forked from lijiext/lammps
update phana tool for USER-PHONON from github
This commit is contained in:
Axel Kohlmeyer
parent
29c50671da
commit
7df8a63045
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@ -1,30 +1,37 @@
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.SUFFIXES : .o .cpp
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# compiler and flags
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CC = g++ -Wall
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LINK = $(CC)
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CC = g++ -Wno-unused-result
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LINK = $(CC) -static
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CFLAGS = -O3 $(DEBUG) $(UFLAG)
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#
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OFLAGS = -O3 $(DEBUG)
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INC = $(LPKINC) $(TCINC) $(SPGINC)
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LIB = $(LPKLIB) $(TCLIB) $(SPGLIB)
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#
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INC = $(LPKINC) $(TCINC) $(SPGINC) $(FFTINC)
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LIB = $(LPKLIB) $(TCLIB) $(SPGLIB) $(FFTLIB)
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# cLapack library needed
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LPKINC =
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LPKLIB =-llapack
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#
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#
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# spglib 1.8.2, used to get the irreducible q-points
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# if UFLAG is not set, spglib won't be used.
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LPKINC = -I/opt/clapack/3.2.1/include
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LPKLIB = -L/opt/clapack/3.2.1/lib -lclapack -lblas -lf2c -lm
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# UFLAG = -DUseSPG
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# SPGINC = -I/opt/libs/spglib/1.8.2/include
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# SPGLIB = -L/opt/libs/spglib/1.8.2/lib -lsymspg
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# Tricubic library needed
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TCINC = -I/opt/tricubic/1.0/include
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TCLIB = -L/opt/tricubic/1.0/lib -ltricubic
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# if spglib other than version 1.8.2 is used, please
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# modify file phonon.cpp, instruction can be found by searching 1.8.2
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# spglib, used to get the irreducible q-points
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# if SFLAG is not set, spglib won't be used.
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SFLAG = -DUseSPG
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SPGINC = -I/opt/spglib/1.9.7/include/spglib
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SPGLIB = -L/opt/spglib/1.9.7/lib -lsymspg
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# FFTW 3， used to deduce the force constants in real space
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# if FFLAG is not set, fftw won't be used.
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FFLAG = -DFFTW3
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FFTINC = -I/opt/fftw/3.3.7/include
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FFTLIB = -L/opt/fftw/3.3.7/lib -lfftw3
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# Debug flags
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#DEBUG = -g -DDEBUG
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# DEBUG = -g -DDEBUG
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UFLAG = $(SFLAG) $(FFLAG)
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#====================================================================
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ROOT = phana
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# executable name
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@ -44,7 +51,7 @@ clean:
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rm -f *.o *~ *.mod ${EXE}
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tar:
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rm -f ${ROOT}.tar; tar -czvf ${ROOT}.tar.gz *.cpp *.h Makefile README
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rm -f ${ROOT}.tar.gz; tar -czvf ${ROOT}.tar.gz *.cpp *.h Makefile README
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ver:
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@echo "#define VERSION `git log|grep '^commit'|wc -l`" > version.h
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@ -58,16 +65,3 @@ ver:
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$(CC) $(CFLAGS) -c $<
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.cpp.o:
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$(CC) $(CFLAGS) $(INC) -c $<
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#====================================================================
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# dependencies
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disp.o: disp.cpp phonon.h dynmat.h memory.h interpolate.h green.h timer.h \
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global.h
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dynmat.o: dynmat.cpp dynmat.h memory.h interpolate.h version.h global.h
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green.o: green.cpp green.h memory.h global.h
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interpolate.o: interpolate.cpp interpolate.h memory.h global.h
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main.o: main.cpp dynmat.h memory.h interpolate.h phonon.h
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memory.o: memory.cpp memory.h
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phonon.o: phonon.cpp phonon.h dynmat.h memory.h interpolate.h green.h \
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timer.h global.h
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timer.o: timer.cpp timer.h
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@ -5,9 +5,13 @@
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analyse the phonon related information.
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#-------------------------------------------------------------------------------
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1. Dependencies
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The LAPACK library is needed to solve the eigen problems.
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http://www.netlib.org/lapack/
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Intel MKL can be used as well.
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The clapack library is needed to solve the eigen problems,
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which could be downloaded from:
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http://www.netlib.org/clapack/
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The tricubic library is also needed to do tricubic interpolations,
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which could now be obtained from:
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https://github.com/nbigaouette/libtricubic/
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The spglib is optionally needed, enabling one to evaluate the
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phonon density of states or vibrational thermal properties
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@ -16,6 +20,12 @@
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automatic mode. Currently, the 1.8.3 version of spglib is used.
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It can be obtained from:
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http://spglib.sourceforge.net/
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FFTW 3 might also be needed if you would like to interface with
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phonopy: necessary input files for phonopy will be prepared so
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that you can make use of the functions provided by phonopy.
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FFTW 3 can be downloaded from:
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http://www.fftw.org
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2. Compilation
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To compile the code, one needs therefore to install the above
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@ -26,17 +36,16 @@
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3. Unit system
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The units of the output frequencies by this code is THz for
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LAMMPS units "real", "si", "metal", and "cgs"; in these cases,
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the frequencies are $\nu$ instead of $\omega$.
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LAMMPS units "real", "si", "metal", "cgs", "micro", "nano";
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in these cases, the frequencies are $\nu$ instead of $\omega$.
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4. Updates
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For updates of phana, please check:
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http://nes.sjtu.edu.cn/english/research/software.htm
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or
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https://github.com/lingtikong/phana.git
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https://github.com/lingtikong/phana.git
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5. Bug report
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If any bug found, please drop a line to: konglt(at)sjtu.edu.cn
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#-------------------------------------------------------------------------------
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Author: Ling-Ti Kong, konglt(at)sjtu.edu.cn
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Oct 2015
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May 2020
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File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
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@ -7,8 +7,6 @@
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#include "memory.h"
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#include "interpolate.h"
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using namespace std;
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class DynMat {
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public:
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@ -17,7 +15,7 @@ public:
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int nx, ny, nz, nucell;
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int sysdim, fftdim;
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double eml2f;
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double eml2f, eml2fc;
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char *funit;
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void getDMq(double *);
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@ -30,7 +28,9 @@ public:
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doublecomplex **DM_q;
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int flag_latinfo;
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int npt, fftdim2;
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double Tmeasure, basevec[9], ibasevec[9];
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double *M_inv_sqrt;
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double **basis;
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int *attyp;
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@ -40,14 +40,12 @@ private:
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Interpolate *interpolate;
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Memory *memory;
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int npt, fftdim2;
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int nasr;
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void EnforceASR();
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char *binfile, *dmfile;
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double boltz, q[3];
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double *M_inv_sqrt;
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doublecomplex **DM_all;
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@ -56,6 +54,8 @@ private:
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void GaussJordan(int, double *);
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void help();
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void ShowInfo();
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void ShowVersion();
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void Define_Conversion_Factor();
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};
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#endif
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@ -38,36 +38,36 @@
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Green::Green(const int ntm, const int sdim, const int niter, const double min, const double max,
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const int ndos, const double eps, double **Hessian, const int itm, double **lpdos)
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{
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const double tpi = 8.*atan(1.);
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natom = ntm; sysdim = sdim; nit = niter; epson = eps;
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wmin = min*tpi; wmax = max*tpi; nw = ndos + (ndos+1)%2;
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H = Hessian; iatom = itm;
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ldos = lpdos;
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memory = new Memory();
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if (natom < 1 || iatom < 0 || iatom >= natom){
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printf("\nError: Wrong number of total atoms or wrong index of interested atom!\n");
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return;
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}
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ndim = natom * sysdim;
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if (nit < 1){printf("\nError: Wrong input of maximum iterations!\n"); return;}
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if (nit > ndim){printf("\nError: # Lanczos iterations is not expected to exceed the degree of freedom!\n"); return;}
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if (nw < 1){printf("\nError: Wrong input of points in LDOS!\n"); return;}
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// initialize variables and allocate local memories
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dw = (wmax - wmin)/double(nw-1);
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memory->create(alpha, sysdim,nit, "Green_Green:alpha");
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memory->create(beta, sysdim,nit+1,"Green_Green:beta");
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//memory->create(ldos, nw,sysdim, "Green_Green:ldos");
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// use Lanczos algorithm to diagonalize the Hessian
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Lanczos();
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// Get the inverser of the treated hessian by continued fractional method
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Recursion();
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return;
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const double tpi = 8.*atan(1.);
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natom = ntm; sysdim = sdim; nit = niter; epson = eps;
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wmin = min*tpi; wmax = max*tpi; nw = ndos + (ndos+1)%2;
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H = Hessian; iatom = itm;
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ldos = lpdos;
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memory = new Memory();
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if (natom < 1 || iatom < 0 || iatom >= natom){
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printf("\nError: Wrong number of total atoms or wrong index of interested atom!\n");
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return;
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}
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ndim = natom * sysdim;
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if (nit < 1){printf("\nError: Wrong input of maximum iterations!\n"); return;}
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if (nit > ndim){printf("\nError: # Lanczos iterations is not expected to exceed the degree of freedom!\n"); return;}
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if (nw < 1){printf("\nError: Wrong input of points in LDOS!\n"); return;}
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// initialize variables and allocate local memories
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dw = (wmax - wmin)/double(nw-1);
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memory->create(alpha, sysdim,nit, "Green_Green:alpha");
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memory->create(beta, sysdim,nit+1,"Green_Green:beta");
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//memory->create(ldos, nw,sysdim, "Green_Green:ldos");
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// use Lanczos algorithm to diagonalize the Hessian
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Lanczos();
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// Get the inverser of the treated hessian by continued fractional method
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Recursion();
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return;
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}
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/*------------------------------------------------------------------------------
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@ -75,14 +75,14 @@ return;
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*----------------------------------------------------------------------------*/
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Green::~Green()
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{
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H = NULL;
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ldos = NULL;
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memory->destroy(alpha);
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memory->destroy(beta);
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delete memory;
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return;
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H = NULL;
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ldos = NULL;
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memory->destroy(alpha);
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memory->destroy(beta);
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delete memory;
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return;
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}
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/*------------------------------------------------------------------------------
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@ -90,159 +90,159 @@ return;
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*----------------------------------------------------------------------------*/
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void Green::Lanczos()
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{
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double *vp, *v, *w, *ptr;
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vp = new double [ndim];
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v = new double [ndim];
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w = new double [ndim];
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int ipos = iatom*sysdim;
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// Loop over dimension
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for (int idim = 0; idim < sysdim; ++idim){
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beta[idim][0] = 0.;
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for (int i = 0; i < ndim; ++i) vp[i] = v[i] = 0.;
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v[ipos+idim] = 1.;
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// Loop on fraction levels
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for (int i = 0; i < nit; ++i){
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double sum_a = 0.;
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for (int j = 0; j < ndim; ++j){
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double sumHv = 0.;
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for (int k = 0; k < ndim; ++k) sumHv += H[j][k]*v[k];
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w[j] = sumHv - beta[idim][i]*vp[j];
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sum_a += w[j]*v[j];
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double *vp, *v, *w, *ptr;
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vp = new double [ndim];
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v = new double [ndim];
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w = new double [ndim];
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int ipos = iatom*sysdim;
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// Loop over dimension
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for (int idim = 0; idim < sysdim; ++idim){
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beta[idim][0] = 0.;
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for (int i = 0; i < ndim; ++i) vp[i] = v[i] = 0.;
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v[ipos+idim] = 1.;
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// Loop on fraction levels
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for (int i = 0; i < nit; ++i){
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double sum_a = 0.;
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for (int j = 0; j < ndim; ++j){
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double sumHv = 0.;
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for (int k = 0; k < ndim; ++k) sumHv += H[j][k]*v[k];
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w[j] = sumHv - beta[idim][i]*vp[j];
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sum_a += w[j]*v[j];
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}
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alpha[idim][i] = sum_a;
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for (int k = 0; k < ndim; ++k) w[k] -= alpha[idim][i]*v[k];
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double gamma = 0.;
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for (int k = 0; k < ndim; ++k) gamma += w[k]*v[k];
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for (int k = 0; k < ndim; ++k) w[k] -= gamma*v[k];
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double sum_b = 0.;
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for (int k = 0; k < ndim; ++k) sum_b += w[k]*w[k];
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beta[idim][i+1] = sqrt(sum_b);
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ptr = vp; vp = v; v = ptr;
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double tmp = 1./beta[idim][i+1];
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for (int k = 0; k < ndim; ++k) v[k] = w[k] * tmp;
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}
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alpha[idim][i] = sum_a;
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for (int k = 0; k < ndim; ++k) w[k] -= alpha[idim][i]*v[k];
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double gamma = 0.;
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for (int k = 0; k < ndim; ++k) gamma += w[k]*v[k];
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for (int k = 0; k < ndim; ++k) w[k] -= gamma*v[k];
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double sum_b = 0.;
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for (int k = 0; k < ndim; ++k) sum_b += w[k]*w[k];
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beta[idim][i+1] = sqrt(sum_b);
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ptr = vp; vp = v; v = ptr;
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double tmp = 1./beta[idim][i+1];
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for (int k = 0; k < ndim; ++k) v[k] = w[k] * tmp;
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}
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}
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ptr = NULL;
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delete []vp;
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delete []v;
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delete []w;
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return;
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}
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ptr = NULL;
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delete []vp;
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delete []v;
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delete []w;
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return;
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}
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/*------------------------------------------------------------------------------
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* Private method to compute the LDOS via the recursive method for system with
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* Private method to compute the LDOS via the recusive method for system with
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* many atoms
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*----------------------------------------------------------------------------*/
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void Green::Recursion()
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{
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// local variables
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double *alpha_inf, *beta_inf, *xmin, *xmax;
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alpha_inf = new double [sysdim];
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beta_inf = new double [sysdim];
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xmin = new double [sysdim];
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xmax = new double [sysdim];
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int nave = nit/4;
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for (int idim = 0; idim < sysdim; ++idim){
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alpha_inf[idim] = beta_inf[idim] = 0.;
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for (int i = nit-nave; i < nit; ++i){
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alpha_inf[idim] += alpha[idim][i];
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beta_inf[idim] += beta[idim][i+1];
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}
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alpha_inf[idim] /= double(nave);
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beta_inf[idim] /= double(nave);
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xmin[idim] = alpha_inf[idim] - 2.*beta_inf[idim];
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xmax[idim] = alpha_inf[idim] + 2.*beta_inf[idim];
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}
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std::complex<double> Z, z_m_a, r_x, rec_x, rec_x_inv;
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double sr, si;
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double w = wmin;
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for (int i = 0; i < nw; ++i){
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double a = w*w, ax, bx;
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Z = std::complex<double>(w*w, epson);
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for (int idim = 0; idim < sysdim; ++idim){
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double two_b = 2.*beta_inf[idim]*beta_inf[idim];
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double rtwob = 1./two_b;
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z_m_a = Z - alpha_inf[idim]*alpha_inf[idim];
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if ( a < xmin[idim] ){
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r_x = sqrt(-2.*two_b + z_m_a);
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ax = std::real(r_x) * rtwob;
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bx = std::imag(r_x) * rtwob;
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} else if (a > xmax[idim]) {
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r_x = sqrt(-2.*two_b + z_m_a);
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ax = -std::real(r_x) * rtwob;
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bx = -std::imag(r_x) * rtwob;
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} else {
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r_x = sqrt(2.*two_b - z_m_a);
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ax = std::imag(r_x) * rtwob;
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bx = -std::real(r_x) * rtwob;
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// local variables
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double *alpha_inf, *beta_inf, *xmin, *xmax;
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alpha_inf = new double [sysdim];
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beta_inf = new double [sysdim];
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xmin = new double [sysdim];
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xmax = new double [sysdim];
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int nave = nit/4;
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for (int idim = 0; idim < sysdim; ++idim){
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alpha_inf[idim] = beta_inf[idim] = 0.;
|
||||
|
||||
for (int i = nit-nave; i < nit; ++i){
|
||||
alpha_inf[idim] += alpha[idim][i];
|
||||
beta_inf[idim] += beta[idim][i+1];
|
||||
}
|
||||
|
||||
sr = (a - alpha_inf[idim])*rtwob + ax;
|
||||
si = epson * rtwob + bx;
|
||||
rec_x = std::complex<double> (sr, si);
|
||||
|
||||
for (int j = 0; j < nit; ++j){
|
||||
rec_x_inv = Z - alpha[idim][nit-j-1] - beta[idim][nit-j]*beta[idim][nit-j]*rec_x;
|
||||
rec_x = 1./rec_x_inv;
|
||||
|
||||
alpha_inf[idim] /= double(nave);
|
||||
beta_inf[idim] /= double(nave);
|
||||
|
||||
xmin[idim] = alpha_inf[idim] - 2.*beta_inf[idim];
|
||||
xmax[idim] = alpha_inf[idim] + 2.*beta_inf[idim];
|
||||
}
|
||||
|
||||
std::complex<double> Z, z_m_a, r_x, rec_x, rec_x_inv;
|
||||
double sr, si;
|
||||
|
||||
double w = wmin;
|
||||
for (int i = 0; i < nw; ++i){
|
||||
double a = w*w, ax, bx;
|
||||
Z = std::complex<double>(w*w, epson);
|
||||
|
||||
for (int idim = 0; idim < sysdim; ++idim){
|
||||
double two_b = 2.*beta_inf[idim]*beta_inf[idim];
|
||||
double rtwob = 1./two_b;
|
||||
|
||||
z_m_a = Z - alpha_inf[idim]*alpha_inf[idim];
|
||||
|
||||
if ( a < xmin[idim] ){
|
||||
r_x = sqrt(-2.*two_b + z_m_a);
|
||||
ax = std::real(r_x) * rtwob;
|
||||
bx = std::imag(r_x) * rtwob;
|
||||
} else if (a > xmax[idim]) {
|
||||
r_x = sqrt(-2.*two_b + z_m_a);
|
||||
ax = -std::real(r_x) * rtwob;
|
||||
bx = -std::imag(r_x) * rtwob;
|
||||
} else {
|
||||
r_x = sqrt(2.*two_b - z_m_a);
|
||||
ax = std::imag(r_x) * rtwob;
|
||||
bx = -std::real(r_x) * rtwob;
|
||||
}
|
||||
|
||||
sr = (a - alpha_inf[idim])*rtwob + ax;
|
||||
si = epson * rtwob + bx;
|
||||
rec_x = std::complex<double> (sr, si);
|
||||
|
||||
for (int j = 0; j < nit; ++j){
|
||||
rec_x_inv = Z - alpha[idim][nit-j-1] - beta[idim][nit-j]*beta[idim][nit-j]*rec_x;
|
||||
rec_x = 1./rec_x_inv;
|
||||
}
|
||||
ldos[i][idim] = std::imag(rec_x)*w;
|
||||
}
|
||||
ldos[i][idim] = std::imag(rec_x)*w;
|
||||
}
|
||||
w += dw;
|
||||
}
|
||||
delete []alpha_inf;
|
||||
delete []beta_inf;
|
||||
delete []xmin;
|
||||
delete []xmax;
|
||||
|
||||
return;
|
||||
w += dw;
|
||||
}
|
||||
delete []alpha_inf;
|
||||
delete []beta_inf;
|
||||
delete []xmin;
|
||||
delete []xmax;
|
||||
|
||||
return;
|
||||
}
|
||||
|
||||
/*------------------------------------------------------------------------------
|
||||
* Private method to compute the LDOS via the recursive method for system with
|
||||
* Private method to compute the LDOS via the recusive method for system with
|
||||
* a few atoms (less than NMAX)
|
||||
*----------------------------------------------------------------------------*/
|
||||
void Green::recursion()
|
||||
{
|
||||
// local variables
|
||||
std::complex<double> Z, rec_x, rec_x_inv;
|
||||
|
||||
double w = wmin;
|
||||
|
||||
for (int i = 0; i < nw; ++i){
|
||||
Z = std::complex<double>(w*w, epson);
|
||||
|
||||
for (int idim = 0; idim < sysdim; ++idim){
|
||||
rec_x = std::complex<double>(0.,0.);
|
||||
|
||||
for (int j = 0; j < nit; ++j){
|
||||
rec_x_inv = Z - alpha[idim][nit-j-1] - beta[idim][nit-j]*beta[idim][nit-j]*rec_x;
|
||||
rec_x = 1./rec_x_inv;
|
||||
// local variables
|
||||
std::complex<double> Z, rec_x, rec_x_inv;
|
||||
std::complex<double> cunit = std::complex<double>(0.,1.);
|
||||
|
||||
double w = wmin;
|
||||
|
||||
for (int i = 0; i < nw; ++i){
|
||||
Z = std::complex<double>(w*w, epson);
|
||||
|
||||
for (int idim = 0; idim < sysdim; ++idim){
|
||||
rec_x = std::complex<double>(0.,0.);
|
||||
|
||||
for (int j = 0; j < nit; ++j){
|
||||
rec_x_inv = Z - alpha[idim][nit-j-1] - beta[idim][nit-j]*beta[idim][nit-j]*rec_x;
|
||||
rec_x = 1./rec_x_inv;
|
||||
}
|
||||
ldos[i][idim] = std::imag(rec_x)*w;
|
||||
}
|
||||
ldos[i][idim] = std::imag(rec_x)*w;
|
||||
}
|
||||
w += dw;
|
||||
}
|
||||
|
||||
return;
|
||||
w += dw;
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
/*------------------------------------------------------------------------------*/
|
||||
|
|
|
|||
|
|
@ -5,21 +5,21 @@
|
|||
|
||||
class Green{
|
||||
public:
|
||||
Green(const int, const int, const int, const double, const double,
|
||||
const int, const double, double **, const int, double **);
|
||||
~Green();
|
||||
Green(const int, const int, const int, const double, const double,
|
||||
const int, const double, double **, const int, double **);
|
||||
~Green();
|
||||
|
||||
private:
|
||||
void Lanczos();
|
||||
void Recursion();
|
||||
void recursion();
|
||||
|
||||
int ndos;
|
||||
double **ldos;
|
||||
|
||||
int natom, iatom, sysdim, nit, nw, ndim;
|
||||
double dw, wmin, wmax, epson;
|
||||
double **alpha, **beta, **H;
|
||||
Memory *memory;
|
||||
void Lanczos();
|
||||
void Recursion();
|
||||
void recursion();
|
||||
|
||||
int ndos;
|
||||
double **ldos;
|
||||
|
||||
int natom, iatom, sysdim, nit, nw, ndim;
|
||||
double dw, wmin, wmax, epson;
|
||||
double **alpha, **beta, **H;
|
||||
Memory *memory;
|
||||
};
|
||||
#endif
|
||||
|
|
|
|||
|
|
@ -1,144 +1,26 @@
|
|||
#include "interpolate.h"
|
||||
#include <math.h>
|
||||
#include "math.h"
|
||||
#include "global.h"
|
||||
|
||||
///////////////////////
|
||||
// tricubic library code
|
||||
static int A[64][64] = {
|
||||
{ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{-3, 3, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 2,-2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 9,-9,-9, 9, 0, 0, 0, 0, 6, 3,-6,-3, 0, 0, 0, 0, 6,-6, 3,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{-6, 6, 6,-6, 0, 0, 0, 0,-3,-3, 3, 3, 0, 0, 0, 0,-4, 4,-2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-2,-1,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{-6, 6, 6,-6, 0, 0, 0, 0,-4,-2, 4, 2, 0, 0, 0, 0,-3, 3,-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-1,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 4,-4,-4, 4, 0, 0, 0, 0, 2, 2,-2,-2, 0, 0, 0, 0, 2,-2, 2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9,-9,-9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 3,-6,-3, 0, 0, 0, 0, 6,-6, 3,-3, 0, 0, 0, 0, 4, 2, 2, 1, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-6, 6, 6,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3,-3, 3, 3, 0, 0, 0, 0,-4, 4,-2, 2, 0, 0, 0, 0,-2,-2,-1,-1, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-6, 6, 6,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4,-2, 4, 2, 0, 0, 0, 0,-3, 3,-3, 3, 0, 0, 0, 0,-2,-1,-2,-1, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4,-4,-4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2,-2,-2, 0, 0, 0, 0, 2,-2, 2,-2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0},
|
||||
{-3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 9,-9, 0, 0,-9, 9, 0, 0, 6, 3, 0, 0,-6,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6,-6, 0, 0, 3,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{-6, 6, 0, 0, 6,-6, 0, 0,-3,-3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4, 4, 0, 0,-2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-2, 0, 0,-1,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0, 0, 0,-1, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9,-9, 0, 0,-9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 3, 0, 0,-6,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6,-6, 0, 0, 3,-3, 0, 0, 4, 2, 0, 0, 2, 1, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-6, 6, 0, 0, 6,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3,-3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4, 4, 0, 0,-2, 2, 0, 0,-2,-2, 0, 0,-1,-1, 0, 0},
|
||||
{ 9, 0,-9, 0,-9, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 3, 0,-6, 0,-3, 0, 6, 0,-6, 0, 3, 0,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 9, 0,-9, 0,-9, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 3, 0,-6, 0,-3, 0, 6, 0,-6, 0, 3, 0,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 1, 0},
|
||||
{-27,27,27,-27,27,-27,-27,27,-18,-9,18, 9,18, 9,-18,-9,-18,18,-9, 9,18,-18, 9,-9,-18,18,18,-18,-9, 9, 9,-9,-12,-6,-6,-3,12, 6, 6, 3,-12,-6,12, 6,-6,-3, 6, 3,-12,12,-6, 6,-6, 6,-3, 3,-8,-4,-4,-2,-4,-2,-2,-1},
|
||||
{18,-18,-18,18,-18,18,18,-18, 9, 9,-9,-9,-9,-9, 9, 9,12,-12, 6,-6,-12,12,-6, 6,12,-12,-12,12, 6,-6,-6, 6, 6, 6, 3, 3,-6,-6,-3,-3, 6, 6,-6,-6, 3, 3,-3,-3, 8,-8, 4,-4, 4,-4, 2,-2, 4, 4, 2, 2, 2, 2, 1, 1},
|
||||
{-6, 0, 6, 0, 6, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0,-3, 0, 3, 0, 3, 0,-4, 0, 4, 0,-2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-2, 0,-1, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0,-6, 0, 6, 0, 6, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0,-3, 0, 3, 0, 3, 0,-4, 0, 4, 0,-2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-2, 0,-1, 0,-1, 0},
|
||||
{18,-18,-18,18,-18,18,18,-18,12, 6,-12,-6,-12,-6,12, 6, 9,-9, 9,-9,-9, 9,-9, 9,12,-12,-12,12, 6,-6,-6, 6, 6, 3, 6, 3,-6,-3,-6,-3, 8, 4,-8,-4, 4, 2,-4,-2, 6,-6, 6,-6, 3,-3, 3,-3, 4, 2, 4, 2, 2, 1, 2, 1},
|
||||
{-12,12,12,-12,12,-12,-12,12,-6,-6, 6, 6, 6, 6,-6,-6,-6, 6,-6, 6, 6,-6, 6,-6,-8, 8, 8,-8,-4, 4, 4,-4,-3,-3,-3,-3, 3, 3, 3, 3,-4,-4, 4, 4,-2,-2, 2, 2,-4, 4,-4, 4,-2, 2,-2, 2,-2,-2,-2,-2,-1,-1,-1,-1},
|
||||
{ 2, 0, 0, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{-6, 6, 0, 0, 6,-6, 0, 0,-4,-2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0,-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 4,-4, 0, 0,-4, 4, 0, 0, 2, 2, 0, 0,-2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-6, 6, 0, 0, 6,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4,-2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0,-3, 3, 0, 0,-2,-1, 0, 0,-2,-1, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4,-4, 0, 0,-4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0,-2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 2,-2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0},
|
||||
{-6, 0, 6, 0, 6, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4, 0,-2, 0, 4, 0, 2, 0,-3, 0, 3, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0,-2, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0,-6, 0, 6, 0, 6, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4, 0,-2, 0, 4, 0, 2, 0,-3, 0, 3, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0,-2, 0,-1, 0},
|
||||
{18,-18,-18,18,-18,18,18,-18,12, 6,-12,-6,-12,-6,12, 6,12,-12, 6,-6,-12,12,-6, 6, 9,-9,-9, 9, 9,-9,-9, 9, 8, 4, 4, 2,-8,-4,-4,-2, 6, 3,-6,-3, 6, 3,-6,-3, 6,-6, 3,-3, 6,-6, 3,-3, 4, 2, 2, 1, 4, 2, 2, 1},
|
||||
{-12,12,12,-12,12,-12,-12,12,-6,-6, 6, 6, 6, 6,-6,-6,-8, 8,-4, 4, 8,-8, 4,-4,-6, 6, 6,-6,-6, 6, 6,-6,-4,-4,-2,-2, 4, 4, 2, 2,-3,-3, 3, 3,-3,-3, 3, 3,-4, 4,-2, 2,-4, 4,-2, 2,-2,-2,-1,-1,-2,-2,-1,-1},
|
||||
{ 4, 0,-4, 0,-4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0,-2, 0,-2, 0, 2, 0,-2, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{ 0, 0, 0, 0, 0, 0, 0, 0, 4, 0,-4, 0,-4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0,-2, 0,-2, 0, 2, 0,-2, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0},
|
||||
{-12,12,12,-12,12,-12,-12,12,-8,-4, 8, 4, 8, 4,-8,-4,-6, 6,-6, 6, 6,-6, 6,-6,-6, 6, 6,-6,-6, 6, 6,-6,-4,-2,-4,-2, 4, 2, 4, 2,-4,-2, 4, 2,-4,-2, 4, 2,-3, 3,-3, 3,-3, 3,-3, 3,-2,-1,-2,-1,-2,-1,-2,-1},
|
||||
{ 8,-8,-8, 8,-8, 8, 8,-8, 4, 4,-4,-4,-4,-4, 4, 4, 4,-4, 4,-4,-4, 4,-4, 4, 4,-4,-4, 4, 4,-4,-4, 4, 2, 2, 2, 2,-2,-2,-2,-2, 2, 2,-2,-2, 2, 2,-2,-2, 2,-2, 2,-2, 2,-2, 2,-2, 1, 1, 1, 1, 1, 1, 1, 1}};
|
||||
|
||||
static int ijk2n(int i, int j, int k) {
|
||||
return(i+4*j+16*k);
|
||||
}
|
||||
|
||||
/* ---------------------------------------------------------------------------- */
|
||||
|
||||
static void tricubic_get_coeff_stacked(double a[64], double x[64]) {
|
||||
int i,j;
|
||||
for (i=0;i<64;i++) {
|
||||
a[i]=(double)(0.0);
|
||||
for (j=0;j<64;j++) {
|
||||
a[i]+=A[i][j]*x[j];
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
static void tricubic_get_coeff(double a[64], double f[8], double dfdx[8], double dfdy[8], double dfdz[8], double d2fdxdy[8], double d2fdxdz[8], double d2fdydz[8], double d3fdxdydz[8]) {
|
||||
int i;
|
||||
double x[64];
|
||||
for (i=0;i<8;i++) {
|
||||
x[0+i]=f[i];
|
||||
x[8+i]=dfdx[i];
|
||||
x[16+i]=dfdy[i];
|
||||
x[24+i]=dfdz[i];
|
||||
x[32+i]=d2fdxdy[i];
|
||||
x[40+i]=d2fdxdz[i];
|
||||
x[48+i]=d2fdydz[i];
|
||||
x[56+i]=d3fdxdydz[i];
|
||||
}
|
||||
tricubic_get_coeff_stacked(a,x);
|
||||
}
|
||||
|
||||
static double tricubic_eval(double a[64], double x, double y, double z) {
|
||||
int i,j,k;
|
||||
double ret=(double)(0.0);
|
||||
/* TRICUBIC EVAL
|
||||
This is the short version of tricubic_eval. It is used to compute
|
||||
the value of the function at a given point (x,y,z). To compute
|
||||
partial derivatives of f, use the full version with the extra args.
|
||||
*/
|
||||
for (i=0;i<4;i++) {
|
||||
for (j=0;j<4;j++) {
|
||||
for (k=0;k<4;k++) {
|
||||
ret+=a[ijk2n(i,j,k)]*pow(x,i)*pow(y,j)*pow(z,k);
|
||||
}
|
||||
}
|
||||
}
|
||||
return(ret);
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------------
|
||||
* Constructor used to get info from caller, and prepare other necessary data
|
||||
* ---------------------------------------------------------------------------- */
|
||||
Interpolate::Interpolate(int nx, int ny, int nz, int ndm, doublecomplex **DM)
|
||||
{
|
||||
Nx = nx;
|
||||
Ny = ny;
|
||||
Nz = nz;
|
||||
Npt = Nx*Ny*Nz;
|
||||
ndim = ndm;
|
||||
memory = new Memory();
|
||||
|
||||
which = UseGamma = 0;
|
||||
|
||||
data = DM;
|
||||
Dfdx = Dfdy = Dfdz = D2fdxdy = D2fdxdz = D2fdydz = D3fdxdydz = NULL;
|
||||
flag_reset_gamma = flag_allocated_dfs = 0;
|
||||
|
||||
return;
|
||||
Nx = nx;
|
||||
Ny = ny;
|
||||
Nz = nz;
|
||||
Npt = Nx*Ny*Nz;
|
||||
ndim = ndm;
|
||||
memory = new Memory();
|
||||
|
||||
which = UseGamma = 0;
|
||||
|
||||
data = DM;
|
||||
Dfdx = Dfdy = Dfdz = D2fdxdy = D2fdxdz = D2fdydz = D3fdxdydz = NULL;
|
||||
flag_reset_gamma = flag_allocated_dfs = 0;
|
||||
|
||||
return;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------------
|
||||
|
|
@ -146,77 +28,76 @@ return;
|
|||
* ---------------------------------------------------------------------------- */
|
||||
void Interpolate::tricubic_init()
|
||||
{
|
||||
// prepare necessary data for tricubic
|
||||
if (flag_allocated_dfs == 0){
|
||||
memory->create(Dfdx, Npt, ndim, "Interpolate_Interpolate:Dfdx");
|
||||
memory->create(Dfdy, Npt, ndim, "Interpolate_Interpolate:Dfdy");
|
||||
memory->create(Dfdz, Npt, ndim, "Interpolate_Interpolate:Dfdz");
|
||||
memory->create(D2fdxdy, Npt, ndim, "Interpolate_Interpolate:D2fdxdy");
|
||||
memory->create(D2fdxdz, Npt, ndim, "Interpolate_Interpolate:D2fdxdz");
|
||||
memory->create(D2fdydz, Npt, ndim, "Interpolate_Interpolate:D2fdydz");
|
||||
memory->create(D3fdxdydz, Npt, ndim, "Interpolate_Interpolate:D2fdxdydz");
|
||||
// prepare necessary data for tricubic
|
||||
if (flag_allocated_dfs == 0){
|
||||
memory->create(Dfdx, Npt, ndim, "Interpolate_Interpolate:Dfdx");
|
||||
memory->create(Dfdy, Npt, ndim, "Interpolate_Interpolate:Dfdy");
|
||||
memory->create(Dfdz, Npt, ndim, "Interpolate_Interpolate:Dfdz");
|
||||
memory->create(D2fdxdy, Npt, ndim, "Interpolate_Interpolate:D2fdxdy");
|
||||
memory->create(D2fdxdz, Npt, ndim, "Interpolate_Interpolate:D2fdxdz");
|
||||
memory->create(D2fdydz, Npt, ndim, "Interpolate_Interpolate:D2fdydz");
|
||||
memory->create(D3fdxdydz, Npt, ndim, "Interpolate_Interpolate:D2fdxdydz");
|
||||
|
||||
flag_allocated_dfs = 1;
|
||||
}
|
||||
|
||||
flag_allocated_dfs = 1;
|
||||
}
|
||||
|
||||
// get the derivatives
|
||||
int n=0;
|
||||
const double half = 0.5, one4 = 0.25, one8 = 0.125;
|
||||
for (int ii = 0; ii < Nx; ++ii)
|
||||
for (int jj = 0; jj < Ny; ++jj)
|
||||
for (int kk = 0; kk < Nz; ++kk){
|
||||
|
||||
int ip = (ii+1)%Nx, jp = (jj+1)%Ny, kp = (kk+1)%Nz;
|
||||
int im = (ii-1+Nx)%Nx, jm = (jj-1+Ny)%Ny, km = (kk-1+Nz)%Nz;
|
||||
|
||||
int p100 = (ip*Ny+jj)*Nz+kk;
|
||||
int p010 = (ii*Ny+jp)*Nz+kk;
|
||||
int p001 = (ii*Ny+jj)*Nz+kp;
|
||||
int p110 = (ip*Ny+jp)*Nz+kk;
|
||||
int p101 = (ip*Ny+jj)*Nz+kp;
|
||||
int p011 = (ii*Ny+jp)*Nz+kp;
|
||||
int pm00 = (im*Ny+jj)*Nz+kk;
|
||||
int p0m0 = (ii*Ny+jm)*Nz+kk;
|
||||
int p00m = (ii*Ny+jj)*Nz+km;
|
||||
int pmm0 = (im*Ny+jm)*Nz+kk;
|
||||
int pm0m = (im*Ny+jj)*Nz+km;
|
||||
int p0mm = (ii*Ny+jm)*Nz+km;
|
||||
int p1m0 = (ip*Ny+jm)*Nz+kk;
|
||||
int p10m = (ip*Ny+jj)*Nz+km;
|
||||
int p01m = (ii*Ny+jp)*Nz+km;
|
||||
int pm10 = (im*Ny+jp)*Nz+kk;
|
||||
int pm01 = (im*Ny+jj)*Nz+kp;
|
||||
int p0m1 = (ii*Ny+jm)*Nz+kp;
|
||||
int p111 = (ip*Ny+jp)*Nz+kp;
|
||||
int pm11 = (im*Ny+jp)*Nz+kp;
|
||||
int p1m1 = (ip*Ny+jm)*Nz+kp;
|
||||
int p11m = (ip*Ny+jp)*Nz+km;
|
||||
int pm1m = (im*Ny+jp)*Nz+km;
|
||||
int p1mm = (ip*Ny+jm)*Nz+km;
|
||||
int pmm1 = (im*Ny+jm)*Nz+kp;
|
||||
int pmmm = (im*Ny+jm)*Nz+km;
|
||||
|
||||
for (int idim=0; idim<ndim; idim++){
|
||||
Dfdx[n][idim].r = (data[p100][idim].r - data[pm00][idim].r) * half;
|
||||
Dfdx[n][idim].i = (data[p100][idim].i - data[pm00][idim].i) * half;
|
||||
Dfdy[n][idim].r = (data[p010][idim].r - data[p0m0][idim].r) * half;
|
||||
Dfdy[n][idim].i = (data[p010][idim].i - data[p0m0][idim].i) * half;
|
||||
Dfdz[n][idim].r = (data[p001][idim].r - data[p00m][idim].r) * half;
|
||||
Dfdz[n][idim].i = (data[p001][idim].i - data[p00m][idim].i) * half;
|
||||
D2fdxdy[n][idim].r = (data[p110][idim].r - data[p1m0][idim].r - data[pm10][idim].r + data[pmm0][idim].r) * one4;
|
||||
D2fdxdy[n][idim].i = (data[p110][idim].i - data[p1m0][idim].i - data[pm10][idim].i + data[pmm0][idim].i) * one4;
|
||||
D2fdxdz[n][idim].r = (data[p101][idim].r - data[p10m][idim].r - data[pm01][idim].r + data[pm0m][idim].r) * one4;
|
||||
D2fdxdz[n][idim].i = (data[p101][idim].i - data[p10m][idim].i - data[pm01][idim].i + data[pm0m][idim].i) * one4;
|
||||
D2fdydz[n][idim].r = (data[p011][idim].r - data[p01m][idim].r - data[p0m1][idim].r + data[p0mm][idim].r) * one4;
|
||||
D2fdydz[n][idim].i = (data[p011][idim].i - data[p01m][idim].i - data[p0m1][idim].i + data[p0mm][idim].i) * one4;
|
||||
D3fdxdydz[n][idim].r = (data[p111][idim].r-data[pm11][idim].r - data[p1m1][idim].r - data[p11m][idim].r +
|
||||
data[p1mm][idim].r+data[pm1m][idim].r + data[pmm1][idim].r - data[pmmm][idim].r) * one8;
|
||||
D3fdxdydz[n][idim].i = (data[p111][idim].i-data[pm11][idim].i - data[p1m1][idim].i - data[p11m][idim].i +
|
||||
data[p1mm][idim].i+data[pm1m][idim].i + data[pmm1][idim].i - data[pmmm][idim].i) * one8;
|
||||
}
|
||||
n++;
|
||||
}
|
||||
return;
|
||||
// get the derivatives
|
||||
int n=0;
|
||||
const double half = 0.5, one4 = 0.25, one8 = 0.125;
|
||||
for (int ii = 0; ii < Nx; ++ii)
|
||||
for (int jj = 0; jj < Ny; ++jj)
|
||||
for (int kk = 0; kk < Nz; ++kk){
|
||||
int ip = (ii+1)%Nx, jp = (jj+1)%Ny, kp = (kk+1)%Nz;
|
||||
int im = (ii-1+Nx)%Nx, jm = (jj-1+Ny)%Ny, km = (kk-1+Nz)%Nz;
|
||||
|
||||
int p100 = (ip*Ny+jj)*Nz+kk;
|
||||
int p010 = (ii*Ny+jp)*Nz+kk;
|
||||
int p001 = (ii*Ny+jj)*Nz+kp;
|
||||
int p110 = (ip*Ny+jp)*Nz+kk;
|
||||
int p101 = (ip*Ny+jj)*Nz+kp;
|
||||
int p011 = (ii*Ny+jp)*Nz+kp;
|
||||
int pm00 = (im*Ny+jj)*Nz+kk;
|
||||
int p0m0 = (ii*Ny+jm)*Nz+kk;
|
||||
int p00m = (ii*Ny+jj)*Nz+km;
|
||||
int pmm0 = (im*Ny+jm)*Nz+kk;
|
||||
int pm0m = (im*Ny+jj)*Nz+km;
|
||||
int p0mm = (ii*Ny+jm)*Nz+km;
|
||||
int p1m0 = (ip*Ny+jm)*Nz+kk;
|
||||
int p10m = (ip*Ny+jj)*Nz+km;
|
||||
int p01m = (ii*Ny+jp)*Nz+km;
|
||||
int pm10 = (im*Ny+jp)*Nz+kk;
|
||||
int pm01 = (im*Ny+jj)*Nz+kp;
|
||||
int p0m1 = (ii*Ny+jm)*Nz+kp;
|
||||
int p111 = (ip*Ny+jp)*Nz+kp;
|
||||
int pm11 = (im*Ny+jp)*Nz+kp;
|
||||
int p1m1 = (ip*Ny+jm)*Nz+kp;
|
||||
int p11m = (ip*Ny+jp)*Nz+km;
|
||||
int pm1m = (im*Ny+jp)*Nz+km;
|
||||
int p1mm = (ip*Ny+jm)*Nz+km;
|
||||
int pmm1 = (im*Ny+jm)*Nz+kp;
|
||||
int pmmm = (im*Ny+jm)*Nz+km;
|
||||
|
||||
for (int idim=0; idim<ndim; idim++){
|
||||
Dfdx[n][idim].r = (data[p100][idim].r - data[pm00][idim].r) * half;
|
||||
Dfdx[n][idim].i = (data[p100][idim].i - data[pm00][idim].i) * half;
|
||||
Dfdy[n][idim].r = (data[p010][idim].r - data[p0m0][idim].r) * half;
|
||||
Dfdy[n][idim].i = (data[p010][idim].i - data[p0m0][idim].i) * half;
|
||||
Dfdz[n][idim].r = (data[p001][idim].r - data[p00m][idim].r) * half;
|
||||
Dfdz[n][idim].i = (data[p001][idim].i - data[p00m][idim].i) * half;
|
||||
D2fdxdy[n][idim].r = (data[p110][idim].r - data[p1m0][idim].r - data[pm10][idim].r + data[pmm0][idim].r) * one4;
|
||||
D2fdxdy[n][idim].i = (data[p110][idim].i - data[p1m0][idim].i - data[pm10][idim].i + data[pmm0][idim].i) * one4;
|
||||
D2fdxdz[n][idim].r = (data[p101][idim].r - data[p10m][idim].r - data[pm01][idim].r + data[pm0m][idim].r) * one4;
|
||||
D2fdxdz[n][idim].i = (data[p101][idim].i - data[p10m][idim].i - data[pm01][idim].i + data[pm0m][idim].i) * one4;
|
||||
D2fdydz[n][idim].r = (data[p011][idim].r - data[p01m][idim].r - data[p0m1][idim].r + data[p0mm][idim].r) * one4;
|
||||
D2fdydz[n][idim].i = (data[p011][idim].i - data[p01m][idim].i - data[p0m1][idim].i + data[p0mm][idim].i) * one4;
|
||||
D3fdxdydz[n][idim].r = (data[p111][idim].r-data[pm11][idim].r - data[p1m1][idim].r - data[p11m][idim].r +
|
||||
data[p1mm][idim].r+data[pm1m][idim].r + data[pmm1][idim].r - data[pmmm][idim].r) * one8;
|
||||
D3fdxdydz[n][idim].i = (data[p111][idim].i-data[pm11][idim].i - data[p1m1][idim].i - data[p11m][idim].i +
|
||||
data[p1mm][idim].i+data[pm1m][idim].i + data[pmm1][idim].i - data[pmmm][idim].i) * one8;
|
||||
}
|
||||
n++;
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------------
|
||||
|
|
@ -224,15 +105,17 @@ return;
|
|||
* ---------------------------------------------------------------------------- */
|
||||
Interpolate::~Interpolate()
|
||||
{
|
||||
data = NULL;
|
||||
memory->destroy(Dfdx);
|
||||
memory->destroy(Dfdy);
|
||||
memory->destroy(Dfdz);
|
||||
memory->destroy(D2fdxdy);
|
||||
memory->destroy(D2fdxdz);
|
||||
memory->destroy(D2fdydz);
|
||||
memory->destroy(D3fdxdydz);
|
||||
delete memory;
|
||||
data = NULL;
|
||||
memory->destroy(Dfdx);
|
||||
memory->destroy(Dfdy);
|
||||
memory->destroy(Dfdz);
|
||||
memory->destroy(D2fdxdy);
|
||||
memory->destroy(D2fdxdz);
|
||||
memory->destroy(D2fdydz);
|
||||
memory->destroy(D3fdxdydz);
|
||||
delete memory;
|
||||
|
||||
return;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------------
|
||||
|
|
@ -240,60 +123,59 @@ Interpolate::~Interpolate()
|
|||
* ---------------------------------------------------------------------------- */
|
||||
void Interpolate::tricubic(double *qin, doublecomplex *DMq)
|
||||
{
|
||||
// qin should be in unit of 2*pi/L
|
||||
double q[3];
|
||||
for (int i = 0; i < 3; ++i) q[i] = qin[i];
|
||||
for (int i = 0; i < 3; ++i){
|
||||
while (q[i] < 0.) q[i] += 1.;
|
||||
while (q[i] >= 1.) q[i] -= 1.;
|
||||
}
|
||||
|
||||
int ix = int(q[0]*double(Nx));
|
||||
int iy = int(q[1]*double(Ny));
|
||||
int iz = int(q[2]*double(Nz));
|
||||
double x = q[0]*double(Nx)-double(ix);
|
||||
double y = q[1]*double(Ny)-double(iy);
|
||||
double z = q[2]*double(Nz)-double(iz);
|
||||
int ixp = (ix+1)%Nx, iyp = (iy+1)%Ny, izp = (iz+1)%Nz;
|
||||
vidx[0] = (ix*Ny+iy)*Nz+iz;
|
||||
vidx[1] = (ixp*Ny+iy)*Nz+iz;
|
||||
vidx[2] = (ix*Ny+iyp)*Nz+iz;
|
||||
vidx[3] = (ixp*Ny+iyp)*Nz+iz;
|
||||
vidx[4] = (ix*Ny+iy)*Nz+izp;
|
||||
vidx[5] = (ixp*Ny+iy)*Nz+izp;
|
||||
vidx[6] = (ix*Ny+iyp)*Nz+izp;
|
||||
vidx[7] = (ixp*Ny+iyp)*Nz+izp;
|
||||
for (int i=0; i<8; i++) if (vidx[i] == 0) UseGamma = 1;
|
||||
|
||||
for (int idim = 0; idim < ndim; ++idim){
|
||||
for (int i = 0; i < 8; ++i){
|
||||
f[i] = data[vidx[i]][idim].r;
|
||||
dfdx[i] = Dfdx[vidx[i]][idim].r;
|
||||
dfdy[i] = Dfdy[vidx[i]][idim].r;
|
||||
dfdz[i] = Dfdz[vidx[i]][idim].r;
|
||||
d2fdxdy[i] = D2fdxdy[vidx[i]][idim].r;
|
||||
d2fdxdz[i] = D2fdxdz[vidx[i]][idim].r;
|
||||
d2fdydz[i] = D2fdydz[vidx[i]][idim].r;
|
||||
d3fdxdydz[i] = D3fdxdydz[vidx[i]][idim].r;
|
||||
}
|
||||
tricubic_get_coeff(&a[0],&f[0],&dfdx[0],&dfdy[0],&dfdz[0],&d2fdxdy[0],&d2fdxdz[0],&d2fdydz[0],&d3fdxdydz[0]);
|
||||
DMq[idim].r = tricubic_eval(&a[0],x,y,z);
|
||||
|
||||
for (int i = 0; i < 8; ++i){
|
||||
f[i] = data[vidx[i]][idim].i;
|
||||
dfdx[i] = Dfdx[vidx[i]][idim].i;
|
||||
dfdy[i] = Dfdy[vidx[i]][idim].i;
|
||||
dfdz[i] = Dfdz[vidx[i]][idim].i;
|
||||
d2fdxdy[i] = D2fdxdy[vidx[i]][idim].i;
|
||||
d2fdxdz[i] = D2fdxdz[vidx[i]][idim].i;
|
||||
d2fdydz[i] = D2fdydz[vidx[i]][idim].i;
|
||||
d3fdxdydz[i] = D3fdxdydz[vidx[i]][idim].i;
|
||||
}
|
||||
tricubic_get_coeff(&a[0],&f[0],&dfdx[0],&dfdy[0],&dfdz[0],&d2fdxdy[0],&d2fdxdz[0],&d2fdydz[0],&d3fdxdydz[0]);
|
||||
DMq[idim].i = tricubic_eval(&a[0],x,y,z);
|
||||
}
|
||||
|
||||
return;
|
||||
// qin should be in unit of 2*pi/L
|
||||
double q[3];
|
||||
for (int i = 0; i < 3; ++i) q[i] = qin[i];
|
||||
for (int i = 0; i < 3; ++i){
|
||||
while (q[i] < 0.) q[i] += 1.;
|
||||
while (q[i] >= 1.) q[i] -= 1.;
|
||||
}
|
||||
|
||||
int ix = int(q[0]*double(Nx));
|
||||
int iy = int(q[1]*double(Ny));
|
||||
int iz = int(q[2]*double(Nz));
|
||||
double x = q[0]*double(Nx)-double(ix);
|
||||
double y = q[1]*double(Ny)-double(iy);
|
||||
double z = q[2]*double(Nz)-double(iz);
|
||||
int ixp = (ix+1)%Nx, iyp = (iy+1)%Ny, izp = (iz+1)%Nz;
|
||||
vidx[0] = (ix*Ny+iy)*Nz+iz;
|
||||
vidx[1] = (ixp*Ny+iy)*Nz+iz;
|
||||
vidx[2] = (ix*Ny+iyp)*Nz+iz;
|
||||
vidx[3] = (ixp*Ny+iyp)*Nz+iz;
|
||||
vidx[4] = (ix*Ny+iy)*Nz+izp;
|
||||
vidx[5] = (ixp*Ny+iy)*Nz+izp;
|
||||
vidx[6] = (ix*Ny+iyp)*Nz+izp;
|
||||
vidx[7] = (ixp*Ny+iyp)*Nz+izp;
|
||||
for (int i=0; i<8; i++) if (vidx[i] == 0) UseGamma = 1;
|
||||
|
||||
for (int idim = 0; idim < ndim; ++idim){
|
||||
for (int i = 0; i < 8; ++i){
|
||||
f[i] = data[vidx[i]][idim].r;
|
||||
dfdx[i] = Dfdx[vidx[i]][idim].r;
|
||||
dfdy[i] = Dfdy[vidx[i]][idim].r;
|
||||
dfdz[i] = Dfdz[vidx[i]][idim].r;
|
||||
d2fdxdy[i] = D2fdxdy[vidx[i]][idim].r;
|
||||
d2fdxdz[i] = D2fdxdz[vidx[i]][idim].r;
|
||||
d2fdydz[i] = D2fdydz[vidx[i]][idim].r;
|
||||
d3fdxdydz[i] = D3fdxdydz[vidx[i]][idim].r;
|
||||
}
|
||||
tricubic_get_coeff(&a[0],&f[0],&dfdx[0],&dfdy[0],&dfdz[0],&d2fdxdy[0],&d2fdxdz[0],&d2fdydz[0],&d3fdxdydz[0]);
|
||||
DMq[idim].r = tricubic_eval(&a[0],x,y,z);
|
||||
|
||||
for (int i = 0; i < 8; ++i){
|
||||
f[i] = data[vidx[i]][idim].i;
|
||||
dfdx[i] = Dfdx[vidx[i]][idim].i;
|
||||
dfdy[i] = Dfdy[vidx[i]][idim].i;
|
||||
dfdz[i] = Dfdz[vidx[i]][idim].i;
|
||||
d2fdxdy[i] = D2fdxdy[vidx[i]][idim].i;
|
||||
d2fdxdz[i] = D2fdxdz[vidx[i]][idim].i;
|
||||
d2fdydz[i] = D2fdydz[vidx[i]][idim].i;
|
||||
d3fdxdydz[i] = D3fdxdydz[vidx[i]][idim].i;
|
||||
}
|
||||
tricubic_get_coeff(&a[0],&f[0],&dfdx[0],&dfdy[0],&dfdz[0],&d2fdxdy[0],&d2fdxdz[0],&d2fdydz[0],&d3fdxdydz[0]);
|
||||
DMq[idim].i = tricubic_eval(&a[0],x,y,z);
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------------
|
||||
|
|
@ -303,63 +185,63 @@ return;
|
|||
* ---------------------------------------------------------------------------- */
|
||||
void Interpolate::trilinear(double *qin, doublecomplex *DMq)
|
||||
{
|
||||
// rescale q[i] into [0 1)
|
||||
double q[3];
|
||||
for (int i = 0; i < 3; ++i) q[i] = qin[i];
|
||||
for (int i = 0; i < 3; ++i){
|
||||
while (q[i] < 0.) q[i] += 1.;
|
||||
while (q[i] >= 1.) q[i] -= 1.;
|
||||
}
|
||||
|
||||
// find the index of the eight vertice
|
||||
int ix, iy, iz, ixp, iyp, izp;
|
||||
double x, y, z;
|
||||
q[0] *= double(Nx);
|
||||
q[1] *= double(Ny);
|
||||
q[2] *= double(Nz);
|
||||
|
||||
ix = int(q[0])%Nx;
|
||||
iy = int(q[1])%Ny;
|
||||
iz = int(q[2])%Nz;
|
||||
ixp = (ix+1)%Nx;
|
||||
iyp = (iy+1)%Ny;
|
||||
izp = (iz+1)%Nz;
|
||||
x = q[0] - double(ix);
|
||||
y = q[1] - double(iy);
|
||||
z = q[2] - double(iz);
|
||||
|
||||
//--------------------------------------
|
||||
vidx[0] = ((ix*Ny)+iy)*Nz + iz;
|
||||
vidx[1] = ((ixp*Ny)+iy)*Nz + iz;
|
||||
vidx[2] = ((ix*Ny)+iyp)*Nz + iz;
|
||||
vidx[3] = ((ix*Ny)+iy)*Nz + izp;
|
||||
vidx[4] = ((ixp*Ny)+iy)*Nz + izp;
|
||||
vidx[5] = ((ix*Ny)+iyp)*Nz + izp;
|
||||
vidx[6] = ((ixp*Ny)+iyp)*Nz + iz;
|
||||
vidx[7] = ((ixp*Ny)+iyp)*Nz + izp;
|
||||
for (int i = 0; i < 8; ++i) if (vidx[i] == 0) UseGamma = 1;
|
||||
|
||||
double fac[8];
|
||||
fac[0] = (1.-x)*(1.-y)*(1.-z);
|
||||
fac[1] = x*(1.-y)*(1.-z);
|
||||
fac[2] = (1.-x)*y*(1.-z);
|
||||
fac[3] = (1.-x)*(1.-y)*z;
|
||||
fac[4] = x*(1.-y)*z;
|
||||
fac[5] = (1.-x)*y*z;
|
||||
fac[6] = x*y*(1.-z);
|
||||
fac[7] = x*y*z;
|
||||
|
||||
// now to do the interpolation
|
||||
for (int idim = 0; idim < ndim; ++idim){
|
||||
DMq[idim].r = 0.;
|
||||
DMq[idim].i = 0.;
|
||||
for (int i = 0; i < 8; ++i){
|
||||
DMq[idim].r += data[vidx[i]][idim].r*fac[i];
|
||||
DMq[idim].i += data[vidx[i]][idim].i*fac[i];
|
||||
}
|
||||
}
|
||||
|
||||
return;
|
||||
// rescale q[i] into [0 1)
|
||||
double q[3];
|
||||
for (int i = 0; i < 3; ++i) q[i] = qin[i];
|
||||
for (int i = 0; i < 3; ++i){
|
||||
while (q[i] < 0.) q[i] += 1.;
|
||||
while (q[i] >= 1.) q[i] -= 1.;
|
||||
}
|
||||
|
||||
// find the index of the eight vertice
|
||||
int ix, iy, iz, ixp, iyp, izp;
|
||||
double x, y, z;
|
||||
q[0] *= double(Nx);
|
||||
q[1] *= double(Ny);
|
||||
q[2] *= double(Nz);
|
||||
|
||||
ix = int(q[0])%Nx;
|
||||
iy = int(q[1])%Ny;
|
||||
iz = int(q[2])%Nz;
|
||||
ixp = (ix+1)%Nx;
|
||||
iyp = (iy+1)%Ny;
|
||||
izp = (iz+1)%Nz;
|
||||
x = q[0] - double(ix);
|
||||
y = q[1] - double(iy);
|
||||
z = q[2] - double(iz);
|
||||
|
||||
//--------------------------------------
|
||||
vidx[0] = ((ix*Ny)+iy)*Nz + iz;
|
||||
vidx[1] = ((ixp*Ny)+iy)*Nz + iz;
|
||||
vidx[2] = ((ix*Ny)+iyp)*Nz + iz;
|
||||
vidx[3] = ((ix*Ny)+iy)*Nz + izp;
|
||||
vidx[4] = ((ixp*Ny)+iy)*Nz + izp;
|
||||
vidx[5] = ((ix*Ny)+iyp)*Nz + izp;
|
||||
vidx[6] = ((ixp*Ny)+iyp)*Nz + iz;
|
||||
vidx[7] = ((ixp*Ny)+iyp)*Nz + izp;
|
||||
for (int i = 0; i < 8; ++i) if (vidx[i] == 0) UseGamma = 1;
|
||||
|
||||
double fac[8];
|
||||
fac[0] = (1.-x)*(1.-y)*(1.-z);
|
||||
fac[1] = x*(1.-y)*(1.-z);
|
||||
fac[2] = (1.-x)*y*(1.-z);
|
||||
fac[3] = (1.-x)*(1.-y)*z;
|
||||
fac[4] = x*(1.-y)*z;
|
||||
fac[5] = (1.-x)*y*z;
|
||||
fac[6] = x*y*(1.-z);
|
||||
fac[7] = x*y*z;
|
||||
|
||||
// now to do the interpolation
|
||||
for (int idim = 0; idim < ndim; ++idim){
|
||||
DMq[idim].r = 0.;
|
||||
DMq[idim].i = 0.;
|
||||
for (int i = 0; i < 8; ++i){
|
||||
DMq[idim].r += data[vidx[i]][idim].r*fac[i];
|
||||
DMq[idim].i += data[vidx[i]][idim].i*fac[i];
|
||||
}
|
||||
}
|
||||
|
||||
return;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------------
|
||||
|
|
@ -367,12 +249,13 @@ return;
|
|||
* ---------------------------------------------------------------------------- */
|
||||
void Interpolate::execute(double *qin, doublecomplex *DMq)
|
||||
{
|
||||
UseGamma = 0;
|
||||
if (which == 1) // 1: tricubic
|
||||
tricubic(qin, DMq);
|
||||
else // otherwise: trilinear
|
||||
trilinear(qin, DMq);
|
||||
return;
|
||||
UseGamma = 0;
|
||||
if (which == 1) // 1: tricubic
|
||||
tricubic(qin, DMq);
|
||||
else // otherwise: trilinear
|
||||
trilinear(qin, DMq);
|
||||
|
||||
return;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------------
|
||||
|
|
@ -380,24 +263,23 @@ return;
|
|||
* ---------------------------------------------------------------------------- */
|
||||
void Interpolate::set_method()
|
||||
{
|
||||
char str[MAXLINE];
|
||||
int im = 1;
|
||||
printf("\n");for(int i=0; i<80; i++) printf("=");
|
||||
printf("\nWhich interpolation method would you like to use?\n");
|
||||
printf(" 1. Tricubic;\n 2. Trilinear;\n");
|
||||
printf("Your choice [1]: ");
|
||||
fgets(str,MAXLINE,stdin);
|
||||
char *ptr = strtok(str," \t\n\r\f");
|
||||
if (ptr) im = atoi(ptr);
|
||||
|
||||
which =2-im%2;
|
||||
printf("Your selection: %d\n", which);
|
||||
for(int i=0; i<80; i++) printf("=");
|
||||
printf("\n\n");
|
||||
|
||||
if (which == 1) tricubic_init();
|
||||
|
||||
return;
|
||||
char str[MAXLINE];
|
||||
int im = 1;
|
||||
printf("\n");for(int i=0; i<80; i++) printf("=");
|
||||
printf("\nWhich interpolation method would you like to use?\n");
|
||||
printf(" 1. Tricubic;\n 2. Trilinear;\n");
|
||||
printf("Your choice [1]: ");
|
||||
fgets(str,MAXLINE,stdin);
|
||||
char *ptr = strtok(str," \t\n\r\f");
|
||||
if (ptr) im = atoi(ptr);
|
||||
|
||||
which =2-im%2;
|
||||
printf("Your selection: %d\n", which);
|
||||
for(int i=0; i<80; i++) printf("="); printf("\n\n");
|
||||
|
||||
if (which == 1) tricubic_init();
|
||||
|
||||
return;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------------
|
||||
|
|
@ -406,22 +288,23 @@ return;
|
|||
* ---------------------------------------------------------------------------- */
|
||||
void Interpolate::reset_gamma()
|
||||
{
|
||||
if (flag_reset_gamma) return;
|
||||
flag_reset_gamma = 1;
|
||||
|
||||
int p1 = 1%Nx, p2 = 2%Nx;
|
||||
int m1 = (Nx-1), m2 = (Nx-2+Nx)%Nx;
|
||||
|
||||
int ip1 = p1*Ny*Nz, ip2 = p2*Ny*Nz;
|
||||
int im1 = m1*Ny*Nz, im2 = m2*Ny*Nz;
|
||||
|
||||
double const one6 = -1./6., two3 = 2./3.;
|
||||
|
||||
for (int idim=0; idim<ndim; idim++){
|
||||
data[0][idim].i = 0.;
|
||||
data[0][idim].r = (data[im2][idim].r + data[ip2][idim].r) * one6
|
||||
+ (data[im1][idim].r + data[ip1][idim].r) * two3;
|
||||
}
|
||||
|
||||
return;
|
||||
if (flag_reset_gamma) return;
|
||||
flag_reset_gamma = 1;
|
||||
|
||||
int p1 = 1%Nx, p2 = 2%Nx;
|
||||
int m1 = (Nx-1), m2 = (Nx-2+Nx)%Nx;
|
||||
|
||||
int ip1 = p1*Ny*Nz, ip2 = p2*Ny*Nz;
|
||||
int im1 = m1*Ny*Nz, im2 = m2*Ny*Nz;
|
||||
|
||||
double const one6 = -1./6., two3 = 2./3.;
|
||||
|
||||
for (int idim=0; idim < ndim; idim++){
|
||||
data[0][idim].i = 0.;
|
||||
data[0][idim].r = (data[im2][idim].r + data[ip2][idim].r) * one6
|
||||
+ (data[im1][idim].r + data[ip1][idim].r) * two3;
|
||||
}
|
||||
|
||||
return;
|
||||
}
|
||||
/* ---------------------------------------------------------------------------- */
|
||||
|
|
|
|||
|
|
@ -5,36 +5,38 @@
|
|||
#include "stdlib.h"
|
||||
#include "string.h"
|
||||
#include "memory.h"
|
||||
#include "tricubic.h"
|
||||
|
||||
extern "C" typedef struct { double r, i; } doublecomplex;
|
||||
|
||||
using namespace std;
|
||||
extern "C"{
|
||||
#include "f2c.h"
|
||||
#include "clapack.h"
|
||||
}
|
||||
|
||||
class Interpolate{
|
||||
public:
|
||||
Interpolate(int, int, int, int, doublecomplex **);
|
||||
~Interpolate();
|
||||
|
||||
void set_method();
|
||||
void execute(double *, doublecomplex *);
|
||||
void reset_gamma();
|
||||
|
||||
int UseGamma;
|
||||
Interpolate(int, int, int, int, doublecomplex **);
|
||||
~Interpolate();
|
||||
|
||||
void set_method();
|
||||
void execute(double *, doublecomplex *);
|
||||
void reset_gamma();
|
||||
|
||||
int UseGamma;
|
||||
|
||||
private:
|
||||
void tricubic_init();
|
||||
void tricubic(double *, doublecomplex *);
|
||||
void trilinear(double *, doublecomplex *);
|
||||
Memory *memory;
|
||||
|
||||
int which;
|
||||
int Nx, Ny, Nz, Npt, ndim;
|
||||
int flag_reset_gamma, flag_allocated_dfs;
|
||||
|
||||
doublecomplex **data;
|
||||
doublecomplex **Dfdx, **Dfdy, **Dfdz, **D2fdxdy, **D2fdxdz, **D2fdydz, **D3fdxdydz;
|
||||
double a[64], f[8], dfdx[8], dfdy[8], dfdz[8], d2fdxdy[8], d2fdxdz[8], d2fdydz[8], d3fdxdydz[8];
|
||||
int vidx[8];
|
||||
void tricubic_init();
|
||||
void tricubic(double *, doublecomplex *);
|
||||
void trilinear(double *, doublecomplex *);
|
||||
Memory *memory;
|
||||
|
||||
int which;
|
||||
int Nx, Ny, Nz, Npt, ndim;
|
||||
int flag_reset_gamma, flag_allocated_dfs;
|
||||
|
||||
doublecomplex **data;
|
||||
doublecomplex **Dfdx, **Dfdy, **Dfdz, **D2fdxdy, **D2fdxdz, **D2fdydz, **D3fdxdydz;
|
||||
double a[64], f[8], dfdx[8], dfdy[8], dfdz[8], d2fdxdy[8], d2fdxdz[8], d2fdydz[8], d3fdxdydz[8];
|
||||
int vidx[8];
|
||||
};
|
||||
|
||||
#endif
|
||||
|
|
|
|||
File diff suppressed because it is too large
Load Diff
|
|
@ -0,0 +1,32 @@
|
|||
#ifndef UseSPG
|
||||
#define KPATH_H
|
||||
#endif
|
||||
#ifndef KPATH_H
|
||||
#define KPATH_H
|
||||
|
||||
#include "qnodes.h"
|
||||
#include "dynmat.h"
|
||||
#include "memory.h"
|
||||
|
||||
class kPath{
|
||||
public:
|
||||
|
||||
kPath(DynMat *, QNodes *);
|
||||
~kPath();
|
||||
|
||||
void kpath();
|
||||
void show_path();
|
||||
void show_info();
|
||||
|
||||
private:
|
||||
|
||||
Memory *memory;
|
||||
|
||||
DynMat *dynmat;
|
||||
QNodes *q;
|
||||
char symbol[11];
|
||||
int spgnum, sysdim, fftdim, num_atom, *attyp;
|
||||
double latvec[3][3], **atpos;
|
||||
|
||||
};
|
||||
#endif
|
||||
File diff suppressed because it is too large
Load Diff
|
|
@ -11,50 +11,50 @@ using namespace std;
|
|||
|
||||
class Phonon{
|
||||
public:
|
||||
Phonon(DynMat *);
|
||||
~Phonon();
|
||||
|
||||
DynMat *dynmat;
|
||||
|
||||
Phonon(DynMat *);
|
||||
~Phonon();
|
||||
|
||||
DynMat *dynmat;
|
||||
|
||||
private:
|
||||
int nq, ndim, sysdim;
|
||||
double **qpts, *wt;
|
||||
double **eigs;
|
||||
|
||||
int ndos, nlocal, *locals;
|
||||
double *dos, fmin, fmax, df, rdf;
|
||||
double ***ldos;
|
||||
|
||||
Memory *memory;
|
||||
|
||||
void QMesh();
|
||||
void ComputeAll();
|
||||
|
||||
void pdos();
|
||||
void pdisp();
|
||||
void therm();
|
||||
|
||||
void ldos_egv();
|
||||
void ldos_rsgf();
|
||||
void local_therm();
|
||||
|
||||
void dmanyq();
|
||||
void vfanyq();
|
||||
void DMdisp();
|
||||
void vecanyq();
|
||||
|
||||
void ShowCell();
|
||||
|
||||
void smooth(double *, const int);
|
||||
void writeDOS();
|
||||
void writeLDOS();
|
||||
void Normalize();
|
||||
|
||||
int count_words(const char *);
|
||||
|
||||
int nq, ndim, sysdim;
|
||||
double **qpts, *wt;
|
||||
double **eigs;
|
||||
|
||||
int ndos, nlocal, *locals;
|
||||
double *dos, fmin, fmax, df, rdf;
|
||||
double ***ldos;
|
||||
|
||||
Memory *memory;
|
||||
|
||||
void QMesh();
|
||||
void ComputeAll();
|
||||
|
||||
void pdos();
|
||||
void pdisp();
|
||||
void therm();
|
||||
|
||||
void ldos_egv();
|
||||
void ldos_rsgf();
|
||||
void local_therm();
|
||||
|
||||
void dmanyq();
|
||||
void vfanyq();
|
||||
void DMdisp();
|
||||
void vecanyq();
|
||||
|
||||
void ShowCell();
|
||||
|
||||
void smooth(double *, const int);
|
||||
void writeDOS();
|
||||
void writeLDOS();
|
||||
void Normalize();
|
||||
|
||||
int count_words(const char *);
|
||||
|
||||
#ifdef UseSPG
|
||||
int num_atom, *attyp;
|
||||
double latvec[3][3], **atpos;
|
||||
int num_atom, *attyp;
|
||||
double latvec[3][3], **atpos;
|
||||
#endif
|
||||
};
|
||||
|
||||
|
|
|
|||
|
|
@ -0,0 +1,320 @@
|
|||
#ifdef FFTW3
|
||||
#include <map>
|
||||
#include "phonopy.h"
|
||||
#include "math.h"
|
||||
#include "kpath.h"
|
||||
#include "fftw3.h"
|
||||
|
||||
/* ----------------------------------------------------------------------------
|
||||
* Class Phonopy is designed to interface with phonopy.
|
||||
* ---------------------------------------------------------------------------- */
|
||||
Phonopy::Phonopy(DynMat *dynmat)
|
||||
{
|
||||
dm = dynmat;
|
||||
memory = new Memory();
|
||||
sysdim = dm->sysdim;
|
||||
fftdim = dm->fftdim;
|
||||
fftdim2 = fftdim * fftdim;
|
||||
nucell = dm->nucell;
|
||||
nx = ny = nz = 5;
|
||||
write(1);
|
||||
|
||||
char str[MAXLINE];
|
||||
if (count_words(fgets(str,MAXLINE,stdin)) >= 3){
|
||||
nx = atoi(strtok(str," \t\n\r\f"));
|
||||
ny = atoi(strtok(NULL," \t\n\r\f"));
|
||||
nz = atoi(strtok(NULL," \t\n\r\f"));
|
||||
}
|
||||
if (dm->nx == 1) nx = 1;
|
||||
if (dm->ny == 1) ny = 1;
|
||||
if (dm->nz == 1) nz = 1;
|
||||
if (nx < 1) nx = 1;
|
||||
if (ny < 1) ny = 1;
|
||||
if (nz < 1) nz = 1;
|
||||
npt = nx * ny * nz;
|
||||
write(2);
|
||||
|
||||
memory->create(mass, nucell, "Phonopy:mass");
|
||||
for (int i = 0; i < nucell; ++i){
|
||||
double m = 1./dm->M_inv_sqrt[i];
|
||||
mass[i] = m * m;
|
||||
}
|
||||
|
||||
memory->create(FC_all, npt, fftdim2, "phonopy:FC_all");
|
||||
|
||||
get_my_FC();
|
||||
|
||||
phonopy();
|
||||
|
||||
return;
|
||||
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------------
|
||||
* Deconstructor, free the memory used.
|
||||
* ---------------------------------------------------------------------------- */
|
||||
Phonopy::~Phonopy()
|
||||
{
|
||||
memory->destroy(mass);
|
||||
memory->destroy(FC_all);
|
||||
delete memory;
|
||||
dm = NULL;
|
||||
return;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------------
|
||||
* Subroutine to write the outputs to screen.
|
||||
* ---------------------------------------------------------------------------- */
|
||||
void Phonopy::write(int flag)
|
||||
{
|
||||
if (flag == 1){ // basic information
|
||||
for (int ii = 0; ii < 80; ++ii) printf("="); printf("\n");
|
||||
printf("Now to prepare the input files for phonopy.\n");
|
||||
printf("The dimension of your present supercell is : %d x %d x %d.\n", dm->nx, dm->ny, dm->nz);
|
||||
printf("The size of the force constant matrix will be: %d x %d.\n", dm->npt*3, dm->npt*3);
|
||||
printf("Please define your desired dimension [5 5 5] : ");
|
||||
|
||||
} else if (flag == 2){
|
||||
printf("\nThe new dimension of the supercell will be : %d x %d x %d.\n", nx, ny, nz);
|
||||
printf("The size of the force constant matrix is then: %d x %d.\n", npt*3, npt*3);
|
||||
|
||||
} else if (flag == 3){
|
||||
printf("\nNow to prepare the phonopy FORCE_CONSTANTS ..."); fflush(stdout);
|
||||
|
||||
} else if (flag == 4){
|
||||
printf("Done!\nThe force constants information is extracted and written to FORCE_CONSTANTS,\n");
|
||||
printf("the primitive cell is written to POSCAR.primitive, and the input file for\n");
|
||||
printf("phonopy band evaluation is written to band.conf.\n");
|
||||
printf("One should be able to obtain the phonon band structure after correcting\n");
|
||||
printf("the element names in POSCAR.primitive and band.conf by running\n");
|
||||
printf("`phonopy --readfc -c POSCAR.primitive -p band.conf`.\n");
|
||||
for (int ii = 0; ii < 80; ++ii) printf("-");
|
||||
printf("\n*** Remember to change the element names. ***\n");
|
||||
#ifdef UseSPG
|
||||
for (int ii = 0; ii < 80; ++ii) printf("-");
|
||||
#endif
|
||||
|
||||
} else if (flag == 5){
|
||||
for (int ii = 0; ii < 80; ++ii) printf("="); printf("\n");
|
||||
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------------
|
||||
* Driver to obtain the force constant matrix
|
||||
* ---------------------------------------------------------------------------- */
|
||||
void Phonopy::get_my_FC()
|
||||
{
|
||||
double q[3];
|
||||
int ipt = 0;
|
||||
for (int ix = 0; ix < nx; ++ix)
|
||||
for (int iy = 0; iy < ny; ++iy)
|
||||
for (int iz = 0; iz < nz; ++iz){
|
||||
q[0] = double(ix)/double(nx);
|
||||
q[1] = double(iy)/double(ny);
|
||||
q[2] = double(iz)/double(nz);
|
||||
|
||||
dm->getDMq(q);
|
||||
|
||||
int ndim = 0;
|
||||
for (int idim = 0; idim < fftdim; ++idim)
|
||||
for (int jdim = 0; jdim < fftdim; ++jdim){
|
||||
FC_all[ipt][ndim] = dm->DM_q[idim][jdim];
|
||||
double m = sqrt(mass[idim/sysdim] * mass[jdim/sysdim]);
|
||||
FC_all[ipt][ndim].r *= m;
|
||||
FC_all[ipt][ndim].i *= m;
|
||||
++ndim;
|
||||
}
|
||||
++ipt;
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------------
|
||||
* Method to write out the force constants and related files for
|
||||
* postprocessing with phonopy.
|
||||
* ---------------------------------------------------------------------------- */
|
||||
void Phonopy::phonopy()
|
||||
{
|
||||
// output info
|
||||
write(3);
|
||||
|
||||
fftw_complex *in, *out;
|
||||
double **fc;
|
||||
memory->create(in, npt, "phonopy:in");
|
||||
memory->create(out, npt, "phonopy:in");
|
||||
memory->create(fc, npt, fftdim2, "phonopy:in");
|
||||
|
||||
fftw_plan plan = fftw_plan_dft_3d(nx, ny, nz, in, out, -1, FFTW_ESTIMATE);
|
||||
|
||||
double factor = dm->eml2fc / double(npt);
|
||||
for (int idim = 0; idim < fftdim2; ++idim){
|
||||
for (int i = 0; i < npt; ++i){
|
||||
in[i][0] = FC_all[i][idim].r;
|
||||
in[i][1] = FC_all[i][idim].i;
|
||||
}
|
||||
fftw_execute(plan);
|
||||
for (int i = 0; i < npt; ++i) fc[i][idim] = out[i][0] * factor;
|
||||
}
|
||||
fftw_destroy_plan(plan);
|
||||
memory->destroy(in);
|
||||
memory->destroy(out);
|
||||
|
||||
// in POSCAR, atoms are sorted/aggregated by type, while for LAMMPS there is no such requirment
|
||||
int type_id[nucell], num_type[nucell], ntype = 0;
|
||||
for (int i = 0; i < nucell; ++i) num_type[i] = 0;
|
||||
for (int i = 0; i < nucell; ++i){
|
||||
int ip = ntype;
|
||||
for (int j = 0; j < ntype; ++j){
|
||||
if (dm->attyp[i] == type_id[j]) ip = j;
|
||||
}
|
||||
if (ip == ntype) type_id[ntype++] = dm->attyp[i];
|
||||
num_type[ip]++;
|
||||
}
|
||||
std::map<int, int> iu_by_type;
|
||||
iu_by_type.clear();
|
||||
int id_new = 0;
|
||||
for (int i = 0; i < ntype; ++i){
|
||||
for (int j = 0; j < nucell; ++j){
|
||||
if (dm->attyp[j] == type_id[i]) iu_by_type[id_new++] = j;
|
||||
}
|
||||
}
|
||||
|
||||
// write the FORCE_CONSTANTS file
|
||||
FILE *fp = fopen("FORCE_CONSTANTS", "w");
|
||||
int natom = npt * nucell;
|
||||
fprintf(fp, "%d %d\n", natom, natom);
|
||||
for (int i = 0; i < natom; ++i){
|
||||
int iu = i / npt;
|
||||
int iz = (i % npt) / (nx * ny);
|
||||
int iy = (i % (nx *ny) ) / nx;
|
||||
int ix = i % nx;
|
||||
iu = iu_by_type[iu];
|
||||
|
||||
for (int j = 0; j < natom; ++j){
|
||||
int ju = j / npt;
|
||||
int jz = (j % npt) / (nx * ny);
|
||||
int jy = (j % (nx *ny) ) / nx;
|
||||
int jx = j % nx;
|
||||
|
||||
int dx = abs(ix - jx);
|
||||
int dy = abs(iy - jy);
|
||||
int dz = abs(iz - jz);
|
||||
|
||||
int id = (dx * ny + dy) * nz + dz;
|
||||
ju = iu_by_type[ju];
|
||||
fprintf(fp, "%d %d\n", i+1, j+1);
|
||||
for (int idim = iu * sysdim; idim < (iu+1)*sysdim; ++idim){
|
||||
for (int jdim = ju * sysdim; jdim < (ju+1)*sysdim; ++jdim){
|
||||
int dd = idim * fftdim + jdim;
|
||||
fprintf(fp, " %lg", fc[id][dd]);
|
||||
}
|
||||
fprintf(fp, "\n");
|
||||
}
|
||||
}
|
||||
}
|
||||
fclose(fp);
|
||||
iu_by_type.clear();
|
||||
memory->destroy(fc);
|
||||
|
||||
// write the primitive cell in POSCAR format
|
||||
fp = fopen("POSCAR.primitive", "w");
|
||||
fprintf(fp, "Fix-phonon unit cell");
|
||||
for (int ip = 0; ip < ntype; ++ip) fprintf(fp, ", Elem-%d: %lg", type_id[ip], mass[ip]);
|
||||
fprintf(fp, "\n1.\n");
|
||||
int ndim = 0;
|
||||
for (int idim = 0; idim < 3; ++idim){
|
||||
for (int jdim = 0; jdim < 3; ++jdim) fprintf(fp, "%lg ", dm->basevec[ndim++]);
|
||||
fprintf(fp, "\n");
|
||||
}
|
||||
for (int ip = 0; ip < ntype; ++ip) fprintf(fp, "Elem-%d ", type_id[ip]); fprintf(fp, "\n");
|
||||
for (int ip = 0; ip < ntype; ++ip) fprintf(fp, "%d ", num_type[ip]);
|
||||
fprintf(fp, "\nDirect\n");
|
||||
for (int ip = 0; ip < ntype; ++ip){
|
||||
for (int i = 0; i < nucell; ++i){
|
||||
if (dm->attyp[i] == type_id[ip]){
|
||||
fprintf(fp, "%lg %lg %lg\n", dm->basis[i][0], dm->basis[i][1], dm->basis[i][2]);
|
||||
}
|
||||
}
|
||||
}
|
||||
fclose(fp);
|
||||
|
||||
#ifdef UseSPG
|
||||
// Get high symmetry k-path
|
||||
QNodes *q = new QNodes();
|
||||
kPath *kp = new kPath(dm, q);
|
||||
kp->kpath();
|
||||
#endif
|
||||
|
||||
// band.conf
|
||||
fp = fopen("band.conf", "w");
|
||||
fprintf(fp, "# From Fix-phonon");
|
||||
for (int ip = 0; ip < ntype; ++ip) fprintf(fp, ", Elem-%d: %lg", type_id[ip], mass[ip]);
|
||||
fprintf(fp, "\n\nATOM_NAME = ");
|
||||
for (int ip = 0; ip < ntype; ++ip) fprintf(fp, "Elem-%d ", type_id[ip]);
|
||||
fprintf(fp, "\nDIM = %d %d %d\nBAND = ", nx, ny, nz);
|
||||
#ifdef UseSPG
|
||||
int nsect = q->qs.size();
|
||||
for (int i = 0; i < nsect; ++i){
|
||||
fprintf(fp, " %lg %lg %lg", q->qs[i][0], q->qs[i][1], q->qs[i][2]);
|
||||
if (i+1 < nsect){
|
||||
double dq = 0.;
|
||||
for (int j = 0; j < 3; ++j) dq += (q->qe[i][j] - q->qs[i+1][j]) * (q->qe[i][j] - q->qs[i+1][j]);
|
||||
if (dq > ZERO) {
|
||||
fprintf(fp, " %lg %lg %lg,", q->qe[i][0], q->qe[i][1], q->qe[i][2]);
|
||||
}
|
||||
} else if (i+1 == nsect){
|
||||
fprintf(fp, " %lg %lg %lg\n", q->qe[i][0], q->qe[i][1], q->qe[i][2]);
|
||||
}
|
||||
}
|
||||
#endif
|
||||
fprintf(fp, "\nBAND_POINTS = 21\nBAND_LABELS =");
|
||||
#ifdef UseSPG
|
||||
for (int i = 0; i < q->ndstr.size(); ++i){
|
||||
std::size_t found = q->ndstr[i].find("{/Symbol G}");
|
||||
if (found != std::string::npos) q->ndstr[i].replace(found, found+11, "$\\Gamma$");
|
||||
found = q->ndstr[i].find("/");
|
||||
if (found != std::string::npos) q->ndstr[i].replace(found, found, " ");
|
||||
fprintf(fp, " %s", q->ndstr[i].c_str());
|
||||
}
|
||||
#endif
|
||||
fprintf(fp, "\nFORCE_CONSTANTS = READ\nBAND_CONNECTION = .TRUE.\n");
|
||||
|
||||
// output info
|
||||
write(4);
|
||||
#ifdef UseSPG
|
||||
kp->show_path();
|
||||
delete kp;
|
||||
delete q;
|
||||
#endif
|
||||
write(5);
|
||||
|
||||
return;
|
||||
}
|
||||
|
||||
/*------------------------------------------------------------------------------
|
||||
* Method to count # of words in a string, without destroying the string
|
||||
*----------------------------------------------------------------------------*/
|
||||
int Phonopy::count_words(const char *line)
|
||||
{
|
||||
int n = strlen(line) + 1;
|
||||
char *copy;
|
||||
memory->create(copy, n, "count_words:copy");
|
||||
strcpy(copy,line);
|
||||
|
||||
char *ptr;
|
||||
if (ptr = strchr(copy,'#')) *ptr = '\0';
|
||||
|
||||
if (strtok(copy," \t\n\r\f") == NULL) {
|
||||
memory->destroy(copy);
|
||||
return 0;
|
||||
}
|
||||
n = 1;
|
||||
while (strtok(NULL," \t\n\r\f")) n++;
|
||||
|
||||
memory->destroy(copy);
|
||||
return n;
|
||||
}
|
||||
/*----------------------------------------------------------------------------*/
|
||||
#endif
|
||||
|
|
@ -0,0 +1,36 @@
|
|||
#ifndef FFTW3
|
||||
#define PHONOPY_H
|
||||
#endif
|
||||
#ifndef PHONOPY_H
|
||||
#define PHONOPY_H
|
||||
|
||||
#include "stdio.h"
|
||||
#include "stdlib.h"
|
||||
#include "string.h"
|
||||
#include "memory.h"
|
||||
#include "qnodes.h"
|
||||
#include "dynmat.h"
|
||||
#include "global.h"
|
||||
|
||||
class Phonopy {
|
||||
public:
|
||||
Phonopy(DynMat *);
|
||||
~Phonopy();
|
||||
|
||||
private:
|
||||
Memory *memory;
|
||||
char str[MAXLINE];
|
||||
int npt, fftdim2; // local variables
|
||||
int nx, ny, nz, nucell; // local variables
|
||||
int sysdim, fftdim; // local variables
|
||||
double *mass;
|
||||
|
||||
doublecomplex **FC_all;
|
||||
|
||||
DynMat *dm;
|
||||
void write(int);
|
||||
void get_my_FC();
|
||||
void phonopy();
|
||||
int count_words(const char *line);
|
||||
};
|
||||
#endif
|
||||
|
|
@ -0,0 +1,30 @@
|
|||
#include "qnodes.h"
|
||||
|
||||
/* ----------------------------------------------------------------------------
|
||||
* Class QNodes stores the high symmetry k-path nodes for a given lattice.
|
||||
* The constructor and the deconstructor simply empties the data.
|
||||
* ---------------------------------------------------------------------------- */
|
||||
QNodes::QNodes()
|
||||
{
|
||||
nodes.clear();
|
||||
ndstr.clear();
|
||||
qs.clear();
|
||||
qe.clear();
|
||||
nqbin.clear();
|
||||
|
||||
return;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------------
|
||||
* The constructor and the deconstructor simply empties the data.
|
||||
* ---------------------------------------------------------------------------- */
|
||||
QNodes::~QNodes()
|
||||
{
|
||||
nodes.clear();
|
||||
ndstr.clear();
|
||||
qs.clear();
|
||||
qe.clear();
|
||||
nqbin.clear();
|
||||
|
||||
return;
|
||||
}
|
||||
|
|
@ -0,0 +1,17 @@
|
|||
#ifndef QNODES_H
|
||||
#define QNODES_H
|
||||
|
||||
#include <vector>
|
||||
#include <string>
|
||||
|
||||
class QNodes {
|
||||
public:
|
||||
QNodes();
|
||||
~QNodes();
|
||||
|
||||
std::vector<double> nodes;
|
||||
std::vector<std::string> ndstr;
|
||||
std::vector<double *> qs, qe;
|
||||
std::vector<int> nqbin;
|
||||
};
|
||||
#endif
|
||||
|
|
@ -4,9 +4,10 @@
|
|||
* -------------------------------------------------------------------------- */
|
||||
Timer::Timer()
|
||||
{
|
||||
flag = 0;
|
||||
start();
|
||||
return;
|
||||
flag = 0;
|
||||
start();
|
||||
|
||||
return;
|
||||
}
|
||||
|
||||
/* -----------------------------------------------------------------------------
|
||||
|
|
@ -14,10 +15,9 @@ return;
|
|||
* -------------------------------------------------------------------------- */
|
||||
void Timer::start()
|
||||
{
|
||||
t1 = clock();
|
||||
flag |= 1;
|
||||
|
||||
return;
|
||||
t1 = clock();
|
||||
flag |= 1;
|
||||
return;
|
||||
}
|
||||
|
||||
/* -----------------------------------------------------------------------------
|
||||
|
|
@ -25,11 +25,11 @@ return;
|
|||
* -------------------------------------------------------------------------- */
|
||||
void Timer::stop()
|
||||
{
|
||||
if ( flag&1 ) {
|
||||
t2 = clock();
|
||||
flag |= 2;
|
||||
}
|
||||
return;
|
||||
if ( flag&1 ) {
|
||||
t2 = clock();
|
||||
flag |= 2;
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
/* -----------------------------------------------------------------------------
|
||||
|
|
@ -37,12 +37,12 @@ return;
|
|||
* -------------------------------------------------------------------------- */
|
||||
void Timer::print()
|
||||
{
|
||||
if ( (flag&3) != 3) return;
|
||||
if ( (flag&3) != 3) return;
|
||||
|
||||
cpu_time_used = ((double) (t2 - t1)) / CLOCKS_PER_SEC;
|
||||
printf("Total CPU time used: %g seconds.\n", cpu_time_used);
|
||||
cpu_time_used = ((double) (t2 - t1)) / CLOCKS_PER_SEC;
|
||||
printf("Total CPU time used: %g seconds.\n", cpu_time_used);
|
||||
|
||||
return;
|
||||
return;
|
||||
}
|
||||
|
||||
/* -----------------------------------------------------------------------------
|
||||
|
|
@ -50,6 +50,6 @@ return;
|
|||
* -------------------------------------------------------------------------- */
|
||||
double Timer::elapse()
|
||||
{
|
||||
if ( (flag&3) != 3) return 0.;
|
||||
else return ((double) (t2 - t1)) / CLOCKS_PER_SEC;
|
||||
if ( (flag&3) != 3) return 0.;
|
||||
else return ((double) (t2 - t1)) / CLOCKS_PER_SEC;
|
||||
}
|
||||
|
|
|
|||
|
|
@ -1 +1 @@
|
|||
#define VERSION 8
|
||||
#define VERSION 21
|
||||
|
|
|
|||
Loading…
Reference in New Issue