im,geotr):
self.ncols=im.shape[1]
self.nrows=im.shape[0]
self.cellsize=geotr[1]
self.xllc=geotr[0]
self.yllc=geotr[3]-self.cellsize*self.nrows
R=make_R(im,geotr)
return im,R
def write_tiff(filename,im,dtype="Float32"):
driver = gdal.GetDriverByName("GTiff")
if np.ndim(im)==3:
outdata = driver.Create(filename, np.shape(im)[1], np.shape(im)[0], np.shape(im)[2], gdal.GDT_Float32)
for i in range(np.shape(im)[2]):
outdata.GetRasterBand(i+1).WriteArray(im[:,:,i].astype("Float32"))
# outdata.GetRasterBand(1).SetNoDataValue(0)##if you want these values transparent
else:
outdata = driver.Create(filename, np.shape(im)[1], np.shape(im)[0], 1, gdal.GDT_Float32)
outdata.GetRasterBand(1).WriteArray(im.astype(dtype))
outdata.FlushCache() ##saves to disk!!
outdata=None
def write_geotiff(filename,im,xmin,ymax,xres,yres,epsg=None,dtype=None,nodata_val=None,band_name=None):
# nodata_val, band_name should be lists/array even if containing one value
if dtype==None: # set data type from given format
dtype=im.dtype.name
if np.ndim(im)<3:
nb=1
im=im[:,:,None]
else:
nb=np.shape(im)[2]
driver = gdal.GetDriverByName('GTiff') # generate driver
outdata = driver.Create(filename, np.shape(im)[1], np.shape(im)[0], nb, gdal.GetDataTypeByName(dtype))
for i in range(nb): # write data
outdata.GetRasterBand(i+1).WriteArray(im[:,:,i].astype(dtype))
outdata.GetRasterBand(i+1).SetNoDataValue(nodata_val[i])
outdata.GetRasterBand(i+1).SetDescription(band_name[i])
# GEOREFERENTIATION
# coords
geotransform = (xmin, # x-coordinate of the upper-left corner of the upper-left pixel.
xres, # W-E pixel resolution / pixel width.
0, #row rotation (typically zero).
ymax, # y-coordinate of the upper-left corner of the upper-left pixel.
0, # column rotation (typically zero).
-yres) # N-S pixel resolution / pixel height (negative value for a north-up image).
outdata.SetGeoTransform(geotransform) # specify coords
srs = osr.SpatialReference() # establish encoding
srs.ImportFromEPSG(epsg) # set CRS from EPSG code
outdata.SetProjection(srs.ExportToWkt())
# save data
outdata.FlushCache()
outdata=None
def extract_grid_points(V, # grid values
xll, # lower left grid CENTER x coord
yll, # lower left grid CENTER y coord (increasing upward)
resx, # x resolution
resy, # y resolution
px, # query point x coordinate [numpy vector or list]
py, # query point y coordinate [numpy vector or list]
plot_xy = False, # if true plot all points and grids
):
# extract pixels values from grid given some of query points (e.g. dataset coordinates).
# it returns an nan if a point is out of the grid
nx = V.shape[1]
ny = V.shape[0]
vx = np.arange(xll, xll + nx*resx, resx)
vy = np.arange(yll, yll + ny*resy, resy)
pv = np.zeros_like(px).astype('float') # grid to point data
pvx = np.copy(pv) # grid to point data x coord
pvy = np.copy(pv) # grid to point data y coord
for i in range(len(pv)):
if px[i]<vx[0] or px[i]>vx[-1] or py[i]<vy[0] or py[i]>vy[-1]:
pv[i] = np.nan
pvx[i] = np.nan
pvy[i] = np.nan
else:
indx = np.argmin(np.abs(px[i]-vx))
indy = np.argmin(np.abs(py[i]-vy))
pv[i] = np.copy(V[ny-indy-1,indx])
pvx[i] = np.copy(vx[indx])
pvy[i] = np.copy(vy[indy])
# plot
if plot_xy ==True:
Gx, Gy = np.meshgrid(vx, vy, sparse=False, indexing='xy')
plt.figure()
plt.imshow(V,extent=[xll-resx/2,xll-resx/2+resx*nx,yll-resy/2,yll-resy/2+resy*ny],label='grid')
plt.scatter(px,py,facecolors='white',edgecolors='green',s=40,label='query points')
plt.scatter(pvx,pvy,marker='s',edgecolors='red',c=pv,s=40,label='extracted grids')
plt.colorbar()
plt.legend()
return pv
def point_vario(x,y,z,nlag,lagseq='lin',q=0.99,maxlag=None):
# x = x coordinate
# y = y coordinate
# z = z coordinate
# nlag = number of lags (scalar)
# lagseq = type of lag sequence linear or log
# q = quantile value of the distance among points to put as max lag limit
# maxlag = given max lag limit (if given, q is not used)
X=np.repeat(x[:,None],len(x),axis=1)
dX=X-np.transpose(X)
del X
Y=np.repeat(y[:,None],len(y),axis=1)
dY=Y-np.transpose(Y)
del Y
D=np.sqrt(dX*dX+dY*dY)
del dX,dY
Z=np.repeat(z[:,None],len(z),axis=1)
dZ=Z-np.transpose(Z)
del Z
if maxlag==None:
maxlag=np.quantile(D,q)
if lagseq=="lin":
lags=np.arange(0,maxlag,maxlag/nlag)
else:
minlag=np.ceil(np.log10(np.min(D[D>0])))
lags=np.logspace(minlag,np.log10(maxlag),num=nlag)
lags=np.append(lags,0)
lags=np.unique(lags)
v=np.empty(len(lags)-1)*np.nan
s=np.empty(len(lags)-1)*np.nan
for i in range(len(lags)-1):
dZtmp=dZ[np.logical_and(D>lags[i],D<=lags[i+1])] # select couples for i-th lag
v[i]=np.nanmean(np.power(dZtmp,2))/2
s[i]=np.nanstd(np.power(dZtmp,2))/2
lags=(lags[:-1]+lags[1:])/2
return lags, maxlag, v, s # lags, maxlag, variogram, vario standard deviation
# variogram model functions: d: x data, return f(x)
def linVario(d, slope, nugget):
return slope * d + nugget
def powerVario(d,scale,exponent,nugget):
return scale * d ** exponent + nugget
def gaussVario(d, psill, range_, nugget):
return psill * (1 - np.exp(-(d ** 2.0) / (range_ * 4.0 / 7.0) ** 2.0)) + nugget
def spheriVario(d, psill, range_, nugget):
return np.piecewise(
d,
[d <= range_, d > range_],
[
lambda x: psill
* ((3.0 * x) / (2.0 * range_) - (x ** 3.0) / (2.0 * range_ ** 3.0))
+ nugget,
psill + nugget,
],
)
def expVario(d, psill, range_, nugget):
return psill * (1.0 - np.exp(-d / (range_ / 3.0))) + nugget
def vario_optim(obs_x,obs_y,obs_data,nlags=20,q=1,lagseq='lin',plot=False):
# automatic choice of variogram model and optimize params
# SAMPLE VARIOGRAM
lags, maxlag, v, s=point_vario(obs_x,obs_y,obs_data,nlags,q=q,lagseq=lagseq)
ind = np.logical_not(np.isnan(v))
lags=lags[ind]
v=v[ind]
# inizialize output params
fp=[] # fitted params
mv=[] # variogram values
err=[] # error
mn=[] # model name
# # LINEAR MODEL
# try:
# # optimize params: slope,nugget
# initialParameters = np.array([0, v[0]])
# lowerBounds = (0,0)#(-np.Inf,-np.Inf)
# upperBounds = (np.Inf,np.Inf)
# parameterBounds = [lowerBounds, upperBounds]
# fittedParams, pcov = curve_fit(linVario, lags, v, initialParameters, bounds = parameterBounds) # fitting
# slope, nugget = fittedParams # fitted params
# fp.append(np.copy(fittedParams))
# vv=linVario(lags,slope, nugget) # # fitted function
# mv.append(vv) # fitted function
# err.append(np.sqrt(np.mean((vv-v)*(vv-v)))) # RMSE
# mn.append('linear')
# except:
# pass
# # POWER MODEL
# try:
# # optimize params: scale, exponent, nugget
# initialParameters = np.array([0, 1,v[0]])
# lowerBounds = (0,0,0) #(-np.Inf,-np.Inf,-np.Inf)
# upperBounds = (np.Inf,1,np.Inf)
# parameterBounds = [lowerBounds, upperBounds]
# fittedParams, pcov = curve_fit(powerVario, lags, v, initialParameters, bounds = parameterBounds) # fitting
# scale, exponent, nugget = fittedParams # fitted params
# fp.append(np.copy(fittedParams))
# vv=powerVario(lags,scale,exponent,nugget) # fitted function
# mv.append(vv) # fitted function
# err.append(np.sqrt(np.mean((vv-v)*(vv-v)))) # RMSE
# mn.append('power')
# except:
# pass
# # GAUSSIAN MODEL
# try:
# # optimize params: psill, range_, nugget
# initialParameters = np.array([np.var(obs_data)/2,max(lags)/2,v[0]])
# lowerBounds = (0,0,0)
# upperBounds = (np.var(obs_data), max(lags), np.var(obs_data))
# parameterBounds = [lowerBounds, upperBounds]
# fittedParams, pcov = curve_fit(gaussVario, lags, v, initialParameters, bounds = parameterBounds) # fitting
# psill, range_, nugget = fittedParams # fitted params
# fp.append(np.copy(fittedParams))
# vv=gaussVario(lags,psill, range_, nugget) # fitted function
# mv.append(vv) # fitted function
# err.append(np.sqrt(np.mean((vv-v)*(vv-v)))) # RMSE
# mn.append('gaussian')
# except:
# pass
# # SPHERICAL MODEL
# try:
# # optimize params: psill, range_, nugget
# initialParameters = np.array([np.var(obs_data)/2,max(lags)/2,v[0]])
# lowerBounds = (0,0,0)
# upperBounds = (np.var(obs_data), max(lags), np.var(obs_data))
# parameterBounds = [lowerBounds, upperBounds]
# fittedParams, pcov = curve_fit(spheriVario, lags, v, initialParameters, bounds = parameterBounds) # fitting
# psill, range_, nugget = fittedParams # fitted params
# fp.append(np.copy(fittedParams))
# vv=gaussVario(lags,psill, range_, nugget) # fitted function
# mv.append(vv) # fitted function
# err.append(np.sqrt(np.mean((vv-v)*(vv-v)))) # RMSE
# mn.append('spherical')
# except:
# pass
# EXPONENTIAL MODEL
# try:
# optimize params: psill, range_, nugget
lowerBounds = np.array([0,0,0])
upperBounds = np.array([np.max(v), max(lags), np.var(obs_data)])
initialParameters = (lowerBounds + upperBounds)/2
parameterBounds = [lowerBounds, upperBounds]
fittedParams, pcov = curve_fit(expVario, lags, v, initialParameters, bounds = parameterBounds) # fitting
psill, range_, nugget = fittedParams # fitted params
fp.append(np.copy(fittedParams))
vv=expVario(lags,psill, range_, nugget)
mv.append(vv) # fitted function
err.append(np.sqrt(np.mean((vv-v)*(vv-v)))) # RMSE
mn.append('exponential')
# except:
# pass
# if len(mn)==0:
# raise Exception('No model could fit the sample variogram!')
# PLOT
if plot==True:
plt.figure()
plt.scatter(lags,v,label='sample variogram')
for i in range(len(mn)):
plt.plot(lags,mv[i],label='%s , RMSE=%.3f' % (mn[i],err[i]))
plt.xlabel('lag [cells]')
plt.ylabel('v(lag)')
plt.title('Sample variogram and model')
plt.legend()
ind=np.argmin(err)
mtype=mn[ind]
mparams=fp[ind]
if mtype=='gaussian' or mtype=='exponential' or mtype=='spherical':
mparams = {'psill':mparams[0],'range':mparams[1],'nugget':mparams[2]}
elif mtype=='linear':
mparams = {'slope':mparams[0],'nugget':mparams[1]}
elif mtype=='power':
mparams = {'scale': mparams[0], 'exponent':mparams[1], 'nugget': mparams[2]}
return mtype, mparams
# reliability plot
def reliability(p,o,q,plot=False):
"""
RELIABILITY
Given a vector of prediction probabibilites p [0-1] and a respective occurrences o [boolean], compute
the frequency of occurrence for q equally spaced classes of probability. A prediction
is considered reliable if for a probability class q_i (e.g. 50%), the occurrence frequency o_i is
~= q_i.
USAGE:
f,qc=reliability(p,o,q) gives the (conditional) occurrence frequency vector for q probabilty classes and
prediction vector p.
f,qc=reliability(p,o,q,plot=True) also output the realiability plot of f vs q
INPUT:
p [float in [0-1]] = Nx1 vector of predicted probability
o [boolean] = Nx1 correspondent vector of occurrences for each prediction
q [int] = number of probability classes used to group the predictions
OUTPUT:
f [float in [0-1]] = qx1 occurrence freqeuency for each probability class, derived from o
qc = qx1 vector of probability class centers
"""
qb=np.linspace(0,1,q+1) # class bounds
qc=(qb[1:]+qb[:-1])/2 # class centers
f=np.empty_like(qc)*np.nan
for i in range(len(qc)): # computin occurrence frequency
o_tmp=o[np.logical_and(p>=qb[i],p<=qb[i+1])]
f[i]=np.sum(o_tmp)/len(o_tmp)
if plot==True:
plt.plot(qc,f,'-o')
plt.xlabel('prediction probability')
plt.ylabel('occurrence probability')
plt.axis('square')
plt.xlim([0,1])
plt.ylim([0,1])
plt.plot([0,1],[0,1],'--')
plt.show()
return qc,f