From cc90003e0bd9a1c318fb72617da0d0718326dae1 Mon Sep 17 00:00:00 2001 From: Yong-Cheol Cho Date: Mon, 21 Aug 2023 12:25:33 -0500 Subject: [PATCH] Changed the script to perform comparison between different versions --- .../ellipsoidal_density_projection.py | 8 +- anisoap/utils/code_timer.py | 38 +- anisoap/utils/cyclic_list.py | 15 +- anisoap/utils/equistore_utils.py | 4 +- tests/ex_input.py | 337 +++--- tests/time_results/comp_result_v0,1.csv | 1044 +++++++++++++++++ 6 files changed, 1291 insertions(+), 155 deletions(-) create mode 100644 tests/time_results/comp_result_v0,1.csv diff --git a/anisoap/representations/ellipsoidal_density_projection.py b/anisoap/representations/ellipsoidal_density_projection.py index cb2497f..6e3a646 100644 --- a/anisoap/representations/ellipsoidal_density_projection.py +++ b/anisoap/representations/ellipsoidal_density_projection.py @@ -39,7 +39,7 @@ def pairwise_ellip_expansion( radial_basis, *, timer: SimpleTimer = None, - moment_fn_lang: str = "rust" + version: int = None ): """ Function to compute the pairwise expansion by combining the moments and the spherical to Cartesian @@ -149,7 +149,7 @@ def pairwise_ellip_expansion( else: internal_timer3 = None - if moment_fn_lang == "rust": + if version is None or version >= 1: # NOTE: This line was replaced with Rust implementation. moments = compute_moments(precision, center, lmax + np.max(num_ns)) # Mark the timers for consistency @@ -475,7 +475,7 @@ def __init__( self.rotation_key = rotation_key - def transform(self, frames, show_progress=False, *, timer: SimpleTimer = None, moment_fn_lang: str = "rust"): # frames: List[Atoms] + def transform(self, frames, show_progress=False, *, version: int = None, timer: SimpleTimer = None): # frames: List[Atoms] """ Computes the features and (if compute_gradients == True) gradients for all the provided frames. The features and gradients are stored in @@ -585,7 +585,7 @@ def transform(self, frames, show_progress=False, *, timer: SimpleTimer = None, m self.sph_to_cart, self.radial_basis, timer=internal_timer, - moment_fn_lang=moment_fn_lang + version=version ) if timer is not None: timer.mark("5-8. pairwise ellip expansion") diff --git a/anisoap/utils/code_timer.py b/anisoap/utils/code_timer.py index bcfcf87..9aed1db 100644 --- a/anisoap/utils/code_timer.py +++ b/anisoap/utils/code_timer.py @@ -1,9 +1,20 @@ import time from collections import defaultdict from typing import Callable +from enum import Enum + + +class SimpleTimerCollectMode(Enum): + AVG = 1, + SUM = 2, + MIN = 3, + MAX = 4, + MED = 5, class SimpleTimer: - default_coll_mode = "avg" + # NOTE: Change this collect_mode default argument to change all measuring across the files + # except the one specified. + default_coll_mode = SimpleTimerCollectMode.AVG def __init__(self): self._internal_time = time.perf_counter() @@ -55,12 +66,10 @@ def collect_trials(self, collect_fn: Callable[[list[float]], float]) -> dict[str coll_dict[key] = collect_fn(val) return coll_dict - # NOTE: Change this collect_mode default argument to change all measuring across the files - # except the one specified. def collect_and_append( self, other: 'SimpleTimer', - collect_mode: str | Callable[[list[float]], float] = None + collect_mode: SimpleTimerCollectMode | Callable[[list[float]], float] = None ): """ Takes another SimpleTimer class as argument and calls average_trials @@ -71,14 +80,16 @@ def collect_and_append( if collect_mode == None: collect_mode = SimpleTimer.default_coll_mode - if collect_mode == "avg": + if collect_mode == SimpleTimerCollectMode.AVG: coll_dict = other.collect_trials(lambda x: sum(x) / len(x)) - elif collect_mode == "sum": + elif collect_mode == SimpleTimerCollectMode.SUM: coll_dict = other.collect_trials(lambda x: sum(x)) - elif collect_mode == "max": + elif collect_mode == SimpleTimerCollectMode.MAX: coll_dict = other.collect_trials(lambda x: max(x)) - elif collect_mode == "min": + elif collect_mode == SimpleTimerCollectMode.MIN: coll_dict = other.collect_trials(lambda x: min(x)) + elif collect_mode == SimpleTimerCollectMode.MED: + coll_dict = other.collect_trials(lambda x: SimpleTimer._median(x)) else: coll_dict = other.collect_trials(lambda x: collect_mode(x)) for key, val in coll_dict.items(): @@ -106,3 +117,14 @@ def _largest_leading_num(text: str) -> float: break return float(int_str) if len(int_str) > 0 else float("inf") + + @staticmethod + def _median(x: list[float]): + sorted_x = sorted(x) + len_x = len(x) + half_index = len_x // 2 # floor + + if len_x % 2 == 0: # even number of elements: + return (sorted_x[half_index - 1] + sorted_x[half_index]) / 2.0 + else: + return sorted_x[half_index] diff --git a/anisoap/utils/cyclic_list.py b/anisoap/utils/cyclic_list.py index 04cc8f2..ad84e11 100644 --- a/anisoap/utils/cyclic_list.py +++ b/anisoap/utils/cyclic_list.py @@ -1,3 +1,5 @@ +from typing import Any + class CGRCacheList: """ This is a simple class that only exists to be used as a "private" cache @@ -11,14 +13,12 @@ def __init__(self, size: int): A constructor that makes an empty cyclic list. """ self._size = size - self._next_ins_index = 0 - self._keys = [] - self._cyclic_list = [None] * size # will be a list of tuples (key, value) + self.clear_cache() def keys(self) -> list: return self._keys - def insert(self, key, value): + def insert(self, key, value) -> None: if key not in self.keys(): # Store (key, value) pair in cyclic list self._cyclic_list[self._next_ins_index] = (key, value) @@ -32,8 +32,13 @@ def insert(self, key, value): # Update the index at which the next element should be inserted. self._next_ins_index = (self._next_ins_index + 1) % self._size - def get_val(self, key): + def get_val(self, key) -> Any: for element in self._cyclic_list: if element is not None and key == element[0]: return element[1] raise IndexError(f"The specified key {key} is not in the list. Current keys in the list are: {self._keys}") + + def clear_cache(self) -> None: + self._next_ins_index = 0 + self._keys = [] + self._cyclic_list = [None] * self._size # will be a list of tuples (key, value) \ No newline at end of file diff --git a/anisoap/utils/equistore_utils.py b/anisoap/utils/equistore_utils.py index 05ed9a4..b39dcab 100644 --- a/anisoap/utils/equistore_utils.py +++ b/anisoap/utils/equistore_utils.py @@ -11,7 +11,7 @@ from .cyclic_list import CGRCacheList class ClebschGordanReal: - def __init__(self, l_max, *, timer: SimpleTimer = None, cache_list: CGRCacheList = None): + def __init__(self, l_max, *, version: int = None, cache_list: CGRCacheList = None, timer: SimpleTimer = None): if timer is not None: timer.mark_start() self._l_max = l_max @@ -29,7 +29,7 @@ def __init__(self, l_max, *, timer: SimpleTimer = None, cache_list: CGRCacheList if timer is not None: timer.mark("8-2. compute r2c and c2r") - if cache_list is not None: + if version >= 1 and cache_list is not None: if l_max in cache_list.keys(): self._cg = cache_list.get_val(l_max) if timer is not None: diff --git a/tests/ex_input.py b/tests/ex_input.py index 30673e6..01a7d07 100644 --- a/tests/ex_input.py +++ b/tests/ex_input.py @@ -1,97 +1,62 @@ import pathlib import time -from anisoap.utils import SimpleTimer +from anisoap.utils.code_timer import SimpleTimer from anisoap.utils.cyclic_list import CGRCacheList +from io import TextIOWrapper +from typing import Any +import gc # for manual garbage collection + +_MOST_RECENT_VER = 1 # ------------------------ Configurations Explanation ------------------------ # """ -_file_name: str - _file_name is used to name the actual file name with - - if _write_mode == "time" - actual_file_name = _file_name + "_" + SimpleTimer.default_coll_mode - elif _write_mode == "result" - actual_file_name = _file_name + "_" + _moment_fn_lang - - The result will be saved to {proj_root}/tests/time_results/.csv - -_write_mode: str ("time", "result") - _write_mode = "time" records the code execution time from SimpleTimer. - _write_mode = "result" records the resulting 2D matrix with each number - represented as signed, 10 decimal digit floats - -SimpleTimer.default_coll_mode: str ("avg", "sum", "min", "max) - or lambda x: ( ... ) with x as a list of floats - When certain bits of code is executed multiple times (due to loops), the - timer records time for each iterations and collects the times into a single - float. Available modes: "avg", "sum", "min", "max", or any lambda functions - of form lambda x: ( ... ) in which x is a list of floats. - This is a static variable inside the SimpleTimer class, hence this notation. - -_coll_mode_name: str - This is used to generate actual save file name when SimpleTimer.default_coll_mode - is a lambda function. Please use a short but descriptive name for your lambda - function. It can be None if SimpleTimer.default_coll_mode was one of the strings. - -_moment_fn_lang: str ("rust" or "python") - Selects a language for computing moments. - "rust" calls compute_moments defined in Rust FFI (see inside anisoap_rust_lib) - "python" calls compute_moments_inefficient_implementation in moments_generator.py - -_test_files: dict[str, int] - A dictionary that determines how many iterations each test files will run. +_comp_version: list[int] + Compares the runtime / SSE for all versions specified. Version 0 (Python + implementation without caching) will always be added as the baseline. + + Simplified changelogs: + Version 0: Initial implementation. Guaranteed to be correct, but it is slow. + Version 1: Ported computation of moments to Rust + CGR matrix is cached for + each l_max. + +_cache_size: int + Determines the cache size for CGRCacheList. It will only be used for version >= 1. + The cache will be reset and recomputed when the version changes. + +_test_files: list[str] + A list that determines which .xyz files to test for. The files must be stored at {proj_root}/benchmarks/two_particle_gb/ directory with .xyz extensions. - - However, when _write_mode == "time", note that the maximum number of single - pass supported is 16. (This is due to limitation of my Excel file used to - analyze the results). Therefore, sum of all integers (next to file names) - must be less than or equal to 16 if _write_mode == "time"; otherwise, it will - not work. - -_cache_list: CGRCacheList(cache_size: int) - A cyclic list used to cache the pre-compted CG matrices for given l_max values. - You can set it to None to disable caching. """ # ------------------------------ Configurations ------------------------------ # # See above for explanations for each variables. -_file_name = "res_cmp" -_write_mode = "result" -SimpleTimer.default_coll_mode = "avg" -_coll_mode_name = None -_moment_fn_lang = "rust" -_test_files = { # file name: repeat number - "ellipsoid_frames": 4, - # "both_rotating_in_z": 1, # Results in key error in frames.arrays['c_q'] - # "face_to_face": 1, - # "random_rotations": 1, - # "side_to_face": 1, - # "side_to_side": 1, - # "single_rotating_in_y": 1, - # "single_rotating_in_z": 1 - } -_cache_list = CGRCacheList(5) - -# --------------------------- Configuration Checks --------------------------- # -if type(_file_name) != str: - raise TypeError("Type of _file_name must be a string") - -if _write_mode not in ["time", "result"]: - raise ValueError("_write_mode currently supports only 'time' or 'result' modes") - -if SimpleTimer.default_coll_mode not in ["avg", "sum", "min", "max"]: - if not callable(SimpleTimer.default_coll_mode): - raise ValueError("SimpleTimer.default_coll_mode has to be of specific types. Please read the hints above") +_comp_version = [_MOST_RECENT_VER] +_cache_size = 5 +_test_files = [ # file name: repeat number + "ellipsoid_frames" + # "both_rotating_in_z", # Results in key error in frames.arrays['c_q'] + # "face_to_face", + # "random_rotations", + # "side_to_face", + # "side_to_side", + # "single_rotating_in_y", + # "single_rotating_in_z" + ] -if _moment_fn_lang not in ["rust", "python"]: - raise ValueError("_moment_fn_lang currently supports only rust or python implementations") +# ------------------------------ Hyperparameter ------------------------------ # +# Performs one iteration for each parameter sets per file. +# lmax σ r_cut, σ1, σ2, σ3 +_params = [[10, 2.0, 5.0, 3.0, 2.0, 1.0], + [10, 3.0, 4.0, 3.0, 2.0, 1.0], + [ 7, 4.0, 6.0, 3.0, 2.0, 1.0], + [ 5, 3.0, 5.0, 5.0, 3.0, 1.0], + [10, 2.0, 5.0, 3.0, 3.0, 0.8]] -if _write_mode == "time" and sum([v for (_, v) in _test_files.items()]) > 16: - raise ValueError("Maximum total iterations supported in 'time' mode is 16.") +# --------------------------- Configuration Checks --------------------------- # +# None +if 0 not in _comp_version: + _comp_version.insert(0, 0) -if type(_cache_list) != CGRCacheList and _cache_list is not None: - raise TypeError("_cache_list must be CGRCacheList (to enable caching) or None (to disable caching)") - # -------------------------------- Main Codes -------------------------------- # start_time = time.perf_counter() from ase.io import read @@ -103,13 +68,22 @@ import_duration = time.perf_counter() - start_time del start_time -def single_pass(file_path: str, *, timer: SimpleTimer = None): +def single_pass( + file_path: str, + params: list[float], *, + version: int = _MOST_RECENT_VER, + cache_list: CGRCacheList = None, + timer: SimpleTimer = None + ) -> (list[list[float]], list[Any]): # returns (result, extra_info) if timer is not None: timer.mark_start() - a1 = 3.0 - a3 = 0.8 - l_max = 10 # ?? + # parameter decomposition + l_max = params[0] + sigma = params[1] + r_cut = params[2] + a1, a2, a3 = params[3:] + if timer is not None: timer.mark("1. variable init") @@ -121,28 +95,29 @@ def single_pass(file_path: str, *, timer: SimpleTimer = None): radial_basis_name='gto', rotation_type='quaternion', rotation_key='c_q', - cutoff_radius=6.0, - radial_gaussian_width=6.0) + cutoff_radius=r_cut, + radial_gaussian_width=sigma) if timer is not None: timer.mark("3. constructing EDP") for frame in frames: frame.arrays["c_diameter[1]"] = a1 * np.ones(len(frame)) - frame.arrays["c_diameter[2]"] = a1 * np.ones(len(frame)) + frame.arrays["c_diameter[2]"] = a2 * np.ones(len(frame)) frame.arrays["c_diameter[3]"] = a3 * np.ones(len(frame)) frame.arrays["quaternions"] = frame.arrays['c_q'] + if timer is not None: timer.mark("4. constructing frames") # timer works internally inside "transform" if timer is not None: internal_timer = SimpleTimer() - rep_raw = representation.transform(frames, show_progress=False, timer=internal_timer, moment_fn_lang=_moment_fn_lang) + rep_raw = representation.transform(frames, show_progress=False, timer=internal_timer, version=version) timer.mark("5. repr transform") timer.collect_and_append(internal_timer) timer.mark_start() else: - rep_raw = representation.transform(frames, show_progress=False, moment_fn_lang=_moment_fn_lang) + rep_raw = representation.transform(frames, show_progress=False, version=version) rep = equistore.operations.mean_over_samples(rep_raw, sample_names="center") if timer is not None: @@ -154,12 +129,12 @@ def single_pass(file_path: str, *, timer: SimpleTimer = None): internal_timer.clear_time() if timer is not None: - my_cg = ClebschGordanReal(l_max, timer=internal_timer, cache_list=_cache_list) + my_cg = ClebschGordanReal(l_max, version=version, cache_list=cache_list, timer=internal_timer) timer.mark("8. constructing CGR") timer.collect_and_append(internal_timer) timer.mark_start() else: - my_cg = ClebschGordanReal(l_max, cache_list=_cache_list) + my_cg = ClebschGordanReal(l_max, version=version, cache_list=cache_list) anisoap_nu2 = cg_combine( anisoap_nu1, @@ -186,54 +161,144 @@ def single_pass(file_path: str, *, timer: SimpleTimer = None): if timer is not None: timer.mark("12. scaler transform") - return x + # NOTE: frame.arrays["quaternions"] seems to output a matrix with two quaternions + # each one represented as a row of the matrix. It also seems that two quaternions + # are identical, so it is set to return only the first row for now. + #! Change the return statement if that changes + return x, [frame.arrays["quaternions"][0]] -if __name__ == "__main__": - if _write_mode == "result": - actual_file_name = _file_name + "_" + _moment_fn_lang - elif _write_mode == "time": - if type(SimpleTimer.default_coll_mode) == str: - actual_file_name = _file_name + "_" + SimpleTimer.default_coll_mode - else: - actual_file_name = _file_name + "_" + _coll_mode_name - else: - actual_file_name = "unknown_mode" +def total_error(result1: list[list[float]], result2: list[list[float]]) -> float: + if len(result1) != len(result2): + raise ValueError("Two matrices must have same number of rows.") + + sse = 0.0 + for i in range(len(result1)): + if len(result1[i]) != len(result2[i]): + raise ValueError(f"Two matrices have different number of columns at row {i}") + + for j in range(len(result1[i])): + sse = (result1[i][j] - result2[i][j]) ** 2 + return sse + +def get_key(ver: int, param_index: int, file: str) -> str: + """ + Get the key of the dictionary, given version, parameter index, and the file name. + Format is: v{ver}_p{param_index}_{file} + """ + return f"v{ver}_p{param_index}_{file}" + +def get_comp_key(key: str) -> str: + """ + Get the key of the equivalent parameter set and file of the original implementation (v0), + given the current key. + """ + return "v0_" + "_".join(key.split("_")[1:]) # replace v"n" with v0 for any number n. + +def keys_in_order() -> list[str]: + """ + Returns a list of all tested combinations, in order. + """ + all_tests_list = [] + for ver in _comp_version: + for file_name in _test_files: + for param_index in range(len(_params)): + all_tests_list.append(get_key(ver, param_index + 1, file_name)) + return all_tests_list + +def write_param_summary(file: TextIOWrapper, extra_info: list[Any]): + file.write("----------------- Parameter Summary -----------------\n") + file.write("Parameter Set,l_max,sigma,r_cut,sigma_1,sigma_2,sigma_3,Rotation Quaternion\n") + quat_vec = ["i", "j", "k"] + for param_index, param in enumerate(_params): + # l_max (param[0]) is an integer, so it will be treated differently from the rest. + other_params = ",".join([f"{val:.01f}" for val in param[1:]]) + file.write(f"p{param_index + 1},{param[0]},{other_params},") + + # NOTE: Since the rotation quaternion does not depend on the file or version + # (considering the constructor of EDP, which does not depend on either), + # we can use v0 and any test_file's (in this case, index 0) rotation quaternion. + quat_key = get_key(0, param_index + 1, _test_files[0]) + quat = extra_info.get(quat_key)[0] + file.write(f"{quat[0]:.4f}") + for i, suffix in enumerate(quat_vec): + if quat[i] < 0: + file.write(" - ") + else: + file.write(" + ") + + file.write(f"{abs(quat[i + 1]):.4f}{suffix}") + file.write("\n") + +def write_result_summary(file: TextIOWrapper, timer: SimpleTimer, err_dict: dict[str, float]): + file.write("------------------ Overall Summary ------------------\n") + all_tests_list = keys_in_order() + file.write("Name,Runtime (sec),Runtime Change (from v0),SSE (from v0)\n") + timer_dict = timer.sorted_dict() + + for key in all_tests_list: + curr_runtime = timer_dict.get(key)[0] + original_runtime = timer_dict.get(get_comp_key(key))[0] + percent_diff = (curr_runtime - original_runtime) / original_runtime * 100 + file.write(f"{key},{curr_runtime:.4f},{percent_diff:.2f}%,{err_dict.get(key):.4e}\n") + + file.write("Note: Negative runtime change means computation was faster compared to the original implementation.\n") + +def write_raw_data(file: TextIOWrapper, raw_data: dict[str, list[list[float]]]): + file.write("----------------- Raw Data (Result) -----------------\n") + all_tests_list = keys_in_order() + for key in all_tests_list: + file.write(f"Output of {key}\n") + result_mat = raw_data.get(key) + for row in result_mat: + file.write(",".join({f"{val:.10f}" for val in row}) + "\n") + file.write("\n") + + +if __name__ == "__main__": + actual_file_name = "comp_result_v" + ",".join([str(ver) for ver in _comp_version]) write_name = str(pathlib.Path(__file__).parent.absolute()) + "/time_results/" + actual_file_name + ".csv" - out_file = open(write_name, "w") - if _write_mode == "result": - out_file.write("Final results\n") - else: - out_file.write("initial import\n") - out_file.write(str(import_duration) + "\n") - - if _write_mode == "time": - flatten_name = [] - for name, iter_val in _test_files.items(): - for iter_num in range(iter_val): - flatten_name.append(name + ": iter" + str(iter_num + 1)) - out_file.write("stage," + ",".join(flatten_name) + "\n") + raw_results = dict() + extra_infos = dict() + errors = dict() - code_timer = SimpleTimer() if _write_mode == "time" else None - for test_file, rep_num in _test_files.items(): - file_path = str(pathlib.Path(__file__).parent.parent.absolute()) + "/benchmarks/two_particle_gb/" + test_file + ".xyz" - for rep_index in range(rep_num): - print(f"Computation for {test_file}, iteration {rep_index + 1} has started") - - if _write_mode == "result": - out_file.write(f"{test_file}: iter {rep_index + 1}\n") - - comp_result = single_pass(file_path, timer=code_timer) + with open(write_name, "w") as out_file: + out_file.write(f"Comparison of versions [{' '.join([str(ver) for ver in _comp_version])}]\n\n") + + out_file.write("---------------- Initialization Info ----------------\n") + out_file.write(f"initial_import time (sec), {import_duration: .04f}\n\n") - if _write_mode == "result": - for row in comp_result: - out_file.write(",".join([f"{val:0.10f}" for val in row])) - out_file.write("\n") - out_file.write("\n") + single_pass_timer = SimpleTimer() + internal_timer = None # disable internal timer - print(f"Computation for {test_file}, iteration {rep_index + 1} has successfully finished") - - if _write_mode == "time": - for key, val in code_timer.sorted_dict().items(): - out_file.write(key + "," + ",".join([str(v) for v in val]) + "\n") - out_file.close() + for ver in _comp_version: + matrix_cache = CGRCacheList(_cache_size) + for test_file in _test_files: + file_path = str(pathlib.Path(__file__).parent.parent.absolute()) + "/benchmarks/two_particle_gb/" + test_file + ".xyz" + + for param_index, param in enumerate(_params): + iter_str = get_key(ver, param_index + 1, test_file) + print(f"Computation for {iter_str} has started") + + single_pass_timer.mark_start() + comp_result, ex_info = single_pass(file_path, param, version=ver, cache_list=matrix_cache,timer=internal_timer) + single_pass_timer.mark(iter_str) + + raw_results.update({iter_str: comp_result}) + extra_infos.update({iter_str: ex_info}) + + # Get SSE based on the original implementation (v0) of equivalent parameter set and the test file + errors.update({iter_str: total_error(raw_results.get(get_comp_key(iter_str)), comp_result)}) + + print(f"Computation for {iter_str} has successfully finished") + + # Make sure garbage collection does not interfere with the next iteration (version change). + matrix_cache.clear_cache() + del matrix_cache + gc.collect() + + write_param_summary(out_file, extra_infos) + out_file.write("\n") + write_result_summary(out_file, single_pass_timer, errors) + out_file.write("\n") + write_raw_data(out_file, raw_results) diff --git a/tests/time_results/comp_result_v0,1.csv b/tests/time_results/comp_result_v0,1.csv new file mode 100644 index 0000000..1da8287 --- /dev/null +++ b/tests/time_results/comp_result_v0,1.csv @@ -0,0 +1,1044 @@ +Comparison of versions [0 1] + +---------------- Initialization Info ---------------- +initial_import time (sec), 0.1592 + +----------------- Parameter Summary ----------------- +num,l_max,sigma,r_cut,sigma_1,sigma_2,sigma_3,rotation quaternion +p1,10,2.0,5.0,3.0,2.0,1.0,-0.7071 - 0.7071i + 0.0000j + 0.0000k +p2,10,3.0,4.0,3.0,2.0,1.0,-0.7071 - 0.7071i + 0.0000j + 0.0000k +p3,7,4.0,6.0,3.0,2.0,1.0,-0.7071 - 0.7071i + 0.0000j + 0.0000k +p4,5,3.0,5.0,5.0,3.0,1.0,-0.7071 - 0.7071i + 0.0000j + 0.0000k +p5,10,2.0,5.0,3.0,3.0,0.8,-0.7071 - 0.7071i + 0.0000j + 0.0000k + +------------------ Overall Summary ------------------ +Name,Runtime (sec),Runtime Change (from v0),SSE (from v0) +v0_p1_ellipsoid_frames,2.5840,0.00%,0.0000e+00 +v0_p2_ellipsoid_frames,1.2459,0.00%,0.0000e+00 +v0_p3_ellipsoid_frames,0.6636,0.00%,0.0000e+00 +v0_p4_ellipsoid_frames,0.3393,0.00%,0.0000e+00 +v0_p5_ellipsoid_frames,1.8488,0.00%,0.0000e+00 +v1_p1_ellipsoid_frames,1.9493,-24.57%,3.7286e-31 +v1_p2_ellipsoid_frames,0.1939,-84.44%,0.0000e+00 +v1_p3_ellipsoid_frames,0.4365,-34.22%,0.0000e+00 +v1_p4_ellipsoid_frames,0.2940,-13.36%,7.7037e-34 +v1_p5_ellipsoid_frames,0.1850,-89.99%,3.0815e-33 +Note: Negative runtime change means computation was faster compared to the original implementation. + +----------------- Raw Data (Result) ----------------- +Output of v0_p1_ellipsoid_frames 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