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check_eos_pth_example.py
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"""
==========================================================================
in-situ density, dynamic enthalpy and derivatives
from Absolute Salinity and Conservative
Temperature, using the computationally-efficient 48-term expression for
density in terms of SA, CT and p (IOC et al., 2010).
==========================================================================
"""
import torch
from typing import Tuple
def gsw_dHdT(sa, ct, p):
"""
d/dT of dynamic enthalpy, analytical derivative
sa : Absolute Salinity [g/kg]
ct : Conservative Temperature [deg C]
p : sea pressure [dbar]
"""
v01 = 9.998420897506056e2
v02 = 2.839940833161907e0
v03 = -3.147759265588511e-2
v04 = 1.181805545074306e-3
v05 = -6.698001071123802e0
v06 = -2.986498947203215e-2
v07 = 2.327859407479162e-4
v08 = -3.988822378968490e-2
v09 = 5.095422573880500e-4
v10 = -1.426984671633621e-5
v11 = 1.645039373682922e-7
v12 = -2.233269627352527e-2
v13 = -3.436090079851880e-4
v14 = 3.726050720345733e-6
v15 = -1.806789763745328e-4
v16 = 6.876837219536232e-7
v17 = -3.087032500374211e-7
v18 = -1.988366587925593e-8
v19 = -1.061519070296458e-11
v20 = 1.550932729220080e-10
v21 = 1.0e0
v22 = 2.775927747785646e-3
v23 = -2.349607444135925e-5
v24 = 1.119513357486743e-6
v25 = 6.743689325042773e-10
v26 = -7.521448093615448e-3
v27 = -2.764306979894411e-5
v28 = 1.262937315098546e-7
v29 = 9.527875081696435e-10
v30 = -1.811147201949891e-11
v31 = -3.303308871386421e-5
v32 = 3.801564588876298e-7
v33 = -7.672876869259043e-9
v34 = -4.634182341116144e-11
v35 = 2.681097235569143e-12
v36 = 5.419326551148740e-6
v37 = -2.742185394906099e-5
v38 = -3.212746477974189e-7
v39 = 3.191413910561627e-9
v40 = -1.931012931541776e-12
v41 = -1.105097577149576e-7
v42 = 6.211426728363857e-10
v43 = -1.119011592875110e-10
v44 = -1.941660213148725e-11
v45 = -1.864826425365600e-14
v46 = 1.119522344879478e-14
v47 = -1.200507748551599e-15
v48 = 6.057902487546866e-17
t1 = v45 * ct
t2 = 0.2e1 * t1
t3 = v46 * sa
t4 = 0.5 * v12
t5 = v14 * ct
t7 = ct * (v13 + t5)
t8 = 0.5 * t7
t11 = sa * (v15 + v16 * ct)
t12 = 0.5 * t11
t13 = t4 + t8 + t12
t15 = v19 * ct
t19 = v17 + ct * (v18 + t15) + v20 * sa
t20 = 1.0 / t19
t24 = v47 + v48 * ct
t25 = 0.5 * v13
t26 = 1.0 * t5
t27 = sa * v16
t28 = 0.5 * t27
t29 = t25 + t26 + t28
t33 = t24 * t13
t34 = t19 ** 2
t35 = 1.0 / t34
t37 = v18 + 2.0 * t15
t38 = t35 * t37
t48 = ct * (v44 + t1 + t3)
t57 = v40 * ct
t59 = ct * (v39 + t57)
t64 = t13 ** 2
t68 = t20 * t29
t71 = t24 * t64
t74 = v04 * ct
t76 = ct * (v03 + t74)
t79 = v07 * ct
t82 = torch.sqrt(sa)
t83 = v11 * ct
t85 = ct * (v10 + t83)
t92 = (
v01
+ ct * (v02 + t76)
+ sa * (v05 + ct * (v06 + t79) + t82 * (v08 + ct * (v09 + t85)))
)
t93 = v48 * t92
t105 = (
v02
+ t76
+ ct * (v03 + 2.0 * t74)
+ sa * (v06 + 2.0 * t79 + t82 * (v09 + t85 + ct * (v10 + 2.0 * t83)))
)
t106 = t24 * t105
t107 = v44 + t2 + t3
t110 = v43 + t48
t117 = t24 * t92
t120 = 4.0 * t71 * t20 - t117 - 2.0 * t110 * t13
t123 = (
v38
+ t59
+ ct * (v39 + 2.0 * t57)
+ sa * v42
+ (
4.0 * v48 * t64 * t20
+ 8.0 * t33 * t68
- 4.0 * t71 * t38
- t93
- t106
- 2.0 * t107 * t13
- 2.0 * t110 * t29
)
* t20
- t120 * t35 * t37
)
t128 = t19 * p
t130 = p * (1.0 * v12 + 1.0 * t7 + 1.0 * t11 + t128)
t131 = 1.0 / t92
t133 = 1.0 + t130 * t131
t134 = torch.log(t133)
t143 = v37 + ct * (v38 + t59) + sa * (v41 + v42 * ct) + t120 * t20
t152 = t37 * p
t156 = t92 ** 2
t165 = v25 * ct
t167 = ct * (v24 + t165)
t169 = ct * (v23 + t167)
t175 = v30 * ct
t177 = ct * (v29 + t175)
t179 = ct * (v28 + t177)
t185 = v35 * ct
t187 = ct * (v34 + t185)
t189 = ct * (v33 + t187)
t199 = t13 * t20
t217 = 2.0 * t117 * t199 - t110 * t92
t234 = (
v21
+ ct * (v22 + t169)
+ sa * (v26 + ct * (v27 + t179) + v36 * sa + t82 * (v31 + ct * (v32 + t189)))
+ t217 * t20
)
t241 = t64 - t92 * t19
t242 = torch.sqrt(t241)
t243 = 1.0 / t242
t244 = t4 + t8 + t12 - t242
t245 = 1.0 / t244
t247 = t4 + t8 + t12 + t242 + t128
t248 = 1.0 / t247
t249 = t242 * t245 * t248
t252 = 1.0 + 2.0 * t128 * t249
t253 = torch.log(t252)
t254 = t243 * t253
t259 = t234 * t19 - t143 * t13
t264 = t259 * t20
t272 = 2.0 * t13 * t29 - t105 * t19 - t92 * t37
t282 = t128 * t242
t283 = t244 ** 2
t287 = t243 * t272 / 2.0
t292 = t247 ** 2
t305 = (
0.1e5
* p
* (
v44
+ t2
+ t3
- 2.0 * v48 * t13 * t20
- 2.0 * t24 * t29 * t20
+ 2.0 * t33 * t38
+ 0.5 * v48 * p
)
* t20
- 0.1e5 * p * (v43 + t48 - 2.0 * t33 * t20 + 0.5 * t24 * p) * t38
+ 0.5e4 * t123 * t20 * t134
- 0.5e4 * t143 * t35 * t134 * t37
+ 0.5e4
* t143
* t20
* (p * (1.0 * v13 + 2.0 * t5 + 1.0 * t27 + t152) * t131 - t130 / t156 * t105)
/ t133
+ 0.5e4
* (
(
v22
+ t169
+ ct * (v23 + t167 + ct * (v24 + 2.0 * t165))
+ sa
* (
v27
+ t179
+ ct * (v28 + t177 + ct * (v29 + 2.0 * t175))
+ t82 * (v32 + t189 + ct * (v33 + t187 + ct * (v34 + 2.0 * t185)))
)
+ (
2.0 * t93 * t199
+ 2.0 * t106 * t199
+ 2.0 * t117 * t68
- 2.0 * t117 * t13 * t35 * t37
- t107 * t92
- t110 * t105
)
* t20
- t217 * t35 * t37
)
* t19
+ t234 * t37
- t123 * t13
- t143 * t29
)
* t20
* t254
- 0.5e4 * t259 * t35 * t254 * t37
- 0.25e4 * t264 / t242 / t241 * t253 * t272
+ 0.5e4
* t264
* t243
* (
2.0 * t152 * t249
+ t128 * t243 * t245 * t248 * t272
- 2.0 * t282 / t283 * t248 * (t25 + t26 + t28 - t287)
- 2.0 * t282 * t245 / t292 * (t25 + t26 + t28 + t287 + t152)
)
/ t252
)
return t305
def prepare_inputs(sa, ct, p, device):
out = [
torch.as_tensor(a, device=device)
for a in (sa, ct, p)
]
if device == "gpu":
torch.cuda.synchronize()
return out
@torch.compile(backend="inductor", fullgraph=True, dynamic=True)
def run(sa, ct, p, device="cpu"):
with torch.no_grad():
out = gsw_dHdT(sa, ct, p)
if device == "gpu":
torch.cuda.synchronize()
return out
def _generate_inputs(size):
import math
import numpy as np
np.random.seed(17)
shape = (
math.ceil(2 * size ** (1/3)),
math.ceil(2 * size ** (1/3)),
math.ceil(0.25 * size ** (1/3)),
)
s = np.random.uniform(1e-2, 10, size=shape)
t = np.random.uniform(-12, 20, size=shape)
p = np.random.uniform(0, 1000, size=(1, 1, shape[-1]))
return s, t, p
class EquationOfState(torch.nn.Module):
def __init__(self):
super(EquationOfState, self).__init__()
def forward(self, s, t, p):
return gsw_dHdT(s, t, p)
DEFAULT_EVAL_BSIZE = 1048576
CANNOT_SET_CUSTOM_OPTIMIZER = True
device = "cpu"
input_size = DEFAULT_EVAL_BSIZE
raw_inputs = _generate_inputs(input_size)
inputs = prepare_inputs(*raw_inputs, device=device)
example_inputs = inputs
model = EquationOfState().to(device=device)
cmodel = torch.compile(model)
with torch.no_grad():
out = cmodel(*example_inputs)