Trigonometric Functions#
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#
; sin
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/sin.shtml
f = 0.5
sin_f = sin(f) ; sin_f = 0.4794255
print(sin_f)
; cos
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/cos.shtml
f = -1.0
cos_f = cos(f) ; cos_f = 0.5403023
print(cos_f)
; tan
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/tan.shtml
f = 5.6
tan_f = tan(f) ; tan_f = -0.8139434
print(tan_f)
; asin
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/asin.shtml
f = 0.5
asin_f = asin(f) ; asin_f = 0.5235988
print(asin_f)
; acos
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/acos.shtml
f = -1.0
acos_f = acos(f) ; acos_f = 3.141593
print(acos_f)
; atan
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/atan.shtml
f = 2.7
atan_f = atan(f) ; atan_f = 1.216091
print(atan_f)
; atan2
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/atan2.shtml
x = 10
y = 5
atan2_f = atan2(y, x) ; atan2_f = 0.4636476
print(atan2_f)
; cosh
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/cosh.shtml
f = -3.2
cosh_f = cosh(f) ; cosh_f = 12.28665
print(cosh_f)
; sinh
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/sinh.shtml
f = 1.4
sinh_f = sinh(f) ; sinh_f = 1.904301
print(sinh_f)
; tanh
; Adapted from https://www.ncl.ucar.edu/Document/Functions/Built-in/tanh.shtml
f = 0.67
tanh_f = tanh(f) ; tanh_f = 0.5849799
print(tanh_f)
Python Functionality#
import math
import numpy as np
results_math = {}
results_np = {}
# sin
f = 0.5
sin_math_f = math.sin(f)
sin_np_f = np.sin(f)
results_math["sin"] = sin_math_f
results_np["sin"] = sin_np_f
# cos
f = -1.0
cos_math_f = math.cos(f)
cos_np_f = np.cos(f)
results_math["cos"] = cos_math_f
results_np["cos"] = cos_np_f
# tan
f = 5.6
tan_math_f = math.tan(f)
tan_np_f = np.tan(f)
results_math["tan"] = tan_math_f
results_np["tan"] = tan_np_f
# asin
f = 0.5
asin_math_f = math.asin(f)
asin_np_f = np.arcsin(f)
results_math["asin"] = asin_math_f
results_np["asin"] = asin_np_f
# acos
f = -1.0
acos_math_f = math.acos(f)
acos_np_f = np.arccos(f)
results_math["acos"] = acos_math_f
results_np["acos"] = acos_np_f
# atan
f = 2.7
atan_math_f = math.atan(f)
atan_np_f = np.arctan(f)
results_math["atan"] = atan_math_f
results_np["atan"] = atan_np_f
# atan2
x = 10.0
y = 5.0
atan2_math_f = math.atan2(y, x)
atan2_np_f = np.arctan2(y, x)
results_math["atan2"] = atan2_math_f
results_np["atan2"] = atan2_np_f
# cosh
f = -3.2
cosh_math_f = math.cosh(f)
cosh_np_f = np.cosh(f)
results_math["cosh"] = cosh_math_f
results_np["cosh"] = cosh_np_f
# sinh
f = 1.4
sinh_math_f = math.sinh(f)
sinh_np_f = np.sinh(f)
results_math["sinh"] = sinh_math_f
results_np["sinh"] = sinh_np_f
# tanh
f = 0.67
tanh_math_f = math.tanh(f)
tanh_np_f = np.tanh(f)
results_math["tanh"] = tanh_math_f
results_np["tanh"] = tanh_np_f
Comparison#
# dictionary of trig functions results
ncl_results = {
"sin": 0.4794255,
"cos": 0.5403023,
"tan": -0.8139434,
"asin": 0.5235988,
"acos": 3.141593,
"atan": 1.216091,
"atan2": 0.4636476,
"cosh": 12.28665,
"sinh": 1.904301,
"tanh": 0.5849799,
}
for c in ncl_results.keys() & results_math.keys() & results_np.keys():
print(
f"{c}: \n\tpython (math):\t{results_math[c]}\n\tpython (numpy):\t{results_np[c]}\n\tncl:\t\t{ncl_results[c]}\n"
)
assert math.isclose(
results_np[c], results_math[c], rel_tol=1e-15
) # within 15 decimal points
assert math.isclose(
ncl_results[c], results_math[c], rel_tol=1e-06
) # within 6 decimal points
assert math.isclose(
ncl_results[c], results_np[c], rel_tol=1e-06
) # within 6 decimal points
atan:
python (math): 1.2160906747839564
python (numpy): 1.2160906747839564
ncl: 1.216091
asin:
python (math): 0.5235987755982989
python (numpy): 0.5235987755982989
ncl: 0.5235988
cosh:
python (math): 12.28664620054386
python (numpy): 12.28664620054386
ncl: 12.28665
sin:
python (math): 0.479425538604203
python (numpy): 0.479425538604203
ncl: 0.4794255
tan:
python (math): -0.8139432836897027
python (numpy): -0.8139432836897027
ncl: -0.8139434
cos:
python (math): 0.5403023058681398
python (numpy): 0.5403023058681398
ncl: 0.5403023
sinh:
python (math): 1.9043015014515339
python (numpy): 1.9043015014515339
ncl: 1.904301
atan2:
python (math): 0.4636476090008061
python (numpy): 0.4636476090008061
ncl: 0.4636476
acos:
python (math): 3.141592653589793
python (numpy): 3.141592653589793
ncl: 3.141593
tanh:
python (math): 0.5849798828807289
python (numpy): 0.5849798828807288
ncl: 0.5849799
Differences#
for c in ncl_results.keys() & results_math.keys() & results_np.keys():
print(f"{c}:")
print(f"\t{results_math[c] - ncl_results[c]}")
print(f"\t{results_np[c] - ncl_results[c]}")
atan:
-3.252160436506557e-07
-3.252160436506557e-07
asin:
-2.440170110418194e-08
-2.440170110418194e-08
cosh:
-3.7994561399301574e-06
-3.7994561399301574e-06
sin:
3.8604203000947024e-08
3.8604203000947024e-08
tan:
1.1631029728231823e-07
1.1631029728231823e-07
cos:
5.868139751896706e-09
5.868139751896706e-09
sinh:
5.014515338519487e-07
5.014515338519487e-07
atan2:
9.000806100445402e-09
9.000806100445402e-09
acos:
-3.4641020674186507e-07
-3.4641020674186507e-07
tanh:
-1.7119271111809553e-08
-1.7119271222831856e-08