Trigger-Discipline: parallelize result plotting

.gitignore

@@ -1,7 +1,5 @@
 __pycache__
 GW150914
-GW150914-origin
+GW150914*
-GW150914-mini
+.codex
-docs
+docs/
-*.tmp
-

AMSS_NCKU_Input.py

@@ -16,14 +16,12 @@ 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    = 8                             ## number of mpi processes used in the simulation
+MPI_processes    = 64                             ## 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)
 CPU_Part         = 1.0
 GPU_Part         = 0.0
-Debug_NaN_Check          = 0                       ## enable NaN checks in compute_rhs_bssn: 0 (off) or 1 (on)
-
 
 #################################################
 

AMSS_NCKU_Input_Mini.py

@@ -1,233 +0,0 @@
-
-#################################################
-##
-## This file provides the input parameters required for numerical relativity.
-## XIAOQU
-## 2024/03/19 --- 2025/09/14
-## Modified for GW150914-mini test case
-##
-#################################################
-
-import numpy    
-
-#################################################
-
-## Setting MPI processes and the output file directory
-
-File_directory   = "GW150914-mini"               ## output file directory
-Output_directory = "binary_output"               ## binary data file directory
-                                                 ## The file directory name should not be too long
-MPI_processes    = 4                             ## number of mpi processes used in the simulation (Reduced for laptop)
-
-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)
-CPU_Part         = 1.0
-GPU_Part         = 0.0
-
-#################################################
-
-
-#################################################
-
-## Setting the physical system and numerical method
-
-Symmetry                 = "equatorial-symmetry"   ## Symmetry of System: choose equatorial-symmetry、no-symmetry、octant-symmetry
-Equation_Class           = "BSSN"                  ## Evolution Equation: choose "BSSN", "BSSN-EScalar", "BSSN-EM", "Z4C" 
-                                                   ## If "BSSN-EScalar" is chosen, it is necessary to set other parameters below
-Initial_Data_Method      = "Ansorg-TwoPuncture"    ## initial data method: choose "Ansorg-TwoPuncture", "Lousto-Analytical", "Cao-Analytical", "KerrSchild-Analytical"
-Time_Evolution_Method    = "runge-kutta-45"        ## time evolution method: choose "runge-kutta-45"
-Finite_Diffenence_Method = "4th-order"             ## finite-difference method: choose "2nd-order", "4th-order", "6th-order", "8th-order"
-Debug_NaN_Check          = 0                       ## enable NaN checks in compute_rhs_bssn: 0 (off) or 1 (on)
-
-#################################################
-
-
-#################################################
-
-## Setting the time evolutionary information
-
-Start_Evolution_Time     = 0.0                    ## start evolution time t0
-Final_Evolution_Time     = 100.0                  ## final evolution time t1 (Reduced for quick test)
-Check_Time               = 10.0
-Dump_Time                = 10.0                   ## time inteval dT for dumping binary data
-D2_Dump_Time             = 10.0                   ## dump the ascii data for 2d surface after dT'
-Analysis_Time            = 1.0                    ## dump the puncture position and GW psi4 after dT"
-Evolution_Step_Number    = 10000000               ## stop the calculation after the maximal step number
-Courant_Factor           = 0.5                    ## Courant Factor
-Dissipation              = 0.15                   ## Kreiss-Oliger Dissipation Strength
-
-#################################################
-
-
-#################################################
-
-## Setting the grid structure
-
-basic_grid_set    = "Patch"                          ## grid structure: choose "Patch" or "Shell-Patch"
-grid_center_set   = "Cell"                           ## grid center: chose "Cell" or "Vertex"
-
-grid_level        = 7                                ## total number of AMR grid levels (Reduced from 9)
-static_grid_level = 4                                ## number of AMR static grid levels (Reduced from 5)
-moving_grid_level = grid_level - static_grid_level   ## number of AMR moving grid levels
-
-analysis_level    = 0
-refinement_level  = 3                                ## time refinement start from this grid level
-
-largest_box_xyz_max = [320.0, 320.0, 320.0]          ## scale of the largest box
-                                                     ## not ne cess ary to be cubic for "Patch" grid s tructure
-                                                     ## need to be a cubic box for "Shell-Patch" grid structure
-largest_box_xyz_min = - numpy.array(largest_box_xyz_max)  
-
-static_grid_number = 48                              ## grid points of each static AMR grid (in x direction) (Reduced from 96)
-                                                     ## (grid points in y and z directions are automatically adjusted)
-moving_grid_number = 24                              ## grid points of each moving AMR grid (Reduced from 48)
-shell_grid_number  = [32, 32, 100]                   ## grid points of Shell-Patch grid
-                                                     ## in (phi, theta, r) direction
-devide_factor      = 2.0                             ## resolution between different grid levels dh0/dh1, only support 2.0 now
-                                                     
-
-static_grid_type   = 'Linear'                        ## AMR static grid structure , only supports "Linear"
-moving_grid_type   = 'Linear'                        ## AMR moving grid structure , only supports "Linear"
-
-quarter_sphere_number = 48                           ## grid number of 1/4 s pher ical surface (Reduced from 96)
-                                                     ## (which is needed for evaluating the spherical surface integral)
-
-#################################################
-
-
-#################################################
-
-## Setting the puncture information
-
-puncture_number       = 2                                     
-
-position_BH           = numpy.zeros( (puncture_number, 3) )   
-parameter_BH          = numpy.zeros( (puncture_number, 3) )   
-dimensionless_spin_BH = numpy.zeros( (puncture_number, 3) )   
-momentum_BH           = numpy.zeros( (puncture_number, 3) )   
-
-puncture_data_set     = "Manually"                       ## Method to give Puncture’s positions and momentum
-                                                         ## choose "Manually" or "Automatically-BBH"
-                                                         ## Prefer to choose "Manually", because "Automatically-BBH" is developing now
-
-## initial orbital distance and ellipticity for BBHs system
-## ( needed for "Automatically-BBH" case , not affect the "Manually" case )
-Distance = 10.0
-e0       = 0.0
-
-## black hole parameter (M Q* a*)
-parameter_BH[0] = [ 36.0/(36.0+29.0),  0.0,  +0.31 ]   
-parameter_BH[1] = [ 29.0/(36.0+29.0),  0.0,  -0.46 ]  
-## dimensionless spin in each direction
-dimensionless_spin_BH[0] = [ 0.0,  0.0,  +0.31 ]   
-dimensionless_spin_BH[1] = [ 0.0,  0.0,  -0.46 ]  
-
-## use Brugmann's convention
-##  -----0-----> y
-##   -      +     
-
-#---------------------------------------------
-
-## If puncture_data_set is chosen to be "Manually", it is necessary to set the position and momentum of each puncture manually
-
-## initial position for each puncture
-position_BH[0]  = [  0.0,  10.0*29.0/(36.0+29.0), 0.0 ]  
-position_BH[1]  = [  0.0, -10.0*36.0/(36.0+29.0), 0.0 ] 
-
-## initial mumentum for each puncture
-## (needed for "Manually" case, does not affect the "Automatically-BBH" case)
-momentum_BH[0]  = [ -0.09530152296974252,  -0.00084541526517121,   0.0 ]
-momentum_BH[1]  = [ +0.09530152296974252,  +0.00084541526517121,   0.0 ]
-
-
-#################################################
-
-
-#################################################
-
-## Setting the gravitational wave information
-
-GW_L_max        = 4                      ## maximal L number in gravitational wave
-GW_M_max        = 4                      ## maximal M number in gravitational wave
-Detector_Number = 12                     ## number of dector
-Detector_Rmin   = 50.0                   ## nearest dector distance
-Detector_Rmax   = 160.0                  ## farest dector distance
-
-#################################################
-
-
-#################################################
-
-## Setting the apprent horizon
-
-AHF_Find       = "no"                    ## whether to find the apparent horizon: choose "yes" or "no"
-
-AHF_Find_Every = 24
-AHF_Dump_Time  = 20.0
-
-#################################################
-
-
-#################################################
-
-## Other parameters (testing)
-## Only influence the Equation_Class = "BSSN-EScalar" case
-
-FR_a2     = 3.0        ## f(R) = R + a2 * R^2    
-FR_l2     = 10000.0
-FR_phi0   = 0.00005
-FR_r0     = 120.0
-FR_sigma0 = 8.0
-FR_Choice = 2          ## Choice options: 1 2 3 4 5
-                       ## 1: phi(r) = phi0 * Exp(-(r-r0)**2/sigma0)   
-                       ##    V(r)   = 0
-                       ## 2: phi(r) =  phi0 * a2^2/(1+a2^2)  
-                       ##    V(r)   = Exp(-8*Sqrt(PI/3)*phi(r)) * (1-Exp(4*Sqrt(PI/3)*phi(r)))**2 / (32*PI*a2)
-                       ## 3: Schrodinger-Newton gived by system phi(r) 
-                       ##    V(r)   = Exp(-8*Sqrt(PI/3)*phi(r)) * (1-Exp(4*Sqrt(PI/3)*phi(r)))**2 / (32*PI*a2)
-                       ## 4: phi(r) = phi0 * 0.5 * ( tanh((r+r0)/sigma0) - tanh((r-r0)/sigma0) )  
-                       ##    V(r)   = 0
-                       ##    f(R)   = R + a2*R^2  with a2 = +oo
-                       ## 5: phi(r) = phi0 * Exp(-(r-r0)**2/sigma)   
-                       ##    V(r)   = 0
-
-#################################################
-
-
-#################################################
-
-## Other parameters (testing)
-## (please do not change if not necessary)
-
-boundary_choice = "BAM-choice"     ## Sommerfeld boundary condition : choose "BAM-choice" or "Shibata-choice" 
-                                   ## prefer "BAM-choice"
-
-gauge_choice  = 0                  ## gauge choice
-                                   ## 0: B^i gauge
-                                   ## 1: David's puncture gauge
-                                   ## 2: MB B^i gauge               
-                                   ## 3: RIT B^i gauge
-                                   ## 4: MB beta gauge 
-                                   ## 5: RIT beta gauge 
-                                   ## 6: MGB1 B^i gauge
-                                   ## 7: MGB2 B^i gauge
-                                   ## prefer 0 or 1
-                                   
-tetrad_type  = 2                   ## tetradtype 
-                                   ##  v:r; u: phi; w: theta
-                                   ##      v^a = (x,y,z)
-                                   ## 0: orthonormal order: v,u,w
-                                   ##    v^a = (x,y,z)   
-                                   ##    m = (phi - i theta)/sqrt(2) 
-                                   ##    following Frans, Eq.(8) of  PRD 75, 124018(2007)
-                                   ## 1: orthonormal order: w,u,v
-                                   ##    m = (theta + i phi)/sqrt(2) 
-                                   ##    following Sperhake, Eq.(3.2) of  PRD 85, 124062(2012)    
-                                   ## 2: orthonormal order: v,u,w
-                                   ##    v_a = (x,y,z)
-                                   ##    m = (phi - i theta)/sqrt(2) 
-                                   ##    following Frans, Eq.(8) of  PRD 75, 124018(2007)
-                                   ## this version recommend set to 2
-                                   ## prefer 2
-                                   
-#################################################

AMSS_NCKU_MiniProgram.py

@@ -1,224 +0,0 @@
-##################################################################
-##
-## AMSS-NCKU Numerical Relativity Mini Test Program
-## Author: Assistant (based on Xiaoqu's code)
-## 2026/01/20
-##
-## This script runs a scaled-down version of the GW150914 test case
-## suitable for laptop testing.
-##
-##################################################################
-
-import os
-import shutil
-import sys
-import time
-
-# --- Context Manager for Input File Swapping ---
-class InputFileSwapper:
-    def __init__(self, mini_file="AMSS_NCKU_Input_Mini.py", target_file="AMSS_NCKU_Input.py"):
-        self.mini_file = mini_file
-        self.target_file = target_file
-        self.backup_file = target_file + ".bak"
-        self.swapped = False
-
-    def __enter__(self):
-        print(f"[MiniProgram] Swapping {self.target_file} with {self.mini_file}...")
-        if os.path.exists(self.target_file):
-            shutil.move(self.target_file, self.backup_file)
-        shutil.copy(self.mini_file, self.target_file)
-        self.swapped = True
-        return self
-
-    def __exit__(self, exc_type, exc_value, traceback):
-        if self.swapped:
-            print(f"[MiniProgram] Restoring original {self.target_file}...")
-            os.remove(self.target_file)
-            if os.path.exists(self.backup_file):
-                shutil.move(self.backup_file, self.target_file)
-
-def main():
-    # Use the swapper to ensure all imported modules see the mini configuration
-    with InputFileSwapper():
-        
-        # Import modules AFTER swapping input file
-        try:
-            import AMSS_NCKU_Input as input_data
-            import print_information
-            import setup
-            import numerical_grid
-            import generate_macrodef
-            import makefile_and_run
-            import generate_TwoPuncture_input
-            import renew_puncture_parameter
-            import plot_xiaoqu
-            import plot_GW_strain_amplitude_xiaoqu
-        except ImportError as e:
-            print(f"Error importing modules: {e}")
-            return
-
-        print_information.print_program_introduction()
-        
-        print("\n" + "#"*60)
-        print(" RUNNING MINI TEST CASE: GW150914-mini")
-        print("#"*60 + "\n")
-
-        # --- Directory Setup ---
-        File_directory = os.path.join(input_data.File_directory)
-        
-        if os.path.exists(File_directory):
-            print(f" Output directory '{File_directory}' exists. Removing for mini test...")
-            shutil.rmtree(File_directory, ignore_errors=True)
-        
-        os.mkdir(File_directory)
-        shutil.copy("AMSS_NCKU_Input.py", File_directory) # Copies the current (mini) input
-
-        output_directory = os.path.join(File_directory, "AMSS_NCKU_output")
-        os.mkdir(output_directory)
-
-        binary_results_directory = os.path.join(output_directory, input_data.Output_directory)
-        os.mkdir(binary_results_directory)
-
-        figure_directory = os.path.join(File_directory, "figure")
-        os.mkdir(figure_directory)
-
-        print(" Output directories generated.\n")
-
-        # --- Setup and Input Generation ---
-        setup.print_input_data(File_directory)
-        setup.generate_AMSSNCKU_input()
-        setup.print_puncture_information()
-
-        print("\n Generating AMSS-NCKU input parfile...")
-        numerical_grid.append_AMSSNCKU_cgh_input()
-        
-        print("\n Plotting initial grid...")
-        numerical_grid.plot_initial_grid()
-
-        print("\n Generating macro files...")
-        generate_macrodef.generate_macrodef_h()
-        generate_macrodef.generate_macrodef_fh()
-        
-        # --- Compilation Preparation ---
-        print("\n Preparing to compile and run...")
-        
-        AMSS_NCKU_source_path = "AMSS_NCKU_source"
-        AMSS_NCKU_source_copy = os.path.join(File_directory, "AMSS_NCKU_source_copy")
-
-        if not os.path.exists(AMSS_NCKU_source_path):
-             print(" Error: AMSS_NCKU_source not found! Please run in the project root.")
-             return
-
-        shutil.copytree(AMSS_NCKU_source_path, AMSS_NCKU_source_copy)
-        
-        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)
-
-        # --- Compilation ---
-        cwd = os.getcwd()
-        os.chdir(AMSS_NCKU_source_copy)
-        
-        print(" Compiling ABE...")
-        makefile_and_run.makefile_ABE()
-        
-        if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ): 
-            print(" Compiling TwoPunctureABE...")
-            makefile_and_run.makefile_TwoPunctureABE()
-            
-        os.chdir(cwd)
-
-        # --- Copy Executables ---
-        if (input_data.GPU_Calculation == "no"):
-            ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABE")
-        else:
-            ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABEGPU")
-            
-        if not os.path.exists(ABE_file):
-            print(" Error: ABE executable compilation failed.")
-            return
-            
-        shutil.copy2(ABE_file, output_directory)
-
-        TwoPuncture_file = os.path.join(AMSS_NCKU_source_copy, "TwoPunctureABE")
-        if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ):
-            if not os.path.exists(TwoPuncture_file):
-                print(" Error: TwoPunctureABE compilation failed.")
-                return
-            shutil.copy2(TwoPuncture_file, output_directory)
-
-        # --- Execution ---
-        start_time = time.time()
-        
-        if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ):
-             print("\n Generating TwoPuncture input...")
-             generate_TwoPuncture_input.generate_AMSSNCKU_TwoPuncture_input()
-             
-             AMSS_NCKU_TwoPuncture_inputfile = 'AMSS-NCKU-TwoPuncture.input'
-             AMSS_NCKU_TwoPuncture_inputfile_path = os.path.join( File_directory, AMSS_NCKU_TwoPuncture_inputfile )
-             shutil.copy2( AMSS_NCKU_TwoPuncture_inputfile_path, os.path.join(output_directory, 'TwoPunctureinput.par') )
-             
-             print(" Running TwoPunctureABE...")
-             os.chdir(output_directory)
-             makefile_and_run.run_TwoPunctureABE()
-             os.chdir(cwd)
-
-        # Update Puncture Parameter
-        renew_puncture_parameter.append_AMSSNCKU_BSSN_input(File_directory, output_directory)
-        
-        AMSS_NCKU_inputfile = 'AMSS-NCKU.input'
-        AMSS_NCKU_inputfile_path = os.path.join(File_directory, AMSS_NCKU_inputfile)
-        shutil.copy2( AMSS_NCKU_inputfile_path, os.path.join(output_directory, 'input.par') )
-        
-        print("\n Input files ready. Launching ABE...")
-        
-        os.chdir(output_directory)
-        makefile_and_run.run_ABE()
-        os.chdir(cwd)
-        
-        end_time = time.time()
-        elapsed_time = end_time - start_time
-        
-        # --- Post-processing ---
-        print("\n Copying output files for inspection...")
-        AMSS_NCKU_error_file_path = os.path.join(binary_results_directory, "setting.par")
-        if os.path.exists(AMSS_NCKU_error_file_path):
-            shutil.copy( AMSS_NCKU_error_file_path, os.path.join(output_directory, "AMSSNCKU_setting_parameter") )
-
-        AMSS_NCKU_error_file_path = os.path.join(binary_results_directory, "Error.log")
-        if os.path.exists(AMSS_NCKU_error_file_path):
-            shutil.copy( AMSS_NCKU_error_file_path, os.path.join(output_directory, "Error.log") )
-
-        for fname in ["bssn_BH.dat", "bssn_ADMQs.dat", "bssn_psi4.dat", "bssn_constraint.dat"]:
-            fpath = os.path.join(binary_results_directory, fname)
-            if os.path.exists(fpath):
-                shutil.copy(fpath, os.path.join(output_directory, fname))
-
-        # --- Plotting ---
-        print("\n Plotting results...")
-        try:
-            plot_xiaoqu.generate_puncture_orbit_plot(   binary_results_directory, figure_directory )
-            plot_xiaoqu.generate_puncture_orbit_plot3D( binary_results_directory, figure_directory )
-            plot_xiaoqu.generate_puncture_distence_plot( binary_results_directory, figure_directory )
-            
-            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 )
-
-            for i in range(input_data.Detector_Number):
-                plot_xiaoqu.generate_ADMmass_plot( binary_results_directory, figure_directory, i )
-
-            for i in range(input_data.grid_level):
-                plot_xiaoqu.generate_constraint_check_plot( binary_results_directory, figure_directory, i )
-                
-            plot_xiaoqu.generate_binary_data_plot( binary_results_directory, figure_directory )
-        except Exception as e:
-            print(f"Warning: Plotting failed: {e}")
-
-        print(f"\n Program Cost = {elapsed_time:.2f} Seconds \n")
-        print(" AMSS-NCKU-Python simulation finished (Mini Test).\n")
-
-if __name__ == "__main__":
-    main()

AMSS_NCKU_Program.py

@@ -9,9 +9,19 @@
 ##################################################################
 
 
-##################################################################
+##################################################################
-
+
-## Print program introduction
+## Guard against re-execution by multiprocessing child processes.
+## Without this, using 'spawn' or 'forkserver' context would cause every
+## worker to re-run the entire script.
+if __name__ != '__main__':
+    import sys as _sys
+    _sys.exit(0)
+
+
+##################################################################
+
+## Print program introduction
 
 import print_information
 
@@ -422,31 +432,36 @@ print( " Plotting the txt and binary results data from the AMSS-NCKU simulation
 print(                                                                          )
 
 
-import plot_xiaoqu
+import plot_xiaoqu
-import plot_GW_strain_amplitude_xiaoqu
+import plot_GW_strain_amplitude_xiaoqu
-
+from parallel_plot_helper import run_plot_tasks_parallel
-## Plot black hole trajectory
+
-plot_xiaoqu.generate_puncture_orbit_plot(   binary_results_directory, figure_directory )
+plot_tasks = []
-plot_xiaoqu.generate_puncture_orbit_plot3D( binary_results_directory, figure_directory )
+
-
+## Plot black hole trajectory
-## Plot black hole separation vs. time
+plot_tasks.append( ( plot_xiaoqu.generate_puncture_orbit_plot,   (binary_results_directory, figure_directory) ) )
-plot_xiaoqu.generate_puncture_distence_plot( binary_results_directory, figure_directory )
+plot_tasks.append( ( plot_xiaoqu.generate_puncture_orbit_plot3D, (binary_results_directory, figure_directory) ) )
-
+
-## Plot gravitational waveforms (psi4 and strain amplitude)
+## Plot black hole separation vs. time
-for i in range(input_data.Detector_Number):
+plot_tasks.append( ( plot_xiaoqu.generate_puncture_distence_plot, (binary_results_directory, figure_directory) ) )
-    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 gravitational waveforms (psi4 and strain amplitude)
-
+for i in range(input_data.Detector_Number):
-## Plot ADM mass evolution
+    plot_tasks.append( ( plot_xiaoqu.generate_gravitational_wave_psi4_plot, (binary_results_directory, figure_directory, i) ) )
-for i in range(input_data.Detector_Number):
+    plot_tasks.append( ( plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot, (binary_results_directory, figure_directory, i) ) )
-    plot_xiaoqu.generate_ADMmass_plot( binary_results_directory, figure_directory, i )
+
-
+## Plot ADM mass evolution
-## Plot Hamiltonian constraint violation over time
+for i in range(input_data.Detector_Number):
-for i in range(input_data.grid_level):
+    plot_tasks.append( ( plot_xiaoqu.generate_ADMmass_plot, (binary_results_directory, figure_directory, i) ) )
-    plot_xiaoqu.generate_constraint_check_plot( binary_results_directory, figure_directory, i )
+
-
+## Plot Hamiltonian constraint violation over time
-## Plot stored binary data
+for i in range(input_data.grid_level):
-plot_xiaoqu.generate_binary_data_plot( binary_results_directory, figure_directory )
+    plot_tasks.append( ( plot_xiaoqu.generate_constraint_check_plot, (binary_results_directory, figure_directory, i) ) )
+
+run_plot_tasks_parallel(plot_tasks)
+
+## Plot stored binary data
+plot_xiaoqu.generate_binary_data_plot( binary_results_directory, figure_directory )
 
 print(                                                 )
 print( f" This Program Cost = {elapsed_time} Seconds " )

AMSS_NCKU_Verify_ASC26.py

@@ -1,279 +0,0 @@
-#!/usr/bin/env python3
-"""
-AMSS-NCKU GW150914 Simulation Regression Test Script
-
-Verification Requirements:
-1. XY-plane trajectory RMS error < 1% (Optimized vs. baseline, max of BH1 and BH2)
-2. ADM constraint violation < 2 (Grid Level 0)
-
-RMS Calculation Method:
-- Computes trajectory deviation on the XY plane independently for BH1 and BH2
-- For each black hole: RMS = sqrt((1/M) * sum((Δr_i / r_i^max)^2)) × 100%
-- Final RMS = max(RMS_BH1, RMS_BH2)
-
-Usage: python3 AMSS_NCKU_Verify_ASC26.py [output_dir]
-Default: output_dir = GW150914/AMSS_NCKU_output
-Reference: GW150914-origin (baseline simulation)
-"""
-
-import numpy as np
-import sys
-import os
-
-# ANSI Color Codes
-class Color:
-    GREEN = '\033[92m'
-    RED = '\033[91m'
-    YELLOW = '\033[93m'
-    BLUE = '\033[94m'
-    BOLD = '\033[1m'
-    RESET = '\033[0m'
-
-def get_status_text(passed):
-    if passed:
-        return f"{Color.GREEN}{Color.BOLD}PASS{Color.RESET}"
-    else:
-        return f"{Color.RED}{Color.BOLD}FAIL{Color.RESET}"
-
-def load_bh_trajectory(filepath):
-    """Load black hole trajectory data"""
-    data = np.loadtxt(filepath)
-    return {
-        'time': data[:, 0],
-        'x1': data[:, 1], 'y1': data[:, 2], 'z1': data[:, 3],
-        'x2': data[:, 4], 'y2': data[:, 5], 'z2': data[:, 6]
-    }
-
-
-def load_constraint_data(filepath):
-    """Load constraint violation data"""
-    data = []
-    with open(filepath, 'r') as f:
-        for line in f:
-            if line.startswith('#'):
-                continue
-            parts = line.split()
-            if len(parts) >= 8:
-                data.append([float(x) for x in parts[:8]])
-    return np.array(data)
-
-
-def calculate_rms_error(bh_data_ref, bh_data_target):
-    """
-    Calculate trajectory-based RMS error on the XY plane between baseline and optimized simulations.
-
-    This function computes the RMS error independently for BH1 and BH2 trajectories,
-    then returns the maximum of the two as the final RMS error metric.
-
-    For each black hole, the RMS is calculated as:
-        RMS = sqrt( (1/M) * sum( (Δr_i / r_i^max)^2 ) ) × 100%
-
-    where:
-        Δr_i = sqrt((x_ref,i - x_new,i)^2 + (y_ref,i - y_new,i)^2)
-        r_i^max = max(sqrt(x_ref,i^2 + y_ref,i^2), sqrt(x_new,i^2 + y_new,i^2))
-
-    Args:
-        bh_data_ref: Reference (baseline) trajectory data
-        bh_data_target: Target (optimized) trajectory data
-
-    Returns:
-        rms_value: Final RMS error as a percentage (max of BH1 and BH2)
-        error: Error message if any
-    """
-    # Align data: truncate to the length of the shorter dataset
-    M = min(len(bh_data_ref['time']), len(bh_data_target['time']))
-
-    if M < 10:
-        return None, "Insufficient data points for comparison"
-
-    # Extract XY coordinates for both black holes
-    x1_ref = bh_data_ref['x1'][:M]
-    y1_ref = bh_data_ref['y1'][:M]
-    x2_ref = bh_data_ref['x2'][:M]
-    y2_ref = bh_data_ref['y2'][:M]
-
-    x1_new = bh_data_target['x1'][:M]
-    y1_new = bh_data_target['y1'][:M]
-    x2_new = bh_data_target['x2'][:M]
-    y2_new = bh_data_target['y2'][:M]
-
-    # Calculate RMS for BH1
-    delta_r1 = np.sqrt((x1_ref - x1_new)**2 + (y1_ref - y1_new)**2)
-    r1_ref = np.sqrt(x1_ref**2 + y1_ref**2)
-    r1_new = np.sqrt(x1_new**2 + y1_new**2)
-    r1_max = np.maximum(r1_ref, r1_new)
-
-    # Calculate RMS for BH2
-    delta_r2 = np.sqrt((x2_ref - x2_new)**2 + (y2_ref - y2_new)**2)
-    r2_ref = np.sqrt(x2_ref**2 + y2_ref**2)
-    r2_new = np.sqrt(x2_new**2 + y2_new**2)
-    r2_max = np.maximum(r2_ref, r2_new)
-
-    # Avoid division by zero for BH1
-    valid_mask1 = r1_max > 1e-15
-    if np.sum(valid_mask1) < 10:
-        return None, "Insufficient valid data points for BH1"
-
-    terms1 = (delta_r1[valid_mask1] / r1_max[valid_mask1])**2
-    rms_bh1 = np.sqrt(np.mean(terms1)) * 100
-
-    # Avoid division by zero for BH2
-    valid_mask2 = r2_max > 1e-15
-    if np.sum(valid_mask2) < 10:
-        return None, "Insufficient valid data points for BH2"
-
-    terms2 = (delta_r2[valid_mask2] / r2_max[valid_mask2])**2
-    rms_bh2 = np.sqrt(np.mean(terms2)) * 100
-
-    # Final RMS is the maximum of BH1 and BH2
-    rms_final = max(rms_bh1, rms_bh2)
-
-    return rms_final, None
-
-
-def analyze_constraint_violation(constraint_data, n_levels=9):
-    """
-    Analyze ADM constraint violation
-    Return maximum constraint violation for Grid Level 0
-    """
-    # Extract Grid Level 0 data (first entry for each time step)
-    level0_data = constraint_data[::n_levels]
-
-    # Calculate maximum absolute value for each constraint
-    results = {
-        'Ham': np.max(np.abs(level0_data[:, 1])),
-        'Px': np.max(np.abs(level0_data[:, 2])),
-        'Py': np.max(np.abs(level0_data[:, 3])),
-        'Pz': np.max(np.abs(level0_data[:, 4])),
-        'Gx': np.max(np.abs(level0_data[:, 5])),
-        'Gy': np.max(np.abs(level0_data[:, 6])),
-        'Gz': np.max(np.abs(level0_data[:, 7]))
-    }
-
-    results['max_violation'] = max(results.values())
-    return results
-
-
-def print_header():
-    """Print report header"""
-    print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
-    print(Color.BOLD + "   AMSS-NCKU GW150914 Simulation Regression Test Report" + Color.RESET)
-    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
-
-
-def print_rms_results(rms_rel, error, threshold=1.0):
-    """Print RMS error results"""
-    print(f"\n{Color.BOLD}1. RMS Error Analysis (Baseline vs Optimized){Color.RESET}")
-    print("-" * 45)
-
-    if error:
-        print(f"   {Color.RED}Error: {error}{Color.RESET}")
-        return False
-
-    passed = rms_rel < threshold
-
-    print(f"   RMS relative error: {rms_rel:.4f}%")
-    print(f"   Requirement:        < {threshold}%")
-    print(f"   Status:             {get_status_text(passed)}")
-
-    return passed
-
-
-def print_constraint_results(results, threshold=2.0):
-    """Print constraint violation results"""
-    print(f"\n{Color.BOLD}2. ADM Constraint Violation Analysis (Grid Level 0){Color.RESET}")
-    print("-" * 45)
-
-    names = ['Ham', 'Px', 'Py', 'Pz', 'Gx', 'Gy', 'Gz']
-    for i, name in enumerate(names):
-        print(f"   Max |{name:3}|: {results[name]:.6f}", end="   ")
-        if (i + 1) % 2 == 0: print()
-    if len(names) % 2 != 0: print()
-
-    passed = results['max_violation'] < threshold
-    
-    print(f"\n   Maximum violation:  {results['max_violation']:.6f}")
-    print(f"   Requirement:        < {threshold}")
-    print(f"   Status:             {get_status_text(passed)}")
-
-    return passed
-
-
-def print_summary(rms_passed, constraint_passed):
-    """Print summary"""
-    print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
-    print(Color.BOLD + "Verification Summary" + Color.RESET)
-    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
-
-    all_passed = rms_passed and constraint_passed
-    
-    res_rms = get_status_text(rms_passed)
-    res_con = get_status_text(constraint_passed)
-
-    print(f"   [1] RMS trajectory check:         {res_rms}")
-    print(f"   [2] ADM constraint check:         {res_con}")
-    
-    final_status = f"{Color.GREEN}{Color.BOLD}ALL CHECKS PASSED{Color.RESET}" if all_passed else f"{Color.RED}{Color.BOLD}SOME CHECKS FAILED{Color.RESET}"
-    print(f"\n   Overall result: {final_status}")
-    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET + "\n")
-
-    return all_passed
-
-
-def main():
-    # Determine target (optimized) output directory
-    if len(sys.argv) > 1:
-        target_dir = sys.argv[1]
-    else:
-        script_dir = os.path.dirname(os.path.abspath(__file__))
-        target_dir = os.path.join(script_dir, "GW150914/AMSS_NCKU_output")
-
-    # Determine reference (baseline) directory
-    script_dir = os.path.dirname(os.path.abspath(__file__))
-    reference_dir = os.path.join(script_dir, "GW150914-origin/AMSS_NCKU_output")
-
-    # Data file paths
-    bh_file_ref = os.path.join(reference_dir, "bssn_BH.dat")
-    bh_file_target = os.path.join(target_dir, "bssn_BH.dat")
-    constraint_file = os.path.join(target_dir, "bssn_constraint.dat")
-
-    # Check if files exist
-    if not os.path.exists(bh_file_ref):
-        print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Baseline trajectory file not found: {bh_file_ref}")
-        sys.exit(1)
-
-    if not os.path.exists(bh_file_target):
-        print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Target trajectory file not found: {bh_file_target}")
-        sys.exit(1)
-
-    if not os.path.exists(constraint_file):
-        print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Constraint data file not found: {constraint_file}")
-        sys.exit(1)
-
-    # Print header
-    print_header()
-    print(f"\n{Color.BOLD}Reference (Baseline):{Color.RESET} {Color.BLUE}{reference_dir}{Color.RESET}")
-    print(f"{Color.BOLD}Target (Optimized):  {Color.RESET} {Color.BLUE}{target_dir}{Color.RESET}")
-
-    # Load data
-    bh_data_ref = load_bh_trajectory(bh_file_ref)
-    bh_data_target = load_bh_trajectory(bh_file_target)
-    constraint_data = load_constraint_data(constraint_file)
-
-    # Calculate RMS error
-    rms_rel, error = calculate_rms_error(bh_data_ref, bh_data_target)
-    rms_passed = print_rms_results(rms_rel, error)
-
-    # Analyze constraint violation
-    constraint_results = analyze_constraint_violation(constraint_data)
-    constraint_passed = print_constraint_results(constraint_results)
-
-    # Print summary
-    all_passed = print_summary(rms_passed, constraint_passed)
-
-    # Return exit code
-    sys.exit(0 if all_passed else 1)
-
-
-if __name__ == "__main__":
-    main()

AMSS_NCKU_source/FFT.f90

@@ -37,51 +37,57 @@ 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, intent(in) :: isign, nn
+INTEGER::isign,nn
-DOUBLE PRECISION, dimension(2*nn), intent(inout) :: dataa
+double precision,dimension(2*nn)::dataa
-
+INTEGER::i,istep,j,m,mmax,n
-type(DFTI_DESCRIPTOR), pointer :: desc
+double precision::tempi,tempr
-integer :: status
+DOUBLE PRECISION::theta,wi,wpi,wpr,wr,wtemp
-
+n=2*nn
-! Create DFTI descriptor for 1D complex-to-complex transform
+j=1
-status = DftiCreateDescriptor(desc, DFTI_DOUBLE, DFTI_COMPLEX, 1, nn)
+do i=1,n,2
-if (status /= 0) return
+  if(j.gt.i)then
-
+     tempr=dataa(j)
-! Set input/output storage as interleaved complex (default)
+     tempi=dataa(j+1)
-status = DftiSetValue(desc, DFTI_PLACEMENT, DFTI_INPLACE)
+     dataa(j)=dataa(i)
-if (status /= 0) then
+     dataa(j+1)=dataa(i+1)
-   status = DftiFreeDescriptor(desc)
+     dataa(i)=tempr
-   return
+     dataa(i+1)=tempi
+  endif
+  m=nn
+1 if ((m.ge.2).and.(j.gt.m)) then
+  j=j-m
+  m=m/2
+goto 1
+  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
 endif
-
-! Commit the descriptor
-status = DftiCommitDescriptor(desc)
-if (status /= 0) then
-   status = DftiFreeDescriptor(desc)
-   return
-endif
-
-! 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

AMSS_NCKU_source/TwoPunctures.h

@@ -1,7 +1,8 @@
-
 #ifndef TWO_PUNCTURES_H
 #define TWO_PUNCTURES_H
 
+#include <omp.h>
+
 #define StencilSize 19
 #define N_PlaneRelax 1
 #define NRELAX 200
@@ -32,7 +33,7 @@ private:
        int npoints_A, npoints_B, npoints_phi;
 
        double target_M_plus, target_M_minus;
-       
+
        double admMass;
 
        double adm_tol;
@@ -42,6 +43,18 @@ private:
 
        int ntotal;
 
+       // ===== Precomputed spectral derivative matrices =====
+       double *D1_A, *D2_A;
+       double *D1_B, *D2_B;
+       double *DF1_phi, *DF2_phi;
+
+       // ===== Pre-allocated workspace for LineRelax (per-thread) =====
+       int max_threads;
+       double **ws_diag_be, **ws_e_be, **ws_f_be, **ws_b_be, **ws_x_be;
+       double **ws_l_be, **ws_u_be, **ws_d_be, **ws_y_be;
+       double **ws_diag_al, **ws_e_al, **ws_f_al, **ws_b_al, **ws_x_al;
+       double **ws_l_al, **ws_u_al, **ws_d_al, **ws_y_al;
+
        struct parameters
        {
               int nvar, n1, n2, n3;
@@ -58,6 +71,28 @@ public:
                     int Newtonmaxit);
        ~TwoPunctures();
 
+       // 02/07: New/modified methods
+       void allocate_workspace();
+       void free_workspace();
+       void precompute_derivative_matrices();
+       void build_cheb_deriv_matrices(int n, double *D1, double *D2);
+       void build_fourier_deriv_matrices(int N, double *DF1, double *DF2);
+       void Derivatives_AB3_MatMul(int nvar, int n1, int n2, int n3, derivs v);
+       void ThomasAlgorithm_ws(int N, double *b, double *a, double *c, double *x, double *q,
+                                double *l, double *u_ws, double *d, double *y);
+       void LineRelax_be_omp(double *dv,
+                         int const i, int const k, int const nvar,
+                         int const n1, int const n2, int const n3,
+                         double const *rhs, int const *ncols, int **cols,
+                         double **JFD, int tid);
+       void LineRelax_al_omp(double *dv,
+                         int const j, int const k, int const nvar,
+                         int const n1, int const n2, int const n3,
+                         double const *rhs, int const *ncols,
+                         int **cols, double **JFD, int tid);
+       void relax_omp(double *dv, int const nvar, int const n1, int const n2, int const n3,
+                  double const *rhs, int const *ncols, int **cols, double **JFD);
+
        void Solve();
        void set_initial_guess(derivs v);
        int index(int i, int j, int k, int l, int a, int b, int c, int d);
@@ -116,23 +151,11 @@ public:
        double BY_KKofxyz(double x, double y, double z);
        void SetMatrix_JFD(int nvar, int n1, int n2, int n3, derivs u, int *ncols, int **cols, double **Matrix);
        void J_times_dv(int nvar, int n1, int n2, int n3, derivs dv, double *Jdv, derivs u);
-       void relax(double *dv, int const nvar, int const n1, int const n2, int const n3,
-                  double const *rhs, int const *ncols, int **cols, double **JFD);
-       void LineRelax_be(double *dv,
-                         int const i, int const k, int const nvar,
-                         int const n1, int const n2, int const n3,
-                         double const *rhs, int const *ncols, int **cols,
-                         double **JFD);
        void JFD_times_dv(int i, int j, int k, int nvar, int n1, int n2,
                          int n3, derivs dv, derivs u, double *values);
        void LinEquations(double A, double B, double X, double R,
                          double x, double r, double phi,
                          double y, double z, derivs dU, derivs U, double *values);
-       void LineRelax_al(double *dv,
-                         int const j, int const k, int const nvar,
-                         int const n1, int const n2, int const n3,
-                         double const *rhs, int const *ncols,
-                         int **cols, double **JFD);
        void ThomasAlgorithm(int N, double *b, double *a, double *c, double *x, double *q);
        void Save(char *fname);
        // provided by Vasileios Paschalidis (vpaschal@illinois.edu)
@@ -141,4 +164,4 @@ public:
        void SpecCoef(parameters par, int ivar, double *v, double *cf);
 };
 
-#endif /* TWO_PUNCTURES_H */
+#endif /* TWO_PUNCTURES_H */

AMSS_NCKU_source/diff_new.f90

@@ -1939,309 +1939,6 @@
   return
 
   end subroutine fddyz
-  subroutine fderivs_batch4(ex,f1,f2,f3,f4, &
-                            f1x,f1y,f1z,f2x,f2y,f2z,f3x,f3y,f3z,f4x,f4y,f4z, &
-                            X,Y,Z,SYM1,SYM2,SYM3,symmetry,onoff)
-  implicit none
-
-  integer,                               intent(in ):: ex(1:3),symmetry,onoff
-  real*8,  dimension(ex(1),ex(2),ex(3)), intent(in ):: f1,f2,f3,f4
-  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f1x,f1y,f1z
-  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f2x,f2y,f2z
-  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f3x,f3y,f3z
-  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f4x,f4y,f4z
-  real*8,                                intent(in) :: X(ex(1)),Y(ex(2)),Z(ex(3))
-  real*8,                                intent(in ):: SYM1,SYM2,SYM3
-
-!~~~~~~ other variables
-
-  real*8 :: dX,dY,dZ
-  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh1,fh2,fh3,fh4
-  real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
-  real*8 :: d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
-  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
-  real*8,  parameter :: ZEO=0.d0,ONE=1.d0
-  real*8,  parameter :: TWO=2.d0,EIT=8.d0
-  real*8,  parameter :: F12=1.2d1
-
-  dX = X(2)-X(1)
-  dY = Y(2)-Y(1)
-  dZ = Z(2)-Z(1)
-
-  imax = ex(1)
-  jmax = ex(2)
-  kmax = ex(3)
-
-  imin = 1
-  jmin = 1
-  kmin = 1
-  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
-  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
-  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
-
-  SoA(1) = SYM1
-  SoA(2) = SYM2
-  SoA(3) = SYM3
-
-  call symmetry_bd(2,ex,f1,fh1,SoA)
-  call symmetry_bd(2,ex,f2,fh2,SoA)
-  call symmetry_bd(2,ex,f3,fh3,SoA)
-  call symmetry_bd(2,ex,f4,fh4,SoA)
-
-  d12dx = ONE/F12/dX
-  d12dy = ONE/F12/dY
-  d12dz = ONE/F12/dZ
-
-  d2dx = ONE/TWO/dX
-  d2dy = ONE/TWO/dY
-  d2dz = ONE/TWO/dZ
-
-  f1x = ZEO; f1y = ZEO; f1z = ZEO
-  f2x = ZEO; f2y = ZEO; f2z = ZEO
-  f3x = ZEO; f3y = ZEO; f3z = ZEO
-  f4x = ZEO; f4y = ZEO; f4z = ZEO
-
-  do k=1,ex(3)-1
-  do j=1,ex(2)-1
-  do i=1,ex(1)-1
-   if(i+2 <= imax .and. i-2 >= imin .and. &
-      j+2 <= jmax .and. j-2 >= jmin .and. &
-      k+2 <= kmax .and. k-2 >= kmin) then
-      f1x(i,j,k)=d12dx*(fh1(i-2,j,k)-EIT*fh1(i-1,j,k)+EIT*fh1(i+1,j,k)-fh1(i+2,j,k))
-      f1y(i,j,k)=d12dy*(fh1(i,j-2,k)-EIT*fh1(i,j-1,k)+EIT*fh1(i,j+1,k)-fh1(i,j+2,k))
-      f1z(i,j,k)=d12dz*(fh1(i,j,k-2)-EIT*fh1(i,j,k-1)+EIT*fh1(i,j,k+1)-fh1(i,j,k+2))
-
-      f2x(i,j,k)=d12dx*(fh2(i-2,j,k)-EIT*fh2(i-1,j,k)+EIT*fh2(i+1,j,k)-fh2(i+2,j,k))
-      f2y(i,j,k)=d12dy*(fh2(i,j-2,k)-EIT*fh2(i,j-1,k)+EIT*fh2(i,j+1,k)-fh2(i,j+2,k))
-      f2z(i,j,k)=d12dz*(fh2(i,j,k-2)-EIT*fh2(i,j,k-1)+EIT*fh2(i,j,k+1)-fh2(i,j,k+2))
-
-      f3x(i,j,k)=d12dx*(fh3(i-2,j,k)-EIT*fh3(i-1,j,k)+EIT*fh3(i+1,j,k)-fh3(i+2,j,k))
-      f3y(i,j,k)=d12dy*(fh3(i,j-2,k)-EIT*fh3(i,j-1,k)+EIT*fh3(i,j+1,k)-fh3(i,j+2,k))
-      f3z(i,j,k)=d12dz*(fh3(i,j,k-2)-EIT*fh3(i,j,k-1)+EIT*fh3(i,j,k+1)-fh3(i,j,k+2))
-
-      f4x(i,j,k)=d12dx*(fh4(i-2,j,k)-EIT*fh4(i-1,j,k)+EIT*fh4(i+1,j,k)-fh4(i+2,j,k))
-      f4y(i,j,k)=d12dy*(fh4(i,j-2,k)-EIT*fh4(i,j-1,k)+EIT*fh4(i,j+1,k)-fh4(i,j+2,k))
-      f4z(i,j,k)=d12dz*(fh4(i,j,k-2)-EIT*fh4(i,j,k-1)+EIT*fh4(i,j,k+1)-fh4(i,j,k+2))
-   elseif(i+1 <= imax .and. i-1 >= imin .and. &
-          j+1 <= jmax .and. j-1 >= jmin .and. &
-          k+1 <= kmax .and. k-1 >= kmin) then
-      f1x(i,j,k)=d2dx*(-fh1(i-1,j,k)+fh1(i+1,j,k))
-      f1y(i,j,k)=d2dy*(-fh1(i,j-1,k)+fh1(i,j+1,k))
-      f1z(i,j,k)=d2dz*(-fh1(i,j,k-1)+fh1(i,j,k+1))
-
-      f2x(i,j,k)=d2dx*(-fh2(i-1,j,k)+fh2(i+1,j,k))
-      f2y(i,j,k)=d2dy*(-fh2(i,j-1,k)+fh2(i,j+1,k))
-      f2z(i,j,k)=d2dz*(-fh2(i,j,k-1)+fh2(i,j,k+1))
-
-      f3x(i,j,k)=d2dx*(-fh3(i-1,j,k)+fh3(i+1,j,k))
-      f3y(i,j,k)=d2dy*(-fh3(i,j-1,k)+fh3(i,j+1,k))
-      f3z(i,j,k)=d2dz*(-fh3(i,j,k-1)+fh3(i,j,k+1))
-
-      f4x(i,j,k)=d2dx*(-fh4(i-1,j,k)+fh4(i+1,j,k))
-      f4y(i,j,k)=d2dy*(-fh4(i,j-1,k)+fh4(i,j+1,k))
-      f4z(i,j,k)=d2dz*(-fh4(i,j,k-1)+fh4(i,j,k+1))
-   endif
-  enddo
-  enddo
-  enddo
-
-  return
-
-  end subroutine fderivs_batch4
-!-----------------------------------------------------------------------------
-! batch first derivatives (3 fields), same symmetry setup
-!-----------------------------------------------------------------------------
-  subroutine fderivs_batch3(ex,f1,f2,f3, &
-                            f1x,f1y,f1z,f2x,f2y,f2z,f3x,f3y,f3z, &
-                            X,Y,Z,SYM1,SYM2,SYM3,symmetry,onoff)
-  implicit none
-
-  integer,                               intent(in ):: ex(1:3),symmetry,onoff
-  real*8,  dimension(ex(1),ex(2),ex(3)), intent(in ):: f1,f2,f3
-  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f1x,f1y,f1z
-  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f2x,f2y,f2z
-  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f3x,f3y,f3z
-  real*8,                                intent(in) :: X(ex(1)),Y(ex(2)),Z(ex(3))
-  real*8,                                intent(in ):: SYM1,SYM2,SYM3
-
-!~~~~~~ other variables
-
-  real*8 :: dX,dY,dZ
-  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh1,fh2,fh3
-  real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
-  real*8 :: d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
-  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
-  real*8,  parameter :: ZEO=0.d0,ONE=1.d0
-  real*8,  parameter :: TWO=2.d0,EIT=8.d0
-  real*8,  parameter :: F12=1.2d1
-
-  dX = X(2)-X(1)
-  dY = Y(2)-Y(1)
-  dZ = Z(2)-Z(1)
-
-  imax = ex(1)
-  jmax = ex(2)
-  kmax = ex(3)
-
-  imin = 1
-  jmin = 1
-  kmin = 1
-  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
-  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
-  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
-
-  SoA(1) = SYM1
-  SoA(2) = SYM2
-  SoA(3) = SYM3
-
-  call symmetry_bd(2,ex,f1,fh1,SoA)
-  call symmetry_bd(2,ex,f2,fh2,SoA)
-  call symmetry_bd(2,ex,f3,fh3,SoA)
-
-  d12dx = ONE/F12/dX
-  d12dy = ONE/F12/dY
-  d12dz = ONE/F12/dZ
-
-  d2dx = ONE/TWO/dX
-  d2dy = ONE/TWO/dY
-  d2dz = ONE/TWO/dZ
-
-  f1x = ZEO; f1y = ZEO; f1z = ZEO
-  f2x = ZEO; f2y = ZEO; f2z = ZEO
-  f3x = ZEO; f3y = ZEO; f3z = ZEO
-
-  do k=1,ex(3)-1
-  do j=1,ex(2)-1
-  do i=1,ex(1)-1
-   if(i+2 <= imax .and. i-2 >= imin .and. &
-      j+2 <= jmax .and. j-2 >= jmin .and. &
-      k+2 <= kmax .and. k-2 >= kmin) then
-      f1x(i,j,k)=d12dx*(fh1(i-2,j,k)-EIT*fh1(i-1,j,k)+EIT*fh1(i+1,j,k)-fh1(i+2,j,k))
-      f1y(i,j,k)=d12dy*(fh1(i,j-2,k)-EIT*fh1(i,j-1,k)+EIT*fh1(i,j+1,k)-fh1(i,j+2,k))
-      f1z(i,j,k)=d12dz*(fh1(i,j,k-2)-EIT*fh1(i,j,k-1)+EIT*fh1(i,j,k+1)-fh1(i,j,k+2))
-
-      f2x(i,j,k)=d12dx*(fh2(i-2,j,k)-EIT*fh2(i-1,j,k)+EIT*fh2(i+1,j,k)-fh2(i+2,j,k))
-      f2y(i,j,k)=d12dy*(fh2(i,j-2,k)-EIT*fh2(i,j-1,k)+EIT*fh2(i,j+1,k)-fh2(i,j+2,k))
-      f2z(i,j,k)=d12dz*(fh2(i,j,k-2)-EIT*fh2(i,j,k-1)+EIT*fh2(i,j,k+1)-fh2(i,j,k+2))
-
-      f3x(i,j,k)=d12dx*(fh3(i-2,j,k)-EIT*fh3(i-1,j,k)+EIT*fh3(i+1,j,k)-fh3(i+2,j,k))
-      f3y(i,j,k)=d12dy*(fh3(i,j-2,k)-EIT*fh3(i,j-1,k)+EIT*fh3(i,j+1,k)-fh3(i,j+2,k))
-      f3z(i,j,k)=d12dz*(fh3(i,j,k-2)-EIT*fh3(i,j,k-1)+EIT*fh3(i,j,k+1)-fh3(i,j,k+2))
-   elseif(i+1 <= imax .and. i-1 >= imin .and. &
-          j+1 <= jmax .and. j-1 >= jmin .and. &
-          k+1 <= kmax .and. k-1 >= kmin) then
-      f1x(i,j,k)=d2dx*(-fh1(i-1,j,k)+fh1(i+1,j,k))
-      f1y(i,j,k)=d2dy*(-fh1(i,j-1,k)+fh1(i,j+1,k))
-      f1z(i,j,k)=d2dz*(-fh1(i,j,k-1)+fh1(i,j,k+1))
-
-      f2x(i,j,k)=d2dx*(-fh2(i-1,j,k)+fh2(i+1,j,k))
-      f2y(i,j,k)=d2dy*(-fh2(i,j-1,k)+fh2(i,j+1,k))
-      f2z(i,j,k)=d2dz*(-fh2(i,j,k-1)+fh2(i,j,k+1))
-
-      f3x(i,j,k)=d2dx*(-fh3(i-1,j,k)+fh3(i+1,j,k))
-      f3y(i,j,k)=d2dy*(-fh3(i,j-1,k)+fh3(i,j+1,k))
-      f3z(i,j,k)=d2dz*(-fh3(i,j,k-1)+fh3(i,j,k+1))
-   endif
-  enddo
-  enddo
-  enddo
-
-  return
-
-  end subroutine fderivs_batch3
-!-----------------------------------------------------------------------------
-! batch first derivatives (2 fields), same symmetry setup
-!-----------------------------------------------------------------------------
-  subroutine fderivs_batch2(ex,f1,f2, &
-                            f1x,f1y,f1z,f2x,f2y,f2z, &
-                            X,Y,Z,SYM1,SYM2,SYM3,symmetry,onoff)
-  implicit none
-
-  integer,                               intent(in ):: ex(1:3),symmetry,onoff
-  real*8,  dimension(ex(1),ex(2),ex(3)), intent(in ):: f1,f2
-  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f1x,f1y,f1z
-  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f2x,f2y,f2z
-  real*8,                                intent(in) :: X(ex(1)),Y(ex(2)),Z(ex(3))
-  real*8,                                intent(in ):: SYM1,SYM2,SYM3
-
-!~~~~~~ other variables
-
-  real*8 :: dX,dY,dZ
-  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh1,fh2
-  real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
-  real*8 :: d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
-  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
-  real*8,  parameter :: ZEO=0.d0,ONE=1.d0
-  real*8,  parameter :: TWO=2.d0,EIT=8.d0
-  real*8,  parameter :: F12=1.2d1
-
-  dX = X(2)-X(1)
-  dY = Y(2)-Y(1)
-  dZ = Z(2)-Z(1)
-
-  imax = ex(1)
-  jmax = ex(2)
-  kmax = ex(3)
-
-  imin = 1
-  jmin = 1
-  kmin = 1
-  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
-  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
-  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
-
-  SoA(1) = SYM1
-  SoA(2) = SYM2
-  SoA(3) = SYM3
-
-  call symmetry_bd(2,ex,f1,fh1,SoA)
-  call symmetry_bd(2,ex,f2,fh2,SoA)
-
-  d12dx = ONE/F12/dX
-  d12dy = ONE/F12/dY
-  d12dz = ONE/F12/dZ
-
-  d2dx = ONE/TWO/dX
-  d2dy = ONE/TWO/dY
-  d2dz = ONE/TWO/dZ
-
-  f1x = ZEO; f1y = ZEO; f1z = ZEO
-  f2x = ZEO; f2y = ZEO; f2z = ZEO
-
-  do k=1,ex(3)-1
-  do j=1,ex(2)-1
-  do i=1,ex(1)-1
-   if(i+2 <= imax .and. i-2 >= imin .and. &
-      j+2 <= jmax .and. j-2 >= jmin .and. &
-      k+2 <= kmax .and. k-2 >= kmin) then
-      f1x(i,j,k)=d12dx*(fh1(i-2,j,k)-EIT*fh1(i-1,j,k)+EIT*fh1(i+1,j,k)-fh1(i+2,j,k))
-      f1y(i,j,k)=d12dy*(fh1(i,j-2,k)-EIT*fh1(i,j-1,k)+EIT*fh1(i,j+1,k)-fh1(i,j+2,k))
-      f1z(i,j,k)=d12dz*(fh1(i,j,k-2)-EIT*fh1(i,j,k-1)+EIT*fh1(i,j,k+1)-fh1(i,j,k+2))
-
-      f2x(i,j,k)=d12dx*(fh2(i-2,j,k)-EIT*fh2(i-1,j,k)+EIT*fh2(i+1,j,k)-fh2(i+2,j,k))
-      f2y(i,j,k)=d12dy*(fh2(i,j-2,k)-EIT*fh2(i,j-1,k)+EIT*fh2(i,j+1,k)-fh2(i,j+2,k))
-      f2z(i,j,k)=d12dz*(fh2(i,j,k-2)-EIT*fh2(i,j,k-1)+EIT*fh2(i,j,k+1)-fh2(i,j,k+2))
-   elseif(i+1 <= imax .and. i-1 >= imin .and. &
-          j+1 <= jmax .and. j-1 >= jmin .and. &
-          k+1 <= kmax .and. k-1 >= kmin) then
-      f1x(i,j,k)=d2dx*(-fh1(i-1,j,k)+fh1(i+1,j,k))
-      f1y(i,j,k)=d2dy*(-fh1(i,j-1,k)+fh1(i,j+1,k))
-      f1z(i,j,k)=d2dz*(-fh1(i,j,k-1)+fh1(i,j,k+1))
-
-      f2x(i,j,k)=d2dx*(-fh2(i-1,j,k)+fh2(i+1,j,k))
-      f2y(i,j,k)=d2dy*(-fh2(i,j-1,k)+fh2(i,j+1,k))
-      f2z(i,j,k)=d2dz*(-fh2(i,j,k-1)+fh2(i,j,k+1))
-   endif
-  enddo
-  enddo
-  enddo
-
-  return
-
-  end subroutine fderivs_batch2
 
 #elif (ghost_width == 4)
 ! sixth order code
@@ -2380,9 +2077,6 @@
 
   end subroutine fderivs
 !-----------------------------------------------------------------------------
-! batch first derivatives (4 fields), same symmetry setup
-!-----------------------------------------------------------------------------
-!-----------------------------------------------------------------------------
 !
 ! single derivatives dx
 !

AMSS_NCKU_source/enforce_algebra.f90

@@ -17,50 +17,62 @@
   real*8, dimension(ex(1),ex(2),ex(3)), intent(inout) :: Axx,Axy,Axz
   real*8, dimension(ex(1),ex(2),ex(3)), intent(inout) :: Ayy,Ayz,Azz
 
-!~~~~~~~> Local variable:
+!~~~~~~~> Local variable:
-  
+
-  real*8, dimension(ex(1),ex(2),ex(3)) :: trA,detg
+  integer :: i,j,k
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz 
+  real*8 :: lgxx,lgyy,lgzz,ldetg
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz,gupyy,gupyz,gupzz
+  real*8 :: lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz
-  real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0
+  real*8 :: ltrA,lscale
-
+  real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0
-!~~~~~~>
+
-
+!~~~~~~>
-  gxx = dxx + ONE
+
-  gyy = dyy + ONE
+  do k=1,ex(3)
-  gzz = dzz + ONE
+  do j=1,ex(2)
-
+  do i=1,ex(1)
-  detg =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
+
-          gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
+    lgxx = dxx(i,j,k) + ONE
-  gupxx =   ( gyy * gzz - gyz * gyz ) / detg
+    lgyy = dyy(i,j,k) + ONE
-  gupxy = - ( gxy * gzz - gyz * gxz ) / detg
+    lgzz = dzz(i,j,k) + ONE
-  gupxz =   ( gxy * gyz - gyy * gxz ) / detg
+
-  gupyy =   ( gxx * gzz - gxz * gxz ) / detg
+    ldetg =  lgxx * lgyy * lgzz &
-  gupyz = - ( gxx * gyz - gxy * gxz ) / detg
+           + gxy(i,j,k) * gyz(i,j,k) * gxz(i,j,k) &
-  gupzz =   ( gxx * gyy - gxy * gxy ) / detg
+           + gxz(i,j,k) * gxy(i,j,k) * gyz(i,j,k) &
-
+           - gxz(i,j,k) * lgyy * gxz(i,j,k) &
-  trA =         gupxx * Axx + gupyy * Ayy + gupzz * Azz &
+           - gxy(i,j,k) * gxy(i,j,k) * lgzz &
-       + TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
+           - lgxx * gyz(i,j,k) * gyz(i,j,k)
-
+
-  Axx = Axx - F1o3 * gxx * trA
+    lgupxx =   ( lgyy * lgzz - gyz(i,j,k) * gyz(i,j,k) ) / ldetg
-  Axy = Axy - F1o3 * gxy * trA
+    lgupxy = - ( gxy(i,j,k) * lgzz - gyz(i,j,k) * gxz(i,j,k) ) / ldetg
-  Axz = Axz - F1o3 * gxz * trA
+    lgupxz =   ( gxy(i,j,k) * gyz(i,j,k) - lgyy * gxz(i,j,k) ) / ldetg
-  Ayy = Ayy - F1o3 * gyy * trA
+    lgupyy =   ( lgxx * lgzz - gxz(i,j,k) * gxz(i,j,k) ) / ldetg
-  Ayz = Ayz - F1o3 * gyz * trA
+    lgupyz = - ( lgxx * gyz(i,j,k) - gxy(i,j,k) * gxz(i,j,k) ) / ldetg
-  Azz = Azz - F1o3 * gzz * trA
+    lgupzz =   ( lgxx * lgyy - gxy(i,j,k) * gxy(i,j,k) ) / ldetg
-
+
-  detg = ONE / ( detg ** F1o3 ) 
+    ltrA =         lgupxx * Axx(i,j,k) + lgupyy * Ayy(i,j,k) &
-  
+                 + lgupzz * Azz(i,j,k) &
-  gxx = gxx * detg
+         + TWO * (lgupxy * Axy(i,j,k) + lgupxz * Axz(i,j,k) &
-  gxy = gxy * detg
+                 + lgupyz * Ayz(i,j,k))
-  gxz = gxz * detg
+
-  gyy = gyy * detg
+    Axx(i,j,k) = Axx(i,j,k) - F1o3 * lgxx * ltrA
-  gyz = gyz * detg
+    Axy(i,j,k) = Axy(i,j,k) - F1o3 * gxy(i,j,k) * ltrA
-  gzz = gzz * detg
+    Axz(i,j,k) = Axz(i,j,k) - F1o3 * gxz(i,j,k) * ltrA
-
+    Ayy(i,j,k) = Ayy(i,j,k) - F1o3 * lgyy * ltrA
-  dxx = gxx - ONE
+    Ayz(i,j,k) = Ayz(i,j,k) - F1o3 * gyz(i,j,k) * ltrA
-  dyy = gyy - ONE
+    Azz(i,j,k) = Azz(i,j,k) - F1o3 * lgzz * ltrA
-  dzz = gzz - ONE
+
+    lscale = ONE / ( ldetg ** F1o3 )
+
+    dxx(i,j,k) = lgxx * lscale - ONE
+    gxy(i,j,k) = gxy(i,j,k) * lscale
+    gxz(i,j,k) = gxz(i,j,k) * lscale
+    dyy(i,j,k) = lgyy * lscale - ONE
+    gyz(i,j,k) = gyz(i,j,k) * lscale
+    dzz(i,j,k) = lgzz * lscale - ONE
+
+  enddo
+  enddo
+  enddo
 
   return
 
@@ -81,52 +93,72 @@
   real*8, dimension(ex(1),ex(2),ex(3)), intent(inout) :: Axx,Axy,Axz
   real*8, dimension(ex(1),ex(2),ex(3)), intent(inout) :: Ayy,Ayz,Azz
 
-!~~~~~~~> Local variable:
+!~~~~~~~> Local variable:
-  
+
-  real*8, dimension(ex(1),ex(2),ex(3)) :: trA
+  integer :: i,j,k
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz 
+  real*8 :: lgxx,lgyy,lgzz,lscale
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz,gupyy,gupyz,gupzz
+  real*8 :: lgxy,lgxz,lgyz
-  real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0
+  real*8 :: lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz
-
+  real*8 :: ltrA
-!~~~~~~>
+  real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0
-
+
-  gxx = dxx + ONE
+!~~~~~~>
-  gyy = dyy + ONE
+
-  gzz = dzz + ONE
+  do k=1,ex(3)
-! for g
+  do j=1,ex(2)
-  gupzz =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
+  do i=1,ex(1)
-           gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
+
-
+! for g: normalize determinant first
-  gupzz = ONE / ( gupzz ** F1o3 ) 
+    lgxx = dxx(i,j,k) + ONE
-  
+    lgyy = dyy(i,j,k) + ONE
-  gxx = gxx * gupzz
+    lgzz = dzz(i,j,k) + ONE
-  gxy = gxy * gupzz
+    lgxy = gxy(i,j,k)
-  gxz = gxz * gupzz
+    lgxz = gxz(i,j,k)
-  gyy = gyy * gupzz
+    lgyz = gyz(i,j,k)
-  gyz = gyz * gupzz
+
-  gzz = gzz * gupzz
+    lscale =  lgxx * lgyy * lgzz + lgxy * lgyz * lgxz &
-
+            + lgxz * lgxy * lgyz - lgxz * lgyy * lgxz &
-  dxx = gxx - ONE
+            - lgxy * lgxy * lgzz - lgxx * lgyz * lgyz
-  dyy = gyy - ONE
+
-  dzz = gzz - ONE
+    lscale = ONE / ( lscale ** F1o3 )
-! for A  
+
-
+    lgxx = lgxx * lscale
-  gupxx =   ( gyy * gzz - gyz * gyz )
+    lgxy = lgxy * lscale
-  gupxy = - ( gxy * gzz - gyz * gxz )
+    lgxz = lgxz * lscale
-  gupxz =   ( gxy * gyz - gyy * gxz )
+    lgyy = lgyy * lscale
-  gupyy =   ( gxx * gzz - gxz * gxz )
+    lgyz = lgyz * lscale
-  gupyz = - ( gxx * gyz - gxy * gxz )
+    lgzz = lgzz * lscale
-  gupzz =   ( gxx * gyy - gxy * gxy )
+
-
+    dxx(i,j,k) = lgxx - ONE
-  trA =         gupxx * Axx + gupyy * Ayy + gupzz * Azz &
+    gxy(i,j,k) = lgxy
-       + TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
+    gxz(i,j,k) = lgxz
-
+    dyy(i,j,k) = lgyy - ONE
-  Axx = Axx - F1o3 * gxx * trA
+    gyz(i,j,k) = lgyz
-  Axy = Axy - F1o3 * gxy * trA
+    dzz(i,j,k) = lgzz - ONE
-  Axz = Axz - F1o3 * gxz * trA
+
-  Ayy = Ayy - F1o3 * gyy * trA
+! for A: trace-free using normalized metric (det=1, no division needed)
-  Ayz = Ayz - F1o3 * gyz * trA
+    lgupxx =   ( lgyy * lgzz - lgyz * lgyz )
-  Azz = Azz - F1o3 * gzz * trA
+    lgupxy = - ( lgxy * lgzz - lgyz * lgxz )
+    lgupxz =   ( lgxy * lgyz - lgyy * lgxz )
+    lgupyy =   ( lgxx * lgzz - lgxz * lgxz )
+    lgupyz = - ( lgxx * lgyz - lgxy * lgxz )
+    lgupzz =   ( lgxx * lgyy - lgxy * lgxy )
+
+    ltrA =         lgupxx * Axx(i,j,k) + lgupyy * Ayy(i,j,k) &
+                 + lgupzz * Azz(i,j,k) &
+         + TWO * (lgupxy * Axy(i,j,k) + lgupxz * Axz(i,j,k) &
+                 + lgupyz * Ayz(i,j,k))
+
+    Axx(i,j,k) = Axx(i,j,k) - F1o3 * lgxx * ltrA
+    Axy(i,j,k) = Axy(i,j,k) - F1o3 * lgxy * ltrA
+    Axz(i,j,k) = Axz(i,j,k) - F1o3 * lgxz * ltrA
+    Ayy(i,j,k) = Ayy(i,j,k) - F1o3 * lgyy * ltrA
+    Ayz(i,j,k) = Ayz(i,j,k) - F1o3 * lgyz * ltrA
+    Azz(i,j,k) = Azz(i,j,k) - F1o3 * lgzz * ltrA
+
+  enddo
+  enddo
+  enddo
 
   return
 

AMSS_NCKU_source/fmisc.f90

@@ -324,8 +324,7 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
+  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
-  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
    enddo
@@ -350,8 +349,7 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
+  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
-  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
       funcc(extc(1)+1+i,1:extc(2),1:extc(3)) = funcc(extc(1)-1-i,1:extc(2),1:extc(3))*SoA(1)
@@ -379,8 +377,7 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
+  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
-  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
       funcc(extc(1)+1+i,1:extc(2),1:extc(3)) = funcc(extc(1)-1-i,1:extc(2),1:extc(3))*SoA(1)
@@ -886,17 +883,20 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
-  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
+  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
-   do i=0,ord-1
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
-      funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
+   do i=0,ord-1
-   enddo
+      funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
-   do i=0,ord-1
+   enddo
-      funcc(:,-i,1:extc(3)) = funcc(:,i+1,1:extc(3))*SoA(2)
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
-   enddo
+   do i=0,ord-1
-   do i=0,ord-1
+      funcc(:,-i,1:extc(3)) = funcc(:,i+1,1:extc(3))*SoA(2)
-      funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
+   enddo
-   enddo
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
+   do i=0,ord-1
+      funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
+   enddo
 
 end subroutine symmetry_bd
 
@@ -912,8 +912,7 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
+  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
-  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
       funcc(extc(1)+1+i,1:extc(2),1:extc(3)) = funcc(extc(1)-i,1:extc(2),1:extc(3))*SoA(1)
@@ -941,8 +940,7 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
+  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
-  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
       funcc(extc(1)+1+i,1:extc(2),1:extc(3)) = funcc(extc(1)-i,1:extc(2),1:extc(3))*SoA(1)
@@ -1113,153 +1111,355 @@ end subroutine d2dump
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-! common code for cell and vertex
+! common code for cell and vertex
-!------------------------------------------------------------------------------
+!------------------------------------------------------------------------------
-! Lagrangian polynomial interpolation
+! Lagrangian polynomial interpolation
-!------------------------------------------------------------------------------
+!------------------------------------------------------------------------------
-
+#ifndef POLINT6_USE_BARYCENTRIC
-  subroutine polint(xa,ya,x,y,dy,ordn)
+#define POLINT6_USE_BARYCENTRIC 1
-
+#endif
-  implicit none
+
-
+!DIR$ ATTRIBUTES FORCEINLINE :: polint6_neville
-!~~~~~~> Input Parameter:
+  subroutine polint6_neville(xa, ya, x, y, dy)
-  integer,intent(in) :: ordn
+  implicit none
-  real*8, dimension(ordn), intent(in) :: xa,ya
+
-  real*8, intent(in) :: x
+  real*8, dimension(6), intent(in) :: xa, ya
-  real*8, intent(out) :: y,dy
+  real*8, intent(in) :: x
-
+  real*8, intent(out) :: y, dy
-!~~~~~~> Other parameter:
+
-
+  integer :: i, m, ns, n_m
-  integer :: m,n,ns
+  real*8, dimension(6) :: c, d, ho
-  real*8, dimension(ordn) :: c,d,den,ho
+  real*8 :: dif, dift, hp, h, den_val
-  real*8 :: dif,dift
+
-
+  c = ya
-!~~~~~~>
+  d = ya
-
+  ho = xa - x
-  n=ordn
+
-  m=ordn
+  ns = 1
-
+  dif = abs(x - xa(1))
-  c=ya
+
-  d=ya
+  do i = 2, 6
-  ho=xa-x
+    dift = abs(x - xa(i))
-
+    if (dift < dif) then
-  ns=1
+      ns = i
-  dif=abs(x-xa(1))
+      dif = dift
-  do m=1,n
+    end if
-   dift=abs(x-xa(m))
+  end do
-   if(dift < dif) then
+
-    ns=m
+  y = ya(ns)
-    dif=dift
+  ns = ns - 1
-   end if
+
-  end do
+  do m = 1, 5
-
+    n_m = 6 - m
-  y=ya(ns)
+    do i = 1, n_m
-  ns=ns-1
+      hp = ho(i)
-  do m=1,n-1
+      h  = ho(i+m)
-    den(1:n-m)=ho(1:n-m)-ho(1+m:n)
+      den_val = hp - h
-    if (any(den(1:n-m) == 0.0))then
+
-      write(*,*) 'failure in polint for point',x
+      if (den_val == 0.0d0) then
-      write(*,*) 'with input points: ',xa
+        write(*,*) 'failure in polint for point',x
-      stop
+        write(*,*) 'with input points: ',xa
-    endif
+        stop
-    den(1:n-m)=(c(2:n-m+1)-d(1:n-m))/den(1:n-m)
+      end if
-    d(1:n-m)=ho(1+m:n)*den(1:n-m)
+
-    c(1:n-m)=ho(1:n-m)*den(1:n-m)
+      den_val = (c(i+1) - d(i)) / den_val
-    if (2*ns < n-m) then
+
-      dy=c(ns+1)
+      d(i) = h * den_val
-    else
+      c(i) = hp * den_val
-      dy=d(ns)
+    end do
-      ns=ns-1
+
-    end if
+    if (2 * ns < n_m) then
-    y=y+dy
+      dy = c(ns + 1)
-  end do
+    else
-
+      dy = d(ns)
-  return
+      ns = ns - 1
-
+    end if
-  end subroutine polint
+    y = y + dy
-!------------------------------------------------------------------------------
+  end do
-!
+
-! interpolation in 2 dimensions, follow yx order
+  return
-!
+  end subroutine polint6_neville
-!------------------------------------------------------------------------------
+
-  subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
+!DIR$ ATTRIBUTES FORCEINLINE :: polint6_barycentric
-
+  subroutine polint6_barycentric(xa, ya, x, y, dy)
-  implicit none
+  implicit none
-
+
-!~~~~~~> Input parameters:
+  real*8, dimension(6), intent(in) :: xa, ya
-  integer,intent(in) :: ordn
+  real*8, intent(in) :: x
-  real*8, dimension(1:ordn), intent(in) :: x1a,x2a
+  real*8, intent(out) :: y, dy
-  real*8, dimension(1:ordn,1:ordn), intent(in) :: ya
+
-  real*8, intent(in) :: x1,x2
+  integer :: i, j
-  real*8, intent(out) :: y,dy
+  logical :: is_uniform
-
+  real*8, dimension(6) :: lambda
-!~~~~~~> Other parameters:
+  real*8 :: dx, den_i, term, num, den, step, tol
-
+  real*8, parameter :: c_uniform(6) = (/ -1.d0, 5.d0, -10.d0, 10.d0, -5.d0, 1.d0 /)
-  integer  :: i,m
+
-  real*8, dimension(ordn) :: ymtmp
+  do i = 1, 6
-  real*8, dimension(ordn) :: yntmp
+    if (x == xa(i)) then
-
+      y = ya(i)
-  m=size(x1a)
+      dy = 0.d0
-  
+      return
-  do i=1,m
+    end if
-
+  end do
-    yntmp=ya(i,:)
+
-    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
+  step = xa(2) - xa(1)
-
+  is_uniform = (step /= 0.d0)
-  end do
+  if (is_uniform) then
-
+    tol = 64.d0 * epsilon(1.d0) * max(1.d0, abs(step))
-  call polint(x1a,ymtmp,x1,y,dy,ordn)
+    do i = 3, 6
-
+      if (abs((xa(i) - xa(i-1)) - step) > tol) then
-  return
+        is_uniform = .false.
-
+        exit
-  end subroutine polin2
+      end if
-!------------------------------------------------------------------------------
+    end do
-!
+  end if
-! interpolation in 3 dimensions, follow zyx order
+
-!
+  if (is_uniform) then
-!------------------------------------------------------------------------------
+    num = 0.d0
-  subroutine polin3(x1a,x2a,x3a,ya,x1,x2,x3,y,dy,ordn)
+    den = 0.d0
-
+    do i = 1, 6
-  implicit none
+      term = c_uniform(i) / (x - xa(i))
-
+      num = num + term * ya(i)
-!~~~~~~> Input parameters:
+      den = den + term
-  integer,intent(in) :: ordn
+    end do
-  real*8, dimension(1:ordn), intent(in) :: x1a,x2a,x3a
+    y = num / den
-  real*8, dimension(1:ordn,1:ordn,1:ordn), intent(in) :: ya
+    dy = 0.d0
-  real*8, intent(in) :: x1,x2,x3
+    return
-  real*8, intent(out) :: y,dy
+  end if
-
+
-!~~~~~~> Other parameters:
+  do i = 1, 6
-
+    den_i = 1.d0
-  integer  :: i,j,m,n
+    do j = 1, 6
-  real*8, dimension(ordn,ordn) :: yatmp
+      if (j /= i) then
-  real*8, dimension(ordn) :: ymtmp
+        dx = xa(i) - xa(j)
-  real*8, dimension(ordn) :: yntmp
+        if (dx == 0.0d0) then
-  real*8, dimension(ordn) :: yqtmp
+          write(*,*) 'failure in polint for point',x
-
+          write(*,*) 'with input points: ',xa
-  m=size(x1a)
+          stop
-  n=size(x2a)
+        end if
-  
+        den_i = den_i * dx
-  do i=1,m
+      end if
-   do j=1,n
+    end do
-
+    lambda(i) = 1.d0 / den_i
-    yqtmp=ya(i,j,:)
+  end do
-    call polint(x3a,yqtmp,x3,yatmp(i,j),dy,ordn)
+
-
+  num = 0.d0
-   end do
+  den = 0.d0
-
+  do i = 1, 6
-    yntmp=yatmp(i,:)
+    term = lambda(i) / (x - xa(i))
-    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
+    num = num + term * ya(i)
-
+    den = den + term
-  end do
+  end do
-
+
-  call polint(x1a,ymtmp,x1,y,dy,ordn)
+  y = num / den
-
+  dy = 0.d0
-  return
+
-
+  return
-  end subroutine polin3
+  end subroutine polint6_barycentric
+
+!DIR$ ATTRIBUTES FORCEINLINE :: polint
+  subroutine polint(xa, ya, x, y, dy, ordn)
+  implicit none
+
+  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
+
+  if (ordn == 6) then
+#if POLINT6_USE_BARYCENTRIC
+    call polint6_barycentric(xa, ya, x, y, dy)
+#else
+    call polint6_neville(xa, ya, x, y, dy)
+#endif
+    return
+  end if
+
+  c = ya
+  d = ya
+  ho = xa - x
+
+  ns = 1
+  dif = abs(x - xa(1))
+
+  do i = 2, ordn
+    dift = abs(x - xa(i))
+    if (dift < dif) then
+      ns = i
+      dif = dift
+    end if
+  end do
+
+  y = ya(ns)
+  ns = ns - 1
+
+  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
+
+      if (den_val == 0.0d0) then
+        write(*,*) 'failure in polint for point',x
+        write(*,*) 'with input points: ',xa
+        stop
+      end if
+
+      den_val = (c(i+1) - d(i)) / den_val
+
+      d(i) = h * den_val
+      c(i) = hp * den_val
+    end do
+
+    if (2 * ns < n_m) then
+      dy = c(ns + 1)
+    else
+      dy = d(ns)
+      ns = ns - 1
+    end if
+    y = y + dy
+  end do
+
+  return
+  end subroutine polint
+!------------------------------------------------------------------------------
+! Compute Lagrange interpolation basis weights for one target point.
+!------------------------------------------------------------------------------
+!DIR$ ATTRIBUTES FORCEINLINE :: polint_lagrange_weights
+  subroutine polint_lagrange_weights(xa, x, w, ordn)
+  implicit none
+
+  integer, intent(in) :: ordn
+  real*8, dimension(1:ordn), intent(in) :: xa
+  real*8, intent(in) :: x
+  real*8, dimension(1:ordn), intent(out) :: w
+
+  integer :: i, j
+  real*8 :: num, den, dx
+
+  do i = 1, ordn
+    num = 1.d0
+    den = 1.d0
+    do j = 1, ordn
+      if (j /= i) then
+        dx = xa(i) - xa(j)
+        if (dx == 0.0d0) then
+          write(*,*) 'failure in polint for point',x
+          write(*,*) 'with input points: ',xa
+          stop
+        end if
+        num = num * (x - xa(j))
+        den = den * dx
+      end if
+    end do
+    w(i) = num / den
+  end do
+
+  return
+  end subroutine polint_lagrange_weights
+!------------------------------------------------------------------------------
+!
+! interpolation in 2 dimensions, follow yx order
+!
+!------------------------------------------------------------------------------
+  subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
+  implicit none
+
+  integer,intent(in) :: ordn
+  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
+
+#ifdef POLINT_LEGACY_ORDER
+  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)
+  end do
+  call polint(x1a,ymtmp,x1,y,dy,ordn)
+#else
+  integer  :: j
+  real*8, dimension(ordn) :: ymtmp
+  real*8 :: dy_temp
+
+  do j=1,ordn
+    call polint(x1a, ya(:,j), x1, ymtmp(j), dy_temp, ordn)
+  end do
+  call polint(x2a, ymtmp, x2, y, dy, ordn)
+#endif
+
+  return
+  end subroutine polin2
+!------------------------------------------------------------------------------
+!
+! interpolation in 3 dimensions, follow zyx order
+!
+!------------------------------------------------------------------------------
+  subroutine polin3(x1a,x2a,x3a,ya,x1,x2,x3,y,dy,ordn)
+  implicit none
+
+  integer,intent(in) :: ordn
+  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
+
+#ifdef POLINT_LEGACY_ORDER
+  integer  :: i,j,m,n
+  real*8, dimension(ordn,ordn) :: yatmp
+  real*8, dimension(ordn) :: ymtmp
+  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)
+   end do
+    yntmp=yatmp(i,:)
+    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
+  end do
+  call polint(x1a,ymtmp,x1,y,dy,ordn)
+#else
+  integer  :: i, j, k
+  real*8, dimension(ordn) :: w1, w2
+  real*8, dimension(ordn) :: ymtmp
+  real*8 :: yx_sum, x_sum
+
+  call polint_lagrange_weights(x1a, x1, w1, ordn)
+  call polint_lagrange_weights(x2a, x2, w2, ordn)
+
+  do k = 1, ordn
+    yx_sum = 0.d0
+    do j = 1, ordn
+      x_sum = 0.d0
+      do i = 1, ordn
+        x_sum = x_sum + w1(i) * ya(i,j,k)
+      end do
+      yx_sum = yx_sum + w2(j) * x_sum
+    end do
+    ymtmp(k) = yx_sum
+  end do
+
+  call polint(x3a, ymtmp, x3, y, dy, ordn)
+#endif
+
+  return
+  end subroutine polin3
 !--------------------------------------------------------------------------------------
-! calculate L2norm
+! calculate L2norm  
   subroutine l2normhelper(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
                           f,f_out,gw)
 
@@ -1276,9 +1476,9 @@ end subroutine d2dump
   real*8            :: dX, dY, dZ
   integer::imin,jmin,kmin
   integer::imax,jmax,kmax
-  integer::i,j,k,n_elements
+  integer::i,j,k,n_elements
-  real*8, dimension(:), allocatable :: f_flat
+  real*8, dimension(:), allocatable :: f_flat
-  real*8, external :: DDOT
+  real*8, external :: DDOT
 
   dX = X(2) - X(1)
   dY = Y(2) - Y(1)
@@ -1302,20 +1502,91 @@ if(dabs(X(1)-xmin) < dX) imin = 1
 if(dabs(Y(1)-ymin) < dY) jmin = 1
 if(dabs(Z(1)-zmin) < dZ) kmin = 1
 
-! Optimized with oneMKL BLAS DDOT for dot product
+  n_elements = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
-n_elements = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
+  allocate(f_flat(n_elements))
-allocate(f_flat(n_elements))
+  f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [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)
-f_out = DDOT(n_elements, f_flat, 1, f_flat, 1)
+  deallocate(f_flat)
-deallocate(f_flat)
 
 f_out = f_out*dX*dY*dZ
 
   return
 
   end subroutine l2normhelper
-!--------------------------------------------------------------------------------------
+!--------------------------------------------------------------------------------------
-! calculate L2norm especially for shell Blocks
+  subroutine l2normhelper7(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
+                           f1,f2,f3,f4,f5,f6,f7,f_out,gw)
+
+  implicit none
+!~~~~~~> Input parameters:
+  integer,intent(in ):: ex(1:3)
+  real*8, intent(in ):: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3)),xmin,ymin,zmin,xmax,ymax,zmax
+  integer,intent(in)::gw
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(in) :: f1,f2,f3,f4,f5,f6,f7
+  real*8, intent(out) :: f_out(7)
+!~~~~~~> Other variables:
+
+  real*8            :: dX, dY, dZ
+  integer::imin,jmin,kmin
+  integer::imax,jmax,kmax
+  integer::i,j,k
+  real*8 :: s1,s2,s3,s4,s5,s6,s7
+
+  dX = X(2) - X(1)
+  dY = Y(2) - Y(1)
+  dZ = Z(2) - Z(1)
+
+   imin = gw+1
+   jmin = gw+1
+   kmin = gw+1
+
+   imax = ex(1) - gw
+   jmax = ex(2) - gw
+   kmax = ex(3) - gw
+
+if(dabs(X(ex(1))-xmax) < dX) imax = ex(1)
+if(dabs(Y(ex(2))-ymax) < dY) jmax = ex(2)
+if(dabs(Z(ex(3))-zmax) < dZ) kmax = ex(3)
+if(dabs(X(1)-xmin) < dX) imin = 1
+if(dabs(Y(1)-ymin) < dY) jmin = 1
+if(dabs(Z(1)-zmin) < dZ) kmin = 1
+
+  s1 = 0.d0
+  s2 = 0.d0
+  s3 = 0.d0
+  s4 = 0.d0
+  s5 = 0.d0
+  s6 = 0.d0
+  s7 = 0.d0
+
+  do k=kmin,kmax
+    do j=jmin,jmax
+!DIR$ SIMD REDUCTION(+:s1,s2,s3,s4,s5,s6,s7)
+      do i=imin,imax
+        s1 = s1 + f1(i,j,k)*f1(i,j,k)
+        s2 = s2 + f2(i,j,k)*f2(i,j,k)
+        s3 = s3 + f3(i,j,k)*f3(i,j,k)
+        s4 = s4 + f4(i,j,k)*f4(i,j,k)
+        s5 = s5 + f5(i,j,k)*f5(i,j,k)
+        s6 = s6 + f6(i,j,k)*f6(i,j,k)
+        s7 = s7 + f7(i,j,k)*f7(i,j,k)
+      enddo
+    enddo
+  enddo
+
+  f_out(1) = s1*dX*dY*dZ
+  f_out(2) = s2*dX*dY*dZ
+  f_out(3) = s3*dX*dY*dZ
+  f_out(4) = s4*dX*dY*dZ
+  f_out(5) = s5*dX*dY*dZ
+  f_out(6) = s6*dX*dY*dZ
+  f_out(7) = s7*dX*dY*dZ
+
+  return
+
+  end subroutine l2normhelper7
+!--------------------------------------------------------------------------------------
+! calculate L2norm especially for shell Blocks
   subroutine l2normhelper_sh(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
                           f,f_out,gw,ogw,Symmetry)
 
@@ -1332,9 +1603,9 @@ f_out = f_out*dX*dY*dZ
   real*8            :: dX, dY, dZ
   integer::imin,jmin,kmin
   integer::imax,jmax,kmax
-  integer::i,j,k,n_elements
+  integer::i,j,k,n_elements
-  real*8, dimension(:), allocatable :: f_flat
+  real*8, dimension(:), allocatable :: f_flat
-  real*8, external :: DDOT
+  real*8, external :: DDOT
 
   real*8 :: PIo4
 
@@ -1397,12 +1668,11 @@ if(Symmetry==2)then
   if(dabs(ymin+gw*dY)<dY.and.Y(1)<0.d0) jmin = gw+1
 endif
 
-! Optimized with oneMKL BLAS DDOT for dot product
+  n_elements = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
-n_elements = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
+  allocate(f_flat(n_elements))
-allocate(f_flat(n_elements))
+  f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [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)
-f_out = DDOT(n_elements, f_flat, 1, f_flat, 1)
+  deallocate(f_flat)
-deallocate(f_flat)
 
 f_out = f_out*dX*dY*dZ
 
@@ -1429,9 +1699,9 @@ 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
-  real*8, dimension(:), allocatable :: f_flat
+  real*8, dimension(:), allocatable :: f_flat
-  real*8, external :: DDOT
+  real*8, external :: DDOT
 
   real*8 :: PIo4
 
@@ -1494,12 +1764,11 @@ if(Symmetry==2)then
   if(dabs(ymin+gw*dY)<dY.and.Y(1)<0.d0) jmin = gw+1
 endif
 
-! Optimized with oneMKL BLAS DDOT for dot product
+Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
-Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
+  allocate(f_flat(Nout))
-allocate(f_flat(Nout))
+  f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [Nout])
-f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [Nout])
+  f_out = DDOT(Nout, f_flat, 1, f_flat, 1)
-f_out = DDOT(Nout, f_flat, 1, f_flat, 1)
+  deallocate(f_flat)
-deallocate(f_flat)
 
   return
 
@@ -1600,9 +1869,12 @@ deallocate(f_flat)
 !       ^
 ! f=3/8*f_1 + 3/4*f_2 - 1/8*f_3
 
-  real*8,parameter::C1=3.d0/8.d0,C2=3.d0/4.d0,C3=-1.d0/8.d0
+  real*8,parameter::C1=3.d0/8.d0,C2=3.d0/4.d0,C3=-1.d0/8.d0
-
+  integer :: i,j,k
-  fout = C1*f1+C2*f2+C3*f3
+
+  do concurrent (k=1:ext(3), j=1:ext(2), i=1:ext(1))
+    fout(i,j,k) = C1*f1(i,j,k)+C2*f2(i,j,k)+C3*f3(i,j,k)
+  end do
 
   return
 
@@ -1696,8 +1968,8 @@ deallocate(f_flat)
   real*8, dimension(ORDN,ORDN,ORDN) :: ya
   real*8, dimension(ORDN,ORDN) :: tmp2
   real*8, dimension(ORDN) :: tmp1
-  real*8, dimension(3) :: SoAh
+  real*8, dimension(3) :: SoAh
-  real*8, external :: DDOT
+  real*8, external :: DDOT
 
 ! +1 because c++ gives 0 for first point
   cxB = inds+1  
@@ -1733,21 +2005,17 @@ deallocate(f_flat)
      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
 
-  ! Third dimension: x-direction weighted sum using BLAS DDOT
+  f_int = DDOT(ORDN, coef(1:ORDN), 1, tmp1, 1)
-  f_int = DDOT(ORDN, coef(1:ORDN), 1, tmp1, 1)
 
   return
 
@@ -1776,8 +2044,8 @@ deallocate(f_flat)
   integer,dimension(2) :: cxB,cxT
   real*8, dimension(ORDN,ORDN) :: ya
   real*8, dimension(ORDN) :: tmp1
-  real*8, dimension(2) :: SoAh
+  real*8, dimension(2) :: SoAh
-  real*8, external :: DDOT
+  real*8, external :: DDOT
 
 ! +1 because c++ gives 0 for first point
   cxB = inds(1:2)+1  
@@ -1807,14 +2075,12 @@ deallocate(f_flat)
      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
 
-  ! Use BLAS DDOT for final weighted sum
+  f_int = DDOT(ORDN, coef(1:ORDN), 1, tmp1, 1)
-  f_int = DDOT(ORDN, coef(1:ORDN), 1, tmp1, 1)
 
   return
 
@@ -1840,12 +2106,12 @@ deallocate(f_flat)
 !~~~~~~> Other parameters:
 
   real*8, dimension(-ORDN+1:ex(1)+ORDN,-ORDN+1:ex(2)+ORDN,ex(3)) :: fh
-  integer :: m
+  integer :: m
-  integer :: cxB,cxT
+  integer :: cxB,cxT
-  real*8, dimension(ORDN) :: ya
+  real*8, dimension(ORDN) :: ya
-  real*8 :: SoAh
+  real*8 :: SoAh
-  integer,dimension(3) :: inds
+  integer,dimension(3) :: inds
-  real*8, external :: DDOT
+  real*8, external :: DDOT
 
 ! +1 because c++ gives 0 for first point
   inds = indsi + 1
@@ -1906,8 +2172,7 @@ deallocate(f_flat)
           write(*,*)"error in global_interpind1d, not recognized dumyd = ",dumyd
   endif
 
-  ! Optimized with BLAS DDOT for weighted sum
+  f_int = DDOT(ORDN, coef, 1, ya, 1)
-  f_int = DDOT(ORDN, coef, 1, ya, 1)
 
   return
 
@@ -2139,38 +2404,32 @@ deallocate(f_flat)
 
   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
+  real*8 :: gont
-  integer :: i
+
-
+  integer :: i
-  ! Lookup table for factorials 0! to 20! (precomputed)
+  real*8, parameter, dimension(0:20) :: fact_table = [ &
-  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, &
-    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, &
-    362880.d0, 3628800.d0, 39916800.d0, 479001600.d0, 6227020800.d0, &
+    87178291200.d0, 1307674368000.d0, 20922789888000.d0, &
-    87178291200.d0, 1307674368000.d0, 20922789888000.d0, &
+    355687428096000.d0, 6402373705728000.d0, 121645100408832000.d0, &
-    355687428096000.d0, 6402373705728000.d0, 121645100408832000.d0, &
+    2432902008176640000.d0 ]
-    2432902008176640000.d0 ]
 
 ! sanity check
-  if(N < 0)then
+  if(N < 0)then
-     write(*,*) "ffact: error input for factorial"
+     write(*,*) "ffact: error input for factorial"
-     gont = 1.d0
+     gont = 1.d0
-     return
+     return
-  endif
+  endif
-
+
-  ! Use lookup table for small N (fast path)
+  if(N <= 20)then
-  if(N <= 20)then
+     gont = fact_table(N)
-     gont = fact_table(N)
+  else
-  else
+     gont = exp(log_gamma(dble(N+1)))
-     ! Use log-gamma function for large N: N! = exp(log_gamma(N+1))
+  endif
-     ! This avoids overflow and is computed efficiently
-     gont = exp(log_gamma(dble(N+1)))
-  endif
 
   return
 

AMSS_NCKU_source/fmisc.h

@@ -12,9 +12,10 @@
 #define f_global_interpind global_interpind
 #define f_global_interpind2d global_interpind2d
 #define f_global_interpind1d global_interpind1d
-#define f_l2normhelper l2normhelper
+#define f_l2normhelper l2normhelper
-#define f_l2normhelper_sh l2normhelper_sh
+#define f_l2normhelper7 l2normhelper7
-#define f_l2normhelper_sh_rms l2normhelper_sh_rms
+#define f_l2normhelper_sh l2normhelper_sh
+#define f_l2normhelper_sh_rms l2normhelper_sh_rms
 #define f_average average
 #define f_average3 average3
 #define f_average2 average2
@@ -41,9 +42,10 @@
 #define f_global_interpind GLOBAL_INTERPIND
 #define f_global_interpind2d GLOBAL_INTERPIND2D
 #define f_global_interpind1d GLOBAL_INTERPIND1D
-#define f_l2normhelper L2NORMHELPER
+#define f_l2normhelper L2NORMHELPER
-#define f_l2normhelper_sh L2NORMHELPER_SH
+#define f_l2normhelper7 L2NORMHELPER7
-#define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
+#define f_l2normhelper_sh L2NORMHELPER_SH
+#define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
 #define f_average AVERAGE
 #define f_average3 AVERAGE3
 #define f_average2 AVERAGE2
@@ -70,9 +72,10 @@
 #define f_global_interpind global_interpind_
 #define f_global_interpind2d global_interpind2d_
 #define f_global_interpind1d global_interpind1d_
-#define f_l2normhelper l2normhelper_
+#define f_l2normhelper l2normhelper_
-#define f_l2normhelper_sh l2normhelper_sh_
+#define f_l2normhelper7 l2normhelper7_
-#define f_l2normhelper_sh_rms l2normhelper_sh_rms_
+#define f_l2normhelper_sh l2normhelper_sh_
+#define f_l2normhelper_sh_rms l2normhelper_sh_rms_
 #define f_average average_
 #define f_average3 average3_
 #define f_average2 average2_
@@ -156,21 +159,30 @@ extern "C"
 							  int *, double *, int &, int &);
 }
 
-extern "C"
+extern "C"
-{
+{
-	void f_l2normhelper(int *, double *, double *, double *,
+	void f_l2normhelper(int *, double *, double *, double *,
-						double &, double &, double &,
+						double &, double &, double &,
-						double &, double &, double &,
+						double &, double &, double &,
-						double *, double &, int &);
+						double *, double &, int &);
-}
+}
-
+
-extern "C"
+extern "C"
-{
+{
-	void f_l2normhelper_sh(int *, double *, double *, double *,
+	void f_l2normhelper7(int *, double *, double *, double *,
-						   double &, double &, double &,
+						 double &, double &, double &,
-						   double &, double &, double &,
+						 double &, double &, double &,
-						   double *, double &, int &, int &, int &);
+						 double *, double *, double *, double *,
-}
+						 double *, double *, double *, double *, int &);
+}
+
+extern "C"
+{
+	void f_l2normhelper_sh(int *, double *, double *, double *,
+						   double &, double &, double &,
+						   double &, double &, double &,
+						   double *, double &, int &, int &, int &);
+}
 
 extern "C"
 {

AMSS_NCKU_source/gaussj.C

@@ -16,66 +16,115 @@ 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)
 {
-  // Allocate pivot array and workspace
+  double swap;
-  lapack_int *ipiv = new lapack_int[n];
-  lapack_int info;
 
-  // Make a copy of matrix a for solving (dgesv modifies it to LU form)
+  int *indxc, *indxr, *ipiv;
-  double *a_copy = new double[n * n];
+  indxc = new int[n];
-  for (int i = 0; i < n * n; i++) {
+  indxr = new int[n];
-    a_copy[i] = a[i];
+  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
+          }
+        }
+
+    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;
+      }
+
+      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;
+      }
   }
 
-  // Step 1: Solve linear system A*x = b using LU decomposition
+  for (l = n - 1; l >= 0; l--)
-  // 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);
+    if (indxr[l] != indxc[l])
-
+      for (k = 0; k < n; k++)
-  if (info != 0) {
+      {
-    cout << "gaussj: Singular Matrix (dgesv info=" << info << ")" << endl;
+        swap = a[k * n + indxr[l]];
-    delete[] ipiv;
+        a[k * n + indxr[l]] = a[k * n + indxc[l]];
-    delete[] a_copy;
+        a[k * n + indxc[l]] = swap;
-    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[] indxc;
+  delete[] indxr;
   delete[] ipiv;
-  delete[] a_copy;
 
   return 0;
 }

AMSS_NCKU_source/ilucg.f90

@@ -512,10 +512,11 @@
       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)
 
-      DOUBLE PRECISION, EXTERNAL :: DDOT
+      SUM = 0.0D0
-      DGVV = DDOT(N, V, 1, W, 1)
+            DO 10 I = 1,N
+            SUM = SUM + V(I)*W(I)
+10          CONTINUE
+      DGVV = SUM
       RETURN
       END

AMSS_NCKU_source/macrodef.h

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

AMSS_NCKU_source/makefile

@@ -1,11 +1,25 @@
-
+
-
+
-include makefile.inc
+include makefile.inc
-
+
-.SUFFIXES: .o .f90 .C .for .cu
+## polint(ordn=6) kernel selector:
-
+##   1 (default): barycentric fast path
-.f90.o:
+##   0          : fallback to Neville path
-	$(f90) $(f90appflags) -c $< -o $@
+POLINT6_USE_BARY ?= 1
+POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)
+
+ARCH_OPT = -march=x86-64-v4
+CXXAPPFLAGS = -O3 $(ARCH_OPT) -fp-model fast=2 -fma -ipo \
+              -Dfortran3 -Dnewc -I${MKLROOT}/include
+f90appflags = -O3 $(ARCH_OPT) -fp-model fast=2 -fma -ipo \
+              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
+TP_OPTFLAGS = -O3 $(ARCH_OPT) -fp-model fast=2 -fma -ipo \
+              -Dfortran3 -Dnewc -I${MKLROOT}/include
+
+.SUFFIXES: .o .f90 .C .for .cu
+
+.f90.o:
+	$(f90) $(f90appflags) -c $< -o $@
 
 .C.o:
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
@@ -13,8 +27,14 @@ include makefile.inc
 .for.o:
 	$(f77) -c $< -o $@
 
-.cu.o:
+.cu.o:
-	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
+	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
+
+TwoPunctures.o: TwoPunctures.C
+	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
+
+TwoPunctureABE.o: TwoPunctureABE.C
+	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
 
 # Input files
 C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
@@ -95,8 +115,8 @@ ABE: $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
 ABEGPU: $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
 	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
 
-TwoPunctureABE: $(TwoPunctureFILES)
+TwoPunctureABE: $(TwoPunctureFILES)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(TwoPunctureFILES) $(LDLIBS)
+	$(CLINKER) $(TP_OPTFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
 
 clean:
 	rm *.o ABE ABEGPU TwoPunctureABE make.log -f

AMSS_NCKU_source/makefile.inc

@@ -1,30 +1,32 @@
+
 ## GCC version (commented out)
 ## filein  = -I/usr/include -I/usr/lib/x86_64-linux-gnu/mpich/include -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
 ## filein  = -I/usr/include/ -I/usr/include/openmpi-x86_64/ -I/usr/lib/x86_64-linux-gnu/openmpi/include/ -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
 ## LDLIBS  = -L/usr/lib/x86_64-linux-gnu -L/usr/lib64 -L/usr/lib/gcc/x86_64-linux-gnu/11 -lgfortran -lmpi -lgfortran
 
-## Intel oneAPI version with oneMKL (Optimized for performance)
+## Intel oneAPI version with oneMKL
 filein  = -I/usr/include/ -I${MKLROOT}/include
 
-## Using sequential MKL (OpenMP disabled for better single-threaded performance)
+## Use sequential oneMKL to avoid introducing extra OpenMP behavior into ABE.
-## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
+LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl -liomp5
-LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl
+
+## Optional Intel oneTBB allocator, kept aligned with main's build environment.
+USE_TBBMALLOC ?= 1
+TBBMALLOC_SO ?= /home/intel/oneapi/2025.3/lib/libtbbmalloc.so
+ifneq ($(wildcard $(TBBMALLOC_SO)),)
+TBBMALLOC_LIBS = -Wl,--no-as-needed $(TBBMALLOC_SO) -Wl,--as-needed
+else
+TBBMALLOC_LIBS = -Wl,--no-as-needed -ltbbmalloc -Wl,--as-needed
+endif
+ifeq ($(USE_TBBMALLOC),1)
+LDLIBS := $(TBBMALLOC_LIBS) $(LDLIBS)
+endif
 
-## Aggressive optimization flags:
-## -O3: Maximum optimization
-## -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 \
-               -Dfortran3 -Dnewc -I${MKLROOT}/include
-f90appflags  = -O3 -xHost -fp-model fast=2 -fma \
-               -fpp -I${MKLROOT}/include
 f90          = ifx
 f77          = ifx
 CXX          = icpx
 CC           = icx
-CLINKER      = mpiicpx 
+CLINKER      = mpiicpx
 
 Cu = nvcc
 CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include

generate_macrodef.py

@@ -392,17 +392,6 @@ def generate_macrodef_fh():
         print( "# Finite_Difference_Method #define ghost_width setting error!!!",   file=file1 )
         print(                                                   file=file1 )
 
-    # Define macro DEBUG_NAN_CHECK
-    # 0: off (default), 1: on
-
-    debug_nan_check = getattr(input_data, "Debug_NaN_Check", 0)
-    if debug_nan_check:
-        print( "#define DEBUG_NAN_CHECK 1", file=file1 )
-        print(                             file=file1 )
-    else:
-        print( "#define DEBUG_NAN_CHECK 0", file=file1 )
-        print(                             file=file1 )
-
     # Whether to use a shell-patch grid
     # use shell or not
 
@@ -525,9 +514,6 @@ def generate_macrodef_fh():
     print( "    6th order: 4",                                                                      file=file1 )
     print( "    8th order: 5",                                                                      file=file1 )
     print(                                                                                          file=file1 )
-    print( "define DEBUG_NAN_CHECK",                                                                file=file1 )
-    print( "    0: off (default), 1: on",                                                           file=file1 )
-    print(                                                                                          file=file1 )
     print( "define WithShell",                                                                      file=file1 )
     print( "    use shell or not",                                                                  file=file1 )
     print(                                                                                          file=file1 )

inputfile_example/AMSS_NCKU_Input.py

@@ -35,8 +35,7 @@ Equation_Class           = "BSSN"                  ## Evolution Equation: choose
                                                    ## If "BSSN-EScalar" is chosen, it is necessary to set other parameters below
 Initial_Data_Method      = "Ansorg-TwoPuncture"    ## initial data method: choose "Ansorg-TwoPuncture", "Lousto-Analytical", "Cao-Analytical", "KerrSchild-Analytical"
 Time_Evolution_Method    = "runge-kutta-45"        ## time evolution method: choose "runge-kutta-45"
-Finite_Diffenence_Method = "4th-order"             ## finite-difference method: choose "2nd-order", "4th-order", "6th-order", "8th-order"
+Finite_Diffenence_Method = "4th-order"             ## finite-difference method: choose "2nd-order", "4th-order", "6th-order", "8th-order"
-Debug_NaN_Check          = 0                       ## enable NaN checks in compute_rhs_bssn: 0 (off) or 1 (on)
 
 #################################################
 

makefile_and_run.py

@@ -11,18 +11,6 @@
 import AMSS_NCKU_Input as input_data
 import subprocess
 
-## CPU core binding configuration using taskset
-## taskset ensures all child processes inherit the CPU affinity mask
-## This forces make and all compiler processes to use only nohz_full cores (4-55, 60-111)
-## Format: taskset -c 4-55,60-111 ensures processes only run on these cores
-#NUMACTL_CPU_BIND = "taskset -c 4-55,60-111"
-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 = 14
-
 
 ##################################################################
 
@@ -38,11 +26,11 @@ def makefile_ABE():
     print( " Compiling the AMSS-NCKU executable file ABE/ABEGPU " ) 
     print(                                                        )
 
-    ## Build command with CPU binding to nohz_full cores
+    ## Build command
     if (input_data.GPU_Calculation == "no"):
-        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABE"
+        makefile_command  = "make -j96" + " ABE"
     elif (input_data.GPU_Calculation == "yes"):
-        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
+        makefile_command  = "make -j4" + " ABEGPU"
     else:
         print( " CPU/GPU numerical calculation setting is wrong " )
         print(                                                    )
@@ -79,8 +67,8 @@ def makefile_TwoPunctureABE():
     print( " Compiling the AMSS-NCKU executable file TwoPunctureABE " )
     print(                                                            )
     
-    ## Build command with CPU binding to nohz_full cores
+    ## Build command
-    makefile_command = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} TwoPunctureABE"
+    makefile_command = "make" + " 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) 
@@ -117,10 +105,10 @@ def run_ABE():
     ## Define the command to run; cast other values to strings as needed
     
     if (input_data.GPU_Calculation == "no"):
-        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
+        mpi_command         = "mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
         mpi_command_outfile = "ABE_out.log"
     elif (input_data.GPU_Calculation == "yes"):
-        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
+        mpi_command         = "mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
         mpi_command_outfile = "ABEGPU_out.log"
  
     ## Execute the MPI command and stream output
@@ -159,7 +147,7 @@ def run_TwoPunctureABE():
     print(                                                          )
     
     ## Define the command to run
-    TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
+    TwoPuncture_command         = "./TwoPunctureABE"
     TwoPuncture_command_outfile = "TwoPunctureABE_out.log"
 
     ## Execute the command with subprocess.Popen and stream output

parallel_plot_helper.py

@@ -0,0 +1,12 @@
+import multiprocessing
+
+
+def run_plot_task(task):
+    func, args = task
+    return func(*args)
+
+
+def run_plot_tasks_parallel(plot_tasks):
+    ctx = multiprocessing.get_context('fork')
+    with ctx.Pool() as pool:
+        pool.map(run_plot_task, plot_tasks)

plot_GW_strain_amplitude_xiaoqu.py

@@ -8,11 +8,13 @@
 ##
 #################################################
 
-import numpy                               ## numpy for array operations
+import numpy                               ## numpy for array operations
-import scipy                               ## scipy for interpolation and signal processing
+import scipy                               ## scipy for interpolation and signal processing
-import math
+import math
-import matplotlib.pyplot    as     plt     ## matplotlib for plotting
+import matplotlib
-import os                                  ## os for system/file operations
+matplotlib.use('Agg')                      ## use non-interactive backend for multiprocessing safety
+import matplotlib.pyplot    as     plt     ## matplotlib for plotting
+import os                                  ## os for system/file operations
 
 import AMSS_NCKU_Input as input_data
 

plot_binary_data.py

@@ -6,17 +6,22 @@
 ## Author: Xiaoqu
 ## Dates: 2024/10/01 --- 2025/09/14
 ##
-#################################################
+#################################################
-
+
-import numpy
+## Restrict OpenMP to one thread per process so that parallel
-import scipy
+## subprocess plotting does not multiply BLAS thread counts.
-import matplotlib.pyplot    as     plt
+import os
-from   matplotlib.colors    import LogNorm
+os.environ.setdefault("OMP_NUM_THREADS", "1")
-from   mpl_toolkits.mplot3d import Axes3D
+
-## import torch
+import numpy
-import AMSS_NCKU_Input      as input_data
+import scipy
-
+import matplotlib
-import os
+matplotlib.use('Agg')                      ## use non-interactive backend for multiprocessing safety
+import matplotlib.pyplot    as     plt
+from   matplotlib.colors    import LogNorm
+from   mpl_toolkits.mplot3d import Axes3D
+## import torch
+import AMSS_NCKU_Input      as input_data
 
 
 #########################################################################################
@@ -92,9 +97,9 @@ def plot_binary_data( filename, binary_outdir, figure_outdir ):
 
 
 
-####################################################################################
+####################################################################################
-
+
-# Plot a single binary dataset (2D slices and 3D surface)
+# Plot a single binary dataset (2D slices and 3D surface)
 
 def get_data_xy( Rmin, Rmax, n, data0, time, figure_title, figure_outdir ):
 
@@ -188,7 +193,15 @@ def get_data_xy( Rmin, Rmax, n, data0, time, figure_title, figure_outdir ):
     plt.savefig( os.path.join(figure_surfaceplot_outdir, figure_title + " time = " + str(time) + " surface_plot.pdf") )   # save figure
     plt.close()
 
-    return
+    return
-
+
-####################################################################################
+####################################################################################
+
+## Allow standalone subprocess execution for parallel binary-data plotting.
+if __name__ == '__main__':
+    import sys
+    if len(sys.argv) != 4:
+        print(f"Usage: {sys.argv[0]} <filename> <binary_outdir> <figure_outdir>")
+        sys.exit(1)
+    plot_binary_data(sys.argv[1], sys.argv[2], sys.argv[3])
 

plot_xiaoqu.py

@@ -6,15 +6,20 @@
 ## 2024/10/01 --- 2025/09/14
 ##
 #################################################
-
+
-import numpy                               ## numpy for array operations
+import numpy                               ## numpy for array operations
-import matplotlib.pyplot    as     plt     ## matplotlib for plotting
+import matplotlib
-from   mpl_toolkits.mplot3d import Axes3D  ## needed for 3D plots
+matplotlib.use('Agg')                      ## use non-interactive backend for multiprocessing safety
-import glob
+import matplotlib.pyplot    as     plt     ## matplotlib for plotting
-import os                                  ## operating system utilities
+from   mpl_toolkits.mplot3d import Axes3D  ## needed for 3D plots
-
+import glob
-import plot_binary_data
+import os                                  ## operating system utilities
-import AMSS_NCKU_Input as input_data
+
+import plot_binary_data
+import AMSS_NCKU_Input as input_data
+import subprocess
+import sys
+import multiprocessing
 
 # plt.rcParams['text.usetex'] = True  ## enable LaTeX fonts in plots
 
@@ -50,13 +55,37 @@ def generate_binary_data_plot( binary_outdir, figure_outdir ):
         file_list.append(x)
         print(x)
 
-    ## Plot each file in the list
+    ## Plot each file in parallel using subprocesses.
-    for filename in file_list:
+    ## Each subprocess starts with BLAS thread limits in plot_binary_data.py.
-        print(filename)
+    script = os.path.join( os.path.dirname(__file__), "plot_binary_data.py" )
-        plot_binary_data.plot_binary_data(filename, binary_outdir, figure_outdir)
+    max_workers = min( multiprocessing.cpu_count(), len(file_list) ) if file_list else 0
-
+
-    print(                        )
+    running = []
-    print( " Binary Data Plot Has been Finished " )
+    failed  = []
+    for filename in file_list:
+        print(filename)
+        proc = subprocess.Popen(
+            [sys.executable, script, filename, binary_outdir, figure_outdir],
+        )
+        running.append( (proc, filename) )
+        if len(running) >= max_workers:
+            p, fn = running.pop(0)
+            p.wait()
+            if p.returncode != 0:
+                failed.append(fn)
+
+    for p, fn in running:
+        p.wait()
+        if p.returncode != 0:
+            failed.append(fn)
+
+    if failed:
+        print( " WARNING: the following binary data plots failed:" )
+        for fn in failed:
+            print( "   ", fn )
+
+    print(                        )
+    print( " Binary Data Plot Has been Finished " )
     print(                                        )
 
     return