def taylor_statistics(p, r):
# Calculate bias (B)
bias = np.mean(p) - np.mean(r)
# Calculate correlation coefficient
ccoef = np.corrcoef(p,r)
ccoef = ccoef[0]
# Calculate centered root-mean-square (RMS) difference (E')^2
crmsd = [0.0, sm.centered_rms_dev(p,r)]
# Calculate standard deviation of predicted field w.r.t N (sigma_p)
sdevp = np.std(p)
# Calculate standard deviation of reference field w.r.t N (sigma_r)
sdevr = np.std(r)
sdev = [sdevr, sdevp];
# Store statistics in a dictionary
stats = {'ccoef': ccoef, 'crmsd': crmsd, 'sdev': sdev, 'bias': bias}
return stats
# Read data from pickle file
data = load_obj('target_data')
pred = data.pred1['data']
ref = data.ref['data']
# Get bias
stats['bias'] = sm.bias(pred, ref)
print('Bias = ' + str(stats['bias']))
# Get Root-Mean-Square-Deviation (RMSD)
stats['rmsd'] = sm.rmsd(pred, ref)
print('RMSD = ' + str(stats['rmsd']))
# Get Centered Root-Mean-Square-Deviation (CRMSD)
stats['crmsd'] = sm.centered_rms_dev(pred, ref)
print('CRMSD = ' + str(stats['crmsd']))
# Get Standard Deviation (SDEV)
stats['sdev'] = np.std(pred)
print('SDEV = ' + str(stats['sdev']))
# Get correlation coefficient (r)
ccoef = np.corrcoef(pred, ref)
stats['ccoef'] = ccoef[0, 1]
print('r = ' + str(stats['ccoef']))
# Get Non-Dimensional Skill Score (SS)
stats['ss'] = sm.skill_score_murphy(pred, ref)
print('SS (Murphy) = ' + str(stats['ss']))
def target_statistics(predicted, reference, field='', norm=False):
'''
Calculates the statistics needed to create a target diagram as
described in Jolliff et al. (2009) using the data provided in the
predicted field (PREDICTED) and the reference field (REFERENCE).
The statistics are returned in the STATS dictionary.
If a dictionary is provided for PREDICTED or REFERENCE, then
the name of the field must be supplied in FIELD.
The function currently supports dictionaries, lists, and np.ndarray,
types for the PREDICTED and REFERENCE variables.
Input:
PREDICTED : predicted field
REFERENCE : reference field
FIELD : name of field to use in PREDICTED and REFERENCE dictionaries
(optional)
NORM : logical flag specifying statistics are to be normalized
with respect to standard deviation of reference field
= True, statistics are normalized
= False, statistics are not normalized
Output:
STATS : dictionary containing statistics
STATS['bias'] : bias (B)
STATS['crmsd'] : centered root-mean-square (RMS) differences (E')
STATS['rmsd'] : total RMS difference (RMSD)
Each of these outputs are one-dimensional with the same length.
Reference:
Jolliff, J. K., J. C. Kindle, I. Shulman, B. Penta, M. Friedrichs,
R. Helber, and R. Arnone (2009), Skill assessment for coupled
biological/physical models of marine systems, J. Mar. Sys., 76(1-2),
64-82, doi:10.1016/j.jmarsys.2008.05.014
Author: Peter A. Rochford
Symplectic, LLC
www.thesymplectic.com
[email protected]
Created on Nov 24, 2016
'''
import numpy as np
from skill_metrics import centered_rms_dev
# Check for valid arguments
if isinstance(predicted, dict):
if field == '':
raise ValueError('FIELD argument not supplied.')
if field in predicted:
p = predicted[field]
else:
raise ValueError('Field is not in PREDICTED dictionary: ' + field)
elif isinstance(predicted, list):
p = np.array(predicted)
elif isinstance(predicted, np.ndarray):
p = predicted
else:
raise ValueError('PREDICTED argument must be a dictionary.')
if isinstance(reference, dict):
if field == '':
raise ValueError('FIELD argument not supplied.')
if field in reference:
r = reference[field]
else:
raise ValueError('Field is not in REFERENCE dictionary: ' + field)
elif isinstance(reference, list):
r = np.array(reference)
elif isinstance(reference, np.ndarray):
r = reference
else:
raise ValueError('REFERENCE argument must be a dictionary.')
# Check that dimensions of predicted and reference fields match
#ToDo: Implement check
# Calculate bias (B)
bias = np.mean(p) - np.mean(r)
# Calculate centered root-mean-square (RMS) difference (E')
crmsd = centered_rms_dev(p, r)
# Calculate RMS difference (RMSD)
rmsd = np.sqrt(np.sum(np.square(np.subtract(p, r))) / float(p.size))
# Normalize if requested
if norm == True:
sigma_ref = np.std(r)
bias = bias / sigma_ref
crmsd = crmsd / sigma_ref
rmsd = rmsd / sigma_ref
# Store statistics in a dictionary
stats = {'bias': bias, 'crmsd': crmsd, 'rmsd': rmsd}
if norm == True:
stats['type'] = 'normalized'
else:
stats['type'] = 'unnormalized'
return stats
def taylor_statistics(predicted, reference, field=''):
'''
Calculates the statistics needed to create a Taylor diagram as
described in Taylor (2001) using the data provided in the predicted
field (PREDICTED) and the reference field (REFERENCE).
The statistics are returned in the STATS dictionary.
If a dictionary is provided for PREDICTED or REFERENCE, then
the name of the field must be supplied in FIELD.
The function currently supports dictionaries, lists, and np.ndarray,
types for the PREDICTED and REFERENCE variables.
Input:
PREDICTED : predicted field
REFERENCE : reference field
FIELD : name of field to use in PREDICTED and REFERENCE dictionaries
(optional)
NORM : logical flag specifying statistics are to be normalized
with respect to standard deviation of reference field
= True, statistics are normalized
= False, statistics are not normalized
Output:
STATS : dictionary containing statistics
STATS['ccoef'] : correlation coefficients (R)
STATS['crmsd'] : centered root-mean-square (RMS) differences (E')
STATS['sdev'] : standard deviations
Each of these outputs are one-dimensional with the same length.
First index corresponds to the reference series for the diagram.
For example SDEV[1] is the standard deviation of the reference
series (sigma_r) and SDEV[2:N] are the standard deviations of the
other (predicted) series.
Reference:
Taylor, K. E. (2001), Summarizing multiple aspects of model
performance in a single diagram, J. Geophys. Res., 106(D7),
7183-7192, doi:10.1029/2000JD900719.
Author: Peter A. Rochford
Symplectic, LLC
www.thesymplectic.com
[email protected]
Created on Dec 3, 2016
'''
import numpy as np
from skill_metrics import centered_rms_dev
# Check for valid arguments
if isinstance(predicted, dict):
if field == '':
raise ValueError('FIELD argument not supplied.')
if field in predicted:
p = predicted[field]
else:
raise ValueError('Field is not in PREDICTED dictionary: ' + field)
elif isinstance(predicted, list):
p = np.array(predicted)
elif isinstance(predicted, np.ndarray):
p = predicted
else:
raise ValueError('PREDICTED argument must be a dictionary.')
if isinstance(reference, dict):
if field == '':
raise ValueError('FIELD argument not supplied.')
if field in reference:
r = reference[field]
else:
raise ValueError('Field is not in REFERENCE dictionary: ' + field)
elif isinstance(reference, list):
r = np.array(reference)
elif isinstance(reference, np.ndarray):
r = reference
else:
raise ValueError('REFERENCE argument must be a dictionary.')
# Check that dimensions of predicted and reference fields match
#ToDo: Implement check
# Calculate correlation coefficient
ccoef = np.corrcoef(p, r)
ccoef = ccoef[0]
# Calculate centered root-mean-square (RMS) difference (E')^2
crmsd = [0.0, centered_rms_dev(p, r)]
# Calculate standard deviation of predicted field w.r.t N (sigma_p)
sdevp = np.std(p)
# Calculate standard deviation of reference field w.r.t N (sigma_r)
sdevr = np.std(r)
sdev = [sdevr, sdevp]
# Store statistics in a dictionary
stats = {'ccoef': ccoef, 'crmsd': crmsd, 'sdev': sdev}
return stats