Genesis4 Benchmark on Perlmutter (NERSC)¶

HPC systems often have special commands to invoke MPI jobs. NERSC uses slurm, which provides srun in place of mpirun.

In [1]:

import os

from genesis.version4 import Genesis4

import os from genesis.version4 import Genesis4

The MPI_RUN class attribute needs to be replaced. For convenience, Genesis4 tries to detect NERSC:

In [2]:

Genesis4.MPI_RUN

Genesis4.MPI_RUN

Out[2]:

'"/Users/klauer/miniforge3/envs/lume-genesis/bin/mpirun" -n {nproc} {command_mpi}'

Additionally, the working directory must be on the scratch disk. This is automatically detected:

In [3]:

Genesis4.WORKDIR

Genesis4.WORKDIR

Create Genesis4 object:

In [4]:

G = Genesis4("data/basic4/cu_hxr.in")

G = Genesis4("data/basic4/cu_hxr.in")

Set up the benchmark

In [7]:

G.input.main.track.zstop = 40

G.input.main.track.zstop = 40

Run with MPI

In [8]:

%%time
G.verbose = False
G.nproc = 0
G.run()

%%time G.verbose = False G.nproc = 0 G.run()

CPU times: user 75.4 ms, sys: 42.2 ms, total: 118 ms
Wall time: 50 s

Out[8]:

Genesis4Output(
  run=RunInfo(
    error_reason='',
    run_script='/Users/klauer/miniforge3/envs/lume-genesis/bin/mpirun -n 0 /Users/klauer/miniforge3/envs/lume-genesis/bin/genesis4 -l hxr.lat genesis4...
    output_log='---------------------------------------------\nGENESIS - Version 4.6.6 has started...\nCompile info: Compiled by runner at 2024-01-11 ...
    start_time=1588289.1093675,
    end_time=1588338.959887,
    run_time=49.850519499974325,
  ),
  beam=OutputBeam(
    units={
      'alphax': pmd_unit('rad', 1, (0, 0, 0, 0, 0, 0, 0)),
      'alphay': pmd_unit('rad', 1, (0, 0, 0, 0, 0, 0, 0)),
      'betax': pmd_unit('m', 1, (1, 0, 0, 0, 0, 0, 0)),
      'betay': pmd_unit('m', 1, (1, 0, 0, 0, 0, 0, 0)),
      'bunchingphase': pmd_unit('rad', 1, (0, 0, 0, 0, 0, 0, 0)),
      'current': pmd_unit('A', 1, (0, 0, 0, 1, 0, 0, 0)),
      'efield': pmd_unit('eV/m', 1.602176634e-19, (1, 1, -2, 0, 0, 0, 0)),
      'emax': pmd_unit('m_ec^2', 8.187105776885341e-14, (2, 1, -2, 0, 0, 0, 0)),
      'emin': pmd_unit('m_ec^2', 8.187105776885341e-14, (2, 1, -2, 0, 0, 0, 0)),
      'emitx': pmd_unit('m', 1, (1, 0, 0, 0, 0, 0, 0)),
      'emity': pmd_unit('m', 1, (1, 0, 0, 0, 0, 0, 0)),
      'energy': pmd_unit('m_ec^2', 8.187105776885341e-14, (2, 1, -2, 0, 0, 0, 0)),
      'energyspread': pmd_unit('m_ec^2', 8.187105776885341e-14, (2, 1, -2, 0, 0, 0, 0)),
      'lsc_field': pmd_unit('eV/m', 1.602176634e-19, (1, 1, -2, 0, 0, 0, 0)),
      'pxmax': pmd_unit('rad', 1, (0, 0, 0, 0, 0, 0, 0)),
      'pxmin': pmd_unit('rad', 1, (0, 0, 0, 0, 0, 0, 0)),
      'pxposition': pmd_unit('rad', 1, (0, 0, 0, 0, 0, 0, 0)),
      'pymax': pmd_unit('rad', 1, (0, 0, 0, 0, 0, 0, 0)),
      'pymin': pmd_unit('rad', 1, (0, 0, 0, 0, 0, 0, 0)),
      'pyposition': pmd_unit('rad', 1, (0, 0, 0, 0, 0, 0, 0)),
      'ssc_field': pmd_unit('eV/m', 1.602176634e-19, (1, 1, -2, 0, 0, 0, 0)),
      'wakefield': pmd_unit('eV/m', 1.602176634e-19, (1, 1, -2, 0, 0, 0, 0)),
      'xmax': pmd_unit('m', 1, (1, 0, 0, 0, 0, 0, 0)),
      'xmin': pmd_unit('m', 1, (1, 0, 0, 0, 0, 0, 0)),
      'xposition': pmd_unit('m', 1, (1, 0, 0, 0, 0, 0, 0)),
      'xsize': pmd_unit('m', 1, (1, 0, 0, 0, 0, 0, 0)),
      'ymax': pmd_unit('m', 1, (1, 0, 0, 0, 0, 0, 0)),
      'ymin': pmd_unit('m', 1, (1, 0, 0, 0, 0, 0, 0)),
      'yposition': pmd_unit('m', 1, (1, 0, 0, 0, 0, 0, 0)),
      'ysize': pmd_unit('m', 1, (1, 0, 0, 0, 0, 0, 0)),
    },
    globals=OutputBeamGlobal(
      units={},
      energy=array([], dtype=float64),
      energyspread=array([], dtype=float64),
      xposition=array([], dtype=float64),
      yposition=array([], dtype=float64),
      xsize=array([], dtype=float64),
      ysize=array([], dtype=float64),
    ),
    bunching=array(shape=(1084, 552), dtype=float64),
    bunchingphase=array(shape=(1084, 552), dtype=float64),
    energy=array(shape=(1084, 552), dtype=float64),
    energyspread=array(shape=(1084, 552), dtype=float64),
    xsize=array(shape=(1084, 552), dtype=float64),
    ysize=array(shape=(1084, 552), dtype=float64),
    lsc_field=array(shape=(1084, 552), dtype=float64),
    ssc_field=array(shape=(1084, 552), dtype=float64),
    efield=array(shape=(1084, 552), dtype=float64),
    wakefield=array(shape=(1084, 552), dtype=float64),
    emin=array(shape=(1084, 552), dtype=float64),
    emax=array(shape=(1084, 552), dtype=float64),
    pxmin=array(shape=(1084, 552), dtype=float64),
    pxmax=array(shape=(1084, 552), dtype=float64),
    pymin=array(shape=(1084, 552), dtype=float64),
    pymax=array(shape=(1084, 552), dtype=float64),
    pxposition=array(shape=(1084, 552), dtype=float64),
    pyposition=array(shape=(1084, 552), dtype=float64),
    xmin=array(shape=(1084, 552), dtype=float64),
    xmax=array(shape=(1084, 552), dtype=float64),
    ymin=array(shape=(1084, 552), dtype=float64),
    ymax=array(shape=(1084, 552), dtype=float64),
    xposition=array(shape=(1084, 552), dtype=float64),
    yposition=array(shape=(1084, 552), dtype=float64),
    alphax=array(shape=(1, 552), dtype=float64),
    alphay=array(shape=(1, 552), dtype=float64),
    betax=array(shape=(1, 552), dtype=float64),
    betay=array(shape=(1, 552), dtype=float64),
    current=array(shape=(1084, 552), dtype=float64),
    emitx=array(shape=(1, 552), dtype=float64),
    emity=array(shape=(1, 552), dtype=float64),
    extra={},
  ),
  field_harmonics={
    '1': OutputField(
      units={
        'intensity_farfield': pmd_unit('W/rad^2', 1, (2, 1, -3, 0, 0, 0, 0)),
        'intensity_nearfield': pmd_unit('W/m^2', 1, (0, 1, -3, 0, 0, 0, 0)),
        'phase_farfield': pmd_unit('rad', 1, (0, 0, 0, 0, 0, 0, 0)),
        'phase_nearfield': pmd_unit('rad', 1, (0, 0, 0, 0, 0, 0, 0)),
        'power': pmd_unit('W', 1, (2, 1, -3, 0, 0, 0, 0)),
        'xdivergence': pmd_unit('rad', 1, (0, 0, 0, 0, 0, 0, 0)),
        'xpointing': pmd_unit('rad', 1, (0, 0, 0, 0, 0, 0, 0)),
        'xposition': pmd_unit('m', 1, (1, 0, 0, 0, 0, 0, 0)),
        'xsize': pmd_unit('m', 1, (1, 0, 0, 0, 0, 0, 0)),
        'ydivergence': pmd_unit('rad', 1, (0, 0, 0, 0, 0, 0, 0)),
        'ypointing': pmd_unit('rad', 1, (0, 0, 0, 0, 0, 0, 0)),
        'yposition': pmd_unit('m', 1, (1, 0, 0, 0, 0, 0, 0)),
        'ysize': pmd_unit('m', 1, (1, 0, 0, 0, 0, 0, 0)),
      },
      globals=OutputFieldGlobal(
        units={},
        energy=array([], dtype=float64),
        intensity_farfield=array([], dtype=float64),
        intensity_nearfield=array([], dtype=float64),
        xdivergence=array([], dtype=float64),
        ydivergence=array([], dtype=float64),
        xpointing=array([], dtype=float64),
        ypointing=array([], dtype=float64),
        xposition=array([], dtype=float64),
        yposition=array([], dtype=float64),
        xsize=array([], dtype=float64),
        ysize=array([], dtype=float64),
        extra={},
      ),
      dgrid=2e-06,
      intensity_farfield=array(shape=(1084, 552), dtype=float64),
      intensity_nearfield=array(shape=(1084, 552), dtype=float64),
      ngrid=101,
      phase_farfield=array(shape=(1084, 552), dtype=float64),
      phase_nearfield=array(shape=(1084, 552), dtype=float64),
      power=array(shape=(1084, 552), dtype=float64),
      xdivergence=array(shape=(1084, 552), dtype=float64),
      ydivergence=array(shape=(1084, 552), dtype=float64),
      xpointing=array(shape=(1084, 552), dtype=float64),
      ypointing=array(shape=(1084, 552), dtype=float64),
      xposition=array(shape=(1084, 552), dtype=float64),
      yposition=array(shape=(1084, 552), dtype=float64),
      xsize=array(shape=(1084, 552), dtype=float64),
      ysize=array(shape=(1084, 552), dtype=float64),
      energy=array(shape=(1084,), dtype=float64),
      extra={},
    ),
  },
  lattice=OutputLattice(
    units={},
    aw=array(shape=(4332,), dtype=float64),
    ax=array(shape=(4332,), dtype=float64),
    ay=array(shape=(4332,), dtype=float64),
    chic_angle=array(shape=(4332,), dtype=float64),
    chic_lb=array(shape=(4332,), dtype=float64),
    chic_ld=array(shape=(4332,), dtype=float64),
    chic_lt=array(shape=(4332,), dtype=float64),
    cx=array(shape=(4332,), dtype=float64),
    cy=array(shape=(4332,), dtype=float64),
    dz=array(shape=(4332,), dtype=float64),
    gradx=array(shape=(4332,), dtype=float64),
    grady=array(shape=(4332,), dtype=float64),
    ku=array(shape=(4332,), dtype=float64),
    kx=array(shape=(4332,), dtype=float64),
    ky=array(shape=(4332,), dtype=float64),
    phaseshift=array(shape=(4332,), dtype=float64),
    qf=array(shape=(4332,), dtype=float64),
    qx=array(shape=(4332,), dtype=float64),
    qy=array(shape=(4332,), dtype=float64),
    slippage=array(shape=(4332,), dtype=float64),
    z=array(shape=(4332,), dtype=float64),
    zplot=array(shape=(1084,), dtype=float64),
    extra={},
  ),
  globals=OutputGlobal(
    units={},
    frequency=array(shape=(552,), dtype=float64),
    gamma0=19174.0776,
    lambdaref=1.3789244869952112e-10,
    s=array(shape=(552,), dtype=float64),
    sample=200.0,
    slen=1.5223326336427133e-05,
    time=True,
    extra={},
  ),
  meta=OutputMeta(
    units={},
    beamdumps=OutputMetaDumps(units={}, extra={}),
    fielddumps=OutputMetaDumps(units={}, extra={}),
    version=OutputMetaVersion(units={}, extra={}),
    extra={},
  ),
  version=OutputMetaVersion(
    units={},
    build_info='Compiled by runner at 2024-01-11 18:10:26 [UTC] from Git Commit ID: ',
    major=4.0,
    minor=6.0,
    revision=6.0,
    extra={},
  ),
  extra={},
  field={},
  particles={},
  alias={
    'alphax': 'beam.alphax',
    'alphay': 'beam.alphay',
    'aw': 'lattice.aw',
    'ax': 'lattice.ax',
    'ay': 'lattice.ay',
    'beam_alphax': 'beam.alphax',
    'beam_alphay': 'beam.alphay',
    'beam_betax': 'beam.betax',
    'beam_betay': 'beam.betay',
    'beam_bunching': 'beam.bunching',
    'beam_bunchingphase': 'beam.bunchingphase',
    'beam_current': 'beam.current',
    'beam_efield': 'beam.efield',
    'beam_emax': 'beam.emax',
    'beam_emin': 'beam.emin',
    'beam_emitx': 'beam.emitx',
    'beam_emity': 'beam.emity',
    'beam_energy': 'beam.energy',
    'beam_energyspread': 'beam.energyspread',
    'beam_globals_energy': 'beam.globals.energy',
    'beam_globals_energyspread': 'beam.globals.energyspread',
    'beam_globals_xposition': 'beam.globals.xposition',
    'beam_globals_xsize': 'beam.globals.xsize',
    'beam_globals_yposition': 'beam.globals.yposition',
    'beam_globals_ysize': 'beam.globals.ysize',
    'beam_lsc_field': 'beam.lsc_field',
    'beam_pxmax': 'beam.pxmax',
    'beam_pxmin': 'beam.pxmin',
    'beam_pxposition': 'beam.pxposition',
    'beam_pymax': 'beam.pymax',
    'beam_pymin': 'beam.pymin',
    'beam_pyposition': 'beam.pyposition',
    'beam_sigma_energy': 'beam.stat.sigma_energy',
    'beam_sigma_x': 'beam.stat.sigma_x',
    'beam_sigma_y': 'beam.stat.sigma_y',
    'beam_ssc_field': 'beam.ssc_field',
    'beam_stat_alphax': 'beam.stat.alphax',
    'beam_stat_alphay': 'beam.stat.alphay',
    'beam_stat_betax': 'beam.stat.betax',
    'beam_stat_betay': 'beam.stat.betay',
    'beam_stat_bunching': 'beam.stat.bunching',
    'beam_stat_bunchingphase': 'beam.stat.bunchingphase',
    'beam_stat_current': 'beam.stat.current',
    'beam_stat_efield': 'beam.stat.efield',
    'beam_stat_emitx': 'beam.stat.emitx',
    'beam_stat_emity': 'beam.stat.emity',
    'beam_stat_energy': 'beam.stat.energy',
    'beam_stat_energyspread': 'beam.stat.energyspread',
    'beam_stat_lsc_field': 'beam.stat.lsc_field',
    'beam_stat_pxmax': 'beam.stat.pxmax',
    'beam_stat_pxmin': 'beam.stat.pxmin',
    'beam_stat_pxposition': 'beam.stat.pxposition',
    'beam_stat_pymax': 'beam.stat.pymax',
    'beam_stat_pymin': 'beam.stat.pymin',
    'beam_stat_pyposition': 'beam.stat.pyposition',
    'beam_stat_sigma_energy': 'beam.stat.sigma_energy',
    'beam_stat_sigma_x': 'beam.stat.sigma_x',
    'beam_stat_sigma_y': 'beam.stat.sigma_y',
    'beam_stat_ssc_field': 'beam.stat.ssc_field',
    'beam_stat_wakefield': 'beam.stat.wakefield',
    'beam_stat_xmax': 'beam.stat.xmax',
    'beam_stat_xmin': 'beam.stat.xmin',
    'beam_stat_xposition': 'beam.stat.xposition',
    'beam_stat_ymax': 'beam.stat.ymax',
    'beam_stat_ymin': 'beam.stat.ymin',
    'beam_stat_yposition': 'beam.stat.yposition',
    'beam_wakefield': 'beam.wakefield',
    'beam_xmax': 'beam.xmax',
    'beam_xmin': 'beam.xmin',
    'beam_xposition': 'beam.xposition',
    'beam_xsize': 'beam.xsize',
    'beam_ymax': 'beam.ymax',
    'beam_ymin': 'beam.ymin',
    'beam_yposition': 'beam.yposition',
    'beam_ysize': 'beam.ysize',
    'betax': 'beam.betax',
    'betay': 'beam.betay',
    'bunching': 'beam.bunching',
    'bunchingphase': 'beam.bunchingphase',
    'chic_angle': 'lattice.chic_angle',
    'chic_lb': 'lattice.chic_lb',
    'chic_ld': 'lattice.chic_ld',
    'chic_lt': 'lattice.chic_lt',
    'current': 'beam.current',
    'cx': 'lattice.cx',
    'cy': 'lattice.cy',
    'dz': 'lattice.dz',
    'efield': 'beam.efield',
    'emax': 'beam.emax',
    'emin': 'beam.emin',
    'emitx': 'beam.emitx',
    'emity': 'beam.emity',
    'field_energy': 'field.energy',
    'field_globals_energy': 'field.globals.energy',
    'field_globals_intensity_farfield': 'field.globals.intensity_farfield',
    'field_globals_intensity_nearfield': 'field.globals.intensity_nearfield',
    'field_globals_xdivergence': 'field.globals.xdivergence',
    'field_globals_xpointing': 'field.globals.xpointing',
    'field_globals_xposition': 'field.globals.xposition',
    'field_globals_xsize': 'field.globals.xsize',
    'field_globals_ydivergence': 'field.globals.ydivergence',
    'field_globals_ypointing': 'field.globals.ypointing',
    'field_globals_yposition': 'field.globals.yposition',
    'field_globals_ysize': 'field.globals.ysize',
    'field_intensity_farfield': 'field.intensity_farfield',
    'field_intensity_nearfield': 'field.intensity_nearfield',
    'field_peak_power': 'field.peak_power',
    'field_phase_farfield': 'field.phase_farfield',
    'field_phase_nearfield': 'field.phase_nearfield',
    'field_power': 'field.power',
    'field_stat_xposition': 'field.stat.xposition',
    'field_stat_xsize': 'field.stat.xsize',
    'field_stat_yposition': 'field.stat.yposition',
    'field_stat_ysize': 'field.stat.ysize',
    'field_xdivergence': 'field.xdivergence',
    'field_xpointing': 'field.xpointing',
    'field_xposition': 'field.xposition',
    'field_xsize': 'field.xsize',
    'field_ydivergence': 'field.ydivergence',
    'field_ypointing': 'field.ypointing',
    'field_yposition': 'field.yposition',
    'field_ysize': 'field.ysize',
    'frequency': 'globals.frequency',
    'globals_frequency': 'globals.frequency',
    'globals_s': 'globals.s',
    'gradx': 'lattice.gradx',
    'grady': 'lattice.grady',
    'ku': 'lattice.ku',
    'kx': 'lattice.kx',
    'ky': 'lattice.ky',
    'lattice_aw': 'lattice.aw',
    'lattice_ax': 'lattice.ax',
    'lattice_ay': 'lattice.ay',
    'lattice_chic_angle': 'lattice.chic_angle',
    'lattice_chic_lb': 'lattice.chic_lb',
    'lattice_chic_ld': 'lattice.chic_ld',
    'lattice_chic_lt': 'lattice.chic_lt',
    'lattice_cx': 'lattice.cx',
    'lattice_cy': 'lattice.cy',
    'lattice_dz': 'lattice.dz',
    'lattice_gradx': 'lattice.gradx',
    'lattice_grady': 'lattice.grady',
    'lattice_ku': 'lattice.ku',
    'lattice_kx': 'lattice.kx',
    'lattice_ky': 'lattice.ky',
    'lattice_phaseshift': 'lattice.phaseshift',
    'lattice_qf': 'lattice.qf',
    'lattice_qx': 'lattice.qx',
    'lattice_qy': 'lattice.qy',
    'lattice_slippage': 'lattice.slippage',
    'lattice_z': 'lattice.z',
    'lattice_zplot': 'lattice.zplot',
    'lsc_field': 'beam.lsc_field',
    'peak_power': 'field.peak_power',
    'phase_farfield': 'field.phase_farfield',
    'phase_nearfield': 'field.phase_nearfield',
    'phaseshift': 'lattice.phaseshift',
    'power': 'field.power',
    'pxmax': 'beam.pxmax',
    'pxmin': 'beam.pxmin',
    'pxposition': 'beam.pxposition',
    'pymax': 'beam.pymax',
    'pymin': 'beam.pymin',
    'pyposition': 'beam.pyposition',
    'qf': 'lattice.qf',
    'qx': 'lattice.qx',
    'qy': 'lattice.qy',
    's': 'globals.s',
    'slippage': 'lattice.slippage',
    'ssc_field': 'beam.ssc_field',
    'wakefield': 'beam.wakefield',
    'xmax': 'beam.xmax',
    'xmin': 'beam.xmin',
    'ymax': 'beam.ymax',
    'ymin': 'beam.ymin',
    'z': 'lattice.z',
    'zplot': 'lattice.zplot',
  },
  field_files={},
  particle_files={},
)

Timing¶

In [ ]:

MAX_CPUS = os.cpu_count()
CPUS_PER_NODE = 128
MIN_CPUS = MAX_CPUS // 8
MAX_CPUS, MIN_CPUS

MAX_CPUS = os.cpu_count() CPUS_PER_NODE = 128 MIN_CPUS = MAX_CPUS // 8 MAX_CPUS, MIN_CPUS

In [ ]:

def time1(nproc):
    G.verbose = False
    G.nproc = nproc
    G.nnode = (nproc - 1) // CPUS_PER_NODE + 1
    G.run()
    return G.output.run.run_time


time1(MAX_CPUS)

def time1(nproc): G.verbose = False G.nproc = nproc G.nnode = (nproc - 1) // CPUS_PER_NODE + 1 G.run() return G.output.run.run_time time1(MAX_CPUS)

In [ ]:

%%time
nlist = []
tlist = []
n_cpu = MAX_CPUS

while n_cpu > 0:
    n = n_cpu
    if n < MIN_CPUS:
        break
    nlist.append(n)
    dt = time1(n)
    tlist.append(dt)
    print(f"{n} cores, {dt:0.1f} s")
    n_cpu = n_cpu // 2

%%time nlist = [] tlist = [] n_cpu = MAX_CPUS while n_cpu > 0: n = n_cpu if n < MIN_CPUS: break nlist.append(n) dt = time1(n) tlist.append(dt) print(f"{n} cores, {dt:0.1f} s") n_cpu = n_cpu // 2

In [ ]:

nlist, tlist

nlist, tlist

Some saved stats¶

In [ ]:

import matplotlib.pyplot as plt
import numpy as np

%config InlineBackend.figure_format = 'retina'

# Perlmutter
nlist, tlist = (
    [256, 128, 64, 32, 16, 8, 4, 2, 1],
    [
        12.407618761062622,
        9.337806940078735,
        15.55810832977295,
        27.734387397766113,
        49.104663372039795,
        113.33639931678772,
        184.2123155593872,
        367.3742334842682,
        555.4603695869446,
    ],
)
nlist = np.array(nlist)[::-1]
tlist = np.array(tlist)[::-1]

tref = tlist[0]

# M1 Max
nlistmac, tlistmac = (
    [8, 4, 2, 1],
    [38.151074171066284, 75.41113114356995, 146.3512842655182, 285.11587405204773],
)
nlistmac = np.array(nlistmac)
tlistmac = np.array(tlistmac)


plt.plot(nlist, tlist / tref, marker=".", label="Genesis4 Perlmutter")
plt.plot(nlistmac, tlistmac / tref, marker=".", label="Genesis4 M1 Max")
plt.plot(nlist, 1 / (nlist / nlist[0]), "--", label="ideal")
plt.xscale("log")
plt.yscale("log")
plt.xlabel("n cores")
plt.ylabel("run time (normalized)")
plt.legend()

import matplotlib.pyplot as plt import numpy as np %config InlineBackend.figure_format = 'retina' # Perlmutter nlist, tlist = ( [256, 128, 64, 32, 16, 8, 4, 2, 1], [ 12.407618761062622, 9.337806940078735, 15.55810832977295, 27.734387397766113, 49.104663372039795, 113.33639931678772, 184.2123155593872, 367.3742334842682, 555.4603695869446, ], ) nlist = np.array(nlist)[::-1] tlist = np.array(tlist)[::-1] tref = tlist[0] # M1 Max nlistmac, tlistmac = ( [8, 4, 2, 1], [38.151074171066284, 75.41113114356995, 146.3512842655182, 285.11587405204773], ) nlistmac = np.array(nlistmac) tlistmac = np.array(tlistmac) plt.plot(nlist, tlist / tref, marker=".", label="Genesis4 Perlmutter") plt.plot(nlistmac, tlistmac / tref, marker=".", label="Genesis4 M1 Max") plt.plot(nlist, 1 / (nlist / nlist[0]), "--", label="ideal") plt.xscale("log") plt.yscale("log") plt.xlabel("n cores") plt.ylabel("run time (normalized)") plt.legend()