Fibonacci numbers¶
In [4]:
def fib(n):
a, b = 0, 1
for _ in range(n):
a, b = b, a+b
return a
In [12]:
%time fib(10_000)
CPU times: total: 15.6 ms Wall time: 999 μs
Out[12]:
33644764876431783266621612005107543310302148460680063906564769974680081442166662368155595513633734025582065332680836159373734790483865268263040892463056431887354544369559827491606602099884183933864652731300088830269235673613135117579297437854413752130520504347701602264758318906527890855154366159582987279682987510631200575428783453215515103870818298969791613127856265033195487140214287532698187962046936097879900350962302291026368131493195275630227837628441540360584402572114334961180023091208287046088923962328835461505776583271252546093591128203925285393434620904245248929403901706233888991085841065183173360437470737908552631764325733993712871937587746897479926305837065742830161637408969178426378624212835258112820516370298089332099905707920064367426202389783111470054074998459250360633560933883831923386783056136435351892133279732908133732642652633989763922723407882928177953580570993691049175470808931841056146322338217465637321248226383092103297701648054726243842374862411453093812206564914032751086643394517512161526545361333111314042436854805106765843493523836959653428071768775328348234345557366719731392746273629108210679280784718035329131176778924659089938635459327894523777674406192240337638674004021330343297496902028328145933418826817683893072003634795623117103101291953169794607632737589253530772552375943788434504067715555779056450443016640119462580972216729758615026968443146952034614932291105970676243268515992834709891284706740862008587135016260312071903172086094081298321581077282076353186624611278245537208532365305775956430072517744315051539600905168603220349163222640885248852433158051534849622434848299380905070483482449327453732624567755879089187190803662058009594743150052402532709746995318770724376825907419939632265984147498193609285223945039707165443156421328157688908058783183404917434556270520223564846495196112460268313970975069382648706613264507665074611512677522748621598642530711298441182622661057163515069260029861704945425047491378115154139941550671256271197133252763631939606902895650288268608362241082050562430701794976171121233066073310059947366875
In [13]:
%time fib(100_000)
CPU times: total: 93.8 ms Wall time: 90.4 ms
--------------------------------------------------------------------------- ValueError Traceback (most recent call last) File C:\Program Files\ArcGIS\Pro\bin\Python\envs\arcgispro-py3\Lib\site-packages\IPython\core\formatters.py:770, in PlainTextFormatter.__call__(self, obj) 763 stream = StringIO() 764 printer = pretty.RepresentationPrinter(stream, self.verbose, 765 self.max_width, self.newline, 766 max_seq_length=self.max_seq_length, 767 singleton_pprinters=self.singleton_printers, 768 type_pprinters=self.type_printers, 769 deferred_pprinters=self.deferred_printers) --> 770 printer.pretty(obj) 771 printer.flush() 772 return stream.getvalue() File C:\Program Files\ArcGIS\Pro\bin\Python\envs\arcgispro-py3\Lib\site-packages\IPython\lib\pretty.py:394, in RepresentationPrinter.pretty(self, obj) 391 for cls in _get_mro(obj_class): 392 if cls in self.type_pprinters: 393 # printer registered in self.type_pprinters --> 394 return self.type_pprinters[cls](obj, self, cycle) 395 else: 396 # deferred printer 397 printer = self._in_deferred_types(cls) File C:\Program Files\ArcGIS\Pro\bin\Python\envs\arcgispro-py3\Lib\site-packages\IPython\lib\pretty.py:794, in _repr_pprint(obj, p, cycle) 792 """A pprint that just redirects to the normal repr function.""" 793 # Find newlines and replace them with p.break_() --> 794 output = repr(obj) 795 lines = output.splitlines() 796 with p.group(): ValueError: Exceeds the limit (4300 digits) for integer string conversion; use sys.set_int_max_str_digits() to increase the limit
In [5]:
import sys
In [6]:
sys.set_int_max_str_digits(10**6) #set the limit for string representation of INTEGER
In [19]:
%time print(len(str(fib(1_000_000))))
208988 CPU times: total: 6.98 s Wall time: 7 s
In [20]:
!pip install cython
Defaulting to user installation because normal site-packages is not writeable Collecting cython Downloading cython-3.2.4-cp311-cp311-win_amd64.whl.metadata (7.7 kB) Downloading cython-3.2.4-cp311-cp311-win_amd64.whl (2.8 MB) ---------------------------------------- 0.0/2.8 MB ? eta -:--:-- ---------------------------------------- 0.0/2.8 MB ? eta -:--:-- ---------------------------------------- 0.0/2.8 MB 325.1 kB/s eta 0:00:09 -- ------------------------------------- 0.2/2.8 MB 1.3 MB/s eta 0:00:02 ------- -------------------------------- 0.5/2.8 MB 3.3 MB/s eta 0:00:01 --------------- ------------------------ 1.1/2.8 MB 5.1 MB/s eta 0:00:01 ------------------------ --------------- 1.7/2.8 MB 6.8 MB/s eta 0:00:01 ------------------------------------ --- 2.6/2.8 MB 8.6 MB/s eta 0:00:01 --------------------------------------- 2.8/2.8 MB 9.3 MB/s eta 0:00:01 ---------------------------------------- 2.8/2.8 MB 7.7 MB/s eta 0:00:00 Installing collected packages: cython Successfully installed cython-3.2.4
WARNING: The scripts cygdb.exe, cython.exe and cythonize.exe are installed in 'C:\Users\student\AppData\Roaming\Python\Python311\Scripts' which is not on PATH. Consider adding this directory to PATH or, if you prefer to suppress this warning, use --no-warn-script-location.
In [1]:
%load_ext cython
In [3]:
%%cython -a
def fib_cython(n):
a, b = 0, 1
for _ in range(n):
a, b = b, a+b
return a
Content of stdout: _cython_magic_0f4cc6ebbb2485effa031413a08c5a20df5d5af666fda0a2c0be23e925ed81e9.c Creating library C:\Users\student\.ipython\cython\Users\student\.ipython\cython\_cython_magic_0f4cc6ebbb2485effa031413a08c5a20df5d5af666fda0a2c0be23e925ed81e9.cp311-win_amd64.lib and object C:\Users\student\.ipython\cython\Users\student\.ipython\cython\_cython_magic_0f4cc6ebbb2485effa031413a08c5a20df5d5af666fda0a2c0be23e925ed81e9.cp311-win_amd64.exp Generating code Finished generating code
Out[3]:
Generated by Cython 3.2.4
Yellow lines hint at Python interaction.
Click on a line that starts with a "+" to see the C code that Cython generated for it.
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In [7]:
%time print(len(str(fib_cython(1_000_000))))
208988 CPU times: total: 7.09 s Wall time: 7.09 s
Primes¶
In [9]:
import cython
def primes(nb_primes: cython.int):
i: cython.int
p: cython.int[10000]
if nb_primes > 10000:
nb_primes = 10000
if not cython.compiled: # Only if regular Python is running
print('NOT COMPILED')
p = [0] * 10000 # Make p work almost like a C array
len_p: cython.int = 0 # The current number of elements in p.
n: cython.int = 2
while len_p < nb_primes:
# Is n prime?
for i in p[:len_p]:
if n % i == 0:
break
# If no break occurred in the loop, we have a prime.
else:
p[len_p] = n
len_p += 1
n += 1
# Let's copy the result into a Python list:
result_as_list = [prime for prime in p[:len_p]]
return result_as_list
In [11]:
print(*primes(100))
NOT COMPILED 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541
In [12]:
%time primes(10000)[-10:]
NOT COMPILED CPU times: total: 3.41 s Wall time: 3.39 s
Out[12]:
[104677, 104681, 104683, 104693, 104701, 104707, 104711, 104717, 104723, 104729]
In [13]:
%%cython -a
import cython
def primes_cython(nb_primes: cython.int):
i: cython.int
p: cython.int[10000]
if nb_primes > 10000:
nb_primes = 10000
if not cython.compiled: # Only if regular Python is running
print('NOT COMPILED')
p = [0] * 10000 # Make p work almost like a C array
len_p: cython.int = 0 # The current number of elements in p.
n: cython.int = 2
while len_p < nb_primes:
# Is n prime?
for i in p[:len_p]:
if n % i == 0:
break
# If no break occurred in the loop, we have a prime.
else:
p[len_p] = n
len_p += 1
n += 1
# Let's copy the result into a Python list:
result_as_list = [prime for prime in p[:len_p]]
return result_as_list
Content of stdout: _cython_magic_1b7829d702aa5b00267382ad93315eefde3d25e18d2b69d27c4b320c3d1da98a.c Creating library C:\Users\student\.ipython\cython\Users\student\.ipython\cython\_cython_magic_1b7829d702aa5b00267382ad93315eefde3d25e18d2b69d27c4b320c3d1da98a.cp311-win_amd64.lib and object C:\Users\student\.ipython\cython\Users\student\.ipython\cython\_cython_magic_1b7829d702aa5b00267382ad93315eefde3d25e18d2b69d27c4b320c3d1da98a.cp311-win_amd64.exp Generating code Finished generating code
Out[13]:
Generated by Cython 3.2.4
Yellow lines hint at Python interaction.
Click on a line that starts with a "+" to see the C code that Cython generated for it.
01:
+02: import cython
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In [14]:
%time primes_cython(10000)[-10:]
CPU times: total: 156 ms Wall time: 136 ms
Out[14]:
[104677, 104681, 104683, 104693, 104701, 104707, 104711, 104717, 104723, 104729]
NOT COMPILED
CPU times: total: 3.41 s
COMPILED:
CPU times: total: 156 msIn [16]:
import numpy as np
from matplotlib import pyplot as plt
%matplotlib inline
plt.rcParams['figure.figsize'] = [15, 5]
plt.rcParams['figure.dpi'] = 100
from numba import jit, vectorize, guvectorize, float64, complex64, int32, float32
def mandelbrot_set(xmin,xmax,ymin,ymax,width,height,maxiter, mandelbrot_func, real=False):
r1 = np.linspace(xmin, xmax, width)
r2 = np.linspace(ymin, ymax, height)
if real:
return [[mandelbrot_func(r, i, maxiter) for r in r1] for i in r2]
return [[mandelbrot_func(complex(r, i), maxiter) for r in r1] for i in r2]
male_hodnoty = (-2.0,0.5,-1.25,1.25,1000,1000,80)
velke_hodnoty = (-0.74877,-0.74872,0.06505,0.06510,1000,1000,2048)
def pds_zobraz(f, real=False):
%time plt.subplot(1, 2, 1).imshow(mandelbrot_set(*male_hodnoty, f, real))
%time plt.subplot(1, 2, 2).imshow(mandelbrot_set(*velke_hodnoty, f, real))
--------------------------------------------------------------------------- ModuleNotFoundError Traceback (most recent call last) Cell In[16], line 8 5 plt.rcParams['figure.figsize'] = [15, 5] 6 plt.rcParams['figure.dpi'] = 100 ----> 8 from numba import jit, vectorize, guvectorize, float64, complex64, int32, float32 10 def mandelbrot_set(xmin,xmax,ymin,ymax,width,height,maxiter, mandelbrot_func, real=False): 11 r1 = np.linspace(xmin, xmax, width) ModuleNotFoundError: No module named 'numba'
In [17]:
!pip install numba
Defaulting to user installation because normal site-packages is not writeable
Collecting numba
Downloading numba-0.64.0-cp311-cp311-win_amd64.whl.metadata (2.8 kB)
Collecting llvmlite<0.47,>=0.46.0dev0 (from numba)
Downloading llvmlite-0.46.0-cp311-cp311-win_amd64.whl.metadata (4.9 kB)
Requirement already satisfied: numpy<2.5,>=1.22 in c:\program files\arcgis\pro\bin\python\envs\arcgispro-py3\lib\site-packages (from numba) (1.26.4)
Downloading numba-0.64.0-cp311-cp311-win_amd64.whl (2.7 MB)
---------------------------------------- 0.0/2.7 MB ? eta -:--:--
---------------------------------------- 0.0/2.7 MB ? eta -:--:--
--------------------------------------- 0.1/2.7 MB 1.1 MB/s eta 0:00:03
------ --------------------------------- 0.5/2.7 MB 4.8 MB/s eta 0:00:01
--------------- ------------------------ 1.0/2.7 MB 7.3 MB/s eta 0:00:01
-------------------------- ------------- 1.8/2.7 MB 9.6 MB/s eta 0:00:01
--------------------------------------- 2.7/2.7 MB 11.6 MB/s eta 0:00:01
---------------------------------------- 2.7/2.7 MB 11.7 MB/s eta 0:00:00
Downloading llvmlite-0.46.0-cp311-cp311-win_amd64.whl (38.1 MB)
---------------------------------------- 0.0/38.1 MB ? eta -:--:--
- -------------------------------------- 1.6/38.1 MB 33.1 MB/s eta 0:00:02
--- ------------------------------------ 3.5/38.1 MB 36.9 MB/s eta 0:00:01
------ --------------------------------- 5.9/38.1 MB 41.7 MB/s eta 0:00:01
--------- ------------------------------ 9.1/38.1 MB 48.7 MB/s eta 0:00:01
-------------- ------------------------- 13.5/38.1 MB 73.1 MB/s eta 0:00:01
------------------- -------------------- 18.9/38.1 MB 108.8 MB/s eta 0:00:01
------------------------- -------------- 24.3/38.1 MB 131.2 MB/s eta 0:00:01
------------------------------- -------- 29.9/38.1 MB 131.2 MB/s eta 0:00:01
------------------------------------- -- 35.4/38.1 MB 131.2 MB/s eta 0:00:01
--------------------------------------- 38.1/38.1 MB 108.8 MB/s eta 0:00:01
--------------------------------------- 38.1/38.1 MB 108.8 MB/s eta 0:00:01
---------------------------------------- 38.1/38.1 MB 54.4 MB/s eta 0:00:00
Installing collected packages: llvmlite, numba
Successfully installed llvmlite-0.46.0 numba-0.64.0
In [20]:
import numpy as np
from matplotlib import pyplot as plt
%matplotlib inline
plt.rcParams['figure.figsize'] = [15, 5]
plt.rcParams['figure.dpi'] = 100
from numba import jit, vectorize, guvectorize, float64, complex64, int32, float32
def mandelbrot_set(xmin,xmax,ymin,ymax,width,height,maxiter, mandelbrot_func, real=False):
r1 = np.linspace(xmin, xmax, width)
r2 = np.linspace(ymin, ymax, height)
if real:
return [[mandelbrot_func(r, i, maxiter) for r in r1] for i in r2]
return [[mandelbrot_func(complex(r, i), maxiter) for r in r1] for i in r2]
male_hodnoty = (-2.0,0.5,-1.25,1.25,1000,1000,80)
velke_hodnoty = (-0.74877,-0.74872,0.06505,0.06510,1000,1000,2048)
def pds_zobraz(f, real=False):
%time plt.subplot(1, 2, 1).imshow(mandelbrot_set(*male_hodnoty, f, real))
%time plt.subplot(1, 2, 2).imshow(mandelbrot_set(*velke_hodnoty, f, real))
In [21]:
def mandelbrot_python(z, maxiter):
c = z
for n in range(maxiter):
if abs(z) > 2:
return n
z = z*z + c
return maxiter
In [22]:
pds_zobraz(mandelbrot_python)
CPU times: total: 3.5 s Wall time: 3.53 s CPU times: total: 1min 20s Wall time: 1min 20s
In [23]:
%%cython -a
def mandelbrot_cython(z, maxiter):
c = z
for n in range(maxiter):
if abs(z) > 2:
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z = z*z + c
return maxiter
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In [24]:
pds_zobraz(mandelbrot_cython)
CPU times: total: 2.28 s Wall time: 2.28 s CPU times: total: 48.6 s Wall time: 48.6 s
In [25]:
@jit
def mandelbrot_numba(z, maxiter):
c = z
for n in range(maxiter):
if abs(z) > 2:
return n
z = z*z + c
return maxiter
In [26]:
pds_zobraz(mandelbrot_numba) #Compiling at first run
CPU times: total: 1.3 s Wall time: 3.73 s CPU times: total: 3.52 s Wall time: 3.51 s
In [27]:
pds_zobraz(mandelbrot_numba)
CPU times: total: 516 ms Wall time: 532 ms CPU times: total: 3.47 s Wall time: 3.46 s
Do not compute square root (for the distance) ...¶
In [29]:
a = complex(3, 4)
In [30]:
abs(a)
Out[30]:
5.0
In [31]:
a.real, a.imag
Out[31]:
(3.0, 4.0)
In [32]:
import math
math.sqrt(a.real**2+a.imag**2)
Out[32]:
5.0
In [33]:
abs(a) > 2
Out[33]:
True
In [34]:
a.real**2+a.imag**2 > 4
Out[34]:
True
In [35]:
@jit
def mandelbrot_numba_sqr(z, maxiter):
c = z
for n in range(maxiter):
if z.real**2+z.imag**2 > 4:
return n
z = z*z + c
return maxiter
In [36]:
pds_zobraz(mandelbrot_numba_sqr)
CPU times: total: 625 ms Wall time: 620 ms CPU times: total: 2.19 s Wall time: 2.18 s
$ z = \texttt{re}+i \cdot \texttt{im}$
$i^2 = -1$
$ z^2 = \left(\texttt{re}+i \cdot \texttt{im}\right)^2 = re^2+2 \cdot \texttt{re} \cdot \texttt{im} \cdot i + i^2 \cdot \texttt{im} = \texttt{re}^2+2 \cdot \texttt{re}\cdot \texttt{im} \cdot i - \texttt{im}$
In [37]:
@jit
def mandelbrot_numba_sqr_real(re, im, maxiter):
c_re, c_im = re, im
for n in range(maxiter):
re2 = re**2
im2 = im**2
if re2+im2 > 4:
return n
# z = z*z+c
re, im = re2-im2+c_re, 2*re*im+c_im
return maxiter
In [39]:
pds_zobraz(mandelbrot_numba_sqr_real, real=True)
CPU times: total: 406 ms Wall time: 411 ms CPU times: total: 2.16 s Wall time: 2.18 s
In [40]:
@jit(int32(complex64, int32))
def mandelbrot_types(c,maxiter):
r = c.real
i = c.imag
for n in range(maxiter):
r2 = r*r
i2 = i*i
if r2 + i2 > 4.0:
return n
i = 2*r*i+c.imag
r = r2-i2+c.real
return maxiter
@guvectorize([(complex64[:], int32, int32[:])], '(n),()->(n)', target='parallel')
def mandelbrot_numpy(c, maxiter, output):
for i in range(c.shape[0]):
output[i] = mandelbrot_types(c[i], maxiter)
def mandelbrot_set2(xmin,xmax,ymin,ymax,width,height,maxiter):
r1 = np.linspace(xmin, xmax, width, dtype=np.float32)
r2 = np.linspace(ymin, ymax, height, dtype=np.float32)
c = r1 + r2[:,None]*1j
return mandelbrot_numpy(c,maxiter)
%time plt.subplot(1, 2, 1).imshow(mandelbrot_set2(*male_hodnoty))
%time plt.subplot(1, 2, 2).imshow(mandelbrot_set2(*velke_hodnoty))
CPU times: total: 156 ms Wall time: 22 ms CPU times: total: 1.91 s Wall time: 179 ms
Out[40]:
<matplotlib.image.AxesImage at 0x20b79980950>
In [41]:
%%time
import numpy as np
from numba import cuda
from numba import *
from matplotlib import pyplot as plt
%matplotlib inline
plt.rcParams['figure.figsize'] = [15, 5]
plt.rcParams['figure.dpi'] = 100
@jit
def mandel(real, imag, max_iters):
cr = real
ci = imag
for n in range(max_iters):
real2 = real*real
imag2 = imag*imag
if real2 + imag2 > 4.0:
return n
imag = 2*real*imag+ci
real = real2-imag2+cr
return max_iters
mandel_gpu = cuda.jit(uint32(float32, float32, uint32), device=True)(mandel)
@cuda.jit((float32, float32, float32, float32, uint32[:,:], uint32))
def mandel_kernel(min_x, max_x, min_y, max_y, image, iters):
height = image.shape[0]
width = image.shape[1]
pixel_size_x = (max_x - min_x) / width
pixel_size_y = (max_y - min_y) / height
startX, startY = cuda.grid(2)
gridX = cuda.gridDim.x * cuda.blockDim.x;
gridY = cuda.gridDim.y * cuda.blockDim.y;
for x in range(startX, width, gridX):
real = min_x + x * pixel_size_x
for y in range(startY, height, gridY):
imag = min_y + y * pixel_size_y
image[y][x] = mandel_gpu(real, imag, iters)
gimage = np.zeros((1000, 1000), dtype = np.uint32)
blockdim = (32, 8)
griddim = (32,16)
d_image = cuda.to_device(gimage)
mandel_kernel[griddim, blockdim](-2.0, 1.0, -1.0, 1.0, d_image, 20)
d_image.copy_to_host(gimage)
plt.subplot(1, 2, 1).imshow(gimage)
d_image = cuda.to_device(gimage)
mandel_kernel[griddim, blockdim](-0.74877,-0.74872,0.06505,0.06510, d_image, 2048)
d_image.copy_to_host(gimage)
plt.subplot(1, 2, 2).imshow(gimage)
--------------------------------------------------------------------------- CudaSupportError Traceback (most recent call last) File <timed exec>:23 File ~\AppData\Roaming\Python\Python311\site-packages\numba\cuda\decorators.py:133, in jit.<locals>._jit(func) 131 from numba.core import typeinfer 132 with typeinfer.register_dispatcher(disp): --> 133 disp.compile_device(argtypes, restype) 134 else: 135 disp.compile(argtypes) File ~\AppData\Roaming\Python\Python311\site-packages\numba\cuda\dispatcher.py:882, in CUDADispatcher.compile_device(self, args, return_type) 875 fastmath = self.targetoptions.get('fastmath') 877 nvvm_options = { 878 'opt': 3 if self.targetoptions.get('opt') else 0, 879 'fastmath': fastmath 880 } --> 882 cc = get_current_device().compute_capability 883 cres = compile_cuda(self.py_func, return_type, args, 884 debug=debug, 885 lineinfo=lineinfo, (...) 888 nvvm_options=nvvm_options, 889 cc=cc) 890 self.overloads[args] = cres File ~\AppData\Roaming\Python\Python311\site-packages\numba\cuda\api.py:443, in get_current_device() 441 def get_current_device(): 442 "Get current device associated with the current thread" --> 443 return current_context().device File ~\AppData\Roaming\Python\Python311\site-packages\numba\cuda\cudadrv\devices.py:220, in get_context(devnum) 216 def get_context(devnum=None): 217 """Get the current device or use a device by device number, and 218 return the CUDA context. 219 """ --> 220 return _runtime.get_or_create_context(devnum) File ~\AppData\Roaming\Python\Python311\site-packages\numba\cuda\cudadrv\devices.py:138, in _Runtime.get_or_create_context(self, devnum) 136 attached_ctx = self._get_attached_context() 137 if attached_ctx is None: --> 138 return self._get_or_create_context_uncached(devnum) 139 else: 140 return attached_ctx File ~\AppData\Roaming\Python\Python311\site-packages\numba\cuda\cudadrv\devices.py:153, in _Runtime._get_or_create_context_uncached(self, devnum) 147 """See also ``get_or_create_context(devnum)``. 148 This version does not read the cache. 149 """ 150 with self._lock: 151 # Try to get the active context in the CUDA stack or 152 # activate GPU-0 with the primary context --> 153 with driver.get_active_context() as ac: 154 if not ac: 155 return self._activate_context_for(0) File ~\AppData\Roaming\Python\Python311\site-packages\numba\cuda\cudadrv\driver.py:499, in _ActiveContext.__enter__(self) 497 else: 498 hctx = drvapi.cu_context(0) --> 499 driver.cuCtxGetCurrent(byref(hctx)) 500 hctx = hctx if hctx.value else None 502 if hctx is None: File ~\AppData\Roaming\Python\Python311\site-packages\numba\cuda\cudadrv\driver.py:295, in Driver.__getattr__(self, fname) 292 self.ensure_initialized() 294 if self.initialization_error is not None: --> 295 raise CudaSupportError("Error at driver init: \n%s:" % 296 self.initialization_error) 298 if USE_NV_BINDING: 299 return self._cuda_python_wrap_fn(fname) CudaSupportError: Error at driver init: CUDA driver library cannot be found. If you are sure that a CUDA driver is installed, try setting environment variable NUMBA_CUDA_DRIVER with the file path of the CUDA driver shared library. :
In [ ]: