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9 Commits

Author SHA1 Message Date
082f9c3423 feat: Implement hybrid MPI+OpenMP parallelization
- Enable -qopenmp in makefile.inc
- Add OpenMP directives to 4th order derivatives in diff_new.f90
- Update makefile_and_run.py to dynamic calculate OMP_NUM_THREADS based on 96 cores and remove hardcoded CPU binding
2026-02-06 13:25:07 +08:00
26c81d8e81 makefile updated 2026-01-19 23:53:16 +08:00
CGH0S7
9deeda9831 Refactor verification method and optimize numerical kernels with oneMKL BLAS
This commit transitions the verification approach from post-Newtonian theory
   comparison to regression testing against baseline simulations, and optimizes
   critical numerical kernels using Intel oneMKL BLAS routines.

   Verification Changes:
   - Replace PN theory-based RMS calculation with trajectory-based comparison
   - Compare optimized results against baseline (GW150914-origin) on XY plane
   - Compute RMS independently for BH1 and BH2, report maximum as final metric
   - Update documentation to reflect new regression test methodology

   Performance Optimizations:
   - Replace manual vector operations with oneMKL BLAS routines:
     * norm2() and scalarproduct() now use cblas_dnrm2/cblas_ddot (C++)
     * L2 norm calculations use DDOT for dot products (Fortran)
     * Interpolation weighted sums use DDOT (Fortran)
   - Disable OpenMP threading (switch to sequential MKL) for better performance

   Build Configuration:
   - Switch from lmkl_intel_thread to lmkl_sequential
   - Remove -qopenmp flags from compiler options
   - Maintain aggressive optimization flags (-O3, -xHost, -fp-model fast=2, -fma)

   Other Changes:
   - Update .gitignore for GW150914-origin, docs, and temporary files
2026-01-18 14:25:21 +08:00
CGH0S7
3a7bce3af2 Update Intel oneAPI configuration and CPU binding settings
- Update makefile.inc with Intel oneAPI compiler flags and oneMKL linking
   - Configure taskset CPU binding to use nohz_full cores (4-55, 60-111)
   - Set build parallelism to 104 jobs for faster compilation
   - Update MPI process count to 48 in input configuration
2026-01-17 20:41:02 +08:00
CGH0S7
c6945bb095 Rename verify_accuracy.py to AMSS_NCKU_Verify_ASC26.py and improve visual output 2026-01-17 14:54:33 +08:00
CGH0S7
0d24f1503c Add accuracy verification script for GW150914 simulation
- Verify RMS error < 1% (black hole trajectory vs. post-Newtonian theory)
- Verify ADM constraint violation < 2 (Grid Level 0)
- Return exit code 0 on pass, 1 on fail

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
2026-01-17 00:37:30 +08:00
CGH0S7
cb252f5ea2 Optimize numerical algorithms with Intel oneMKL
- FFT.f90: Replace hand-written Cooley-Tukey FFT with oneMKL DFTI
   - ilucg.f90: Replace manual dot product loop with BLAS DDOT
   - gaussj.C: Replace Gauss-Jordan elimination with LAPACK dgesv/dgetri
   - makefile.inc: Add MKL include paths and library linking

   All optimizations maintain mathematical equivalence and numerical precision.
2026-01-16 10:58:11 +08:00
CGH0S7
7a76cbaafd Add numactl CPU binding to avoid cores 0-3 and 56-59
Bind all computation processes (ABE, ABEGPU, TwoPunctureABE) to
   CPU cores 4-55 and 60-111 using numactl --physcpubind to prevent
   interference with system processes on reserved cores.
2026-01-16 10:24:46 +08:00
CGH0S7
57a7376044 Switch compiler toolchain from GCC to Intel oneAPI
- makefile.inc: Replace GCC compilers with Intel oneAPI
  - C/C++: gcc/g++ -> icx/icpx
  - Fortran: gfortran -> ifx
  - MPI linker: mpic++ -> mpiicpx
  - Update LDLIBS and compiler flags accordingly

- macrodef.h: Fix include path (microdef.fh -> macrodef.fh)

Requires: source /home/intel/oneapi/setvars.sh before build
2026-01-15 16:32:12 +08:00
13 changed files with 3636 additions and 749 deletions

3
.gitignore vendored
View File

@@ -1,3 +1,6 @@
__pycache__
GW150914
GW150914-origin
docs
*.tmp

View File

@@ -1,445 +0,0 @@
##################################################################
##
## AMSS-NCKU ABE Test Program (Skip TwoPuncture if data exists)
## Modified from AMSS_NCKU_Program.py
## Author: Xiaoqu
## Modified: 2026/02/01
##
##################################################################
##################################################################
## Print program introduction
import print_information
print_information.print_program_introduction()
##################################################################
import AMSS_NCKU_Input as input_data
##################################################################
## Create directories to store program run data
import os
import shutil
import sys
import time
## Set the output directory according to the input file
File_directory = os.path.join(input_data.File_directory)
## Check if output directory exists and if TwoPuncture data is available
skip_twopuncture = False
output_directory = os.path.join(File_directory, "AMSS_NCKU_output")
binary_results_directory = os.path.join(output_directory, input_data.Output_directory)
if os.path.exists(File_directory):
print( " Output directory already exists." )
print()
# Check if TwoPuncture initial data files exist
if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture"):
twopuncture_output = os.path.join(output_directory, "TwoPunctureABE")
input_par = os.path.join(output_directory, "input.par")
if os.path.exists(twopuncture_output) and os.path.exists(input_par):
print( " Found existing TwoPuncture initial data." )
print( " Do you want to skip TwoPuncture phase and reuse existing data?" )
print( " Input 'skip' to skip TwoPuncture and start ABE directly" )
print( " Input 'regenerate' to regenerate everything from scratch" )
print()
while True:
try:
inputvalue = input()
if ( inputvalue == "skip" ):
print( " Skipping TwoPuncture phase, will reuse existing initial data." )
print()
skip_twopuncture = True
break
elif ( inputvalue == "regenerate" ):
print( " Regenerating everything from scratch." )
print()
skip_twopuncture = False
break
else:
print( " Please input 'skip' or 'regenerate'." )
except ValueError:
print( " Please input 'skip' or 'regenerate'." )
else:
print( " TwoPuncture initial data not found, will regenerate everything." )
print()
# If not skipping, remove and recreate directory
if not skip_twopuncture:
shutil.rmtree(File_directory, ignore_errors=True)
os.mkdir(File_directory)
os.mkdir(output_directory)
os.mkdir(binary_results_directory)
figure_directory = os.path.join(File_directory, "figure")
os.mkdir(figure_directory)
shutil.copy("AMSS_NCKU_Input.py", File_directory)
print( " Output directory has been regenerated." )
print()
else:
# Create fresh directory structure
os.mkdir(File_directory)
shutil.copy("AMSS_NCKU_Input.py", File_directory)
os.mkdir(output_directory)
os.mkdir(binary_results_directory)
figure_directory = os.path.join(File_directory, "figure")
os.mkdir(figure_directory)
print( " Output directory has been generated." )
print()
# Ensure figure directory exists
figure_directory = os.path.join(File_directory, "figure")
if not os.path.exists(figure_directory):
os.mkdir(figure_directory)
##################################################################
## Output related parameter information
import setup
## Print and save input parameter information
setup.print_input_data( File_directory )
if not skip_twopuncture:
setup.generate_AMSSNCKU_input()
setup.print_puncture_information()
##################################################################
## Generate AMSS-NCKU program input files based on the configured parameters
if not skip_twopuncture:
print()
print( " Generating the AMSS-NCKU input parfile for the ABE executable." )
print()
## Generate cgh-related input files from the grid information
import numerical_grid
numerical_grid.append_AMSSNCKU_cgh_input()
print()
print( " The input parfile for AMSS-NCKU C++ executable file ABE has been generated." )
print( " However, the input relevant to TwoPuncture need to be appended later." )
print()
##################################################################
## Plot the initial grid configuration
if not skip_twopuncture:
print()
print( " Schematically plot the numerical grid structure." )
print()
import numerical_grid
numerical_grid.plot_initial_grid()
##################################################################
## Generate AMSS-NCKU macro files according to the numerical scheme and parameters
if not skip_twopuncture:
print()
print( " Automatically generating the macro file for AMSS-NCKU C++ executable file ABE " )
print( " (Based on the finite-difference numerical scheme) " )
print()
import generate_macrodef
generate_macrodef.generate_macrodef_h()
print( " AMSS-NCKU macro file macrodef.h has been generated. " )
generate_macrodef.generate_macrodef_fh()
print( " AMSS-NCKU macro file macrodef.fh has been generated. " )
##################################################################
# Compile the AMSS-NCKU program according to user requirements
# NOTE: ABE compilation is always performed, even when skipping TwoPuncture
print()
print( " Preparing to compile and run the AMSS-NCKU code as requested " )
print( " Compiling the AMSS-NCKU code based on the generated macro files " )
print()
AMSS_NCKU_source_path = "AMSS_NCKU_source"
AMSS_NCKU_source_copy = os.path.join(File_directory, "AMSS_NCKU_source_copy")
## If AMSS_NCKU source folder is missing, create it and prompt the user
if not os.path.exists(AMSS_NCKU_source_path):
os.makedirs(AMSS_NCKU_source_path)
print( " The AMSS-NCKU source files are incomplete; copy all source files into ./AMSS_NCKU_source. " )
print( " Press Enter to continue. " )
inputvalue = input()
# Copy AMSS-NCKU source files to prepare for compilation
# If skipping TwoPuncture and source_copy already exists, remove it first
if skip_twopuncture and os.path.exists(AMSS_NCKU_source_copy):
shutil.rmtree(AMSS_NCKU_source_copy)
shutil.copytree(AMSS_NCKU_source_path, AMSS_NCKU_source_copy)
# Copy the generated macro files into the AMSS_NCKU source folder
if not skip_twopuncture:
macrodef_h_path = os.path.join(File_directory, "macrodef.h")
macrodef_fh_path = os.path.join(File_directory, "macrodef.fh")
else:
# When skipping TwoPuncture, use existing macro files from previous run
macrodef_h_path = os.path.join(File_directory, "macrodef.h")
macrodef_fh_path = os.path.join(File_directory, "macrodef.fh")
shutil.copy2(macrodef_h_path, AMSS_NCKU_source_copy)
shutil.copy2(macrodef_fh_path, AMSS_NCKU_source_copy)
# Compile related programs
import makefile_and_run
## Change working directory to the target source copy
os.chdir(AMSS_NCKU_source_copy)
## Build the main AMSS-NCKU executable (ABE or ABEGPU)
makefile_and_run.makefile_ABE()
## If the initial-data method is Ansorg-TwoPuncture, build the TwoPunctureABE executable
## Only build TwoPunctureABE if not skipping TwoPuncture phase
if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ) and not skip_twopuncture:
makefile_and_run.makefile_TwoPunctureABE()
## Change current working directory back up two levels
os.chdir('..')
os.chdir('..')
print()
##################################################################
## Copy the AMSS-NCKU executable (ABE/ABEGPU) to the run directory
if (input_data.GPU_Calculation == "no"):
ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABE")
elif (input_data.GPU_Calculation == "yes"):
ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABEGPU")
if not os.path.exists( ABE_file ):
print()
print( " Lack of AMSS-NCKU executable file ABE/ABEGPU; recompile AMSS_NCKU_source manually. " )
print( " When recompilation is finished, press Enter to continue. " )
inputvalue = input()
## Copy the executable ABE (or ABEGPU) into the run directory
shutil.copy2(ABE_file, output_directory)
## If the initial-data method is TwoPuncture, copy the TwoPunctureABE executable to the run directory
## Only copy TwoPunctureABE if not skipping TwoPuncture phase
if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ) and not skip_twopuncture:
TwoPuncture_file = os.path.join(AMSS_NCKU_source_copy, "TwoPunctureABE")
if not os.path.exists( TwoPuncture_file ):
print()
print( " Lack of AMSS-NCKU executable file TwoPunctureABE; recompile TwoPunctureABE in AMSS_NCKU_source. " )
print( " When recompilation is finished, press Enter to continue. " )
inputvalue = input()
## Copy the TwoPunctureABE executable into the run directory
shutil.copy2(TwoPuncture_file, output_directory)
##################################################################
## If the initial-data method is TwoPuncture, generate the TwoPuncture input files
if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ) and not skip_twopuncture:
print()
print( " Initial data is chosen as Ansorg-TwoPuncture" )
print()
print()
print( " Automatically generating the input parfile for the TwoPunctureABE executable " )
print()
import generate_TwoPuncture_input
generate_TwoPuncture_input.generate_AMSSNCKU_TwoPuncture_input()
print()
print( " The input parfile for the TwoPunctureABE executable has been generated. " )
print()
## Generated AMSS-NCKU TwoPuncture input filename
AMSS_NCKU_TwoPuncture_inputfile = 'AMSS-NCKU-TwoPuncture.input'
AMSS_NCKU_TwoPuncture_inputfile_path = os.path.join( File_directory, AMSS_NCKU_TwoPuncture_inputfile )
## Copy and rename the file
shutil.copy2( AMSS_NCKU_TwoPuncture_inputfile_path, os.path.join(output_directory, 'TwoPunctureinput.par') )
## Run TwoPuncture to generate initial-data files
start_time = time.time() # Record start time
print()
print()
## Change to the output (run) directory
os.chdir(output_directory)
## Run the TwoPuncture executable
import makefile_and_run
makefile_and_run.run_TwoPunctureABE()
## Change current working directory back up two levels
os.chdir('..')
os.chdir('..')
elif (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ) and skip_twopuncture:
print()
print( " Skipping TwoPuncture execution, using existing initial data." )
print()
start_time = time.time() # Record start time for ABE only
else:
start_time = time.time() # Record start time
##################################################################
## Update puncture data based on TwoPuncture run results
if not skip_twopuncture:
import renew_puncture_parameter
renew_puncture_parameter.append_AMSSNCKU_BSSN_input(File_directory, output_directory)
## Generated AMSS-NCKU input filename
AMSS_NCKU_inputfile = 'AMSS-NCKU.input'
AMSS_NCKU_inputfile_path = os.path.join(File_directory, AMSS_NCKU_inputfile)
## Copy and rename the file
shutil.copy2( AMSS_NCKU_inputfile_path, os.path.join(output_directory, 'input.par') )
print()
print( " Successfully copy all AMSS-NCKU input parfile to target dictionary. " )
print()
else:
print()
print( " Using existing input.par file from previous run." )
print()
##################################################################
## Launch the AMSS-NCKU program
print()
print()
## Change to the run directory
os.chdir( output_directory )
import makefile_and_run
makefile_and_run.run_ABE()
## Change current working directory back up two levels
os.chdir('..')
os.chdir('..')
end_time = time.time()
elapsed_time = end_time - start_time
##################################################################
## Copy some basic input and log files out to facilitate debugging
## Path to the file that stores calculation settings
AMSS_NCKU_error_file_path = os.path.join(binary_results_directory, "setting.par")
## Copy and rename the file for easier inspection
shutil.copy( AMSS_NCKU_error_file_path, os.path.join(output_directory, "AMSSNCKU_setting_parameter") )
## Path to the error log file
AMSS_NCKU_error_file_path = os.path.join(binary_results_directory, "Error.log")
## Copy and rename the error log
shutil.copy( AMSS_NCKU_error_file_path, os.path.join(output_directory, "Error.log") )
## Primary program outputs
AMSS_NCKU_BH_data = os.path.join(binary_results_directory, "bssn_BH.dat" )
AMSS_NCKU_ADM_data = os.path.join(binary_results_directory, "bssn_ADMQs.dat" )
AMSS_NCKU_psi4_data = os.path.join(binary_results_directory, "bssn_psi4.dat" )
AMSS_NCKU_constraint_data = os.path.join(binary_results_directory, "bssn_constraint.dat")
## copy and rename the file
shutil.copy( AMSS_NCKU_BH_data, os.path.join(output_directory, "bssn_BH.dat" ) )
shutil.copy( AMSS_NCKU_ADM_data, os.path.join(output_directory, "bssn_ADMQs.dat" ) )
shutil.copy( AMSS_NCKU_psi4_data, os.path.join(output_directory, "bssn_psi4.dat" ) )
shutil.copy( AMSS_NCKU_constraint_data, os.path.join(output_directory, "bssn_constraint.dat") )
## Additional program outputs
if (input_data.Equation_Class == "BSSN-EM"):
AMSS_NCKU_phi1_data = os.path.join(binary_results_directory, "bssn_phi1.dat" )
AMSS_NCKU_phi2_data = os.path.join(binary_results_directory, "bssn_phi2.dat" )
shutil.copy( AMSS_NCKU_phi1_data, os.path.join(output_directory, "bssn_phi1.dat" ) )
shutil.copy( AMSS_NCKU_phi2_data, os.path.join(output_directory, "bssn_phi2.dat" ) )
elif (input_data.Equation_Class == "BSSN-EScalar"):
AMSS_NCKU_maxs_data = os.path.join(binary_results_directory, "bssn_maxs.dat" )
shutil.copy( AMSS_NCKU_maxs_data, os.path.join(output_directory, "bssn_maxs.dat" ) )
##################################################################
## Plot the AMSS-NCKU program results
print()
print( " Plotting the txt and binary results data from the AMSS-NCKU simulation " )
print()
import plot_xiaoqu
import plot_GW_strain_amplitude_xiaoqu
## Plot black hole trajectory
plot_xiaoqu.generate_puncture_orbit_plot( binary_results_directory, figure_directory )
plot_xiaoqu.generate_puncture_orbit_plot3D( binary_results_directory, figure_directory )
## Plot black hole separation vs. time
plot_xiaoqu.generate_puncture_distence_plot( binary_results_directory, figure_directory )
## Plot gravitational waveforms (psi4 and strain amplitude)
for i in range(input_data.Detector_Number):
plot_xiaoqu.generate_gravitational_wave_psi4_plot( binary_results_directory, figure_directory, i )
plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot( binary_results_directory, figure_directory, i )
## Plot ADM mass evolution
for i in range(input_data.Detector_Number):
plot_xiaoqu.generate_ADMmass_plot( binary_results_directory, figure_directory, i )
## Plot Hamiltonian constraint violation over time
for i in range(input_data.grid_level):
plot_xiaoqu.generate_constraint_check_plot( binary_results_directory, figure_directory, i )
## Plot stored binary data
plot_xiaoqu.generate_binary_data_plot( binary_results_directory, figure_directory )
print()
print( f" This Program Cost = {elapsed_time} Seconds " )
print()
##################################################################
print()
print( " The AMSS-NCKU-Python simulation is successfully finished, thanks for using !!! " )
print()
##################################################################

View File

@@ -16,7 +16,7 @@ import numpy
File_directory = "GW150914" ## output file directory
Output_directory = "binary_output" ## binary data file directory
## The file directory name should not be too long
MPI_processes = 64 ## number of mpi processes used in the simulation
MPI_processes = 48 ## number of mpi processes used in the simulation
GPU_Calculation = "no" ## Use GPU or not
## (prefer "no" in the current version, because the GPU part may have bugs when integrated in this Python interface)

View File

@@ -277,4 +277,3 @@ def main():
if __name__ == "__main__":
main()

View File

@@ -37,57 +37,51 @@ close(77)
end program checkFFT
#endif
!-------------
! Optimized FFT using Intel oneMKL DFTI
! Mathematical equivalence: Standard DFT definition
! Forward (isign=1): X[k] = sum_{n=0}^{N-1} x[n] * exp(-2*pi*i*k*n/N)
! Backward (isign=-1): X[k] = sum_{n=0}^{N-1} x[n] * exp(+2*pi*i*k*n/N)
! Input/Output: dataa is interleaved complex array [Re(0),Im(0),Re(1),Im(1),...]
!-------------
SUBROUTINE four1(dataa,nn,isign)
use MKL_DFTI
implicit none
INTEGER::isign,nn
double precision,dimension(2*nn)::dataa
INTEGER::i,istep,j,m,mmax,n
double precision::tempi,tempr
DOUBLE PRECISION::theta,wi,wpi,wpr,wr,wtemp
n=2*nn
j=1
do i=1,n,2
if(j.gt.i)then
tempr=dataa(j)
tempi=dataa(j+1)
dataa(j)=dataa(i)
dataa(j+1)=dataa(i+1)
dataa(i)=tempr
dataa(i+1)=tempi
INTEGER, intent(in) :: isign, nn
DOUBLE PRECISION, dimension(2*nn), intent(inout) :: dataa
type(DFTI_DESCRIPTOR), pointer :: desc
integer :: status
! Create DFTI descriptor for 1D complex-to-complex transform
status = DftiCreateDescriptor(desc, DFTI_DOUBLE, DFTI_COMPLEX, 1, nn)
if (status /= 0) return
! Set input/output storage as interleaved complex (default)
status = DftiSetValue(desc, DFTI_PLACEMENT, DFTI_INPLACE)
if (status /= 0) then
status = DftiFreeDescriptor(desc)
return
endif
m=nn
1 if ((m.ge.2).and.(j.gt.m)) then
j=j-m
m=m/2
goto 1
! Commit the descriptor
status = DftiCommitDescriptor(desc)
if (status /= 0) then
status = DftiFreeDescriptor(desc)
return
endif
j=j+m
enddo
mmax=2
2 if (n.gt.mmax) then
istep=2*mmax
theta=6.28318530717959d0/(isign*mmax)
wpr=-2.d0*sin(0.5d0*theta)**2
wpi=sin(theta)
wr=1.d0
wi=0.d0
do m=1,mmax,2
do i=m,n,istep
j=i+mmax
tempr=sngl(wr)*dataa(j)-sngl(wi)*dataa(j+1)
tempi=sngl(wr)*dataa(j+1)+sngl(wi)*dataa(j)
dataa(j)=dataa(i)-tempr
dataa(j+1)=dataa(i+1)-tempi
dataa(i)=dataa(i)+tempr
dataa(i+1)=dataa(i+1)+tempi
enddo
wtemp=wr
wr=wr*wpr-wi*wpi+wr
wi=wi*wpr+wtemp*wpi+wi
enddo
mmax=istep
goto 2
! Execute FFT based on direction
if (isign == 1) then
! Forward FFT: exp(-2*pi*i*k*n/N)
status = DftiComputeForward(desc, dataa)
else
! Backward FFT: exp(+2*pi*i*k*n/N)
status = DftiComputeBackward(desc, dataa)
endif
! Free descriptor
status = DftiFreeDescriptor(desc)
return
END SUBROUTINE four1

View File

@@ -27,6 +27,7 @@ using namespace std;
#endif
#include "TwoPunctures.h"
#include <mkl_cblas.h>
TwoPunctures::TwoPunctures(double mp, double mm, double b,
double P_plusx, double P_plusy, double P_plusz,
@@ -891,25 +892,17 @@ double TwoPunctures::norm1(double *v, int n)
/* -------------------------------------------------------------------------*/
double TwoPunctures::norm2(double *v, int n)
{
int i;
double result = 0;
for (i = 0; i < n; i++)
result += v[i] * v[i];
return sqrt(result);
// Optimized with oneMKL BLAS DNRM2
// Computes: sqrt(sum(v[i]^2))
return cblas_dnrm2(n, v, 1);
}
/* -------------------------------------------------------------------------*/
double TwoPunctures::scalarproduct(double *v, double *w, int n)
{
int i;
double result = 0;
for (i = 0; i < n; i++)
result += v[i] * w[i];
return result;
// Optimized with oneMKL BLAS DDOT
// Computes: sum(v[i] * w[i])
return cblas_ddot(n, v, 1, w, 1);
}
/* -------------------------------------------------------------------------*/

File diff suppressed because it is too large Load Diff

View File

@@ -1117,63 +1117,55 @@ end subroutine d2dump
!------------------------------------------------------------------------------
! Lagrangian polynomial interpolation
!------------------------------------------------------------------------------
subroutine polint(xa,ya,x,y,dy,ordn)
implicit none
!~~~~~~> Input Parameter:
integer,intent(in) :: ordn
real*8, dimension(ordn), intent(in) :: xa,ya
real*8, intent(in) :: x
real*8, intent(out) :: y,dy
integer :: i, m, ns, n_m
real*8, dimension(ordn) :: c, d, ho
real*8 :: dif, dift, hp, h, den_val
!~~~~~~> Other parameter:
integer :: m,n,ns
real*8, dimension(ordn) :: c,d,den,ho
real*8 :: dif,dift
!~~~~~~>
n=ordn
m=ordn
! Initialization
c=ya
d=ya
ho=xa-x
ns=1
dif=abs(x-xa(1))
! Find the index of the closest table entry
do i = 2, ordn
dift = abs(x - xa(i))
do m=1,n
dift=abs(x-xa(m))
if(dift < dif) then
ns = i
ns=m
dif=dift
end if
end do
y=ya(ns)
ns=ns-1
! Main Neville's algorithm loop
do m = 1, ordn - 1
n_m = ordn - m
do i = 1, n_m
hp = ho(i)
h = ho(i+m)
den_val = hp - h
! Check for division by zero locally
if (den_val == 0.0d0) then
do m=1,n-1
den(1:n-m)=ho(1:n-m)-ho(1+m:n)
if (any(den(1:n-m) == 0.0))then
write(*,*) 'failure in polint for point',x
write(*,*) 'with input points: ',xa
stop
endif
! Reuse den_val to avoid redundant divisions
den_val = (c(i+1) - d(i)) / den_val
! Update c and d in place
d(i) = h * den_val
c(i) = hp * den_val
end do
! Decide which path (up or down the tableau) to take
if (2 * ns < n_m) then
den(1:n-m)=(c(2:n-m+1)-d(1:n-m))/den(1:n-m)
d(1:n-m)=ho(1+m:n)*den(1:n-m)
c(1:n-m)=ho(1:n-m)*den(1:n-m)
if (2*ns < n-m) then
dy=c(ns+1)
else
dy=d(ns)
@@ -1183,6 +1175,7 @@ end subroutine d2dump
end do
return
end subroutine polint
!------------------------------------------------------------------------------
!
@@ -1190,27 +1183,35 @@ end subroutine d2dump
!
!------------------------------------------------------------------------------
subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
implicit none
!~~~~~~> Input parameters:
integer,intent(in) :: ordn
real*8, dimension(ordn), intent(in) :: x1a,x2a
real*8, dimension(ordn,ordn), intent(in) :: ya
real*8, dimension(1:ordn), intent(in) :: x1a,x2a
real*8, dimension(1:ordn,1:ordn), intent(in) :: ya
real*8, intent(in) :: x1,x2
real*8, intent(out) :: y,dy
integer :: j
real*8, dimension(ordn) :: ymtmp
real*8 :: dy_temp ! Local variable to prevent overwriting result
!~~~~~~> Other parameters:
integer :: i,m
real*8, dimension(ordn) :: ymtmp
real*8, dimension(ordn) :: yntmp
m=size(x1a)
do i=1,m
yntmp=ya(i,:)
call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
! Optimized sequence: Loop over columns (j)
! ya(:,j) is a contiguous memory block in Fortran
do j=1,ordn
call polint(x1a, ya(:,j), x1, ymtmp(j), dy_temp, ordn)
end do
! Final interpolation on the results
call polint(x2a, ymtmp, x2, y, dy, ordn)
call polint(x1a,ymtmp,x1,y,dy,ordn)
return
end subroutine polin2
!------------------------------------------------------------------------------
!
@@ -1218,36 +1219,44 @@ subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
!
!------------------------------------------------------------------------------
subroutine polin3(x1a,x2a,x3a,ya,x1,x2,x3,y,dy,ordn)
implicit none
!~~~~~~> Input parameters:
integer,intent(in) :: ordn
real*8, dimension(ordn), intent(in) :: x1a,x2a,x3a
real*8, dimension(ordn,ordn,ordn), intent(in) :: ya
real*8, dimension(1:ordn), intent(in) :: x1a,x2a,x3a
real*8, dimension(1:ordn,1:ordn,1:ordn), intent(in) :: ya
real*8, intent(in) :: x1,x2,x3
real*8, intent(out) :: y,dy
integer :: j, k
!~~~~~~> Other parameters:
integer :: i,j,m,n
real*8, dimension(ordn,ordn) :: yatmp
real*8, dimension(ordn) :: ymtmp
real*8 :: dy_temp
real*8, dimension(ordn) :: yntmp
real*8, dimension(ordn) :: yqtmp
m=size(x1a)
n=size(x2a)
do i=1,m
do j=1,n
yqtmp=ya(i,j,:)
call polint(x3a,yqtmp,x3,yatmp(i,j),dy,ordn)
! Sequence change: Process the contiguous first dimension (x1) first.
! We loop through the 'slow' planes (j, k) to extract 'fast' columns.
do k=1,ordn
do j=1,ordn
! ya(:,j,k) is contiguous; much faster than ya(i,j,:)
call polint(x1a, ya(:,j,k), x1, yatmp(j,k), dy_temp, ordn)
end do
end do
! Now process the second dimension
do k=1,ordn
call polint(x2a, yatmp(:,k), x2, ymtmp(k), dy_temp, ordn)
yntmp=yatmp(i,:)
call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
end do
! Final dimension
call polint(x3a, ymtmp, x3, y, dy, ordn)
call polint(x1a,ymtmp,x1,y,dy,ordn)
return
end subroutine polin3
!--------------------------------------------------------------------------------------
! calculate L2norm
@@ -1267,7 +1276,9 @@ subroutine polin3(x1a,x2a,x3a,ya,x1,x2,x3,y,dy,ordn)
real*8 :: dX, dY, dZ
integer::imin,jmin,kmin
integer::imax,jmax,kmax
integer::i,j,k
integer::i,j,k,n_elements
real*8, dimension(:), allocatable :: f_flat
real*8, external :: DDOT
dX = X(2) - X(1)
dY = Y(2) - Y(1)
@@ -1291,7 +1302,12 @@ if(dabs(X(1)-xmin) < dX) imin = 1
if(dabs(Y(1)-ymin) < dY) jmin = 1
if(dabs(Z(1)-zmin) < dZ) kmin = 1
f_out = sum(f(imin:imax,jmin:jmax,kmin:kmax)*f(imin:imax,jmin:jmax,kmin:kmax))
! Optimized with oneMKL BLAS DDOT for dot product
n_elements = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
allocate(f_flat(n_elements))
f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [n_elements])
f_out = DDOT(n_elements, f_flat, 1, f_flat, 1)
deallocate(f_flat)
f_out = f_out*dX*dY*dZ
@@ -1316,7 +1332,9 @@ f_out = f_out*dX*dY*dZ
real*8 :: dX, dY, dZ
integer::imin,jmin,kmin
integer::imax,jmax,kmax
integer::i,j,k
integer::i,j,k,n_elements
real*8, dimension(:), allocatable :: f_flat
real*8, external :: DDOT
real*8 :: PIo4
@@ -1379,7 +1397,12 @@ if(Symmetry==2)then
if(dabs(ymin+gw*dY)<dY.and.Y(1)<0.d0) jmin = gw+1
endif
f_out = sum(f(imin:imax,jmin:jmax,kmin:kmax)*f(imin:imax,jmin:jmax,kmin:kmax))
! Optimized with oneMKL BLAS DDOT for dot product
n_elements = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
allocate(f_flat(n_elements))
f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [n_elements])
f_out = DDOT(n_elements, f_flat, 1, f_flat, 1)
deallocate(f_flat)
f_out = f_out*dX*dY*dZ
@@ -1407,6 +1430,8 @@ f_out = f_out*dX*dY*dZ
integer::imin,jmin,kmin
integer::imax,jmax,kmax
integer::i,j,k
real*8, dimension(:), allocatable :: f_flat
real*8, external :: DDOT
real*8 :: PIo4
@@ -1469,11 +1494,12 @@ if(Symmetry==2)then
if(dabs(ymin+gw*dY)<dY.and.Y(1)<0.d0) jmin = gw+1
endif
f_out = sum(f(imin:imax,jmin:jmax,kmin:kmax)*f(imin:imax,jmin:jmax,kmin:kmax))
f_out = f_out
! Optimized with oneMKL BLAS DDOT for dot product
Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
allocate(f_flat(Nout))
f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [Nout])
f_out = DDOT(Nout, f_flat, 1, f_flat, 1)
deallocate(f_flat)
return
@@ -1671,6 +1697,7 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
real*8, dimension(ORDN,ORDN) :: tmp2
real*8, dimension(ORDN) :: tmp1
real*8, dimension(3) :: SoAh
real*8, external :: DDOT
! +1 because c++ gives 0 for first point
cxB = inds+1
@@ -1706,20 +1733,21 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
ya=fh(cxB(1):cxT(1),cxB(2):cxT(2),cxB(3):cxT(3))
endif
! Optimized with BLAS operations for better performance
! First dimension: z-direction weighted sum
tmp2=0
do m=1,ORDN
tmp2 = tmp2 + coef(2*ORDN+m)*ya(:,:,m)
enddo
! Second dimension: y-direction weighted sum
tmp1=0
do m=1,ORDN
tmp1 = tmp1 + coef(ORDN+m)*tmp2(:,m)
enddo
f_int=0
do m=1,ORDN
f_int = f_int + coef(m)*tmp1(m)
enddo
! Third dimension: x-direction weighted sum using BLAS DDOT
f_int = DDOT(ORDN, coef(1:ORDN), 1, tmp1, 1)
return
@@ -1749,6 +1777,7 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
real*8, dimension(ORDN,ORDN) :: ya
real*8, dimension(ORDN) :: tmp1
real*8, dimension(2) :: SoAh
real*8, external :: DDOT
! +1 because c++ gives 0 for first point
cxB = inds(1:2)+1
@@ -1778,15 +1807,14 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
ya=fh(cxB(1):cxT(1),cxB(2):cxT(2),inds(3))
endif
! Optimized with BLAS operations
tmp1=0
do m=1,ORDN
tmp1 = tmp1 + coef(ORDN+m)*ya(:,m)
enddo
f_int=0
do m=1,ORDN
f_int = f_int + coef(m)*tmp1(m)
enddo
! Use BLAS DDOT for final weighted sum
f_int = DDOT(ORDN, coef(1:ORDN), 1, tmp1, 1)
return
@@ -1817,6 +1845,7 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
real*8, dimension(ORDN) :: ya
real*8 :: SoAh
integer,dimension(3) :: inds
real*8, external :: DDOT
! +1 because c++ gives 0 for first point
inds = indsi + 1
@@ -1877,10 +1906,8 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
write(*,*)"error in global_interpind1d, not recognized dumyd = ",dumyd
endif
f_int=0
do m=1,ORDN
f_int = f_int + coef(m)*ya(m)
enddo
! Optimized with BLAS DDOT for weighted sum
f_int = DDOT(ORDN, coef, 1, ya, 1)
return
@@ -2112,24 +2139,38 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
end function fWigner_d_function
!----------------------------------
! Optimized factorial function using lookup table for small N
! and log-gamma for large N to avoid overflow
function ffact(N) result(gont)
implicit none
integer,intent(in) :: N
real*8 :: gont
integer :: i
! Lookup table for factorials 0! to 20! (precomputed)
real*8, parameter, dimension(0:20) :: fact_table = [ &
1.d0, 1.d0, 2.d0, 6.d0, 24.d0, 120.d0, 720.d0, 5040.d0, 40320.d0, &
362880.d0, 3628800.d0, 39916800.d0, 479001600.d0, 6227020800.d0, &
87178291200.d0, 1307674368000.d0, 20922789888000.d0, &
355687428096000.d0, 6402373705728000.d0, 121645100408832000.d0, &
2432902008176640000.d0 ]
! sanity check
if(N < 0)then
write(*,*) "ffact: error input for factorial"
gont = 1.d0
return
endif
gont = 1.d0
do i=1,N
gont = gont*i
enddo
! Use lookup table for small N (fast path)
if(N <= 20)then
gont = fact_table(N)
else
! Use log-gamma function for large N: N! = exp(log_gamma(N+1))
! This avoids overflow and is computed efficiently
gont = exp(log_gamma(dble(N+1)))
endif
return
@@ -2263,4 +2304,3 @@ subroutine find_maximum(ext,X,Y,Z,fun,val,pos,llb,uub)
return
end subroutine

View File

@@ -16,115 +16,66 @@ using namespace std;
#include <string.h>
#include <math.h>
#endif
/* Linear equation solution by Gauss-Jordan elimination.
// Intel oneMKL LAPACK interface
#include <mkl_lapacke.h>
/* Linear equation solution using Intel oneMKL LAPACK.
a[0..n-1][0..n-1] is the input matrix. b[0..n-1] is input
containing the right-hand side vectors. On output a is
replaced by its matrix inverse, and b is replaced by the
corresponding set of solution vectors */
corresponding set of solution vectors.
Mathematical equivalence:
Solves: A * x = b => x = A^(-1) * b
Original Gauss-Jordan and LAPACK dgesv/dgetri produce identical results
within numerical precision. */
int gaussj(double *a, double *b, int n)
{
double swap;
// Allocate pivot array and workspace
lapack_int *ipiv = new lapack_int[n];
lapack_int info;
int *indxc, *indxr, *ipiv;
indxc = new int[n];
indxr = new int[n];
ipiv = new int[n];
int i, icol, irow, j, k, l, ll;
double big, dum, pivinv, temp;
for (j = 0; j < n; j++)
ipiv[j] = 0;
for (i = 0; i < n; i++)
{
big = 0.0;
for (j = 0; j < n; j++)
if (ipiv[j] != 1)
for (k = 0; k < n; k++)
{
if (ipiv[k] == 0)
{
if (fabs(a[j * n + k]) >= big)
{
big = fabs(a[j * n + k]);
irow = j;
icol = k;
}
}
else if (ipiv[k] > 1)
{
cout << "gaussj: Singular Matrix-1" << endl;
for (int ii = 0; ii < n; ii++)
{
for (int jj = 0; jj < n; jj++)
cout << a[ii * n + jj] << " ";
cout << endl;
}
return 1; // error return
}
// Make a copy of matrix a for solving (dgesv modifies it to LU form)
double *a_copy = new double[n * n];
for (int i = 0; i < n * n; i++) {
a_copy[i] = a[i];
}
ipiv[icol] = ipiv[icol] + 1;
if (irow != icol)
{
for (l = 0; l < n; l++)
{
swap = a[irow * n + l];
a[irow * n + l] = a[icol * n + l];
a[icol * n + l] = swap;
}
// Step 1: Solve linear system A*x = b using LU decomposition
// LAPACKE_dgesv uses column-major by default, but we use row-major
info = LAPACKE_dgesv(LAPACK_ROW_MAJOR, n, 1, a_copy, n, ipiv, b, 1);
swap = b[irow];
b[irow] = b[icol];
b[icol] = swap;
}
indxr[i] = irow;
indxc[i] = icol;
if (a[icol * n + icol] == 0.0)
{
cout << "gaussj: Singular Matrix-2" << endl;
for (int ii = 0; ii < n; ii++)
{
for (int jj = 0; jj < n; jj++)
cout << a[ii * n + jj] << " ";
cout << endl;
}
return 1; // error return
}
pivinv = 1.0 / a[icol * n + icol];
a[icol * n + icol] = 1.0;
for (l = 0; l < n; l++)
a[icol * n + l] *= pivinv;
b[icol] *= pivinv;
for (ll = 0; ll < n; ll++)
if (ll != icol)
{
dum = a[ll * n + icol];
a[ll * n + icol] = 0.0;
for (l = 0; l < n; l++)
a[ll * n + l] -= a[icol * n + l] * dum;
b[ll] -= b[icol] * dum;
}
}
for (l = n - 1; l >= 0; l--)
{
if (indxr[l] != indxc[l])
for (k = 0; k < n; k++)
{
swap = a[k * n + indxr[l]];
a[k * n + indxr[l]] = a[k * n + indxc[l]];
a[k * n + indxc[l]] = swap;
}
}
delete[] indxc;
delete[] indxr;
if (info != 0) {
cout << "gaussj: Singular Matrix (dgesv info=" << info << ")" << endl;
delete[] ipiv;
delete[] a_copy;
return 1;
}
// Step 2: Compute matrix inverse A^(-1) using LU factorization
// First do LU factorization of original matrix a
info = LAPACKE_dgetrf(LAPACK_ROW_MAJOR, n, n, a, n, ipiv);
if (info != 0) {
cout << "gaussj: Singular Matrix (dgetrf info=" << info << ")" << endl;
delete[] ipiv;
delete[] a_copy;
return 1;
}
// Then compute inverse from LU factorization
info = LAPACKE_dgetri(LAPACK_ROW_MAJOR, n, a, n, ipiv);
if (info != 0) {
cout << "gaussj: Singular Matrix (dgetri info=" << info << ")" << endl;
delete[] ipiv;
delete[] a_copy;
return 1;
}
delete[] ipiv;
delete[] a_copy;
return 0;
}

View File

@@ -512,11 +512,10 @@
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION V(N),W(N)
! SUBROUTINE TO COMPUTE DOUBLE PRECISION VECTOR DOT PRODUCT.
! Optimized using Intel oneMKL BLAS ddot
! Mathematical equivalence: DGVV = sum_{i=1}^{N} V(i)*W(i)
SUM = 0.0D0
DO 10 I = 1,N
SUM = SUM + V(I)*W(I)
10 CONTINUE
DGVV = SUM
DOUBLE PRECISION, EXTERNAL :: DDOT
DGVV = DDOT(N, V, 1, W, 1)
RETURN
END

View File

@@ -2,7 +2,7 @@
#ifndef MICRODEF_H
#define MICRODEF_H
#include "microdef.fh"
#include "macrodef.fh"
// application parameters

View File

@@ -15,19 +15,18 @@ LDLIBS = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore
## -xHost: Optimize for the host CPU architecture (Intel/AMD compatible)
## -fp-model fast=2: Aggressive floating-point optimizations
## -fma: Enable fused multiply-add instructions
## Note: OpenMP has been disabled (-qopenmp removed) due to performance issues
CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma \
## Note: OpenMP enabled for hybrid MPI+OpenMP
CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -qopenmp \
-Dfortran3 -Dnewc -I${MKLROOT}/include
f90appflags = -O3 -xHost -fp-model fast=2 -fma \
f90appflags = -O3 -xHost -fp-model fast=2 -fma -qopenmp \
-fpp -I${MKLROOT}/include
f90 = ifx
f77 = ifx
CXX = icpx
CC = icx
CLINKER = mpiicpx
CLINKER = mpiicpx -qopenmp
Cu = nvcc
CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include
#CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -arch compute_13 -code compute_13,sm_13 -Dfortran3 -Dnewc
CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -Dfortran3 -Dnewc

View File

@@ -11,6 +11,15 @@
import AMSS_NCKU_Input as input_data
import subprocess
## CPU core binding configuration
## Removed hardcoded taskset to allow full utilization of 96 cores via MPI+OpenMP
NUMACTL_CPU_BIND = ""
## Build parallelism configuration
## Use nohz_full cores (4-55, 60-111) for compilation: 52 + 52 = 104 cores
## Set make -j to utilize available cores for faster builds
BUILD_JOBS = 96
##################################################################
@@ -28,9 +37,9 @@ def makefile_ABE():
## Build command
if (input_data.GPU_Calculation == "no"):
makefile_command = "make -j4" + " ABE"
makefile_command = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABE"
elif (input_data.GPU_Calculation == "yes"):
makefile_command = "make -j4" + " ABEGPU"
makefile_command = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
else:
print( " CPU/GPU numerical calculation setting is wrong " )
print( )
@@ -68,7 +77,7 @@ def makefile_TwoPunctureABE():
print( )
## Build command
makefile_command = "make" + " TwoPunctureABE"
makefile_command = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} TwoPunctureABE"
## Execute the command with subprocess.Popen and stream output
makefile_process = subprocess.Popen(makefile_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True)
@@ -102,13 +111,23 @@ def run_ABE():
print( " Running the AMSS-NCKU executable file ABE/ABEGPU " )
print( )
## Calculate OMP_NUM_THREADS
## User has 96 cores. Calculate threads per MPI process.
total_physical_cores = 96
omp_num_threads = total_physical_cores // input_data.MPI_processes
if omp_num_threads < 1:
omp_num_threads = 1
print( f" Configuration: {input_data.MPI_processes} MPI processes, {omp_num_threads} OpenMP threads per process." )
print( f" Total cores utilized: {input_data.MPI_processes * omp_num_threads}" )
## Define the command to run; cast other values to strings as needed
if (input_data.GPU_Calculation == "no"):
mpi_command = "mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
mpi_command = f"{NUMACTL_CPU_BIND} mpirun -genv OMP_NUM_THREADS {omp_num_threads} -np {input_data.MPI_processes} ./ABE"
mpi_command_outfile = "ABE_out.log"
elif (input_data.GPU_Calculation == "yes"):
mpi_command = "mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
mpi_command = f"{NUMACTL_CPU_BIND} mpirun -genv OMP_NUM_THREADS {omp_num_threads} -np {input_data.MPI_processes} ./ABEGPU"
mpi_command_outfile = "ABEGPU_out.log"
## Execute the MPI command and stream output
@@ -147,7 +166,7 @@ def run_TwoPunctureABE():
print( )
## Define the command to run
TwoPuncture_command = "./TwoPunctureABE"
TwoPuncture_command = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
TwoPuncture_command_outfile = "TwoPunctureABE_out.log"
## Execute the command with subprocess.Popen and stream output