#!/usr/local/bin/env python

#=============================================================================================
# MODULE DOCSTRING
#=============================================================================================

"""
Test energy for alchemically decoupled ligand using CustomGBForce.

DESCRIPTION

COPYRIGHT

@author John D. Chodera <jchodera@gmail.com>

All code in this repository is released under the GNU General Public License.

This program is free software: you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free Software
Foundation, either version 3 of the License, or (at your option) any later
version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
PARTICULAR PURPOSE.  See the GNU General Public License for more details.
 
You should have received a copy of the GNU General Public License along with
this program.  If not, see <http://www.gnu.org/licenses/>.

TODO

"""

#=============================================================================================
# GLOBAL IMPORTS
#=============================================================================================

import os
import os.path
import sys
import math
import copy
import time

import numpy

import simtk
import simtk.unit as units
import simtk.openmm as openmm

#=============================================================================================
# SUBROUTINES
#=============================================================================================

def norm(n01):
    return n01.unit * numpy.sqrt(numpy.dot(n01/n01.unit, n01/n01.unit))

#=============================================================================================
# ALCHEMICAL MODIFICATIONS
#=============================================================================================

def createCustomSoftcoreGBOBC(solventDielectric, soluteDielectric, igb):

    custom = openmm.CustomGBForce()

    custom.addPerParticleParameter("q");
    custom.addPerParticleParameter("radius");
    custom.addPerParticleParameter("scale");
    custom.addPerParticleParameter("lambda");
    custom.addGlobalParameter("solventDielectric", solventDielectric);
    custom.addGlobalParameter("soluteDielectric", soluteDielectric);
    custom.addGlobalParameter("offset", 0.009)
    custom.addComputedValue("I",  "lambda2*step(r+sr2-or1)*0.5*(1/L-1/U+0.25*(r-sr2^2/r)*(1/(U^2)-1/(L^2))+0.5*log(L/U)/r);"
                                  "U=r+sr2;"
                                  "L=max(or1, D);"
                                  "D=abs(r-sr2);"
                                  "sr2 = scale2*or2;"
                                  "or1 = radius1-offset; or2 = radius2-offset", openmm.CustomGBForce.ParticlePairNoExclusions)

#    custom.addComputedValue("I", "lambda1*lambda2*step(r+sr2-or1)*0.5*(1/L-1/U+0.25*(1/U^2-1/L^2)*(r-sr2*sr2/r)+0.5*log(L/U)/r+C);"
#                            "U=r+sr2;"
#                            "C=2*(1/or1-1/L)*step(sr2-r-or1);"
#                            "L=max(or1, D);"
#                            "D=abs(r-sr2);"
#                            "sr2 = scale2*or2;"
#                            "or1 = radius1-offset; or2 = radius2-offset", openmm.CustomGBForce.ParticlePairNoExclusions);
    

    if igb == 2:
        custom.addComputedValue("B", "1/(1/or-tanh(0.8*psi+2.909125*psi^3)/radius);"
                                  "psi=I*or; or=radius-offset", openmm.CustomGBForce.SingleParticle)

    elif igb == 5:
        custom.addComputedValue("B", "1/(1/or-tanh(psi-0.8*psi^2+4.85*psi^3)/radius);"
                                  "psi=I*or; or=radius-offset", openmm.CustomGBForce.SingleParticle)

    else:
        print "ERROR: Incorrect igb# input for 'createCustomGBOBC'"
        print "Exiting..."
        sys.exit()

#    custom.addEnergyTerm("-0.5*138.935485*lambda*(1/soluteDielectric-1/solventDielectric)*q^2/B", openmm.CustomGBForce.SingleParticle)
#    custom.addEnergyTerm("-138.935485*lambda1*lambda2*(1/soluteDielectric-1/solventDielectric)*q1*q2/f;"
#                           "f=sqrt(r^2+B1*B2*exp(-r^2/(4*B1*B2)))", openmm.CustomGBForce.ParticlePair)

    custom.addEnergyTerm("lambda*28.3919551*(radius+0.14)^2*(radius/B)^6-0.5*138.935485*(1/soluteDielectric-1/solventDielectric)*q^2/B", openmm.CustomGBForce.SingleParticle);
    custom.addEnergyTerm("-138.935485*(1/soluteDielectric-1/solventDielectric)*q1*q2/f;"
                          "f=sqrt(r^2+B1*B2*exp(-r^2/(4*B1*B2)))", openmm.CustomGBForce.ParticlePairNoExclusions);
        

    return custom

def build_softcore_system(reference_system, receptor_atoms, ligand_atoms, valence_lambda, coulomb_lambda, vdw_lambda, annihilate=True):
    """
    Build alchemically-modified system where ligand is decoupled or annihilated using *SoftcoreForce classes.
    
    """

    # Create new system.
    system = openmm.System()

    # Set periodic box vectors.
    [a,b,c] = reference_system.getDefaultPeriodicBoxVectors()
    system.setDefaultPeriodicBoxVectors(a,b,c)

    # Add atoms.
    for atom_index in range(reference_system.getNumParticles()):
        mass = reference_system.getParticleMass(atom_index)
        system.addParticle(mass)

    # Add constraints
    for constraint_index in range(reference_system.getNumConstraints()):
        [iatom, jatom, r0] = reference_system.getConstraintParameters(constraint_index)
        system.addConstraint(iatom, jatom, r0)    

    # Perturb force terms.
    for force_index in range(reference_system.getNumForces()):
        reference_force = reference_system.getForce(force_index)
        # Dispatch forces
        if isinstance(reference_force, openmm.HarmonicBondForce):
            # HarmonicBondForce
            force = openmm.HarmonicBondForce()
            for bond_index in range(reference_force.getNumBonds()):
                # Retrieve parameters.
                [iatom, jatom, r0, K] = reference_force.getBondParameters(bond_index)
                # Annihilate if directed.
                if annihilate and (iatom in ligand_atoms) and (jatom in ligand_atoms):
                    K *= valence_lambda
                # Add bond parameters.
                force.addBond(iatom, jatom, r0, K)
            # Add force to new system.
            system.addForce(force)
        elif isinstance(reference_force, openmm.HarmonicAngleForce):
            # HarmonicAngleForce
            force = openmm.HarmonicAngleForce()
            for angle_index in range(reference_force.getNumAngles()):
                # Retrieve parameters.
                [iatom, jatom, katom, theta0, Ktheta] = reference_force.getAngleParameters(angle_index)
                # Annihilate if directed:
                if annihilate and (iatom in ligand_atoms) and (jatom in ligand_atoms) and (katom in ligand_atoms):
                    Ktheta *= valence_lambda
                # Add parameters.
                force.addAngle(iatom, jatom, katom, theta0, Ktheta)
            # Add force to system.                
            system.addForce(force)
        elif isinstance(reference_force, openmm.PeriodicTorsionForce):
            # PeriodicTorsionForce
            force = openmm.PeriodicTorsionForce()
            for torsion_index in range(reference_force.getNumTorsions()):
                # Retrieve parmaeters.
                [particle1, particle2, particle3, particle4, periodicity, phase, k] = reference_force.getTorsionParameters(torsion_index)
                # Annihilate if directed:
                if annihilate and (particle1 in ligand_atoms) and (particle2 in ligand_atoms) and (particle3 in ligand_atoms) and (particle4 in ligand_atoms):
                    k *= valence_lambda
                # Add parameters.
                force.addTorsion(particle1, particle2, particle3, particle4, periodicity, phase, k)
            # Add force to system.
            system.addForce(force)            
        elif isinstance(reference_force, openmm.NonbondedForce):
            # NonbondedForce
            force = openmm.NonbondedSoftcoreForce()
            for particle_index in range(reference_force.getNumParticles()):
                # Retrieve parameters.
                [charge, sigma, epsilon] = reference_force.getParticleParameters(particle_index)
                # Alchemically modify parameters.
                if particle_index in ligand_atoms:
                    charge *= coulomb_lambda
                    epsilon *= vdw_lambda
                    # Add modified particle parameters.
                    force.addParticle(charge, sigma, epsilon, vdw_lambda)
                else:
                    # Add unmodified particle parameters.
                    force.addParticle(charge, sigma, epsilon, 1.0)
            for exception_index in range(reference_force.getNumExceptions()):
                # Retrieve parameters.
                [iatom, jatom, chargeprod, sigma, epsilon] = reference_force.getExceptionParameters(exception_index)
                # Alchemically modify epsilon and chargeprod.
                if (iatom in ligand_atoms) and (jatom in ligand_atoms):
                    if annihilate:
                        epsilon *= vdw_lambda 
                        chargeprod *= coulomb_lambda
                    # Add modified exception parameters.
                    force.addException(iatom, jatom, chargeprod, sigma, epsilon, vdw_lambda)
                else:
                    # Add unmodified exception parameters.
                    force.addException(iatom, jatom, chargeprod, sigma, epsilon, 1.0)                    
            # Set parameters.
            force.setNonbondedMethod( reference_force.getNonbondedMethod() )
            force.setCutoffDistance( reference_force.getCutoffDistance() )
            force.setReactionFieldDielectric( reference_force.getReactionFieldDielectric() )
            #force.setEwaldErrorTolerance( reference_force.getEwaldErrorTolerance() )
            # Add force to new system.
            system.addForce(force)
            
        elif isinstance(reference_force, openmm.GBSAOBCForce):
            # GBSAOBCForce
            force = openmm.GBSAOBCSoftcoreForce()

            force.setSolventDielectric( reference_force.getSolventDielectric() )
            force.setSoluteDielectric( reference_force.getSoluteDielectric() )

            for particle_index in range(reference_force.getNumParticles()):
                # Retrieve parameters.
                [charge, radius, scaling_factor] = reference_force.getParticleParameters(particle_index)
                # Alchemically modify parameters.
                if particle_index in ligand_atoms:
                    # Scale charge and contribution to GB integrals.
                    force.addParticle(charge*coulomb_lambda, radius, scaling_factor, coulomb_lambda)
                else:
                    # Don't modulate GB.
                    force.addParticle(charge, radius, scaling_factor, 1.0)

            # Add force to new system.
            system.addForce(force)
        else:
            # Don't add unrecognized forces.
            pass

    return system

def build_custom_system(reference_system, receptor_atoms, ligand_atoms, valence_lambda, coulomb_lambda, vdw_lambda, annihilate=True):
    """
    Build alchemically-modified system where ligand is decoupled or annihilated using Custom*Force classes.
    
    """

    # Create new system.
    system = openmm.System()

    # Set periodic box vectors.
    [a,b,c] = reference_system.getDefaultPeriodicBoxVectors()
    system.setDefaultPeriodicBoxVectors(a,b,c)

    # Add atoms.
    for atom_index in range(reference_system.getNumParticles()):
        mass = reference_system.getParticleMass(atom_index)
        system.addParticle(mass)

    # Add constraints
    for constraint_index in range(reference_system.getNumConstraints()):
        [iatom, jatom, r0] = reference_system.getConstraintParameters(constraint_index)
        system.addConstraint(iatom, jatom, r0)    

    # Perturb force terms.
    for force_index in range(reference_system.getNumForces()):
        reference_force = reference_system.getForce(force_index)
        # Dispatch forces
        if isinstance(reference_force, openmm.HarmonicBondForce):
            # HarmonicBondForce
            force = openmm.HarmonicBondForce()
            for bond_index in range(reference_force.getNumBonds()):
                # Retrieve parameters.
                [iatom, jatom, r0, K] = reference_force.getBondParameters(bond_index)
                # Annihilate if directed.
                if annihilate and (iatom in ligand_atoms) and (jatom in ligand_atoms):
                    K *= valence_lambda
                # Add bond parameters.
                force.addBond(iatom, jatom, r0, K)
            # Add force to new system.
            system.addForce(force)
        elif isinstance(reference_force, openmm.HarmonicAngleForce):
            # HarmonicAngleForce
            force = openmm.HarmonicAngleForce()
            for angle_index in range(reference_force.getNumAngles()):
                # Retrieve parameters.
                [iatom, jatom, katom, theta0, Ktheta] = reference_force.getAngleParameters(angle_index)
                # Annihilate if directed:
                if annihilate and (iatom in ligand_atoms) and (jatom in ligand_atoms) and (katom in ligand_atoms):
                    Ktheta *= valence_lambda
                # Add parameters.
                force.addAngle(iatom, jatom, katom, theta0, Ktheta)
            # Add force to system.                
            system.addForce(force)
        elif isinstance(reference_force, openmm.PeriodicTorsionForce):
            # PeriodicTorsionForce
            force = openmm.PeriodicTorsionForce()
            for torsion_index in range(reference_force.getNumTorsions()):
                # Retrieve parmaeters.
                [particle1, particle2, particle3, particle4, periodicity, phase, k] = reference_force.getTorsionParameters(torsion_index)
                # Annihilate if directed:
                if annihilate and (particle1 in ligand_atoms) and (particle2 in ligand_atoms) and (particle3 in ligand_atoms) and (particle4 in ligand_atoms):
                    k *= valence_lambda
                # Add parameters.
                force.addTorsion(particle1, particle2, particle3, particle4, periodicity, phase, k)
            # Add force to system.
            system.addForce(force)            
        elif isinstance(reference_force, openmm.NonbondedForce):
            # NonbondedForce will handle charges and exception interactions.
            force = openmm.NonbondedForce()
            for particle_index in range(reference_force.getNumParticles()):
                # Retrieve parameters.
                [charge, sigma, epsilon] = reference_force.getParticleParameters(particle_index)
                # Remove Lennard-Jones interactions, which will be handled by CustomNonbondedForce.
                epsilon *= 0.0
                # Alchemically modify charges.
                if particle_index in ligand_atoms:
                    charge *= coulomb_lambda
                # Add modified particle parameters.
                force.addParticle(charge, sigma, epsilon)
            for exception_index in range(reference_force.getNumExceptions()):
                # Retrieve parameters.
                [iatom, jatom, chargeprod, sigma, epsilon] = reference_force.getExceptionParameters(exception_index)
                # Alchemically modify epsilon and chargeprod.
                # Note that exceptions are handled by NonbondedForce and not CustomNonbondedForce.
                if (iatom in ligand_atoms) and (jatom in ligand_atoms):
                    if annihilate:
                        epsilon *= vdw_lambda 
                        chargeprod *= coulomb_lambda
                # Add modified exception parameters.
                force.addException(iatom, jatom, chargeprod, sigma, epsilon)
            # Set parameters.
            force.setNonbondedMethod( reference_force.getNonbondedMethod() )
            force.setCutoffDistance( reference_force.getCutoffDistance() )
            force.setReactionFieldDielectric( reference_force.getReactionFieldDielectric() )
            force.setEwaldErrorTolerance( reference_force.getEwaldErrorTolerance() )
            # Add force to new system.
            system.addForce(force)

            # CustomNonbondedForce
            # Softcore potential.
            energy_expression = "4*epsilon*lambda*x*(x-1.0);"
            energy_expression += "x = 1.0/(alpha*(1.0-lambda) + (r/sigma)^6);"
            energy_expression += "epsilon = sqrt(epsilon1*epsilon2);"
            energy_expression += "sigma = 0.5*(sigma1 + sigma2);"
            energy_expression += "lambda = lambda1*lambda2;"

            force = openmm.CustomNonbondedForce(energy_expression)            
            alpha = 0.5 # softcore parameter
            force.addGlobalParameter("alpha", alpha);
            force.addPerParticleParameter("sigma")
            force.addPerParticleParameter("epsilon")
            force.addPerParticleParameter("lambda"); 
            for particle_index in range(reference_force.getNumParticles()):
                # Retrieve parameters.
                [charge, sigma, epsilon] = reference_force.getParticleParameters(particle_index)
                # Alchemically modify parameters.
                if particle_index in ligand_atoms:
                    force.addParticle([sigma, epsilon, vdw_lambda])
                else:
                    force.addParticle([sigma, epsilon, 1.0])
            for exception_index in range(reference_force.getNumExceptions()):
                # Retrieve parameters.
                [iatom, jatom, chargeprod, sigma, epsilon] = reference_force.getExceptionParameters(exception_index)
                # All exceptions are handled by NonbondedForce, so we exclude all these here.
                force.addExclusion(iatom, jatom)
            force.setNonbondedMethod( reference_force.getNonbondedMethod() )
            force.setCutoffDistance( reference_force.getCutoffDistance() )
            system.addForce(force)
            
        elif isinstance(reference_force, openmm.GBSAOBCForce):
            # GBSAOBCForce
            solvent_dielectric = reference_force.getSolventDielectric()
            solute_dielectric = reference_force.getSoluteDielectric()
            force = createCustomSoftcoreGBOBC(solvent_dielectric, solute_dielectric, igb=5)
            for particle_index in range(reference_force.getNumParticles()):
                # Retrieve parameters.
                [charge, radius, scaling_factor] = reference_force.getParticleParameters(particle_index)
                # Alchemically modify parameters.
                if particle_index in ligand_atoms:
                    # Scale charge and contribution to GB integrals.
                    force.addParticle([charge*coulomb_lambda, radius, scaling_factor, coulomb_lambda])
                else:
                    # Don't modulate GB.
                    force.addParticle([charge, radius, scaling_factor, 1.0])

            # Add force to new system.
            system.addForce(force)
        else:
            # Don't add unrecognized forces.
            pass

    return system

#=============================================================================================
# MAIN AND TESTS
#=============================================================================================

if __name__ == "__main__":
    # Create system
    system = openmm.System()

    timestep = 2.0 * units.femtoseconds

    # Set whether to use GB model or not.
    gbmodel = 'OBC' # use OBC GBSA (gives finite error)
    #gbmodel = 'none' # no solvent model (gives zero error)
    
    # PARAMETERS
    complex_prmtop_filename = 'complex.prmtop'
    complex_crd_filename = 'complex-minimized.crd'
    receptor_prmtop_filename = 'receptor.prmtop'
    receptor_crd_filename = 'receptor-minimized.crd'
#    receptor_atoms = range(0,12) # benzene
#    ligand_atoms = range(12,27) # toluene
    receptor_atoms = range(0,2603) # T4 lysozyme L99A
    ligand_atoms = range(2603,2621) # p-xylene
    platform_names = ['Reference', 'Cuda', 'OpenCL']
    #platform_names = ['Cuda', 'OpenCL']    

    # Create force type variants of systems.
    force_types = ['standard', 'softcore-full', 'softcore-half', 'softcore-annihilated', 'custom-full', 'custom-half', 'custom-annihilated'] # Different force types
    system_types = ['complex', 'receptor']
    systems = dict()
    for system_type in system_types:
        systems[system_type] = dict()        
    # Load standard systems.
    import simtk.pyopenmm.amber.amber_file_parser as amber    
    systems['complex']['standard'] = amber.readAmberSystem(complex_prmtop_filename, mm=openmm, gbmodel=gbmodel, shake='h-bonds')
    systems['receptor']['standard'] = amber.readAmberSystem(receptor_prmtop_filename, mm=openmm, gbmodel=gbmodel, shake='h-bonds')
    # Create softcore force type variants.
    for system_type in system_types:
        systems[system_type]['softcore-full'] = build_softcore_system(systems[system_type]['standard'], receptor_atoms, ligand_atoms, 1.0, 1.0, 1.0)
        systems[system_type]['softcore-half'] = build_softcore_system(systems[system_type]['standard'], receptor_atoms, ligand_atoms, 1.0, 0.5, 1.0)
        systems[system_type]['softcore-annihilated'] = build_softcore_system(systems[system_type]['standard'], receptor_atoms, ligand_atoms, 0.0, 0.0, 0.0)
    # Create custom force type variants.
    for system_type in system_types:
        systems[system_type]['custom-full'] = build_custom_system(systems[system_type]['standard'], receptor_atoms, ligand_atoms, 1.0, 1.0, 1.0)
        systems[system_type]['custom-half'] = build_custom_system(systems[system_type]['standard'], receptor_atoms, ligand_atoms, 1.0, 0.5, 1.0)
        systems[system_type]['custom-annihilated'] = build_custom_system(systems[system_type]['standard'], receptor_atoms, ligand_atoms, 0.0, 0.0, 0.0)

    # Read coordinates.
    coordinates = dict()
    coordinates['complex'] = amber.readAmberCoordinates(complex_crd_filename, asNumpy=True)
    coordinates['receptor'] = coordinates['complex'][receptor_atoms,:]

    #==============================================================================================
    # Compute potentials.
    #==============================================================================================
        
    potential = dict()
    for platform_name in platform_names:
        potential[platform_name] = dict()

        # Select platform to use.
        platform = openmm.Platform.getPlatformByName(platform_name)

        for system_type in system_types:
            potential[platform_name][system_type] = dict()

            for force_type in force_types:
                potential[platform_name][system_type][force_type] = dict()                        

                # Compute full complex energy.
                print "Computing potential for system '%(system_type)s' force type '%(force_type)s' on platform '%(platform_name)s'" % vars()
                try:                
                    integrator = openmm.VerletIntegrator(timestep)
                    context = openmm.Context(systems[system_type][force_type], integrator, platform)
                    context.setPositions(coordinates[system_type])
                    state = context.getState(getEnergy=True)
                    potential[platform_name][system_type][force_type] = state.getPotentialEnergy()
                    del integrator, context
                except Exception as e:
                    print e
                    potential[platform_name][system_type][force_type] = None

    #==============================================================================================
    # Show results.
    #==============================================================================================

    print "%24s : " % "Platforms:",
    for platform_name in platform_names: print "%54s" % (platform_name),
    print ""

    # fully interacting
    print "-----------------------------"
    print "Interacting ligand in complex"
    for force_type in ['standard', 'softcore-full', 'custom-full']:
        print "%24s : " % (force_type),
        for platform_name in platform_names:
            energy = potential[platform_name]['complex'][force_type]
            if energy is None:
                print "%24s       " % "N/A",                
            else:
                print "%24.8f kJ/mol" % (energy / units.kilojoules_per_mole),
        print ""

    # non-interacting complex
    print "-----------------------------"
    print "Annihilated ligand in complex - should be same as 'receptor only' below"

    for force_type in ['softcore-annihilated', 'custom-annihilated']:
        print "%24s : " % (force_type),
        for platform_name in platform_names:
            energy = potential[platform_name]['complex'][force_type]
            if energy is None:
                print "%24s       " % "N/A",
            else:
                print "%24.8f kJ/mol" % (energy / units.kilojoules_per_mole),
        print ""

    # non-interacting complex
    print "-----------------------------"
    print "Partially annihilated ligand in complex - should match between custom and softcore"

    for force_type in ['softcore-half', 'custom-half']:
        print "%24s : " % (force_type),
        for platform_name in platform_names:
            energy = potential[platform_name]['complex'][force_type]
            if energy is None:
                print "%24s       " % "N/A",
            else:
                print "%24.8f kJ/mol" % (energy / units.kilojoules_per_mole),
        print ""

    print "-----------------------------"
    print "Receptor only (no ligand)"
    
    for force_type in force_types:
        print "%24s : " % (force_type),
        for platform_name in platform_names:
            energy = potential[platform_name]['receptor'][force_type]
            if energy is None:
                print "%24s       " % "N/A",                
            else:
                print "%24.8f kJ/mol" % (energy / units.kilojoules_per_mole),
        print ""
        
    stop

    #==============================================================================================
    # Run timings
    #==============================================================================================

    nsteps = 50

    elapsed_times = dict() # elapsed_times[platform_name] is time for nsteps of dynamics
    system_type = 'complex'
    for platform_name in platform_names:
        # Select platform to use.
        platform = openmm.Platform.getPlatformByName(platform_name)

        elapsed_times[platform_name] = dict()
        for force_type in force_types:

            print "Running system '%(system_type)s' force type '%(force_type)s' for %(nsteps)d steps of dynamics on platform '%(platform_name)s'..." % vars()
            try:
                integrator = openmm.VerletIntegrator(timestep)
                context = openmm.Context(systems[system_type][force_type], integrator, platform)
                context.setPositions(coordinates[system_type])
                initial_time = time.time()
                integrator.step(nsteps)
                final_time = time.time()
                elapsed_time = final_time - initial_time
                elapsed_times[platform_name][force_type] = elapsed_time
                del integrator, context
            except:
                elapsed_times[platform_name][force_type] = None

    print "-----------------------------"
    print "Timings for system '%s'" % (system_type)
    
    for force_type in force_types:
        print "%48s : " % (force_type),
        for platform_name in platform_names:
            elapsed_time = elapsed_times[platform_name][force_type]
            if elapsed_time is None:
                print "%24s%24s      " % ("N/A",""),
            else:
                ns_per_day =  (float(nsteps) * timestep / (elapsed_time * units.seconds)) / (units.nanoseconds / units.day)                
                print "%12.3f s (%12.6f ns/day)                  " % (elapsed_time, ns_per_day),
        print ""
