General Applied Math#
Warning
This is not meant to be a standalone notebook. This notebook is part of the process we have for adding entries to the NCL Index and is not meant to be used as tutorial or example code.
Functions covered#
NCL code#
; abs
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/abs.shtml
f = -5
abs_f = abs(f) ; abs_f = 5
print(abs_f)
f_array = (/-3, -2, -1, 0, 1, 2, 3/)
abs_f = abs(f_array)
print(abs_f)
; (0) 3
; (1) 2
; (2) 1
; (3) 0
; (4) 1
; (5) 2
; (6) 3
; avg
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/avg.shtml
f = (/ (/1,2,3/), (/4,5,6/)/)
avg_f = avg(f) ; avg_f = 3.5
print(avg_f)
; ceil
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/ceil.shtml
f = 6.4
ceil_f = ceil(f) ; ceil_f = 7
print(ceil_f)
; cumsum
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/cumsum.shtml
f = (/1,2,3,4,5/)
cumsum_f = cumsum(f, 0) ; cumsum_f = (/1 3 6 10 15/)
print(cumsum_f)
; (0) 1
; (1) 3
; (2) 6
; (3) 10
; (4) 15
; decimalPlaces
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Contributed/decimalPlaces.shtml
f = 12.345678
decimalPlaces_f = decimalPlaces(f, 2, True) ; decimalPlaces_f = 12.35
; exp
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/exp.shtml
f = -0.2
exp_f = exp(f) ; exp_f = 0.8187308
print(exp_f)
; fabs
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/fabs.shtml
iarray = (/-3.5, -2.2, -1.0, 0.0, 1.2, 2.4, 3.9/)
jarray = fabs(iarray) ; jarray = (/3.5, 2.2, 1, 0, 1.2, 2.4, 3.9/)
print(jarray)
; floor
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/floor.shtml
f = -6.4
floor_f = floor(f) ; floor_f = 6
print(floor_f )
; get_d2r
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Contributed/get_d2r.shtml
d2r = get_d2r("double") ; d2r = 0.0174532925199433
; get_r2d
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Contributed/get_r2d.shtml
r2d = get_r2d("double") ; r2d = 57.29577951308232
; get_pi
; Adapted from https://www.ncl.ucar.edu/D
pi = get_pi("double") ; pi = 3.141592653589793
; log
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/log.shtml
f = 3.6
log_f = log(f) ; log_f = 1.280934
print(log_f
; log10
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/log10.shtml
f = 3.4
log10_f = log10(f) ; log10_f = 0.5314789
print(log10_f)
; max
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/max.shtml
f = (/2.1, 3.2, 4.3, 5.4, 6.5, 7.6, 8.7, 9.8/)
max_f = max(f) ; max_f = 9.8
print(max_f)
; min
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/min.shtml
f = (/2.1, 3.2, 4.3, 5.4, 6.5, 7.6, 8.7, 9.8/)
min_f = min(f) ; min_f = 2.1
print(min_f)
; mod
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Contributed/mod.shtml
mod_f = mod(17, 3) ; mod_f = 2
print(mod_f)
; product
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/product.shtml
x = (/ (/1,-99/), (/3,4/), (/-99,6/) /)
x@_FillValue = -99
xproduct = product(x) ; xproduct = 72
print(xproduct)
; qsort
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/qsort.shtml
x = (/4.3, 0.9, 5.2, 7.7, 2.3, -4.7, -9.1/)
qsort(x)
print(x) ; x = (/-9.1, -4.7, 0.9, 2.3, 4.3, 5.2, 7.7/)
; round
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/round.shtml
f = 5.7
round_f = round(f, 0)
print(round_f) ; round_f = 6
; sign_matlab
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Contributed/sign_matlab.shtml
i = (/-3.5, 0.0, 1.2/)
matlab_i = sqrt(matlab_i)
print(matlab_i) ; matlab_i = (/-1, 0, 1/)
; sqrt
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/sqrt.shtml
f = 12.5
sqrt_f = sqrt(f)
print(sqrt_f) ; sqrt = 3.535534
; sqsort
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/sqsort.shtml
s = (/"Auf Wiedersehen", "Goodbye", "Hasta Luego", "Ciao"/)
sqsort(s)
print(s) ; s= (/"Auf Wiedersehen", "Ciao", "Goodbye", "Hasta Luego"/)
; sum
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/sum.shtml
x = (/ (/1,-99/), (/3,4/), (/-99,6/) /)
x@_FillValue = -99
xsum = sum(x) ; xsum = 14
print(xsum)
Python Functionality#
import math
import numpy as np
results_math = {}
results_np = {}
# abs
f = -5
results_math["abs"] = abs(f)
results_np["abs"] = np.absolute(f)
# avg
f = [[1, 2, 3], [4, 5, 6]]
results_np["avg"] = np.mean(f)
# ceil
f = 6.4
results_math["ceil"] = math.ceil(f)
results_np["ceil"] = np.ceil(f)
# cumsum
f = [1, 2, 3, 4, 5]
results_np["cumsum"] = np.cumsum(f, axis=0)
# decimalPlaces
f = 12.345678
results_math["decimalPlaces"] = round(f, 2)
results_np["decimalPlaces"] = np.round(f, 2)
# exp
f = -0.2
results_math["exp"] = math.exp(f)
results_np["exp"] = np.exp(f)
# fabs
f = [-3.5, -2.2, -1.0, 0.0, 1.2, 2.4, 3.9]
results_np["fabs"] = np.absolute(f)
# floor
f = 6.4
results_math["floor"] = math.floor(f)
results_np["floor"] = np.floor(f)
# get_d2r
results_math["get_d2r"] = math.pi / 180
results_np["get_d2r"] = np.pi / 180
# get_r2d
results_math["get_r2d"] = 180 / math.pi
results_np["get_r2d"] = 180 / np.pi
# get_pi
results_math["get_pi"] = math.pi
results_np["get_pi"] = np.pi
# log
f = 3.6
results_math["log"] = math.log(f)
results_np["log"] = np.log(f)
# log10
f = 3.4
results_math["log10"] = math.log10(f)
results_np["log10"] = np.log10(f)
# max
f = [2.1, 3.2, 4.3, 5.4, 6.5, 7.6, 8.7, 9.8]
results_math["max"] = max(f)
results_np["max"] = np.max(f)
# min
f = [2.1, 3.2, 4.3, 5.4, 6.5, 7.6, 8.7, 9.8]
results_math["min"] = min(f)
results_np["min"] = np.min(f)
# mod
results_math["mod"] = 17 % 3
results_np["mod"] = np.mod([17], [3])[0]
# product
f = [1, 3, 4, 6]
results_math["product"] = math.prod(f)
results_np["product"] = np.prod(f)
# qsort
f = [4.3, 0.9, 5.2, 7.7, 2.3, -4.7, -9.1]
results_math["qsort"] = sorted(f)
h = [4.3, 0.9, 5.2, 7.7, 2.3, -4.7, -9.1]
results_np["qsort"] = np.sort(h)
# round
f = 5.7
results_math["round"] = round(f)
results_np["round"] = np.round(f)
# sign_matlab
f = [-3.5, 0.0, 1.2]
results_np["sign_matlab"] = np.sign(f)
# sqrt
f = 12.5
results_math["sqrt"] = math.sqrt(f)
results_np["sqrt"] = np.sqrt(f)
# sqsort
s = ["Auf Wiedersehen", "Goodbye", "Hasta Luego", "Ciao"]
results_math["sqsort"] = sorted(s)
q = ["Auf Wiedersehen", "Goodbye", "Hasta Luego", "Ciao"]
results_np["sqsort"] = np.sort(q)
# sum
f = [1, 3, 4, 6]
results_math["sum"] = sum(f)
results_np["sum"] = np.sum(f)
Comparison#
ncl_results = {
"abs": 5,
"avg": 3.5,
"ceil": 7,
"cumsum": np.array([1, 3, 6, 10, 15]),
"decimalPlaces": 12.35,
"exp": 0.8187308,
"fabs": [3.5, 2.2, 1, 0, 1.2, 2.4, 3.9],
"floor": 6,
"get_d2r": 0.0174532925199433,
"get_r2d": 57.29577951308232,
"get_pi": 3.141592653589793,
"log": 1.280934,
"log10": 0.5314789,
"max": 9.8,
"min": 2.1,
"mod": 2,
"product": 72,
"qsort": np.array([-9.1, -4.7, 0.9, 2.3, 4.3, 5.2, 7.7]),
"round": 6,
"sign_matlab": [-1, 0, 1],
"sqsort": np.array(["Auf Wiedersehen", "Ciao", "Goodbye", "Hasta Luego"]),
"sqrt": 3.535534,
"sum": 14,
}
for key in ncl_results.keys():
if key == "sqsort":
# compare string outputs
assert np.all(ncl_results[key] == results_math[key])
assert np.all(ncl_results[key] == results_np[key])
assert np.all(results_math[key] == results_np[key])
elif key in results_math.keys() and key in results_np.keys():
print(
f"{key}: \n\tncl:\t\t{ncl_results[key]}\n\tpython (math):\t{results_math[key]}\n\tpython (numpy):\t{results_np[key]}\n"
)
try:
assert math.isclose(
results_np[key], results_math[key], rel_tol=1e-15
) # within 15 decimal points
assert math.isclose(
ncl_results[key], results_math[key], rel_tol=1e-06
) # within 6 decimal points
assert math.isclose(
ncl_results[key], results_np[key], rel_tol=1e-06
) # within 6 decimal points
except Exception:
assert np.all(
np.isclose(ncl_results[key], results_math[key], rtol=1e-06)
) # within 6 decimal points
assert np.all(
np.isclose(results_np[key], results_math[key], rtol=1e-15)
) # within 15 decimal points
assert np.all(
np.isclose(ncl_results[key], results_np[key], rtol=1e-06)
) # within 6 decimal points
elif key in results_math.keys() and key not in results_np.keys():
print(
f"{key}: \n\tncl:\t\t{ncl_results[key]}\n\tpython (math):\t{results_math[key]}\n"
)
try:
assert math.isclose(
ncl_results[key], results_math[key], rel_tol=1e-06
) # within 6 decimal points
except Exception:
assert np.all(
np.isclose(ncl_results[key], results_np[key], rtol=1e-06)
) # within 6 decimal points
elif key in results_np.keys() and key not in results_math.keys():
print(
f"{key}: \n\tncl:\t\t{ncl_results[key]}\n\tpython (numpy):\t{results_np[key]}\n"
)
try:
assert math.isclose(
ncl_results[key], results_np[key], rel_tol=1e-06
) # within 6 decimal points
except Exception:
assert np.all(
np.isclose(ncl_results[key], results_np[key], rtol=1e-06)
) # within 6 decimal points
abs:
ncl: 5
python (math): 5
python (numpy): 5
avg:
ncl: 3.5
python (numpy): 3.5
ceil:
ncl: 7
python (math): 7
python (numpy): 7.0
cumsum:
ncl: [ 1 3 6 10 15]
python (numpy): [ 1 3 6 10 15]
decimalPlaces:
ncl: 12.35
python (math): 12.35
python (numpy): 12.35
exp:
ncl: 0.8187308
python (math): 0.8187307530779818
python (numpy): 0.8187307530779818
fabs:
ncl: [3.5, 2.2, 1, 0, 1.2, 2.4, 3.9]
python (numpy): [3.5 2.2 1. 0. 1.2 2.4 3.9]
floor:
ncl: 6
python (math): 6
python (numpy): 6.0
get_d2r:
ncl: 0.0174532925199433
python (math): 0.017453292519943295
python (numpy): 0.017453292519943295
get_r2d:
ncl: 57.29577951308232
python (math): 57.29577951308232
python (numpy): 57.29577951308232
get_pi:
ncl: 3.141592653589793
python (math): 3.141592653589793
python (numpy): 3.141592653589793
log:
ncl: 1.280934
python (math): 1.2809338454620642
python (numpy): 1.2809338454620642
log10:
ncl: 0.5314789
python (math): 0.5314789170422551
python (numpy): 0.5314789170422551
max:
ncl: 9.8
python (math): 9.8
python (numpy): 9.8
min:
ncl: 2.1
python (math): 2.1
python (numpy): 2.1
mod:
ncl: 2
python (math): 2
python (numpy): 2
product:
ncl: 72
python (math): 72
python (numpy): 72
qsort:
ncl: [-9.1 -4.7 0.9 2.3 4.3 5.2 7.7]
python (math): [-9.1, -4.7, 0.9, 2.3, 4.3, 5.2, 7.7]
python (numpy): [-9.1 -4.7 0.9 2.3 4.3 5.2 7.7]
round:
ncl: 6
python (math): 6
python (numpy): 6.0
sign_matlab:
ncl: [-1, 0, 1]
python (numpy): [-1. 0. 1.]
sqrt:
ncl: 3.535534
python (math): 3.5355339059327378
python (numpy): 3.5355339059327378
sum:
ncl: 14
python (math): 14
python (numpy): 14
Differences#
for key in ncl_results.keys():
if key == "sqsort":
# ignore string comparison
continue
elif key in results_math.keys() and key in results_np.keys():
print(f"{key}:")
print(f"\t{results_math[key] - ncl_results[key]}")
print(f"\t{results_np[key] - ncl_results[key]}")
elif key in results_math.keys() and key not in results_np.keys():
print(f"{key}:")
print(f"\t{results_math[key] - ncl_results[key]}")
elif key in results_np.keys() and key not in results_math.keys():
print(f"{key}:")
print(f"\t{results_np[key] - ncl_results[key]}")
for key in ncl_results.keys() & results_math.keys() & results_np.keys():
if key == "sqsort":
# ignore string comparison
continue
else:
print(f"{key}:")
print(f"\t{results_math[key] - ncl_results[key]}")
print(f"\t{results_np[key] - ncl_results[key]}")
abs:
0
0
avg:
0.0
ceil:
0
0.0
cumsum:
[0 0 0 0 0]
decimalPlaces:
0.0
0.0
exp:
-4.6922018159811785e-08
-4.6922018159811785e-08
fabs:
[0. 0. 0. 0. 0. 0. 0.]
floor:
0
0.0
get_d2r:
-3.469446951953614e-18
-3.469446951953614e-18
get_r2d:
0.0
0.0
get_pi:
0.0
0.0
log:
-1.5453793578146247e-07
-1.5453793578146247e-07
log10:
1.704225516263591e-08
1.704225516263591e-08
max:
0.0
0.0
min:
0.0
0.0
mod:
0
0
product:
0
0
qsort:
[0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0.]
round:
0
0.0
sign_matlab:
[0. 0. 0.]
sqrt:
-9.406726242389141e-08
-9.406726242389141e-08
sum:
0
0
get_pi:
0.0
0.0
exp:
-4.6922018159811785e-08
-4.6922018159811785e-08
product:
0
0
sqrt:
-9.406726242389141e-08
-9.406726242389141e-08
min:
0.0
0.0
get_d2r:
-3.469446951953614e-18
-3.469446951953614e-18
abs:
0
0
log:
-1.5453793578146247e-07
-1.5453793578146247e-07
qsort:
[0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0.]
max:
0.0
0.0
decimalPlaces:
0.0
0.0
get_r2d:
0.0
0.0
floor:
0
0.0
log10:
1.704225516263591e-08
1.704225516263591e-08
round:
0
0.0
sum:
0
0
mod:
0
0
ceil:
0
0.0