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vecteur.cc
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vecteur.cc
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// -*- mode:C++ ; compile-command: "g++ -I. -I.. -I../include -g -c vecteur.cc -fno-strict-aliasing -DGIAC_GENERIC_CONSTANTS -DHAVE_CONFIG_H -DIN_GIAC" -*-
#include "giacPCH.h"
/*
* Copyright (C) 2000,14 B. Parisse, Institut Fourier, 38402 St Martin d'Heres
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
using namespace std;
#include <cmath>
#include <stdexcept>
#include <map>
#include <iostream>
#if defined HAVE_SSTREAM || defined FXCG
#include <sstream>
#else
#include <strstream>
#endif
#if !defined GIAC_HAS_STO_38 && !defined NSPIRE && !defined FXCG
#include <fstream>
#endif
#include "gen.h"
#include "vecteur.h"
#include "modpoly.h"
#include "unary.h"
#include "symbolic.h"
#include "usual.h"
#include "sym2poly.h"
#include "solve.h"
#include "prog.h"
#include "subst.h"
#include "permu.h"
#include "plot.h"
#include "misc.h"
#include "ti89.h"
#include "csturm.h"
#include "sparse.h"
#include "modfactor.h"
#include "quater.h"
#include "giacintl.h"
#include "signalprocessing.h"
#ifdef HAVE_LIBGSL
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_eigen.h>
#include <gsl/gsl_poly.h>
#endif
// vector class version 1 by Agner Fog https://github.com/vectorclass
// this might be faster for CPU with AVX512DQ instruction set
// (fast multiplication of Vec4q)
#ifdef HAVE_VCL1_VECTORCLASS_H
#include <vcl1/vectorclass.h>
#endif
// Apple has the Accelerate framework for lapack if you did not install Atlas/lapack
// (link with -framewrok Accelerate)
// it is not used by default because the Accelerate version is slower
// than the current Atlas, at least on OSX.6, and is also slower than giac built-in
#if !defined(APPLE_SMART) && !defined(DONT_USE_LIBLAPLACK)
#if defined __APPLE__ && !defined(HAVE_LIBLAPACK) && !defined(USE_GMP_REPLACEMENTS)
#define HAVE_LIBLAPACK
#endif
// for pocketcas compat.
#if defined(HAVE_LIBCLAPACK) && !defined(HAVE_LIBLAPACK)
#define HAVE_LIBLAPACK
#endif
#endif // APPLE_SMART
// Note that Atlas is slower than built-in for real matrices diago for n < about 1000
// and complex matrices diago for n<300
// the global variable CALL_LAPACK is set to 1111 by default
// can be modified from icas/xcas using lapack_limit() or shell variable GIAC_LAPACK
// #undef HAVE_LIBLAPACK
#ifdef HAVE_LIBLAPACK
#include <f2c.h>
#include <clapack.h>
#ifdef POCKETCAS
#include "f2c.h"
#include "clapack.h"
#include <Accelerate/Accelerate.h>
#endif // POCKETCAS
#undef abs
#undef min
#endif
#if defined __i386__ && !defined PIC && !defined __APPLE__ && !defined _I386_
//#define _I386_
// commented because it will fail with -O2 optimizations under gcc >= 4.3
// on Ubuntu 11.04 in Mac VirtualBox
#endif
#ifdef USTL
namespace ustl {
inline bool operator > (const giac::index_t & a,const giac::index_t & b){
if (a.size()!=b.size())
return a.size()>b.size();
return !giac::all_inf_equal(a,b);
}
inline bool operator < (const giac::index_t & a,const giac::index_t & b){
if (a.size()!=b.size())
return a.size()<b.size();
return !giac::all_sup_equal(a,b);
}
}
#endif
#ifndef NO_NAMESPACE_GIAC
namespace giac {
#endif // ndef NO_NAMESPACE_GIAC
unsigned nbits(const gen & g){
if (g.type==_INT_)
return sizeinbase2(g.val>0?g.val:-g.val);
if (g.type==_ZINT)
return mpz_sizeinbase(*g._ZINTptr,2);
gen G=_ceil(g,context0);
if (is_integer(G))
return nbits(G);
return RAND_MAX;
}
#if defined(GIAC_HAS_STO_38) && defined(VISUALC)
static const int rand_max=2147483647;
#else
static const int rand_max=RAND_MAX;
#endif
#ifdef _I386_
// a->a+b*c mod m
inline void mod(int & a,int b,int c,int m){
if (c){
asm volatile("testl %%ebx,%%ebx\n\t" /* sign bit=1 if negative */
"jns .Lok%=\n\t"
"addl %%edi,%%ebx\n" /* a+=m*/
".Lok%=:\t"
"imull %%ecx; \n\t" /* b*c in edx:eax */
"addl %%ebx,%%eax; \n\t" /* b*c+a */
"adcl $0x0,%%edx; \n\t" /* b*c+a carry */
"idivl %%edi; \n\t"
:"=d"(a)
:"a"(b),"b"(a),"c"(c),"D"(m)
);
}
}
// a->a+b*c mod m
inline int smod(int a,int b,int c,int m){
if (c){
if (a<0) a+=m;
asm volatile("imull %%ecx; \n\t" /* b*c in edx:eax */
"addl %%ebx,%%eax; \n\t" /* b*c+a */
"adcl $0x0,%%edx; \n\t" /* b*c+a carry */
"idivl %%edi; \n\t"
:"=d"(a)
:"a"(b),"b"(a),"c"(c),"D"(m)
);
}
return a;
}
#else
// a->a+b*c mod m
inline void mod(int & a,int b,int c,int m){
a = (a + longlong(b)*c)%m;
}
// a->a+b*c mod m
inline int smod(int a,int b,int c,int m){
return (a + longlong(b)*c)%m;
}
#endif
vecteur makevecteur(const gen & a,const gen & b){
vecteur v(2);
v[0]=a;
v[1]=b;
return v;
}
vecteur makevecteur(const gen & a,const gen & b,const gen & c){
vecteur v(3);
v[0]=a;
v[1]=b;
v[2]=c;
return v;
}
vecteur makevecteur(const gen & a){
return vecteur(1,a);
}
vecteur makevecteur(const gen & a,const gen & b,const gen & c,const gen & d){
vecteur v(4);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
return v;
}
vecteur makevecteur(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e){
vecteur v(5);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
v[4]=e;
return v;
}
vecteur makevecteur(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f){
vecteur v(6);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
v[4]=e;
v[5]=f;
return v;
}
vecteur makevecteur(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f,const gen & g){
vecteur v(7);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
v[4]=e;
v[5]=f;
v[6]=g;
return v;
}
vecteur makevecteur(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f,const gen & g,const gen & h){
vecteur v(8);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
v[4]=e;
v[5]=f;
v[6]=g;
v[7]=h;
return v;
}
vecteur makevecteur(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f,const gen & g,const gen & h,const gen & i){
vecteur v(9);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
v[4]=e;
v[5]=f;
v[6]=g;
v[7]=h;
v[8]=i;
return v;
}
vecteur makevecteur(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f,const gen & g,const gen & h,const gen & i,const gen &j){
vecteur v(10);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
v[4]=e;
v[5]=f;
v[6]=g;
v[7]=h;
v[8]=i;
v[9]=j;
return v;
}
vecteur makevecteur(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f,const gen & g,const gen & h,const gen & i,const gen &j,const gen & k){
vecteur v(11);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
v[4]=e;
v[5]=f;
v[6]=g;
v[7]=h;
v[8]=i;
v[9]=j;
v[10]=k;
return v;
}
vecteur makevecteur(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f,const gen & g,const gen & h,const gen & i,const gen &j,const gen & k,const gen & l){
vecteur v(12);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
v[4]=e;
v[5]=f;
v[6]=g;
v[7]=h;
v[8]=i;
v[9]=j;
v[10]=k;
v[11]=l;
return v;
}
vecteur makevecteur(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f,const gen & g,const gen & h,const gen & i,const gen &j,const gen & k,const gen & l,const gen & m){
vecteur v(13);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
v[4]=e;
v[5]=f;
v[6]=g;
v[7]=h;
v[8]=i;
v[9]=j;
v[10]=k;
v[11]=l;
v[12]=m;
return v;
}
vecteur makevecteur(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f,const gen & g,const gen & h,const gen & i,const gen &j,const gen & k,const gen & l,const gen & m,const gen& n){
vecteur v(14);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
v[4]=e;
v[5]=f;
v[6]=g;
v[7]=h;
v[8]=i;
v[9]=j;
v[10]=k;
v[11]=l;
v[12]=m;
v[13]=n;
return v;
}
gen makesequence(const gen & a){
return gen(vecteur(1,a),_SEQ__VECT);
}
gen makesequence(const gen & a,const gen & b){
vecteur v(2);
v[0]=a;
v[1]=b;
return gen(v,_SEQ__VECT);
}
gen makesequence(const gen & a,const gen & b,const gen & c){
vecteur v(3);
v[0]=a;
v[1]=b;
v[2]=c;
return gen(v,_SEQ__VECT);
}
gen makesequence(const gen & a,const gen & b,const gen & c,const gen & d){
vecteur v(4);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
return gen(v,_SEQ__VECT);
}
gen makesequence(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e){
vecteur v(5);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
v[4]=e;
return gen(v,_SEQ__VECT);
}
gen makesequence(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f){
vecteur v(6);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
v[4]=e;
v[5]=f;
return gen(v,_SEQ__VECT);
}
gen makesequence(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f,const gen & g){
vecteur v(7);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
v[4]=e;
v[5]=f;
v[6]=g;
return gen(v,_SEQ__VECT);
}
gen makesequence(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f,const gen & g,const gen & h){
vecteur v(8);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
v[4]=e;
v[5]=f;
v[6]=g;
v[7]=h;
return gen(v,_SEQ__VECT);
}
gen makesequence(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f,const gen & g,const gen & h,const gen & i){
vecteur v(9);
v[0]=a;
v[1]=b;
v[2]=c;
v[3]=d;
v[4]=e;
v[5]=f;
v[6]=g;
v[7]=h;
v[8]=i;
return gen(v,_SEQ__VECT);
}
ref_vecteur * makenewvecteur(const gen & a){
return new_ref_vecteur(vecteur(1,a));
}
ref_vecteur * makenewvecteur(const gen & a,const gen & b){
ref_vecteur *vptr=new_ref_vecteur(0);
vptr->v.reserve(2);
vptr->v.push_back(a);
vptr->v.push_back(b);
return vptr;
}
ref_vecteur * makenewvecteur(const gen & a,const gen & b,const gen & c){
ref_vecteur * vptr=new_ref_vecteur(0);
vptr->v.reserve(3);
vptr->v.push_back(a);
vptr->v.push_back(b);
vptr->v.push_back(c);
return vptr;
}
ref_vecteur * makenewvecteur(const gen & a,const gen & b,const gen & c,const gen & d){
ref_vecteur * vptr=new_ref_vecteur(0);
vptr->v.reserve(4);
vptr->v.push_back(a);
vptr->v.push_back(b);
vptr->v.push_back(c);
vptr->v.push_back(d);
return vptr;
}
ref_vecteur * makenewvecteur(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e){
ref_vecteur * vptr=new_ref_vecteur(0);
vptr->v.reserve(5);
vptr->v.push_back(a);
vptr->v.push_back(b);
vptr->v.push_back(c);
vptr->v.push_back(d);
vptr->v.push_back(e);
return vptr;
}
ref_vecteur * makenewvecteur(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f){
ref_vecteur * vptr=new_ref_vecteur(0);
vptr->v.reserve(6);
vptr->v.push_back(a);
vptr->v.push_back(b);
vptr->v.push_back(c);
vptr->v.push_back(d);
vptr->v.push_back(e);
vptr->v.push_back(f);
return vptr;
}
ref_vecteur * makenewvecteur(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f,const gen & g){
ref_vecteur * vptr=new_ref_vecteur(0);
vptr->v.reserve(7);
vptr->v.push_back(a);
vptr->v.push_back(b);
vptr->v.push_back(c);
vptr->v.push_back(d);
vptr->v.push_back(e);
vptr->v.push_back(f);
vptr->v.push_back(g);
return vptr;
}
ref_vecteur * makenewvecteur(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f,const gen & g,const gen & h){
ref_vecteur * vptr=new_ref_vecteur(0);
vptr->v.reserve(8);
vptr->v.push_back(a);
vptr->v.push_back(b);
vptr->v.push_back(c);
vptr->v.push_back(d);
vptr->v.push_back(e);
vptr->v.push_back(f);
vptr->v.push_back(g);
vptr->v.push_back(h);
return vptr;
}
ref_vecteur * makenewvecteur(const gen & a,const gen & b,const gen & c,const gen & d,const gen & e,const gen & f,const gen & g,const gen & h,const gen & i){
ref_vecteur * vptr=new_ref_vecteur(0);
vptr->v.reserve(9);
vptr->v.push_back(a);
vptr->v.push_back(b);
vptr->v.push_back(c);
vptr->v.push_back(d);
vptr->v.push_back(e);
vptr->v.push_back(f);
vptr->v.push_back(g);
vptr->v.push_back(h);
vptr->v.push_back(i);
return vptr;
}
// make a matrix with free rows
// (i.e. it is possible to modify the answer in place)
matrice makefreematrice(const matrice & m){
matrice res(m);
int s=int(m.size());
for (int i=0;i<s;++i){
if (m[i].type==_VECT){
res[i]=makefreematrice(*m[i]._VECTptr);
}
}
return res;
}
void transpose_double(const matrix_double & a,int r0,int r1,int c0,int c1,matrix_double & at){
int L=int(a.size()),C=int(a.front().size());
if (r0<0) r0=0;
if (r1<=r0)
r1=L;
if (c1<0) c1=0;
if (c1<=c0)
c1=C;
if (r1>L) r1=L;
if (c1>C) c1=C;
L=r1-r0; C=c1-c0;
at.resize(C);
for (int i=0;i<C;++i)
at[i].resize(L);
for (int i=0;i<L;++i){
const vector<giac_double> & ai=a[r0+i];
for (int j=0;j<C;++j){
at[j][i]=ai[c0+j];
}
}
}
// square matrix inplace transpose
void transpose_double(matrix_double &P){
int Ps=int(P.size());
for (int i=0;i<Ps;++i){
for (int j=0;j<i;++j){
giac_double t=P[i][j];
P[i][j]=P[j][i];
P[j][i]=t;
}
}
}
int alphaposcell(const string & s,int & r){
int ss=int(s.size());
r=0;
int i=0;
for (;i<ss;++i){
if ( (s[i]>='A') && (s[i]<='Z') )
r=r*26+(s[i]-'A')+1;
else {
if ( (s[i]>='a') && (s[i]<='q') )
r=r*26+(s[i]-'a')+1;
else
break;
}
}
--r;
return i;
}
bool iscell(const gen & g,int & r,int & c,GIAC_CONTEXT){
if (g.type!=_IDNT)
return false;
const string & s=g._IDNTptr->name();
int ss=int(s.size());
if (ss<2)
return false;
int i=alphaposcell(s,r);
if (!i || (i==ss) )
return false;
c=0;
for (;i<ss;++i){
if ( (s[i]>='0') && (s[i]<='9') )
c=c*10+(s[i]-'0');
else
break;
}
if (array_start(contextptr))
--c;
return (i==ss);
}
// find all identifiers in g, check if they are of the form
// Alpha_number, replace them by spread(i,j) if this is the case
gen spread_convert(const gen & g,int g_row,int g_col,GIAC_CONTEXT){
// relative cell
vecteur l(gen2vecteur(_lname(g,contextptr)));
const_iterateur it=l.begin(),itend=l.end();
vecteur sub_in,sub_out;
int r,c;
for (;it!=itend;++it){
if (iscell(*it,c,r,contextptr)){
sub_in.push_back(*it);
sub_out.push_back(symbolic(at_cell,makevecteur(makevecteur(r-g_row),makevecteur(c-g_col))));
}
}
// absolute cell
l=lop(g,at_dollar);
itend=l.end();
for (it=l.begin();it!=itend;++it){
gen & f=it->_SYMBptr->feuille;
// CERR << "absolute cell "<< f << '\n';
if ( (f.type!=_VECT) ){
if (iscell(f,c,r,contextptr)){
sub_in.push_back(*it);
sub_out.push_back(symbolic(at_cell,makevecteur(makevecteur(r-g_row),c)));
}
continue;
}
vecteur & v=*f._VECTptr;
if (v.size()==2){
gen & a=v.front();
gen & b=v.back();
// CERR << "absolute cell "<< a << " " << b <<'\n';
if (b.type!=_INT_)
continue;
if (array_start(contextptr))
r=b.val-1;
else
r=b.val;
if (a.type==_IDNT){
const string & chaine=a._IDNTptr->name();
int i=alphaposcell(chaine,c);
if (i==signed(chaine.size())){
sub_in.push_back(*it);
sub_out.push_back(symbolic(at_cell,makevecteur(r,makevecteur(c-g_col))));
}
continue;
}
if ( (a.type==_SYMB) && (a._SYMBptr->sommet==at_dollar) && (a._SYMBptr->feuille.type==_IDNT) ){
const string & chaine = a._SYMBptr->feuille._IDNTptr->name();
int i=alphaposcell(chaine,c);
if (i==signed(chaine.size())){
sub_in.push_back(*it);
sub_out.push_back(symbolic(at_cell,makevecteur(r,c)));
}
}
}
}
if (sub_in.empty())
return g;
gen tmp(quotesubst(g,sub_in,sub_out,contextptr));
tmp.subtype=_SPREAD__SYMB;
return tmp;
}
string printcell(const vecteur & v,GIAC_CONTEXT){
// CERR << "printcell" << printcell_current_row << " " << printcell_current_col << " " << v << '\n';
string debut,tmp,fin;
int i;
// Note: in popular spreadsheet, the column index comes before the row
// Therefore we translate v.back before v.front
if (v.back().type==_INT_){
i=v.back().val;
debut="$";
}
else
i=v.back()._VECTptr->front().val+printcell_current_col(contextptr);
if (i<0)
return print_INT_(i);
for(int j=0;;++j){
tmp=char('A'+i%26-(j!=0))+tmp;
i=i/26;
if (!i)
break;
}
debut=debut+tmp;
if (v.front().type==_INT_){
i=v.front().val;
debut=debut+"$";
}
else
i=v.front()._VECTptr->front().val+printcell_current_row(contextptr);
if (array_start(contextptr))
++i;
if (i<0)
return debut+print_INT_(i);
for (;;){
fin=char('0'+i%10)+fin;
i=i/10;
if (!i)
break;
}
return debut+fin;
}
string printascell(const gen & feuille,const char * sommetstr,GIAC_CONTEXT){
if ( (feuille.type!=_VECT) || (feuille._VECTptr->size()!=2) )
return sommetstr+("("+feuille.print(contextptr)+")");
return printcell(*feuille._VECTptr,contextptr);
}
gen _cell(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if ( (args.type!=_VECT) || (args._VECTptr->size()!=2) )
return gensizeerr(contextptr);
return symbolic(at_cell,args);
}
static const char _cell_s []="cell";
static define_unary_function_eval2 (__cell,&_cell,_cell_s,&printascell);
define_unary_function_ptr5( at_cell ,alias_at_cell,&__cell,0,true);
static void lcell(const gen & g,vecteur & res){
if (g.type==_VECT){
if (g.subtype==_CELL__VECT){
if (res.empty())
res=*g._VECTptr;
else { // assumes g._VECTptr has much more elements than res
vecteur tmp=res;
res=*g._VECTptr;
const_iterateur it=tmp.begin(),itend=tmp.end();
for (;it!=itend;++it){
if (!equalposcomp(res,*it))
res.push_back(*it);
}
}
}
else {
const_iterateur it=g._VECTptr->begin(),itend=g._VECTptr->end();
for (;it!=itend;++it)
lcell(*it,res);
}
}
if (g.type==_SYMB){
if (g._SYMBptr->sommet==at_cell || g._SYMBptr->sommet==at_deuxpoints){
if (!equalposcomp(res,g))
res.push_back(g);
}
else
lcell(g._SYMBptr->feuille,res);
}
}
vecteur lcell(const gen & g){
vecteur res;
lcell(g,res);
return res;
}
// given g=cell() or its argument at row i, column j
// return 0 if not a cell, 1 if a cell, then compute r and c s.t. g refers to (r,c),
// return 2 if g is e.g. A1:B4 compute ref of A1 and B4
int cell2pos(const gen & g,int i,int j,int & r,int & c,int & r2,int & c2){
if (g.is_symb_of_sommet(at_deuxpoints) && g._SYMBptr->feuille.type==_VECT ){
vecteur & gf=*g._SYMBptr->feuille._VECTptr;
if (gf.size()!=2)
return 0;
int r1,c1;
if (cell2pos(gf[0],i,j,r,c,r1,c1)==1 && cell2pos(gf[1],i,j,r2,c2,r1,c1)==1)
return 2;
return 0;
}
vecteur v;
if ( (g.type==_SYMB) && (g._SYMBptr->sommet==at_cell))
v=*g._SYMBptr->feuille._VECTptr;
else {
if ( (g.type!=_VECT) || (g._VECTptr->size()!=2) )
return 0;
v=*g._VECTptr;
}
if (v.front().type==_INT_)
r=v.front().val;
else
r=i+v.front()._VECTptr->front().val;
if (v.back().type==_INT_)
c=v.back().val;
else
c=j+v.back()._VECTptr->front().val;
return 1;
}
// return cell(r,c) argument at (i,j) with same absolute/relative addressing
// as g
gen pos2cell(const gen & g,int i,int j,int r,int c,int r2,int c2){
if (g.is_symb_of_sommet(at_deuxpoints) && g._SYMBptr->feuille.type==_VECT){
vecteur & gf=*g._SYMBptr->feuille._VECTptr;
if (gf.size()!=2)
return gensizeerr(gettext("pos2cell"));
return symbolic(at_deuxpoints,makevecteur(pos2cell(gf[0],i,j,r,c,r,c),pos2cell(gf[1],i,j,r2,c2,r2,c2)));
}
vecteur v;
if ( (g.type==_SYMB) && (g._SYMBptr->sommet==at_cell))
v=*g._SYMBptr->feuille._VECTptr;
else {
if ( (g.type!=_VECT) || (g._VECTptr->size()!=2) )
return gensizeerr(gettext("pos2cell"));
v=*g._VECTptr;
}
vecteur w(2);
if (v.front().type==_INT_)
w.front()=r;
else
w.front()=vecteur(1,r-i);
if (v.back().type==_INT_)
w.back()=c;
else
w.back()=vecteur(1,c-j);
return _cell(w,context0);
}
gen freecopy(const gen & g){
if (g.type!=_VECT)
return g;
else
return *g._VECTptr;
}
// insert nrows/ncols of fill in m, e.g. fill= [0,0,2] for a spreadsheet
// or ["","",2] or 0 for a matrix
matrice matrice_insert(const matrice & m,int insert_row,int insert_col,int nrows,int ncols,const gen & fill_,GIAC_CONTEXT){
int r,c,cell_r,cell_c;
int decal_i=0,decal_j;
mdims(m,r,c);
gen fill(fill_);
if (is_undef(fill)){
if (m[0][0].type==_VECT)
fill=makevecteur(string2gen("",false),string2gen("",false),2);
else
fill=0;
}
matrice res;
res.reserve(r+nrows);
// i,j position in the old matrix; i+decal_i,i+decal_j in the new
for (int i=0;i<r;++i){
vecteur tmp;
tmp.reserve(c+ncols);
if (i==insert_row){ // insert nrows of fill
for (int j=0;j<nrows;++j){
// we must recreate the line each time to have a free line
for (int k=0;k<c+ncols;++k)
tmp.push_back(freecopy(fill));
res.push_back(tmp);
tmp.clear();
}
decal_i=nrows;
}
decal_j=0;
for (int j=0;j<c;++j){
if (j==insert_col){
for (int k=0;k<ncols;k++)
tmp.push_back(freecopy(fill));
decal_j=ncols;
}
gen g=m[i][j];
// find all cells in g
vecteur sub_in(lcell(g.type==_VECT?g[0]:g)),sub_out;
if (sub_in.empty()){
tmp.push_back(g);
continue;
}
const_iterateur it=sub_in.begin(),itend=sub_in.end();
for (;it!=itend;++it){
int cell_r2,cell_c2,type=cell2pos(*it,i,j,cell_r,cell_c,cell_r2,cell_c2);
if (type){
if (cell_r>=insert_row)
cell_r += nrows;
if (cell_c>=insert_col)
cell_c += ncols;
if (cell_r2>=insert_row)
cell_r2 += nrows;
if (cell_c2>=insert_col)
cell_c2 += ncols;
sub_out.push_back(pos2cell(*it,i+decal_i,j+decal_j,cell_r,cell_c,cell_r2,cell_c2));
}
else
sub_out.push_back(*it);
}
g=quotesubst(g,sub_in,sub_out,contextptr);
if (g.type==_VECT && !g._VECTptr->empty())
g._VECTptr->front().subtype=m[i][j][0].subtype;
tmp.push_back(g);
} // end for j
res.push_back(tmp);
} // end for i
return res;
}
// erase nrows/ncols
matrice matrice_erase(const matrice & m,int insert_row,int insert_col,int nrows,int ncols,GIAC_CONTEXT){
int r,c,cell_r,cell_c;
int decal_i=0,decal_j;
mdims(m,r,c);
matrice res;
if ( (r<=nrows) || (c<=ncols) )
return res;
res.reserve(r-nrows);
for (int i=0;i<r;++i){
if (i==insert_row){
i+=nrows;
if (i>=r)
break;
decal_i=nrows;
}
vecteur tmp;
tmp.reserve(c-ncols);
decal_j=0;
for (int j=0;j<c;++j){
if (j==insert_col){
j+=ncols;
if (j>=c)
break;
decal_j=ncols;
}
gen g=m[i][j];
// find all cells in g
vecteur sub_in(lcell(g)),sub_out;
if (sub_in.empty()){
tmp.push_back(g);
continue;
}
const_iterateur it=sub_in.begin(),itend=sub_in.end();
for (;it!=itend;++it){
int cell_r2,cell_c2,type=cell2pos(*it,i,j,cell_r,cell_c,cell_r2,cell_c2);
if (type){
if (cell_r>=insert_row)
cell_r -= nrows;
if (cell_c>=insert_col)
cell_c -= ncols;
if (cell_r2>=insert_row)
cell_r2 -= nrows;
if (cell_c2>=insert_col)
cell_c2 -= ncols;
sub_out.push_back(pos2cell(*it,i-decal_i,j-decal_j,cell_r,cell_c,cell_r2,cell_c2));
}
else
sub_out.push_back(*it);
}
tmp.push_back(quotesubst(g,sub_in,sub_out,contextptr));
} // end for j
res.push_back(tmp);
} // end for i
return res;
}
// extract submatrix
matrice matrice_extract(const matrice & m,int insert_row,int insert_col,int nrows,int ncols){
if ( (!nrows) || (!ncols))
return vecteur(1,vecteur(1,gensizeerr(gettext("matrice_extract"))));
int mr,mc;
mdims(m,mr,mc);
if (mr>insert_row+nrows)
mr=insert_row+nrows;
if (mc>insert_col+ncols)
mc=insert_col+ncols;
matrice res;
res.reserve(nrows);
for (int i=insert_row;i<mr;++i){
const_iterateur it=m[i]._VECTptr->begin();
res.push_back(vecteur(it+insert_col,it+mc));
}
return res;
}
// convert m to a spreadsheet matrix if necessary
// each cell must be a vector of length 3: v[0] is the formula
// v[1] is the value and v[2] is 0 (not evaluated), 1 (in eval), 2 (evaled)