def conjugate_gradient(A, b, x0=None, imax=10000, tol=1.0e-8, atol=1.0e-14,
iprint=None, output_stats=False, use_c_cg=False, precon='None'):
"""
Try to solve linear equation Ax = b using
conjugate gradient method
If b is an array, solve it as if it was a set of vectors, solving each
vector.
"""
if use_c_cg:
from anuga.utilities.sparse import Sparse_CSR
msg = ('c implementation of conjugate gradient requires that matrix A\
be of type %s') % (str(Sparse_CSR))
assert isinstance(A, Sparse_CSR), msg
if x0 is None:
x0 = num.zeros(b.shape, dtype=num.float)
else:
x0 = num.array(x0, dtype=num.float)
b = num.array(b, dtype=num.float)
err = 0
# preconditioner
# Padarn Note: currently a fairly lazy implementation, needs fixing
M = None
if precon == 'Jacobi':
M = num.zeros(b.shape[0])
jacobi_precon_c(A, M)
x0 = b.copy()
if len(b.shape) != 1:
for i in range(b.shape[1]):
if not use_c_cg:
x0[:, i], stats = _conjugate_gradient_preconditioned(A, b[:, i], x0[:, i], M,
imax, tol, atol, iprint, Type="Jacobi")
else:
# need to copy into new array to ensure contiguous access
xnew = x0[:, i].copy()
err = cg_solve_c_precon(A, xnew, b[:, i].copy(), imax, tol, atol, b.shape[1], M)
x0[:, i] = xnew
else:
if not use_c_cg:
x0, stats = _conjugate_gradient_preconditioned(A, b, x0, M, imax, tol, atol, iprint, Type="Jacobi")
else:
err = cg_solve_c_precon(A, x0, b, imax, tol, atol, 1, M)
else:
if len(b.shape) != 1:
for i in range(b.shape[1]):
if not use_c_cg:
x0[:, i], stats = _conjugate_gradient(A, b[:, i], x0[:, i],
imax, tol, atol, iprint)
else:
# need to copy into new array to ensure contiguous access
xnew = x0[:, i].copy()
err = cg_solve_c(A, xnew, b[:, i].copy(), imax, tol, atol, b.shape[1])
x0[:, i] = xnew
else:
if not use_c_cg:
x0, stats = _conjugate_gradient(A, b, x0, imax, tol, atol, iprint)
else:
x0 = b.copy()
err = cg_solve_c(A, x0, b, imax, tol, atol, 1)
if err == -1:
log.warning('max number of iterations attained from c cg')
msg = 'Conjugate gradient solver did not converge'
raise ConvergenceError, msg
if output_stats:
return x0, stats
else:
return x0
def _conjugate_gradient_preconditioned(A, b, x0, M,
imax=10000, tol=1.0e-8, atol=1.0e-10, iprint=None, Type='None'):
"""
Try to solve linear equation Ax = b using
preconditioned conjugate gradient method
Input
A: matrix or function which applies a matrix, assumed symmetric
A can be either dense or sparse or a function
(__mul__ just needs to be defined)
b: right hand side
x0: inital guess (default the 0 vector)
imax: max number of iterations
tol: tolerance used for residual
Output
x: approximate solution
"""
# Padarn note: This is temporary while the Jacboi preconditioner is the only
# one avaliable.
D=[]
if not Type=='Jacobi':
log.warning('Only the Jacobi Preconditioner is impletment cg_solve python')
msg = 'Only the Jacobi Preconditioner is impletment in cg_solve python'
raise PreconditionerError, msg
else:
D=Sparse(A.M, A.M)
for i in range(A.M):
D[i,i]=1/M[i]
D=Sparse_CSR(D)
stats = Stats()
b = num.array(b, dtype=num.float)
if len(b.shape) != 1:
raise VectorShapeError, 'input vector should consist of only one column'
if x0 is None:
x0 = num.zeros(b.shape, dtype=num.float)
else:
x0 = num.array(x0, dtype=num.float)
stats.x0 = num.linalg.norm(x0)
if iprint is None or iprint == 0:
iprint = imax
dx = 0.0
i = 1
x = x0
r = b - A * x
z = D * r
d = r
rTr = num.dot(r, z)
rTr0 = rTr
stats.rTr0 = rTr0
#FIXME Let the iterations stop if starting with a small residual
while (i < imax and rTr > tol ** 2 * rTr0 and rTr > atol ** 2):
q = A * d
alpha = rTr / num.dot(d, q)
xold = x
x = x + alpha * d
dx = num.linalg.norm(x-xold)
#if dx < atol :
# break
# Padarn Note 26/11/12: This modification to the algorithm seems
# unnecessary, but also seem to have been implemented incorrectly -
# it was set to perform the more expensive r = b - A * x routine in
# 49/50 iterations. Suggest this being either removed completely or
# changed to 'if i%50==0' (or equvialent).
#if i % 50:
if False:
r = b - A * x
else:
r = r - alpha * q
rTrOld = rTr
z = D * r
rTr = num.dot(r, z)
bt = rTr / rTrOld
d = z + bt * d
i = i + 1
if i % iprint == 0:
log.info('i = %g rTr = %15.8e dx = %15.8e' % (i, rTr, dx))
if i == imax:
log.warning('max number of iterations attained')
msg = 'Conjugate gradient solver did not converge: rTr==%20.15e' % rTr
raise ConvergenceError, msg
stats.x = num.linalg.norm(x)
stats.iter = i
stats.rTr = rTr
stats.dx = dx
return x, stats
if is_opened[point_i] == False:
points_writer = writer(file(dir_name + sep + gauge_file
+ point_name[point_i] + '.csv', "wb"))
points_writer.writerow(heading)
is_opened[point_i] = True
else:
points_writer = writer(file(dir_name + sep + gauge_file
+ point_name[point_i] + '.csv', "ab"))
points_list = [quake_time, quake_time/3600.] + _quantities2csv(quantities, point_quantities, callable_sww.centroids, point_i)
points_writer.writerow(points_list)
else:
if verbose:
msg = 'gauge' + point_name[point_i] + 'falls off the mesh in file ' + sww_file + '.'
log.warning(msg)
def sww2timeseries(swwfiles,
gauge_filename,
production_dirs,
report=None,
reportname=None,
plot_quantity=None,
generate_fig=False,
surface=None,
time_min=None,
time_max=None,
time_thinning=1,
time_unit=None,
title_on=None,
use_cache=False,
def sww2csv_gauges(sww_file,
gauge_file,
out_name='gauge_',
quantities=['stage', 'depth', 'elevation',
'xmomentum', 'ymomentum'],
verbose=False,
use_cache=True,
output_centroids=False):
"""
Inputs:
NOTE: if using csv2timeseries_graphs after creating csv file,
it is essential to export quantities 'depth' and 'elevation'.
'depth' is good to analyse gauges on land and elevation is used
automatically by csv2timeseries_graphs in the legend.
sww_file: path to any sww file
gauge_file: Assumes that it follows this format
name, easting, northing, elevation
point1, 100.3, 50.2, 10.0
point2, 10.3, 70.3, 78.0
NOTE: order of column can change but names eg 'easting', 'elevation'
must be the same! ALL lowercaps!
out_name: prefix for output file name (default is 'gauge_')
Outputs:
one file for each gauge/point location in the points file. They
will be named with this format in the same directory as the 'sww_file'
<out_name><name>.csv
eg gauge_point1.csv if <out_name> not supplied
myfile_2_point1.csv if <out_name> ='myfile_2_'
They will all have a header
Usage: sww2csv_gauges(sww_file='test1.sww',
quantities = ['stage', 'elevation','depth','bearing'],
gauge_file='gauge.txt')
Interpolate the quantities at a given set of locations, given
an sww file.
The results are written to a csv file.
In the future let points be a points file.
And the user choose the quantities.
This is currently quite specific.
If it needs to be more general, change things.
This is really returning speed, not velocity.
"""
from csv import reader,writer
from anuga.utilities.numerical_tools import ensure_numeric, mean, NAN
import string
from anuga.utilities.file_utils import get_all_swwfiles
from anuga.abstract_2d_finite_volumes.util import file_function
assert isinstance(gauge_file,string_types) or isinstance(gauge_file, str), 'Gauge filename must be a string or unicode'
assert isinstance(out_name,string_types) or isinstance(out_name, str), 'Output filename prefix must be a string'
try:
gid = open(gauge_file)
point_reader = reader(gid)
gid.close()
except Exception as e:
msg = 'File "%s" could not be opened: Error="%s"' % (gauge_file, e)
raise Exception(msg)
if verbose: log.critical('Gauges obtained from: %s' % gauge_file)
gid = open(gauge_file)
point_reader = reader(gid)
points = []
point_name = []
# read point info from file
for i,row in enumerate(point_reader):
# read header and determine the column numbers to read correctly.
if i==0:
for j,value in enumerate(row):
if value.strip()=='easting':easting=j
if value.strip()=='northing':northing=j
if value.strip()=='name':name=j
if value.strip()=='elevation':elevation=j
else:
#points.append([float(row[easting]),float(row[northing])])
points.append([float(row[easting]),float(row[northing])])
point_name.append(row[name])
gid.close()
#convert to array for file_function
points_array = num.array(points,num.float)
points_array = ensure_absolute(points_array)
#print 'points_array', points_array
dir_name, base = os.path.split(sww_file)
#need to get current directory so when path and file
#are "joined" below the directory is correct
if dir_name == '':
dir_name =getcwd()
if access(sww_file,R_OK):
if verbose: log.critical('File %s exists' % sww_file)
else:
msg = 'File "%s" could not be opened: no read permission' % sww_file
raise Exception(msg)
sww_files = get_all_swwfiles(look_in_dir=dir_name,
base_name=base,
verbose=verbose)
# fudge to get SWW files in 'correct' order, oldest on the left
sww_files.sort()
if verbose:
log.critical('sww files=%s' % sww_files)
#to make all the quantities lower case for file_function
quantities = [quantity.lower() for quantity in quantities]
# what is quantities are needed from sww file to calculate output quantities
# also
core_quantities = ['stage', 'elevation', 'xmomentum', 'ymomentum']
gauge_file = out_name
heading = [quantity for quantity in quantities]
heading.insert(0,'time')
heading.insert(1,'hours')
if verbose: log.critical('Writing csv files')
quake_offset_time = None
is_opened = [False]*len(points_array)
for sww_file in sww_files:
sww_file = join(dir_name, sww_file+'.sww')
callable_sww = file_function(sww_file,
quantities=core_quantities,
interpolation_points=points_array,
verbose=verbose,
use_cache=use_cache,
output_centroids = output_centroids)
if quake_offset_time is None:
quake_offset_time = callable_sww.starttime
for point_i, point in enumerate(points_array):
for time in callable_sww.get_time():
# add domain starttime to relative time.
quake_time = time + quake_offset_time
point_quantities = callable_sww(time, point_i) # __call__ is overridden
if point_quantities[0] != NAN:
if is_opened[point_i] == False:
points_handle = open(dir_name + sep + gauge_file
+ point_name[point_i] + '.csv', 'w')
points_writer = writer(points_handle)
points_writer.writerow(heading)
is_opened[point_i] = True
else:
points_handle = open(dir_name + sep + gauge_file
+ point_name[point_i] + '.csv', 'a')
points_writer = writer(points_handle)
points_list = [quake_time, quake_time/3600.] + _quantities2csv(quantities, point_quantities, callable_sww.centroids, point_i)
points_writer.writerow(points_list)
points_handle.close()
else:
if verbose:
msg = 'gauge' + point_name[point_i] + 'falls off the mesh in file ' + sww_file + '.'
log.warning(msg)
else:
points_writer = writer(
file(
dir_name + sep + gauge_file +
point_name[point_i] + '.csv', "ab"))
points_list = [quake_time,
quake_time / 3600.] + _quantities2csv(
quantities, point_quantities,
callable_sww.centroids, point_i)
points_writer.writerow(points_list)
else:
if verbose:
msg = 'gauge' + point_name[
point_i] + 'falls off the mesh in file ' + sww_file + '.'
log.warning(msg)
def sww2timeseries(swwfiles,
gauge_filename,
production_dirs,
report=None,
reportname=None,
plot_quantity=None,
generate_fig=False,
surface=None,
time_min=None,
time_max=None,
time_thinning=1,
time_unit=None,
title_on=None,