libmgl-dev 2.2.2.1-3+b2 / usr / include / mgl2 / data.h

/***************************************************************************
 * data.h is part of Math Graphic Library
 * Copyright (C) 2007-2014 Alexey Balakin <mathgl.abalakin@gmail.ru>       *
 *                                                                         *
 *   This program is free software; you can redistribute it and/or modify  *
 *   it under the terms of the GNU Library General Public License as       *
 *   published by the Free Software Foundation; either version 3 of the    *
 *   License, or (at your option) any later version.                       *
 *                                                                         *
 *   This program is distributed in the hope that it will be useful,       *
 *   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
 *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *
 *   GNU General Public License for more details.                          *
 *                                                                         *
 *   You should have received a copy of the GNU Library General Public     *
 *   License along with this program; if not, write to the                 *
 *   Free Software Foundation, Inc.,                                       *
 *   59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.             *
 ***************************************************************************/
#ifndef _MGL_DATA_H_
#define _MGL_DATA_H_

#include "mgl2/data_cf.h"
#include "mgl2/pde.h"
#ifdef __cplusplus
//-----------------------------------------------------------------------------
#include <vector>
#include <string>
//-----------------------------------------------------------------------------
/// Class for working with data array
#if MGL_NO_DATA_A
class MGL_EXPORT mglData
#else
class MGL_EXPORT mglData : public mglDataA
#endif
{
public:

	long nx;		///< number of points in 1st dimensions ('x' dimension)
	long ny;		///< number of points in 2nd dimensions ('y' dimension)
	long nz;		///< number of points in 3d dimensions ('z' dimension)
	mreal *a;		///< data array
	std::string id;	///< column (or slice) names
	bool link;		///< use external data (i.e. don't free it)

	/// Initiate by other mglData variable
	inline mglData(const mglData &d)	{	a=0;	mgl_data_set(this,&d);		}	// NOTE: must be constructor for mglData& to exclude copy one
	inline mglData(const mglDataA *d)	{	a=0;	mgl_data_set(this, d);		}
	inline mglData(bool, mglData *d)	// NOTE: Variable d will be deleted!!!
	{	if(d)
		{	nx=d->nx;	ny=d->ny;	nz=d->nz;	a=d->a;	d->a=0;
			id=d->id;	link=d->link;	delete d;	}
		else	{	a=0;	Create(1);	}	}
	/// Initiate by flat array
	inline mglData(int size, const float *d)	{	a=0;	Set(d,size);	}
	inline mglData(int rows, int cols, const float *d)	{	a=0;	Set(d,cols,rows);	}
	inline mglData(int size, const double *d)	{	a=0;	Set(d,size);	}
	inline mglData(int rows, int cols, const double *d)	{	a=0;	Set(d,cols,rows);	}
	inline mglData(const double *d, int size)	{	a=0;	Set(d,size);	}
	inline mglData(const double *d, int rows, int cols)	{	a=0;	Set(d,cols,rows);	}
	/// Read data from file
	inline mglData(const char *fname)			{	a=0;	Read(fname);	}
	/// Allocate the memory for data array and initialize it zero
	inline mglData(long xx=1,long yy=1,long zz=1)	{	a=0;	Create(xx,yy,zz);	}
	/// Delete the array
	virtual ~mglData()	{	if(!link && a)	delete []a;	}
	inline mreal GetVal(long i, long j=0, long k=0)
	{	return mgl_data_get_value(this,i,j,k);}
	inline void SetVal(mreal f, long i, long j=0, long k=0)
	{	mgl_data_set_value(this,f,i,j,k);	}
	/// Get sizes
	inline long GetNx() const	{	return nx;	}
	inline long GetNy() const	{	return ny;	}
	inline long GetNz() const	{	return nz;	}

	/// Link external data array (don't delete it at exit)
	inline void Link(mreal *A, long NX, long NY=1, long NZ=1)
	{	mgl_data_link(this,A,NX,NY,NZ);	}
	inline void Link(mglData &d)	{	Link(d.a,d.nx,d.ny,d.nz);	}
	/// Allocate memory and copy the data from the gsl_vector
	inline void Set(gsl_vector *m)	{	mgl_data_set_vector(this,m);	}
	/// Allocate memory and copy the data from the gsl_matrix
	inline void Set(gsl_matrix *m)	{	mgl_data_set_matrix(this,m);	}

	/// Allocate memory and copy the data from the (float *) array
	inline void Set(const float *A,long NX,long NY=1,long NZ=1)
	{	mgl_data_set_float(this,A,NX,NY,NZ);	}
	/// Allocate memory and copy the data from the (double *) array
	inline void Set(const double *A,long NX,long NY=1,long NZ=1)
	{	mgl_data_set_double(this,A,NX,NY,NZ);	}
	/// Allocate memory and copy the data from the (float **) array
	inline void Set(float const * const *A,long N1,long N2)
	{	mgl_data_set_float2(this,A,N1,N2);	}
	/// Allocate memory and copy the data from the (double **) array
	inline void Set(double const * const *A,long N1,long N2)
	{	mgl_data_set_double2(this,A,N1,N2);	}
	/// Allocate memory and copy the data from the (float ***) array
	inline void Set(float const * const * const *A,long N1,long N2,long N3)
	{	mgl_data_set_float3(this,A,N1,N2,N3);	}
	/// Allocate memory and copy the data from the (double ***) array
	inline void Set(double const * const * const *A,long N1,long N2,long N3)
	{	mgl_data_set_double3(this,A,N1,N2,N3);	}
	/// Allocate memory and scanf the data from the string
	inline void Set(const char *str,long NX,long NY=1,long NZ=1)
	{	mgl_data_set_values(this,str,NX,NY,NZ);	}
	/// Import data from abstract type
	inline void Set(HCDT dat)	{	mgl_data_set(this, dat);	}
	inline void Set(const mglDataA &dat)	{	mgl_data_set(this, &dat);	}
	/// Allocate memory and copy data from std::vector<T>
	inline void Set(const std::vector<int> &d)
	{	if(d.size()<1)	return;
		Create(d.size());	for(long i=0;i<nx;i++)	a[i] = d[i];	}
	inline void Set(const std::vector<float> &d)
	{	if(d.size()<1)	return;
		Create(d.size());	for(long i=0;i<nx;i++)	a[i] = d[i];	}
	inline void Set(const std::vector<double> &d)
	{	if(d.size()<1)	return;
		Create(d.size());	for(long i=0;i<nx;i++)	a[i] = d[i];	}

	/// Create or recreate the array with specified size and fill it by zero
	inline void Create(long mx,long my=1,long mz=1)
	{	mgl_data_create(this,mx,my,mz);	}
	/// Rearange data dimensions
	inline void Rearrange(long mx, long my=0, long mz=0)
	{	mgl_data_rearrange(this,mx,my,mz);	}
	/// Transpose dimensions of the data (generalization of Transpose)
	inline void Transpose(const char *dim="yx")
	{	mgl_data_transpose(this,dim);	}
	/// Extend data dimensions
	inline void Extend(long n1, long n2=0)
	{	mgl_data_extend(this,n1,n2);	}
	/// Reduce size of the data
	inline void Squeeze(long rx,long ry=1,long rz=1,bool smooth=false)
	{	mgl_data_squeeze(this,rx,ry,rz,smooth);	}
	/// Crop the data
	inline void Crop(long n1, long n2,char dir='x')
	{	mgl_data_crop(this,n1,n2,dir);	}
	/// Insert data rows/columns/slices
	inline void Insert(char dir, long at=0, long num=1)
	{	mgl_data_insert(this,dir,at,num);	}
	/// Delete data rows/columns/slices
	inline void Delete(char dir, long at=0, long num=1)
	{	mgl_data_delete(this,dir,at,num);	}
	/// Remove rows with duplicate values in column id
	inline void Clean(long id)
	{	mgl_data_clean(this,id);	}
	/// Join with another data array
	inline void Join(const mglDataA &d)
	{	mgl_data_join(this,&d);	}

	/// Modify the data by specified formula
	inline void Modify(const char *eq,long dim=0)
	{	mgl_data_modify(this, eq, dim);	}
	/// Modify the data by specified formula
	inline void Modify(const char *eq,const mglDataA &vdat, const mglDataA &wdat)
	{	mgl_data_modify_vw(this,eq,&vdat,&wdat);	}
	/// Modify the data by specified formula
	inline void Modify(const char *eq,const mglDataA &vdat)
	{	mgl_data_modify_vw(this,eq,&vdat,0);	}
	/// Modify the data by specified formula assuming x,y,z in range [r1,r2]
	inline void Fill(mglBase *gr, const char *eq, const char *opt="")
	{	mgl_data_fill_eq(gr,this,eq,0,0,opt);	}
	inline void Fill(mglBase *gr, const char *eq, const mglDataA &vdat, const char *opt="")
	{	mgl_data_fill_eq(gr,this,eq,&vdat,0,opt);	}
	inline void Fill(mglBase *gr, const char *eq, const mglDataA &vdat, const mglDataA &wdat,const char *opt="")
	{	mgl_data_fill_eq(gr,this,eq,&vdat,&wdat,opt);	}
	/// Equidistantly fill the data to range [x1,x2] in direction dir
	inline void Fill(mreal x1,mreal x2=NaN,char dir='x')
	{	return mgl_data_fill(this,x1,x2,dir);	}
	/// Fill the data by interpolated values of vdat parametrically depended on xdat,ydat,zdat for x,y,z in range [p1,p2]
	inline void Refill(const mglDataA &xdat, const mglDataA &vdat, mreal x1, mreal x2,long sl=-1)
	{	mgl_data_refill_x(this,&xdat,&vdat,x1,x2,sl);	}
	inline void Refill(const mglDataA &xdat, const mglDataA &vdat, mglPoint p1, mglPoint p2,long sl=-1)
	{	mgl_data_refill_x(this,&xdat,&vdat,p1.x,p2.x,sl);	}
	inline void Refill(const mglDataA &xdat, const mglDataA &ydat, const mglDataA &vdat, mglPoint p1, mglPoint p2,long sl=-1)
	{	mgl_data_refill_xy(this,&xdat,&ydat,&vdat,p1.x,p2.x,p1.y,p2.y,sl);	}
	inline void Refill(const mglDataA &xdat, const mglDataA &ydat, const mglDataA &zdat, const mglDataA &vdat, mglPoint p1, mglPoint p2)
	{	mgl_data_refill_xyz(this,&xdat,&ydat,&zdat,&vdat,p1.x,p2.x,p1.y,p2.y,p1.z,p2.z);	}
	/// Fill the data by interpolated values of vdat parametrically depended on xdat,ydat,zdat for x,y,z in axis range of gr
	inline void Refill(mglBase *gr, const mglDataA &xdat, const mglDataA &vdat, long sl=-1, const char *opt="")
	{	mgl_data_refill_gr(gr,this,&xdat,0,0,&vdat,sl,opt);	}
	inline void Refill(mglBase *gr, const mglDataA &xdat, const mglDataA &ydat, const mglDataA &vdat, long sl=-1, const char *opt="")
	{	mgl_data_refill_gr(gr,this,&xdat,&ydat,0,&vdat,sl,opt);	}
	inline void Refill(mglBase *gr, const mglDataA &xdat, const mglDataA &ydat, const mglDataA &zdat, const mglDataA &vdat, const char *opt="")
	{	mgl_data_refill_gr(gr,this,&xdat,&ydat,&zdat,&vdat,-1,opt);	}
	/// Set the data by triangulated surface values assuming x,y,z in axis range of gr
	inline void Grid(mglBase *gr, const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *opt="")
	{	mgl_data_grid(gr,this,&x,&y,&z,opt);	}
	/// Set the data by triangulated surface values assuming x,y,z in range [p1, p2]
	inline void Grid(const mglDataA &xdat, const mglDataA &ydat, const mglDataA &vdat, mglPoint p1, mglPoint p2)
	{	mgl_data_grid_xy(this,&xdat,&ydat,&vdat,p1.x,p2.x,p1.y,p2.y);	}
	/// Put value to data element(s)
	inline void Put(mreal val, long i=-1, long j=-1, long k=-1)
	{	mgl_data_put_val(this,val,i,j,k);	}
	/// Put array to data element(s)
	inline void Put(const mglDataA &dat, long i=-1, long j=-1, long k=-1)
	{	mgl_data_put_dat(this,&dat,i,j,k);	}
	/// Set names for columns (slices)
	inline void SetColumnId(const char *ids)
	{	mgl_data_set_id(this,ids);	}
	/// Make new id
	inline void NewId()	{	id.clear();	}

	/// Read data from tab-separated text file with auto determining size
	inline bool Read(const char *fname)
	{	return mgl_data_read(this,fname); }
	/// Read data from text file with specifeid size
	inline bool Read(const char *fname,long mx,long my=1,long mz=1)
	{	return mgl_data_read_dim(this,fname,mx,my,mz);	}
	/// Save whole data array (for ns=-1) or only ns-th slice to text file
	inline void Save(const char *fname,long ns=-1) const
	{	mgl_data_save(this,fname,ns);	}
	/// Export data array (for ns=-1) or only ns-th slice to PNG file according color scheme
	inline void Export(const char *fname,const char *scheme,mreal v1=0,mreal v2=0,long ns=-1) const
	{	mgl_data_export(this,fname,scheme,v1,v2,ns);	}
	/// Import data array from PNG file according color scheme
	inline void Import(const char *fname,const char *scheme,mreal v1=0,mreal v2=1)
	{	mgl_data_import(this,fname,scheme,v1,v2);	}
	/// Read data from tab-separated text files with auto determining size which filenames are result of sprintf(fname,templ,t) where t=from:step:to
	inline bool ReadRange(const char *templ, double from, double to, double step=1, bool as_slice=false)
	{	return mgl_data_read_range(this,templ,from,to,step,as_slice);	}
	/// Read data from tab-separated text files with auto determining size which filenames are satisfied to template (like "t_*.dat")
	inline bool ReadAll(const char *templ, bool as_slice=false)
	{	return mgl_data_read_all(this, templ, as_slice);	}
	/// Read data from text file with size specified at beginning of the file
	inline bool ReadMat(const char *fname, long dim=2)
	{	return mgl_data_read_mat(this,fname,dim);	}
	/// Read data array from HDF file (parse HDF4 and HDF5 files)
	inline int ReadHDF(const char *fname,const char *data)
	{	return mgl_data_read_hdf(this,fname,data);	}
	/// Save data to HDF file
	inline void SaveHDF(const char *fname,const char *data,bool rewrite=false) const
	{	mgl_data_save_hdf(this,fname,data,rewrite);	}
	/// Put HDF data names into buf as '\t' separated.
	inline static int DatasHDF(const char *fname, char *buf, long size)
	{	return mgl_datas_hdf(fname,buf,size);	}

	/// Get column (or slice) of the data filled by formulas of named columns
	inline mglData Column(const char *eq) const
	{	return mglData(true,mgl_data_column(this,eq));	}
	/// Get momentum (1D-array) of data along direction 'dir'. String looks like "x1" for median in x-direction, "x2" for width in x-dir and so on.
	inline mglData Momentum(char dir, const char *how) const
	{	return mglData(true,mgl_data_momentum(this,dir,how));	}
	/// Get sub-array of the data with given fixed indexes
	inline mglData SubData(long xx,long yy=-1,long zz=-1) const
	{	return mglData(true,mgl_data_subdata(this,xx,yy,zz));	}
	inline mglData SubData(const mglDataA &xx, const mglDataA &yy, const mglDataA &zz) const
	{	return mglData(true,mgl_data_subdata_ext(this,&xx,&yy,&zz));	}
	/// Get trace of the data array
	inline mglData Trace() const
	{	return mglData(true,mgl_data_trace(this));	}
	/// Create n-th points distribution of this data values in range [v1, v2]
	inline mglData Hist(long n,mreal v1=0,mreal v2=1, long nsub=0) const
	{	return mglData(true,mgl_data_hist(this,n,v1,v2,nsub));	}
	/// Create n-th points distribution of this data values in range [v1, v2] with weight w
	inline mglData Hist(const mglDataA &w, long n,mreal v1=0,mreal v2=1, long nsub=0) const
	{	return mglData(true,mgl_data_hist_w(this,&w,n,v1,v2,nsub));	}
	/// Get array which is result of summation in given direction or directions
	inline mglData Sum(const char *dir) const
	{	return mglData(true,mgl_data_sum(this,dir));	}
	/// Get array which is result of maximal values in given direction or directions
	inline mglData Max(const char *dir) const
	{	return mglData(true,mgl_data_max_dir(this,dir));	}
	/// Get array which is result of minimal values in given direction or directions
	inline mglData Min(const char *dir) const
	{	return mglData(true,mgl_data_min_dir(this,dir));	}
	/// Get the data which is direct multiplication (like, d[i,j] = this[i]*a[j] and so on)
	inline mglData Combine(const mglDataA &dat) const
	{	return mglData(true,mgl_data_combine(this,&dat));	}
	/// Resize the data to new size of box [x1,x2]*[y1,y2]*[z1,z2]
	inline mglData Resize(long mx,long my=0,long mz=0, mreal x1=0,mreal x2=1, mreal y1=0,mreal y2=1, mreal z1=0,mreal z2=1) const
	{	return mglData(true,mgl_data_resize_box(this,mx,my,mz,x1,x2,y1,y2,z1,z2));	}
	/// Get array which values is result of interpolation this for coordinates from other arrays
	inline mglData Evaluate(const mglData &idat, bool norm=true) const
	{	return mglData(true,mgl_data_evaluate(this,&idat,0,0,norm));	}
	inline mglData Evaluate(const mglData &idat, const mglData &jdat, bool norm=true) const
	{	return mglData(true,mgl_data_evaluate(this,&idat,&jdat,0,norm));	}
	inline mglData Evaluate(const mglData &idat, const mglData &jdat, const mglData &kdat, bool norm=true) const
	{	return mglData(true,mgl_data_evaluate(this,&idat,&jdat,&kdat,norm));	}
	/// Find roots for set of nonlinear equations defined by textual formula
	inline mglData Roots(const char *func, char var='x') const
	{	return mglData(true,mgl_data_roots(func, this, var));	}
	/// Find correlation with another data arrays
	inline mglData Correl(const mglDataA &dat, const char *dir) const
	{	return mglData(true,mgl_data_correl(this,&dat,dir));	}
	/// Find auto correlation function
	inline mglData AutoCorrel(const char *dir) const
	{	return mglData(true,mgl_data_correl(this,this,dir));	}

	/// Cumulative summation the data in given direction or directions
	inline void CumSum(const char *dir)	{	mgl_data_cumsum(this,dir);	}
	/// Integrate (cumulative summation) the data in given direction or directions
	inline void Integral(const char *dir)	{	mgl_data_integral(this,dir);	}
	/// Differentiate the data in given direction or directions
	inline void Diff(const char *dir)	{	mgl_data_diff(this,dir);	}
	/// Differentiate the parametrically specified data along direction v1 with v2=const
	inline void Diff(const mglDataA &v1, const mglDataA &v2)
	{	mgl_data_diff_par(this,&v1,&v2,0);	}
	/// Differentiate the parametrically specified data along direction v1 with v2,v3=const
	inline void Diff(const mglDataA &v1, const mglDataA &v2, const mglDataA &v3)
	{	mgl_data_diff_par(this,&v1,&v2,&v3);	}
	/// Double-differentiate (like Laplace operator) the data in given direction
	inline void Diff2(const char *dir)	{	mgl_data_diff2(this,dir);	}

	/// Swap left and right part of the data in given direction (useful for Fourier spectrum)
	inline void Swap(const char *dir)		{	mgl_data_swap(this,dir);	}
	/// Roll data along direction dir by num slices
	inline void Roll(char dir, long num)	{	mgl_data_roll(this,dir,num);	}
	/// Mirror the data in given direction (useful for Fourier spectrum)
	inline void Mirror(const char *dir)		{	mgl_data_mirror(this,dir);	}
	/// Sort rows (or slices) by values of specified column
	inline void Sort(long idx, long idy=-1)	{	mgl_data_sort(this,idx,idy);	}

	/// Set as the data envelop
	inline void Envelop(char dir='x')
	{	mgl_data_envelop(this,dir);	}
	/// Remove phase jump
	inline void Sew(const char *dirs="xyz", mreal da=2*Pi)
	{	mgl_data_sew(this,dirs,da);	}
	/// Smooth the data on specified direction or directions
	inline void Smooth(const char *dirs="xyz",mreal delta=0)
	{	mgl_data_smooth(this,dirs,delta);	}
	/// Normalize the data to range [v1,v2]
	inline void Norm(mreal v1=0,mreal v2=1,bool sym=false,long dim=0)
	{	mgl_data_norm(this,v1,v2,sym,dim);	}
	/// Normalize the data to range [v1,v2] slice by slice
	inline void NormSl(mreal v1=0,mreal v2=1,char dir='z',bool keep_en=true,bool sym=false)
	{	mgl_data_norm_slice(this,v1,v2,dir,keep_en,sym);	}

	/// Apply Hankel transform
	inline void Hankel(const char *dir)	{	mgl_data_hankel(this,dir);	}
	/// Apply Sin-Fourier transform
	inline void SinFFT(const char *dir)	{	mgl_data_sinfft(this,dir);	}
	/// Apply Cos-Fourier transform
	inline void CosFFT(const char *dir)	{	mgl_data_cosfft(this,dir);	}
	/// Fill data by 'x'/'k' samples for Hankel ('h') or Fourier ('f') transform
	inline void FillSample(const char *how)
	{	mgl_data_fill_sample(this,how);	}

	/// Interpolate by cubic spline the data to given point x=[0...nx-1], y=[0...ny-1], z=[0...nz-1]
	inline mreal Spline(mreal x,mreal y=0,mreal z=0) const
	{	return mgl_data_spline(this, x,y,z);	}
	/// Interpolate by cubic spline the data to given point x,\a y,\a z which normalized in range [0, 1]
	inline mreal Spline1(mreal x,mreal y=0,mreal z=0) const
	{	return mgl_data_spline(this, x*(nx-1),y*(ny-1),z*(nz-1));	}
	/// Interpolate by linear function the data to given point x=[0...nx-1], y=[0...ny-1], z=[0...nz-1]
	inline mreal Linear(mreal x,mreal y=0,mreal z=0)	const
	{	return mgl_data_linear(this,x,y,z);	}
	/// Interpolate by line the data to given point x,\a y,\a z which normalized in range [0, 1]
	inline mreal Linear1(mreal x,mreal y=0,mreal z=0) const
	{	return mgl_data_linear(this,x*(nx-1),y*(ny-1),z*(nz-1));	}
	/// Return an approximated x-value (root) when dat(x) = val
	inline mreal Solve(mreal val, bool use_spline=true, long i0=0) const
	{	return mgl_data_solve_1d(this, val, use_spline, i0);		}
	/// Return an approximated value (root) when dat(x) = val
	inline mglData Solve(mreal val, char dir, bool norm=true) const
	{	return mglData(true,mgl_data_solve(this, val, dir, 0, norm));	}
	inline mglData Solve(mreal val, char dir, const mglData &i0, bool norm=true) const
	{	return mglData(true,mgl_data_solve(this, val, dir, &i0, norm));	}

	/// Interpolate by cubic spline the data and return its derivatives at given point x=[0...nx-1], y=[0...ny-1], z=[0...nz-1]
	inline mreal Spline(mglPoint &dif, mreal x,mreal y=0,mreal z=0) const
	{	return mgl_data_spline_ext(this, x,y,z, &(dif.x),&(dif.y), &(dif.z));	}
	/// Interpolate by cubic spline the data and return its derivatives at given point x,\a y,\a z which normalized in range [0, 1]
	inline mreal Spline1(mglPoint &dif, mreal x,mreal y=0,mreal z=0) const
	{	mreal res=mgl_data_spline_ext(this, x*(nx-1),y*(ny-1),z*(nz-1), &(dif.x),&(dif.y), &(dif.z));
		dif.x*=nx>1?nx-1:1;	dif.y*=ny>1?ny-1:1;	dif.z*=nz>1?nz-1:1;	return res;	}
	/// Interpolate by linear function the data and return its derivatives at given point x=[0...nx-1], y=[0...ny-1], z=[0...nz-1]
	inline mreal Linear(mglPoint &dif, mreal x,mreal y=0,mreal z=0)	const
	{	return mgl_data_linear_ext(this,x,y,z, &(dif.x),&(dif.y), &(dif.z));	}
	/// Interpolate by line the data and return its derivatives at given point x,\a y,\a z which normalized in range [0, 1]
	inline mreal Linear1(mglPoint &dif, mreal x,mreal y=0,mreal z=0) const
	{	mreal res=mgl_data_linear_ext(this,x*(nx-1),y*(ny-1),z*(nz-1), &(dif.x),&(dif.y), &(dif.z));
		dif.x*=nx>1?nx-1:1;	dif.y*=ny>1?ny-1:1;	dif.z*=nz>1?nz-1:1;	return res;	}

	/// Get information about the data (sizes and momentum) to string
	inline const char *PrintInfo() const	{	return mgl_data_info(this);	}
	/// Print information about the data (sizes and momentum) to FILE (for example, stdout)
	inline void PrintInfo(FILE *fp) const
	{	if(fp)	{	fprintf(fp,"%s",mgl_data_info(this));	fflush(fp);	}	}
	/// Get maximal value of the data
	inline mreal Maximal() const	{	return mgl_data_max(this);	}
	/// Get minimal value of the data
	inline mreal Minimal() const	{	return mgl_data_min(this);	}
	/// Get maximal value of the data which is less than 0
	inline mreal MaximalNeg() const	{	return mgl_data_neg_max(this);	}
	/// Get minimal value of the data which is larger than 0
	inline mreal MinimalPos() const	{	return mgl_data_pos_min(this);	}
	/// Get maximal value of the data and its position
	inline mreal Maximal(long &i,long &j,long &k) const
	{	return mgl_data_max_int(this,&i,&j,&k);	}
	/// Get minimal value of the data and its position
	inline mreal Minimal(long &i,long &j,long &k) const
	{	return mgl_data_min_int(this,&i,&j,&k);	}
	/// Get maximal value of the data and its approximated position
	inline mreal Maximal(mreal &x,mreal &y,mreal &z) const
	{	return mgl_data_max_real(this,&x,&y,&z);	}
	/// Get minimal value of the data and its approximated position
	inline mreal Minimal(mreal &x,mreal &y,mreal &z) const
	{	return mgl_data_min_real(this,&x,&y,&z);	}
	/// Get "energy" and find first (median) and second (width) momenta of data
	inline mreal Momentum(char dir,mreal &m,mreal &w) const
	{	return mgl_data_momentum_val(this,dir,&m,&w,0,0);	}
	/// Get "energy and find 4 momenta of data: median, width, skewness, kurtosis
	inline mreal Momentum(char dir,mreal &m,mreal &w,mreal &s,mreal &k) const
	{	return mgl_data_momentum_val(this,dir,&m,&w,&s,&k);	}
	/// Find position (after specified in i,j,k) of first nonzero value of formula
	inline mreal Find(const char *cond, long &i, long &j, long &k) const
	{	return mgl_data_first(this,cond,&i,&j,&k);	}
	/// Find position (before specified in i,j,k) of last nonzero value of formula
	inline mreal Last(const char *cond, long &i, long &j, long &k) const
	{	return mgl_data_last(this,cond,&i,&j,&k);	}
	/// Find position of first in direction 'dir' nonzero value of formula
	inline long Find(const char *cond, char dir, long i=0, long j=0, long k=0) const
	{	return mgl_data_find(this,cond,dir,i,j,k);	}
	/// Find if any nonzero value of formula
	inline bool FindAny(const char *cond) const
	{	return mgl_data_find_any(this,cond);	}

	/// Copy data from other mglData variable
	inline mglData &operator=(const mglData &d)
	{	if(this!=&d)	Set(d.a,d.nx,d.ny,d.nz);	return *this;	}
	inline mreal operator=(mreal val)
	{	for(long i=0;i<nx*ny*nz;i++)	a[i]=val;	return val;	}
	/// Multiply the data by other one for each element
	inline void operator*=(const mglDataA &d)	{	mgl_data_mul_dat(this,&d);	}
	/// Divide the data by other one for each element
	inline void operator/=(const mglDataA &d)	{	mgl_data_div_dat(this,&d);	}
	/// Add the other data
	inline void operator+=(const mglDataA &d)	{	mgl_data_add_dat(this,&d);	}
	/// Subtract the other data
	inline void operator-=(const mglDataA &d)	{	mgl_data_sub_dat(this,&d);	}
	/// Multiply each element by the number
	inline void operator*=(mreal d)		{	mgl_data_mul_num(this,d);	}
	/// Divide each element by the number
	inline void operator/=(mreal d)		{	mgl_data_div_num(this,d);	}
	/// Add the number
	inline void operator+=(mreal d)		{	mgl_data_add_num(this,d);	}
	/// Subtract the number
	inline void operator-=(mreal d)		{	mgl_data_sub_num(this,d);	}
#ifndef SWIG
	/// Direct access to the data cell
	inline mreal &operator[](long i)	{	return a[i];	}
	// NOTE see 13.10 for operator(), operator[] -- m.b. I should add it ???
#endif
#if MGL_NO_DATA_A
	inline long GetNN() const {	return nx*ny*nz;	}
#endif
	/// Get the value in given cell of the data without border checking
	inline mreal v(long i,long j=0,long k=0) const
#ifndef DEBUG
	{	return a[i+nx*(j+ny*k)];	}
#else
	{	if(i<0 || j<0 || k<0 || i>=nx || j>=ny || k>=nz)	printf("Wrong index in mglData");
		return a[i+nx*(j+ny*k)];	}
#endif
	inline mreal vthr(long i) const {	return a[i];	}
	// add for speeding up !!!
	inline mreal dvx(long i,long j=0,long k=0) const
	{   register long i0=i+nx*(j+ny*k);
		return i>0? (i<nx-1? (a[i0+1]-a[i0-1])/2:a[i0]-a[i0-1]) : a[i0+1]-a[i0];	}
	inline mreal dvy(long i,long j=0,long k=0) const
	{   register long i0=i+nx*(j+ny*k);
		return j>0? (j<ny-1? (a[i0+nx]-a[i0-nx])/2:a[i0]-a[i0-nx]) : a[i0+nx]-a[i0];}
	inline mreal dvz(long i,long j=0,long k=0) const
	{   register long i0=i+nx*(j+ny*k), n=nx*ny;
		return k>0? (k<nz-1? (a[i0+n]-a[i0-n])/2:a[i0]-a[i0-n]) : a[i0+n]-a[i0];	}
};
//-----------------------------------------------------------------------------
#ifndef SWIG
inline mglData operator*(const mglDataA &b, const mglDataA &d)
{	mglData a(&b);	a*=d;	return a;	}
inline mglData operator*(mreal b, const mglDataA &d)
{	mglData a(&d);	a*=b;	return a;	}
inline mglData operator*(const mglDataA &d, mreal b)
{	mglData a(&d);	a*=b;	return a;	}
inline mglData operator-(const mglDataA &b, const mglDataA &d)
{	mglData a(&b);	a-=d;	return a;	}
inline mglData operator-(mreal b, const mglDataA &d)
{	mglData a(&d);	a-=b;	return a;	}
inline mglData operator-(const mglDataA &d, mreal b)
{	mglData a(&d);	a-=b;	return a;	}
inline mglData operator+(const mglDataA &b, const mglDataA &d)
{	mglData a(&b);	a+=d;	return a;	}
inline mglData operator+(mreal b, const mglDataA &d)
{	mglData a(&d);	a+=b;	return a;	}
inline mglData operator+(const mglDataA &d, mreal b)
{	mglData a(&d);	a+=b;	return a;	}
inline mglData operator/(const mglDataA &b, const mglDataA &d)
{	mglData a(&b);	a/=d;	return a;	}
inline mglData operator/(const mglDataA &d, mreal b)
{	mglData a(&d);	a/=b;	return a;	}
inline bool operator==(const mglData &b, const mglData &d)
{	if(b.nx!=d.nx || b.ny!=d.ny || b.ny!=d.ny)	return false;
	return !memcmp(b.a,d.a,b.nx*b.ny*b.nz*sizeof(mreal));	}
inline bool operator<(const mglDataA &b, const mglDataA &d)
{	return b.Maximal()<d.Maximal();	}
inline bool operator>(const mglDataA &b, const mglDataA &d)
{	return b.Minimal()>d.Minimal();	}
#endif
//-----------------------------------------------------------------------------
#ifndef SWIG
mreal mglLinear(const mreal *a, long nx, long ny, long nz, mreal x, mreal y, mreal z);
mreal mglSpline3(const mreal *a, long nx, long ny, long nz, mreal x, mreal y, mreal z,mreal *dx=0, mreal *dy=0, mreal *dz=0);
#endif
//-----------------------------------------------------------------------------
/// Integral data transformation (like Fourier 'f' or 'i', Hankel 'h' or None 'n') for amplitude and phase
inline mglData mglTransformA(const mglDataA &am, const mglDataA &ph, const char *tr)
{	return mglData(true,mgl_transform_a(&am,&ph,tr));	}
/// Integral data transformation (like Fourier 'f' or 'i', Hankel 'h' or None 'n') for real and imaginary parts
inline mglData mglTransform(const mglDataA &re, const mglDataA &im, const char *tr)
{	return mglData(true,mgl_transform(&re,&im,tr));	}
/// Apply Fourier transform for the data and save result into it
inline void mglFourier(mglData &re, mglData &im, const char *dir)
{	mgl_data_fourier(&re,&im,dir);	}
/// Short time Fourier analysis for real and imaginary parts. Output is amplitude of partial Fourier (result will have size {dn, floor(nx/dn), ny} for dir='x'
inline mglData mglSTFA(const mglDataA &re, const mglDataA &im, long dn, char dir='x')
{	return mglData(true, mgl_data_stfa(&re,&im,dn,dir));	}
//-----------------------------------------------------------------------------
/// Saves result of PDE solving (|u|^2) for "Hamiltonian" ham with initial conditions ini
inline mglData mglPDE(mglBase *gr, const char *ham, const mglDataA &ini_re, const mglDataA &ini_im, mreal dz=0.1, mreal k0=100,const char *opt="")
{	return mglData(true, mgl_pde_solve(gr,ham, &ini_re, &ini_im, dz, k0,opt));	}
/// Saves result of PDE solving for "Hamiltonian" ham with initial conditions ini along a curve ray (must have nx>=7 - x,y,z,px,py,pz,tau or nx=5 - x,y,px,py,tau)
inline mglData mglQO2d(const char *ham, const mglDataA &ini_re, const mglDataA &ini_im, const mglDataA &ray, mreal r=1, mreal k0=100)
{	return mglData(true, mgl_qo2d_solve(ham, &ini_re, &ini_im, &ray, r, k0, 0, 0));	}
inline mglData mglQO2d(const char *ham, const mglDataA &ini_re, const mglDataA &ini_im, const mglDataA &ray, mglData &xx, mglData &yy, mreal r=1, mreal k0=100)
{	return mglData(true, mgl_qo2d_solve(ham, &ini_re, &ini_im, &ray, r, k0, &xx, &yy));	}
/// Saves result of PDE solving for "Hamiltonian" ham with initial conditions ini along a curve ray (must have nx>=7 - x,y,z,px,py,pz,tau or nx=5 - x,y,px,py,tau)
inline mglData mglQO3d(const char *ham, const mglDataA &ini_re, const mglDataA &ini_im, const mglDataA &ray, mreal r=1, mreal k0=100)
{	return mglData(true, mgl_qo3d_solve(ham, &ini_re, &ini_im, &ray, r, k0, 0, 0, 0));	}
inline mglData mglQO3d(const char *ham, const mglDataA &ini_re, const mglDataA &ini_im, const mglDataA &ray, mglData &xx, mglData &yy, mglData &zz, mreal r=1, mreal k0=100)
{	return mglData(true, mgl_qo3d_solve(ham, &ini_re, &ini_im, &ray, r, k0, &xx, &yy, &zz));	}
/// Finds ray with starting point r0, p0 (and prepares ray data for mglQO2d)
inline mglData mglRay(const char *ham, mglPoint r0, mglPoint p0, mreal dt=0.1, mreal tmax=10)
{	return mglData(true, mgl_ray_trace(ham, r0.x, r0.y, r0.z, p0.x, p0.y, p0.z, dt, tmax));	}
/// Calculate Jacobian determinant for D{x(u,v), y(u,v)} = dx/du*dy/dv-dx/dv*dy/du
inline mglData mglJacobian(const mglDataA &x, const mglDataA &y)
{	return mglData(true, mgl_jacobian_2d(&x, &y));	}
/// Calculate Jacobian determinant for D{x(u,v,w), y(u,v,w), z(u,v,w)}
inline mglData mglJacobian(const mglDataA &x, const mglDataA &y, const mglDataA &z)
{	return mglData(true, mgl_jacobian_3d(&x, &y, &z));	}
/// Do something like Delone triangulation
inline mglData mglTriangulation(const mglDataA &x, const mglDataA &y, const mglDataA &z)
{	return mglData(true,mgl_triangulation_3d(&x,&y,&z));	}
inline mglData mglTriangulation(const mglDataA &x, const mglDataA &y)
{	return mglData(true,mgl_triangulation_2d(&x,&y));	}
//-----------------------------------------------------------------------------
/// Wrapper class expression evaluating
class MGL_EXPORT mglExpr
{
	HMEX ex;
public:
	mglExpr(const char *expr)		{	ex = mgl_create_expr(expr);	}
	~mglExpr()	{	mgl_delete_expr(ex);	}
	/// Return value of expression for given x,y,z variables
	inline double Eval(double x, double y=0, double z=0)
	{	return mgl_expr_eval(ex,x,y,z);	}
	/// Return value of expression differentiation over variable dir for given x,y,z variables
	inline double Diff(char dir, double x, double y=0, double z=0)
	{	return mgl_expr_diff(ex,dir, x,y,z);	}
#ifndef SWIG
	/// Return value of expression for given variables
	inline double Eval(mreal var[26])
	{	return mgl_expr_eval_v(ex,var);	}
	/// Return value of expression differentiation over variable dir for given variables
	inline double Diff(char dir, mreal var[26])
	{	return mgl_expr_diff_v(ex,dir, var);	}
#endif
};
//-----------------------------------------------------------------------------
#ifndef SWIG
/// Structure for handling named mglData (used by mglParse class).
class MGL_EXPORT mglVar : public mglData
{
public:
	std::wstring s;	///< Data name
	void *o; 		///< Pointer to external object
	mglVar *next;	///< Pointer to next instance in list
	mglVar *prev;	///< Pointer to previous instance in list
	bool temp;		///< This is temporary variable
	void (*func)(void *);	///< Callback function for destroying

	mglVar(std::wstring name=L""):mglData()
	{	o=0;	next=prev=0;	func=0;	temp=false;	s=name;	}
	mglVar(mglVar **head, std::wstring name=L""):mglData()
	{	o=0;	next=*head;	prev=0;	*head=this;	func=0;	temp=false;	s=name;	}
	mglVar(mglVar **head, const mglData &dat, std::wstring name):mglData(dat)
	{	o=0;	next=*head;	prev=0;	*head=this;	func=0;	temp=false;	s=name;	}
	mglVar(mglVar **head, HCDT dat, std::wstring name):mglData(dat)
	{	o=0;	next=*head;	prev=0;	*head=this;	func=0;	temp=false;	s=name;	}
	mglVar(mglVar *v, std::wstring name, bool link=true):mglData()	// NOTE: use carefully due to Link()!
	{	if(!v)	throw mglWarnZero;
		if(link)	Link(*v);	else	Set(*v);
		o=0;	temp=false;	s=name;	func = v->func;
		prev = v;	next = v->next;	v->next = this;
		if(next)	next->prev = this;	}
	virtual ~mglVar()
	{
		if(func)	func(o);
		if(prev)	prev->next = next;
		if(next)	next->prev = prev;
	}
	/// Make copy which link on the same data but have different name. NOTE: use carefully due to Link()!
	inline void Duplicate(std::wstring name)
	{	mglVar *v=new mglVar(name);	v->Link(*this);	v->MoveAfter(this);	}
	/// Move variable after var and copy func from var (if func is 0)
	inline void MoveAfter(mglVar *var)
	{
		if(prev)	prev->next = next;
		if(next)	next->prev = prev;
		prev = next = 0;
		if(var)
		{
			prev = var;	next = var->next;
			var->next = this;
			if(func==0)	func = var->func;
		}
		if(next)	next->prev = this;
	}
};
#endif
//-----------------------------------------------------------------------------
#endif
#endif