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/* License in license.txt. */

/* */

/* Adverbs: a ind}z for sparse z & ind is box a0;a1;a2;... or integer */

/* am1e a is the sparse element */

/* am1a a is an arbitrary dense array */

/* am1sp a an arbitrary sparse array */

#include "j.h"

static A jtistd1(J jt,A z,A ind){A*iv,j,*jv,x;I d,i,id,n,r,*s;

RZ(z&&ind);

ASSERT(1>=AR(ind),EVRANK);

if(AN(ind)&&!(BOX&AT(ind))){ASSERT(NUMERIC&AT(ind),EVINDEX); RZ(ind=every(ind,0L,jtright1));}

s=AS(z); n=AN(ind); iv=AAV(ind); id=(I)ind*ARELATIVE(ind);

ASSERT(n<=AR(z),EVINDEX);

d=n; DO(n, --d; x=IVR(d); if(!equ(x,ace))break;); n=n?1+d:d;

GA(j,BOX,n,1,0); jv=AAV(j);

for(i=0;i<n;++i){

x=IVR(i); d=s[i];

if(BOX&AT(x)){

ASSERT(!AR(x),EVINDEX);

x=AAV0(x); r=AR(x);

RZ(jv[i]=!AN(x)&&1==r?ace:less(IX(d),pind(d,x)));

}else RZ(jv[i]=pind(d,x));

}

R j;

} /* convert index list ind into standard form */

static A jtastd1(J jt,A a,A z,A ind){A*iv,q,r,s,s1,*sv,x;B b;I ar,*as,d,id,j,m,n,*rv,zr,*zs;P*zp; I*s1v;

ar=AR(a); as=AS(a);

zr=AR(z); zs=AS(z); zp=PAV(z);

if(!ar)R a;

n=AN(ind); iv=AAV(ind); id=(I)ind*ARELATIVE(ind);

GA(r,INT,zr,1,0); rv= AV(r);

GA(s,BOX,zr,1,0); sv=AAV(s);

m=0; j=n;

DO(n, x=IVR(i); b=x==ace; m+=rv[i]=b?1:AR(x); RZ(sv[i]=b?sc(zs[i]):shape(x)););

DO(zr-n, rv[j]=1; RZ(sv[j]=sc(zs[j])); ++j;);

d=m+zr-n; ASSERT(ar<=d,EVRANK);

RZ(s1=raze(s)); s1v=AV(s1);

ASSERT(!ICMP(as,AV(s1)+d-ar,ar),EVLENGTH);

if(ar<d)RZ(a=reshape(s1,a));

RZ(q=dgrade1(eps(repeat(r,IX(zr)),SPA(zp,a))));

R equ(q,IX(d))?a:cant2(q,a);

} /* convert replacement array a into standard form relative to index list ind */

static A jtssel(J jt,A z,A ind){A a,*iv,p,q,x,y;B*b;I*av,c,i,id,j,m,n,*u,*v,*yv;P*zp;

zp=PAV(z);

y=SPA(zp,i); v=AS(y); m=v[0]; c=v[1]; yv=AV(y);

a=SPA(zp,a); n=AN(a); av=AV(a);

GA(p,B01,m,1,0); b=BAV(p); memset(b,C1,m);

GA(q,INT,m,1,0); v=AV(q); iv=AAV(ind); id=(I)ind*ARELATIVE(ind);

for(i=0;i<n;++i){

j=av[i]; if(j>=AN(ind))break;

x=IVR(j);

if(x!=ace){

u=yv+i; DO(m, v[i]=b[i]?*u:-1; u+=c;);

RZ(p=eps(q,1<AR(x)?ravel(x):x)); b=BAV(p);

}}

R p;

} /* which rows of the index matrix of z are selected by index list ind? */

static B jtipart(J jt,A z,A ind,A*i1,A*i2){A*iv,p,*pv,q,*qv,x;B*b;I c,d,id,n;P*zp;

n=AN(ind); iv=AAV(ind); id=(I)ind*ARELATIVE(ind); zp=PAV(z);

RZ(b=bfi(AR(z),SPA(zp,a),1));

c=0; DO(n, if(b[i])++c;); d=n-c;

GA(p,BOX,c,1,0); pv=AAV(p); *i1=p;

GA(q,BOX,d,1,0); qv=AAV(q); *i2=q;

DO(n, x=IVR(i); if(b[i])*pv++=x; else *qv++=x;);

R 1;

} /* partition index into sparse and dense parts */

static A jtdcube(J jt,A z,A i2){A*iv,x,y;I i,id,m,n,*s;P*zp;

n=AN(i2); iv=AAV(i2); id=(I)i2*ARELATIVE(i2);

zp=PAV(z); x=SPA(zp,x); s=1+AS(x);

m=1; y=IVR(n-1); if(y==ace)RZ(y=IX(s[n-1]));

for(i=n-2;0<=i;--i){

m*=s[1+i]; x=IVR(i);

RZ(y=irs2(tymes(sc(m),x==ace?IX(s[i]):x),y,0L,0L,RMAX,jtplus));

}

R y;

} /* index cube relative to dense axes */

static A jtscuba(J jt,A z,A i1,B u){A*iv,q=0,x;I c,d,id,j,n,*s,*v;P*zp;

n=AN(i1);

if(!n)R mtm;

iv=AAV(i1); id=(I)i1*ARELATIVE(i1); s=AS(z); zp=PAV(z); x=SPA(zp,a); v=AV(x);

for(j=n-1;0<=j;--j){

x=IVR(j);

if(x==ace)RZ(x=IX(s[v[j]]))else{if(1<AR(x))RZ(x=ravel(x)); if(u)RZ(x=nub(x));}

c=AN(x);

if(q){d=*AS(q); RZ(q=stitch(repeat(sc(d),x),reitem(sc(c*d),q)));}

else RZ(q=reshape(v2(c,1L),x));

}

R q;

} /* index cube relative to sparse axes; 1=u iff unique (remove duplicates) */

static A jtscubb(J jt,A z,A i1){A a,q,x,y;I c,d,h,j,*s,*v,*xv;P*zp;

RZ(q=scuba(z,i1,1));

if(!*AS(q))R mtm;

s=AS(z); zp=PAV(z); y=SPA(zp,i); a=SPA(zp,a); v=AV(a);

c=*(1+AS(q)); d=*(1+AS(y)); h=d-c;

if(c==d)R less(q,y);

RZ(q=less(q,taker(c,y)));

GA(x,INT,h,1,0); xv=AV(x); j=c; DO(h, xv[i]=s[v[j++]];);

RZ(x=odom(2L,h,xv));

c=*AS(q); d=*AS(x);

R stitch(repeat(sc(d),q),reitem(sc(c*d),x));

} /* new rows for the index matrix of z for brand new cells */

static A jtscubc(J jt,A z,A i1,A p){A a,q,s,y,y1;B*qv;I c,d,h,j=-1,m,n,*sv,*u,*v;P*zp;

zp=PAV(z); a=SPA(zp,a); n=AN(i1); h=AN(a)-n;

if(!h)R mtm;

GA(s,INT,h,1,0); sv=AV(s);

d=1; u=AS(z); v=AV(a); DO(h, d*=sv[i]=u[v[n+i]];);

RZ(y=repeat(p,SPA(zp,i))); m=*AS(y);

RZ(y1=take(v2(m,n),y)); v=AV(y1);

GA(q,B01,m,1,0); qv=BAV(q);

if(m){memset(qv,C0,m); DO(m-1, if(ICMP(v,v+n,n)){if(d>i-j)qv[i]=1; j=i;} v+=n;); if(d>(m-1)-j)qv[m-1]=1;}

RZ(y1=repeat(q,y1)); c=*AS(y1);

if(!c)R mtm;

R less(stitch(repeat(sc(d),y1),reitem(sc(c*d),odom(2L,h,sv))),y);

} /* new rows for the index matrix of z for existing cells */

static A jtscube(J jt,A z,A i1,A p){A a,y;P*zp;

zp=PAV(z); a=SPA(zp,a); y=SPA(zp,i);

R !AN(a)&&!*AS(y)?take(one,mtm):over(scubb(z,i1),scubc(z,i1,p));

} /* new rows for the index matrix of z */

static A jtiindx(J jt,A z,A i1){A q,j,j1,y;I c,d,e,h,i,*jv,m,n,*qv,*v,*yv;P*zp;

c=AN(i1); zp=PAV(z); y=SPA(zp,i);

if(c==*(1+AS(y)))R indexof(y,scuba(z,i1,0));

/* when y has excess columns, do progressive indexing */

RZ(y=taker(c,y));

RZ(j=indexof(y,scuba(z,i1,0))); /* j: group indices */

n= AN(j); jv=AV(j);

m=*AS(y); yv=AV(y);

GA(q,INT,n,1,0); qv=AV(q); /* q: # members in each group */

for(i=h=0;i<n;++i){

e=1; d=jv[i]; v=yv+c*d;

DO(m-d-1, if(ICMP(v,v+c,c))break; ++e; v+=c;);

qv[i]=e; h+=e;

}

GA(j1,INT,h,1,0); v=AV(j1);

DO(n, e=qv[i]; d=jv[i]; DO(e, *v++=d++;););

R j1;

} /* index of index list in the index matrix of z */

static A jtzpad1(J jt,A z,A t,B ip){A q,s,x,x0,y,y0;I m;P*zp;

RZ(z&&t);

if(m=*AS(t)){ /* new cells being added */

zp=PAV(z);

y0=SPA(zp,i); RZ(y=over(y0,t)); RZ(q=grade1(y)); RZ(y=from(q,y));

x0=SPA(zp,x); RZ(s=shape(x0)); *AV(s)=m; RZ(x=from(q,over(x0,reshape(s,SPA(zp,e)))));

if(ip){ra(y); ra(x); fa(y0); fa(x0);}

SPB(zp,i,y); SPB(zp,x,x);

}

R z;

} /* pad z with new rows t for its index matrix */

static B mtind(A ind){A*iv,x;I id;

iv=AAV(ind); id=(I)ind*ARELATIVE(ind);

DO(AN(ind), x=IVR(i); if(!AN(x))R 1;);

R 0;

} /* 1 iff standardized index ind is an empty selection */

A jtam1e(J jt,A a,A z,A ind,B ip){A e,i1,i2,p,x,y;B*pv;C*u,*v;I*iv,k,m,n,r,*s,vk,xk;P*zp;

RZ(a&&(ind=istd1(z,ind)));

r=AR(z); zp=PAV(z); x=SPA(zp,x); y=SPA(zp,i); e=SPA(zp,e);

RZ(p=ssel(z,ind)); pv=BAV(p);

RZ(ipart(z,ind,&i1,&i2));

m=AN(p); n=AN(i2); u=CAV(e); v=CAV(x);

r=AR(x); s=AS(x); k=bp(AT(x)); xk=k*prod(r-(n+1),s+(n+1)); vk=k*prod(r-1,s+1);

if(!n)DO(m, if(pv[i])mvc(xk,v,k,u); v+=vk;)

else{

RZ(i2=dcube(z,i2)); iv=AV(i2); n=AN(i2);

DO(m, if(pv[i])DO(n, mvc(xk,v+iv[i]*xk,k,u);); v+=vk;);

}

R z;

} /* a (<ind)}z; sparse z; ind is index list; sparse element a replacement */

A jtam1a(J jt,A a,A z,A ind,B ip){A a0=a,a1,e,i1,i2,t,x,y;C*u,*v,*xv;I ar,c,*iv,*jv,k,m,n,r,*s,uk,vk,xk;P*zp;

RZ(a&&(ind=istd1(z,ind)));

RZ(a=astd1(a,z,ind));

if(mtind(ind))R z;

RZ(ipart(z,ind,&i1,&i2));

RZ(z=zpad1(z,scube(z,i1,ssel(z,ind)),ip));

zp=PAV(z); x=SPA(zp,x); y=SPA(zp,i); e=SPA(zp,e);

ar=AR(a); n=AN(i2); r=AR(x); s=AS(x);

k=bp(AT(x)); xk=k*prod(r-1-n,s+1+n); vk=k*prod(r-1,s+1); uk=!ar?k:n?xk:vk;

u=CAV(a); xv=v=CAV(x);

RZ(t=iindx(z,i1)); iv=AV(t); m=AN(t);

if(!n&&!m){a1=SPA(zp,a); R ar?sparseit(a0,a1,e):sparseit(reshape(shape(z),a),a1,a);}

if(n){RZ(t=dcube(z,i2)); jv=AV(t); c=AN(t); v=xv-vk;}

if(!n) DO(m, mvc(vk,v+vk*iv[i],uk,u); if(ar)u+=uk; )

else if(m)DO(m, v=xv+vk*iv[i]; DO(c, mvc(xk,v+xk*jv[i],uk,u); if(ar)u+=uk;);)

else DO(*AS(x), v+=vk; DO(c, mvc(xk,v+xk*jv[i],uk,u); if(ar)u+=uk;););

R z;

} /* a (<ind)}z; sparse z; ind is index list; arbitrary dense array a replacement */

A jtam1sp(J jt,A a,A z,A ind,B ip){R amnsp(a,z,ope(catalog(istd1(z,ind))),ip);}

/* a (<ind)}z; sparse z; ind is index list; arbitrary sparse array a replacement */