Introduction to `Operator` `apply` and `arguments`

This tutorial describes two fundamental user APIs:

Operator.apply
Operator.arguments

We will use a trivial Operator that, at each time step, increments by 1 all points in the physical domain.



In [1]:

    
from devito import Grid, TimeFunction, Eq, Operator

grid = Grid(shape=(4, 4))
u = TimeFunction(name='u', grid=grid, save=3)
op = Operator(Eq(u.forward, u + 1))

To run op, we have to "apply" it.



In [2]:

    
#NBVAL_IGNORE_OUTPUT
summary = op.apply()









    



Operator `Kernel` run in 0.00 s

Under-the-hood, some code has been generated (print(op) to display the generated code), JIT-compiled, and executed. Since no additional arguments have been passed, op has used u as input. We can verify that the content of u.data is as expected



In [3]:

    
u.dimensions, u.shape









    Out[3]:





((time, x, y), (3, 4, 4))



In [4]:

    
u.data









    Out[4]:





Data([[[0., 0., 0., 0.],
       [0., 0., 0., 0.],
       [0., 0., 0., 0.],
       [0., 0., 0., 0.]],

      [[1., 1., 1., 1.],
       [1., 1., 1., 1.],
       [1., 1., 1., 1.],
       [1., 1., 1., 1.]],

      [[2., 2., 2., 2.],
       [2., 2., 2., 2.],
       [2., 2., 2., 2.],
       [2., 2., 2., 2.]]], dtype=float32)

In particular, we observe that:

u has size 3 along the time dimension, since it was built with save=3. Therefore op could only execute 2 timesteps, namely time=0 and time=1; given Eq(u.forward, u + 1), executing time=2 would cause out-of-bounds access errors. Devito figures this out automatically and sets appropriate minimum and maximum iteration points.
All 16 points in each timeslice of the 4x4 Grid have been computed.

To access all default arguments used by op without running the Operator, one can run



In [5]:

    
#NBVAL_IGNORE_OUTPUT
op.arguments()









    Out[5]:





{'u': <cparam 'P' (0x7fb0d01d45a8)>,
 'time_m': 0,
 'time_size': 3,
 'time_M': 1,
 'x_m': 0,
 'x_size': 4,
 'x_M': 3,
 'y_m': 0,
 'y_size': 4,
 'y_M': 3,
 'timers': <cparam 'P' (0x7fb0d0550918)>}

'u' stores a pointer to the allocated data; 'timers' stores a pointer to a data structure used for C-level performance profiling.

One may want to replace some of these default arguments. For example, we could increase the minimum iteration point along the spatial Dimensions x and y, and execute only the very first timestep:



In [6]:

    
#NBVAL_IGNORE_OUTPUT
u.data[:] = 0.  # Explicit reset to initial value
summary = op.apply(x_m=2, y_m=2, time_M=0)









    



Operator `Kernel` run in 0.00 s

We look again at the computed data to convince ourselves that everything went as intended to go



In [7]:

    
u.data









    Out[7]:





Data([[[0., 0., 0., 0.],
       [0., 0., 0., 0.],
       [0., 0., 0., 0.],
       [0., 0., 0., 0.]],

      [[0., 0., 0., 0.],
       [0., 0., 0., 0.],
       [0., 0., 1., 1.],
       [0., 0., 1., 1.]],

      [[0., 0., 0., 0.],
       [0., 0., 0., 0.],
       [0., 0., 0., 0.],
       [0., 0., 0., 0.]]], dtype=float32)

Given a generic Dimension d, the naming convention is such that:

d_m is the minimum iteration point
d_M is the maximum iteration point

Hence, op.apply(..., d_m=4, d_M=7, ...) will run op in the compact interval [4, 7] along d. For historical reasons, d=... aliases to d_M=...; in many Devito examples it happens to see op.apply(..., time=10, ...) -- this is just equivalent to op.apply(..., time_M=10, ...).

If we try to specify an invalid iteration extreme, Devito will raise an exception.



In [8]:

    
from devito.exceptions import InvalidArgument
try:
    op.apply(time_M=2)
except InvalidArgument as e:
    print(e)









    



OOB detected due to time_M=2

The same Operator can be applied to a different TimeFunction. For example:



In [9]:

    
#NBVAL_IGNORE_OUTPUT
u2 = TimeFunction(name='u', grid=grid, save=5)
summary = op.apply(u=u2)









    



Operator `Kernel` run in 0.00 s



In [10]:

    
u2.data









    Out[10]:





Data([[[0., 0., 0., 0.],
       [0., 0., 0., 0.],
       [0., 0., 0., 0.],
       [0., 0., 0., 0.]],

      [[1., 1., 1., 1.],
       [1., 1., 1., 1.],
       [1., 1., 1., 1.],
       [1., 1., 1., 1.]],

      [[2., 2., 2., 2.],
       [2., 2., 2., 2.],
       [2., 2., 2., 2.],
       [2., 2., 2., 2.]],

      [[3., 3., 3., 3.],
       [3., 3., 3., 3.],
       [3., 3., 3., 3.],
       [3., 3., 3., 3.]],

      [[4., 4., 4., 4.],
       [4., 4., 4., 4.],
       [4., 4., 4., 4.],
       [4., 4., 4., 4.]]], dtype=float32)

Note that this was the third call to op.apply, but code generation and JIT-compilation only occurred upon the very first call.

There is one relevant case in which the maximum iteration point along the time dimension must be specified -- whenever save is unset, as in such a case the Operator wouldn't know for how many iterations to run.



In [11]:

    
v = TimeFunction(name='v', grid=grid)
op2 = Operator(Eq(v.forward, v + 1))
try:
    op2.apply()
except ValueError as e:
    print(e)









    



No value found for parameter time_M



In [12]:

    
#NBVAL_IGNORE_OUTPUT
summary = op2.apply(time_M=4)









    



Operator `Kernel` run in 0.00 s



In [13]:

    
v.data









    Out[13]:





Data([[[4., 4., 4., 4.],
       [4., 4., 4., 4.],
       [4., 4., 4., 4.],
       [4., 4., 4., 4.]],

      [[5., 5., 5., 5.],
       [5., 5., 5., 5.],
       [5., 5., 5., 5.],
       [5., 5., 5., 5.]]], dtype=float32)

The summary variable can be inspected to retrieve performance metrics.



In [14]:

    
#NBVAL_IGNORE_OUTPUT
summary









    Out[14]:





PerformanceSummary([('section0',
                     PerfEntry(time=3e-06, gflopss=0.0, gpointss=0.0, oi=0.0, ops=0, itershapes=[]))])

We observe that basically all entries except for the execution time are fixed at 0. This is because by default Devito avoids to compute performance metrics, to minimize the processing time before returning control to the user (in complex Operators, the processing time to retrieve, for instance, the operation count or the memory footprint could be significant). To compute all performance metrics, a user could either export the environment variable DEVITO_PROFILING to 'advanced' or change the profiling level programmatically before the Operator is constructed



In [15]:

    
#NBVAL_IGNORE_OUTPUT
from devito import configuration
configuration['profiling'] = 'advanced'

op = Operator(Eq(u.forward, u*u + 1.))
op.apply()









    



Operator `Kernel` run in 0.00 s






    Out[15]:





PerformanceSummary([('section0',
                     PerfEntry(time=3e-06, gflopss=0.021333333333333333, gpointss=0.010666666666666666, oi=0.16666666666666666, ops=2, itershapes=[(2, 4, 4)]))])

A PerformanceSummary will contain as many entries as "sections" in the generated code. Currently, there is no way to automatically tie a compiler-generated section to the user-provided Eqs (in general, there can be more than one Eq in a section). The only option is to look at the generated code and search for bodies of code wrapped within C comments such as

/* Begin section0 */
<code>
/* End section0 \*/"

For example



In [16]:

    
# Uncomment me and search for /* Begin section0 */ ... /* End section0 */
# print(op)

In the PerformanceSummary, associated to section0 is a PerfEntry, whose entries represent:

time: The time, in seconds, to execute the section.
gflopss: Performance of the section in Gigaflops per second.
gpointss: Performance of the section in Gigapoints per second.
oi: Operational intensity.
ops: Floating point operations at each (innermost loop) iteration.
itershape: The shape of the iteration space.

Introduction to Operator apply and arguments

Introduction to `Operator` `apply` and `arguments`