{load_file("stdgui.hoc")}
// utility to help compute computational complexity of a cell
// and determine best split locations
begintemplate LoadBalance
public cell_complexity, subtree_complexity, secref, resolutions
public ExperimentalMechComplex, distrib, multisplit, read_load_balance_info, cpu_complexity
public sec_complex_, roots_complex_, cell_complexity_, m_complex_, ion_complex_, cplx
public srlist, backbone_cx_, mt, compute_roots, parent_vec_
public host, gid, splitx, spliti, splitb, unsplitx, splitbit, read_mcomplex
public thread_partition, slthread, thread_cxbal_, npiece_, pieces_cx, lpt
external hoc_obj_, hoc_sf_, cvode
objref srlist, sec_complex_, roots_complex_, parent_vec_, save_capac_
objref mt[2], m_complex_[2], cplx, this, pc, ion_complex_
objref slthread[1]
objref cx_piece_indices, bb_piece_cx
strdef mname
// temporaries for distrib
objref cvec, splitxlist, splitixlist, cpu, splitcplx, splitindex, allocated, sorted, sp, si
objref splitbrlist, splitbres, sb
objref gid, splitx, spliti, splitb, host
objref unsplitx


proc init() {local i, j  localobj ms
	if (numarg() == 0) {
		pc = new ParallelContext()
	}else{
		pc = $o1
	}
	backbone_cx_ = .6 // extra complexity due to backbone segments
	thread_cxbal_ = 1.0
	splitbit = 2^28
	sec_complex_ = new Vector()
	roots_complex_ = new Vector()
	parent_vec_ = new Vector()
	for j=0, 1 {
		mt[j] = new MechanismType(j)
		m_complex_[j] = new Vector(mt[j].count)
		if (j == 0) {ion_complex_ = new Vector(mt[0].count)}
		for i=0, mt[j].count-1 {
			if (j == 1) if(mt[j].is_artificial(i) == 1) continue
			mt[j].select(i)
			mt[j].selected(mname)
			ms = new MechanismStandard(mname, 3)
			m_complex_[j].x[i] = 1 + ms.count
//			printf("complexity %d for %s\n", m_complex_[j].x[i], mname)
			if (j == 0 && hoc_sf_.substr(mname, "_ion") != -1) {
				m_complex_[j].x[i] = 0
				ion_complex_.x[i] = 1
			}
		}
	}
}

iterator sections() {local i
	for i=0, srlist.count-1 srlist.object(i).sec {
		$&1 = i
		iterator_statement
	}
}

// least processing time algorithm
// $o1 is vector of weights  $2 is number of partitions
// return is vector of partition indices parallel to weights
obfunc lpt() {local i, j  localobj wx, ix, pw
	if ($3) {
		print $o1.size, " piece weights"
		$o1.printf
	}
	wx = $o1.sortindex.reverse
	ix = new Vector($o1.size)
	pw = new Vector($2)
	for i=0, $o1.size-1 {
		j = wx.x[i]
		w = $o1.x[j]
		ip = pw.min_ind
		pw.x[ip] += w
		ix.x[j] = ip
	}
	if ($3) {
		print $2, " partition complexities"
		pw.printf
	}
	if (pw.mean) {
		thread_cxbal_ = pw.max/(pw.mean)
	}else{
		thread_cxbal_ = 1
	}
	return ix
}

// piece complexities can only be called after srlist exists
obfunc pieces_cx() {local i  localobj cx, srl, sr, roots
	cx = new Vector()
	roots = new List()
	srl = srlist
	for i = 0, srl.count-1 {
		sr = srl.object(i)
		if (!sr.has_parent) sr.sec {
			roots.append(sr)
			cx.append(cell_complexity())
		}
	}
	if (numarg() == 1) { $o1 = roots }
	return cx
}

// lpt distribution of pieces on all the threads
proc thread_partition() { local i  localobj roots, cx, tid
	cx = pieces_cx(roots)
	npiece_ = roots.count()
//	if (pc.nthread == 1) { return } // do not bother
	tid = lpt(cx, pc.nthread, $1)
	objref slthread[pc.nthread]
	for i=0, pc.nthread - 1 {
		slthread[i] = new SectionList()
	}
	for i=0, tid.size-1 {
		roots.object(i).sec slthread[tid.x[i]].append()
	}
	for i=0, pc.nthread - 1 {
		pc.partition(i, slthread[i])
	}
}

func is_nernst() {
	return int(ion_style($s1)/64)%2
}

// complexity of currently accessed section
func sec_complexity() {local c, i, x  localobj pp
	c = m_complex_[0].x[0] // one zero area node
	for i=1, mt[0].count-1 {
		mt[0].select(i)
		mt[0].selected(mname)
		if (ismembrane(mname)) {
			x = m_complex_[0].x[i]
			if (ion_complex_.x[i] > 0) if (is_nernst(mname)) {
				x = ion_complex_.x[i]
			}
			c += x * nseg
		}
	}
	for i=0, mt[1].count-1 {
		mt[1].select(i)
		for (pp = mt[1].pp_begin; object_id(pp); pp = mt[1].pp_next) {
			c += m_complex_[1].x[i]
		}
	}
	return c
}

// complexity of entire cell containing currently accessed section
// or, if there is an arg, the complexity of the cell object.
// keep the individual section complexities in a parallel vector
// for split analysis
func cell_complexity() {local x, i, c  localobj sl, sr
	sl = new SectionList()
	if (numarg() == 1) {
		if (!execute1("{all}", $o1, 0)) {
			srlist = new List()
			sec_complex_.resize(0)
			return 0
		}
		forsec $o1.all {
			if (object_id(sr) == 0) {
				sr = new SectionRef()
			}
		}
		sr.sec { sl.wholetree() }
	}else{
		sl.wholetree() // note this is root to leaf order
	}
	return cplx_helper(sl) + m_complex_[0].x[0]
}
func cpu_complexity() { local n  localobj s, sl
	s = new String()
	srlist = new SectionList()
	srlist.allroots()
	n = 0 forsec srlist { n += 1 }
	sl = new SectionList()
	forsec srlist { sl.wholetree() }
	return cplx_helper(sl) + n * m_complex_[0].x[0]
}
func cplx_helper() {local x, i, c  localobj sl
	sl = $o1
	srlist = new List()
	forsec sl { srlist.append(new SectionRef()) }
	sec_complex_.resize(srlist.count)
	c = 0
	for sections(&i) {
		x = sec_complexity()	
		sec_complex_.x[i] = x
		c += x
	}
	cell_complexity_ = c
	return c
}

proc compute_roots() {local i
	// construct a trueparent index vector
	save_capac()
	for sections(&i) { cm(.0001) = i }
	parent_vec_.resize(srlist.count)
	for i=0, srlist.count-1 {
		if (srlist.object(i).has_trueparent) {
			srlist.object(i).trueparent {parent_vec_.x[i] = cm(.0001)}
		}else if (srlist.object(i).has_parent) {
			srlist.object(i).parent {parent_vec_.x[i] = cm(.0001)}
		}else{
			parent_vec_.x[i] = -1
		}		
	}
	restore_capac()

	// accumulate the subtree complexities
	roots_complex_.copy(sec_complex_)
	for (i = srlist.count-1; i > 0; i -= 1) {
		if (parent_vec_.x[i] >= 0) {
			roots_complex_.x[parent_vec_.x[i]] += roots_complex_.x[i]
		}
	}
}

// returns the index of the complexity that is closest to the desired
// complexity (argument 1) but less than
// or equal to the upper bound complexity (argument 2)
// Note if scalar reference arg3 returns as 0 then the subtree
// rooted at that section index is the one referred to. If 1, then
// subtree rerooted at the parent is the on referred to.
func subtree_complexity() {local i, j, k, min
	compute_roots()
	min = 1e9
	for i = 0, srlist.count-1 {
		c = roots_complex_.x[i]
		if (c < $2 && abs(c - $1) < min) {
			j = i  k = 0  min = abs(c - $1)
		}
		c = cell_complexity_ - c
		if (c < $2 && abs(c - $1) < min) {
			j = i  k = 1  min = abs(c - $1)
		}
	}
	$&3 = k
	return j
}

//returns the SectionRef of the section associated with index (arg1)
obfunc secref() {
	return srlist.object($1)
}

//returns a vector with the distinct possible resolutions
//the indices of these resolutions are returned as a new parallel vector in $o1
// and the branch set index as a vector in $o2.
// note that at a branch point where n sections connect together
// with m different complexities,
// there are n!/(n - m)! - 1 potentially distinct complexity resolutions.
// For complicated trees, e.g. 3d reconstructions, most often n = 3 and
// so there are generally 5 resolutions available. The TCR Traub
// cell has 10 subtrees each of weight 418 connected to a soma/axon
// subtree of weight 4306 - 10*418 = 126 so there would be
// 11*10 - 1 possible resolutions at the 1 end of the soma.

obfunc resolutions() {local i, j, ibegin, pbegin, c, oldres \
    localobj si, res, v1, v2, bres, corder
	compute_roots()

	v1 = new Vector()
	v2 = new Vector()
	res = new Vector()
	bres = new Vector()
	corder = new Vector()
	if (srlist.count == 0) {
		$o1 = v2
		$o2 = bres
		return v1
	}

	si = parent_vec_.sortindex
	ibegin = 0
	pbegin = parent_vec_.x[si.x[ibegin]]

	for i=0, si.size-1 {
		if (parent_vec_.x[si.x[i]] == pbegin) {continue}
	    if (parent_vec_.x[si.x[ibegin]] >= 0) { // do not allow split at root
		n = i - ibegin
		res.resize(n)
		corder.resize(n)
		// child resolutions of the pbegin index
		for j=0, n-1 {
			res.x[j] = roots_complex_.x[si.x[j + ibegin]]
			corder.x[j] = si.x[j + ibegin]
		}
		// want the res to be in child order
		corder = corder.sortindex
		res.index(res, corder)
		// the parent tree is implicit with respect to the
		// remainder

		// for simplicity, instead of analyzing all the
		// possiblities, just do all individual and the sums
		// (and, of course, the remainders). Associate every
		// resolution with ibegin and a index for the
		// specific branch set. Note that this gets all of
		// the binary branch combinations and is good
		// for stylized multibranches where all are identical

		// individuals
		c = cell_complexity_
		for j=0, n-1 {
			v1.append(res.x[j])
			v1.append(c - res.x[j])	
			v2.append(si.x[ibegin])
			v2.append(si.x[ibegin])
			bres.append(j+1)
			bres.append(-(j+1))
		}
		// sums
		oldres = res.x[0]
		for j=1, n-1 {
			oldres += res.x[j]
			if (oldres < c) {
				v1.append(oldres)
				v1.append(c - oldres)	
				v2.append(si.x[ibegin])
				v2.append(si.x[ibegin])
				bres.append(n+j)
				bres.append(-(n+j))
			}
		}
	    }
		ibegin = i
		pbegin = parent_vec_.x[si.x[ibegin]]
	}
	// now only the distinct ones
	si = v1.sortindex
	v1.index(v1, si)
	v2.index(v2, si)
	bres.index(bres, si)
	for (i=v1.size-1; i >= 1; i -= 1) {
		if (v1.x[i] == v1.x[i-1]) {
			v1.remove(i)
			v2.remove(i)
			bres.remove(i)
		}
	}
	$o1 = v2
	$o2 = bres
	return v1
}

proc save_capac() {local i
	save_capac_ = new Vector(sec_complex_.size)
	for sections(&i) {
		save_capac_.x[i] = cm(.0001)
	}
}

proc restore_capac() {local i
	for sections(&i) {
		cm(.0001) = save_capac_.x[i]
	}
}

// all the mechanism type 0 then 1, then base and ion with style eadvance (64 bit set)
// generate a vector of computation time and a list of type vectors of types inserted

proc setcol() {local i
	for i=0, $o1.nrow-1 {
		$o1.x[i][$2] = $3
	}
}

proc ExperimentalMechComplex() {local i, j, k, b, ts, ns, baseindex, irun, par \
  localobj s, cmd, sr, ionindices, ct, names, ninstance, pc, ionname, f, dvec, vcnts, dvec1
	//if something uses a mechanism of type i then if ionindices.x[i] > 0 then
	// the mechanism is an ion and if the eadvance bit is set for the ionstyle
	// then the index for the element is ionindices.x[i]
	pc = new ParallelContext()
	par = 0 if (pc.nhost > 1) { par = 1 dvec = new Vector() }
//printf("id=%d nhost=%d\n", pc.id, pc.nhost)
	baseindex = mt[0].count + mt[1].count
	j = baseindex + 1
	ionindices = new Vector(mt[0].count)
	s = new String()
	ionname = new String()
	for i=0, mt[0].count-1 {
		mt[0].select(i)
		mt[0].selected(s.s)
		if (hoc_sf_.substr(s.s, "_ion") != -1) {
			ionindices.x[i] = j
			j += 1
		}
	}
	// start empty
	forall delete_section()
	// do three runs for each mechanism
	ct = new Matrix(j, 3)
	names = new List()
	for i=0, ct.nrow-1 {
		names.append(new String())
	}
	ninstance = new Matrix(j, j, 2)
	// fixed step with cache efficiency
	cvode.active(0)
	cvode.cache_efficient(1)

	cmd = new String()
	ts = 100
	ns = 100
	for irun=0, ct.ncol-1 {
		ct.x[baseindex][irun] = dorun(ts)
	}
//	setcol(ninstance,baseindex,1) // everyone has the overhead
	names.o(baseindex).s = "overhead"
	// morphology and capacitance go together by default. But treat 0 and 1
	// as 100 empty sections with one segment and 1 empty section with 100
	// segments respectively
	sr = makesec(ns, 1)
	for irun=0, ct.ncol-1 {
		ct.x[0][irun] = dorun(ts)
	}
//	setcol(ninstance, 0, 2) // everyone has 2 zero area nodes except
//	ninstance.x[0][0] = 1 + ns // this one is sausage of ns sections
//	ninstance.x[baseindex][0] = 0 // overhead has none
	names.o(0).s = "zero_area_node"
	sr = makesec(1, ns)
	for irun=0, ct.ncol-1 {
		ct.x[1][irun] = dorun(ts)
	}	
//	setcol(ninstance, 1, ns) // everyone has capacitance
	names.o(1).s = "capacitance"
	// from now on 1 section ns segments
	for j=0, 1 for k = 0, mt[j].count-1 {
		if (j == 0 && k < 2) { continue }
		kk = k + j*mt[0].count
		mt[j].select(k)
		mt[j].selected(s.s)
		names.o(kk).s = s.s
		// parallelism added on top of working version
		b = 1
		if (kk%pc.nhost != pc.id) {
			b = 0
		}
		// ions must be done on id 0 (because names for
		// ionindices.x[k] needs to be assigned )
		if (j == 0) if (ionindices.x[k] > 0) {
			if (pc.id == 0) {
				b = 1
			}else{
				b = 0
			}
		}
		if (b == 0) {
			continue
		}
//printf("%d %s\n", pc.id, s.s)
		sr = makesec(1, ns)
		b = 0
		for i=1, numarg() {
			if (hoc_sf_.substr(s.s, $si) != -1) { b = 1 }
		}
		if (b) { continue }
		
		if (j == 0) {
			sprint(cmd.s, "insert %s", s.s)
		}else{
			if (mt[j].is_artificial(k)) { continue }
			hoc_obj_ = new List(ns)
sprint(cmd.s, "for (hoc_ac_, 0) hoc_obj_.append(new %s(hoc_ac_))", s.s)
		}
		sr.sec execute(cmd.s)
		if (dorun(1) == 1000) {
			printf("mcomplex failed for %s\n", s.s)
			continue
		}
		
		if (par) { dvec.append(kk) }
		for irun=0, ct.ncol-1 {
			ct.x[kk][irun] = dorun(ts)
			if (par) { dvec.append(ct.x[kk][irun]) }
		}
//		ninstance.x[kk][kk] = ns
		// if it is an ion, do again with style eadvance
		b = 0
		if (j == 0) if (ionindices.x[k] > 0) { b = 1 }
		if (b) {
			ion_style(s.s, 3, 2, 1, 1, 0)
			for irun=0, ct.ncol-1 {
				ct.x[ionindices.x[k]][irun] = dorun(ts)
			}
			ninstance.x[ionindices.x[k]][ionindices.x[k]] = ns
			names.o(ionindices.x[k]).s = s.s
		}else{ // otherwise, what ions are used with what style
			for i=2, ionindices.size-1 if (ionindices.x[i] > 0) {
				mt[0].select(i)
				mt[0].selected(ionname.s)
				sr.sec if (ismembrane(ionname.s)) {
					if (int(ion_style(ionname.s)/64)%2) {
						//eadvance is 1
						ninstance.x[kk][ionindices.x[i]] = ns
					}else{
						ninstance.x[kk][i] = ns
					}
				}
			}
		}
	}
	execute("objref hoc_obj_[2]")
	if (object_id(sr)) sr.sec delete_section()
	if (par) {// now do an alltoall so id 0 has all the info
		vcnts = new Vector(pc.nhost)
		if (pc.id == 0) {dvec.resize(0)}
		vcnts.x[0] = dvec.size
		dvec1 = new Vector()
		pc.alltoall(dvec, vcnts, dvec1)
		for (i=0; i < dvec1.size; i += ct.ncol+1) {
			kk = dvec1.x[i]
			for irun=0, ct.ncol-1 {
				ct.x[kk][irun] = dvec1.x[i+irun+1]
			}
		}
		if (pc.id > 0) { // the id==0 barrier is at the end
			pc.barrier()
			return
		}
	}
	// lastly, get some indication of time it takes to solve a backbone
	if (0) {
		pc.gid_clear()
		sr.sec delete_section()
		sr = makesec(ns)	
		sr.sec {
			pc.multisplit(0, 1, 2)
			pc.multisplit(1, 2, 2)
		}		
		pc.multisplit()
		cx = (dorun(ts)-base)/base
		if (cx < 0) { cx = 0 }
		printf("backbone %g\n", cx)
		pc.gid_clear()
		sr.sec delete_section()
	}
	// subtract the overhead
	f = ct.getrow(baseindex)
	for i=0, ct.nrow-1 if (i != baseindex) {
		ct.setrow(i, ct.getrow(i).sub(f))
	}
	// the capacitance contains the zero area node contribution. subtract from mech
	f = ct.getrow(1)
	for i=2, ct.nrow-1 if (i != baseindex) {
		ct.setrow(i, ct.getrow(i).sub(f))
	}
	// separate the zero-area_node and the capacitance
	ct.setrow(0, ct.getrow(0).sub(ct.getrow(1)).div(ns-1)) // single zero-area-node
	ct.setrow(1, ct.getrow(1).sub(ct.getrow(0).mul(2)).div(ns)) // single capacitance after subtract two zero nodes

	// subtract ions from mechanisms
	for i=2, baseindex-1 {
		for k = 0, ninstance.sprowlen(i)-1 {
			ninstance.spgetrowval(i, k, &j)
			ct.setrow(i, ct.getrow(i).sub(ct.getrow(j)))
		}
	}
	// unit values
	for i=2, ct.nrow-1 if (i != baseindex) {
		ct.setrow(i, ct.getrow(i).div(ns))
	}

	f = new File()
	f.wopen("mcomplex.dat")
	// scale to capacitance
	j = ct.getrow(1).mean
	for i=0, ct.nrow-1 {
		// take average. negative is artificial and undone
		k = ct.getrow(i).mean
		if (k < 0) { k = 0 }
		f.printf("%g %s\n", k/j, names.o(i).s)
	}
	f.close()
	if (par) { pc.barrier() }
}

proc read_mcomplex() {local i, j, k, c  localobj f, s, s2, pc
	pc = new ParallelContext()
	f = new File()
	if (!f.ropen("mcomplex.dat")) { return }
	s = new String()
	s2 = new String()
	for j=0,1 {
		k = 0
		for i=0, mt[j].count - 1 {
			c = f.scanvar()
			f.scanstr(s2.s)
			mt[j].select(i)
			mt[j].selected(s.s)
			if (pc.id == 0) if (j == 0 && k == 0) {
  if (strcmp("zero_area_node", s2.s) != 0) { execerror(s2.s, " should be zero_area_node") }
			}else{
			  if (strcmp(s.s, s2.s) != 0) { execerror(s2.s, " not loaded") }
			}
			m_complex_[j].x[k] = c
			k += 1
		}
	}
	c = f.scanvar() f.scanstr(s2.s)
	if (strcmp(s2.s, "overhead") != 0) { execerror(s2.s, "should be overhead")}
	while (f.gets(s.s) != -1) if (hoc_sf_.substr(s.s, "_ion") != -1) {
		sscanf(s.s, "%lf %s", &c, s2.s)
		mt[0].select(s2.s)
		ion_complex_.x[mt[0].selected()] = c
	}
	if (0) {
		for i=0, mt[0].count-1 {
			printf("%g %g\n", m_complex_[0].x[i], ion_complex_.x[i])
		}
		for i=0, mt[1].count-1 {
			printf("%g\n", m_complex_[1].x[i])
		}
	}
}

func dorun() {
	xrun_ = $1
	if (execute1("xrun()", this) == 0) { return 1000 }
	return xrun_
}

proc xrun() {local tstop  localobj pc
	tstop = xrun_
	pc = new ParallelContext()
	finitialize(-70)
	xrun_ = pc.time
	batch_run(tstop, tstop)
	xrun_ = pc.time - xrun_
}

obfunc makesec() {localobj s, sr
	s = new String()
	sprint(s.s, "create tempsec[%d]", $1)
	execute(s.s)
	sprint(s.s, "forall nseg=%d", $2)
	execute(s.s)
	sprint(s.s, "for i=1, %d { connect tempsec[i](0), tempsec[i-1](1) }", $1-1)
	execute(s.s)
	sprint(s.s, "tempsec[0] hoc_obj_[1] = new SectionRef()")
	execute(s.s)
	sr = hoc_obj_[1]
	cvode.use_mxb(0) // extracellular would turn this on
	cvode.cache_efficient(1) // extracellular would turn this off
	return sr
}


//args
//input $1=#ncpu, $o2=Vector of complexity values, $o3=List of Vectors of split point complexities
//   $o4=List of Vectors of split point indices
//   $o8 = List of Vectors of split point branch set indices
//output (parallel to $o2) $o5 = Vector of cpu indices, $o6 = Vector of split point complexity
//   $o7 = Vector of split point indices
//   $o9 = Vector of split point branch set indices
// if a return split point complexity is -1 then means it was not split
// return % load balance error
func distrib() {local i, n
	$o5.resize($o2.size)
	$o6.resize($o2.size)
	$o7.resize($o2.size)
	$o9.resize($o2.size)
	cplx = new Vector()
	for i = 0, 50 {
		cvec = $o2
		splitxlist = $o3
		splitixlist = $o4
		cpu = $o5
		splitcplx = $o6
		splitindex = $o7
		splitbrlist = $o8
		splitbres = $o9
		n = distrib_trial($1, i+.5)
//printf("i=%d n=%d\n", i, n)
		if (n <= $1) { break }
	}
//print "distrib returning with i=",i
	return int((cplx.max*$1/$o2.sum - 1)*100 + .5)
}

func distrib_trial() {local i, i1, j1, j2, j, k, c, cmax, cmin, climit, n, ncpu, margin
	ncpu = $1
	margin = (1 + $2/100)
	
	splitcplx.fill(-1)
	splitindex.fill(0)
	splitbres.fill(0)
	allocated = new Vector(cvec.size)
	sorted = cvec.sortindex
	cplx.resize(0)
	i = 0
	j = sorted.size - 1		
	n = 0
	c = 0
	climit = cvec.sum/ncpu
//printf("climit = %g climit*margin = %g\n", climit, climit*margin)
	while (i <= j) {
		i1 = sorted.x[i] // smallest
		j1 = sorted.x[j] // largest
		if (allocated.x[i1]) { i += 1  continue }
		if (allocated.x[j1]) { j -= 1 continue }
		cmax = cvec.x[j1]
		cmin = cvec.x[i1]
		if (c + cmax <= climit*margin) { // largest whole cell fits into cpu
			cpu.x[j1] = n    // hopefully the most common case
//printf("largest fits j=%d j1=%d cold=%d cmax=%d cnew=%d n=%d\n", j, j1, c, cmax, c+cmax, n)
			c += cmax
			allocated.x[j1] = 1
		}else{ // if (cmax > climit) { // must split
			if (c + cmax > 2*climit) { // may want to defer til c==0
				if (c == 0) { // no choice but to split as evenly as possible
					// and put the largest part first
					cpu.x[j1] = n
					allocated.x[j1] = 1
					sp = splitxlist.object(j1)
					si = splitixlist.object(j1)
					sb = splitbrlist.object(j1)
					k = sp.indwhere(">=", cmax/2)
					splitcplx.x[j1] = sp.x[k]
					splitindex.x[j1] = si.x[k]
					splitbres.x[j1] = sb.x[k]
					c += sp.x[k]
//printf("no choice even split j=%d j1=%d c=%d cmax=%d othersplit=%d", j, j1, c, cmax, cmax-c, n)
					n = addone(n, ncpu, c)
					c = cmax - c
					if (c > climit) {
						// satisfied if n is full
						n = addone(n, ncpu, c)
						c = 0
					}else if ( greedy(i, j, c, climit, margin, &j2, &k) ) {
		// see if there is a cell available which will fill this
		// and the next cpu to within the margin.
						cpu.x[j2] = n
						allocated.x[j2] = 1
						sp = splitxlist.object(j2)
						si = splitixlist.object(j2)
						sb = splitbrlist.object(j2)
						splitcplx.x[j2] = sp.x[k]
						splitindex.x[j2] = si.x[k]
						splitbres.x[j2] = sb.x[k]
						c += sp.x[k]
						n = addone(n, ncpu, c)
						c = cvec.x[j2] - sp.x[k]
						n = addone(n, ncpu, c)
						c = 0
					}else{
						// not clear what to do.
						// attempt to fill more?
						// probably pretty close to full
//printf("fail %d %d\n", n, c)
						n = addone(n, ncpu, c)
						c = 0
					}
				}else if ( greedy(i, j, c, climit, margin, &j2, &k) ) {
		// see if there is a cell available which will fill this
		// and the next cpu to within the margin.
					cpu.x[j2] = n
					allocated.x[j2] = 1
					sp = splitxlist.object(j2)
					si = splitixlist.object(j2)
					sb = splitbrlist.object(j2)
					splitcplx.x[j2] = sp.x[k]
					splitindex.x[j2] = si.x[k]
					splitbres.x[j2] = sb.x[k]
					c += sp.x[k]
					n = addone(n, ncpu, c)
					c = cvec.x[j2] - sp.x[k]
					n = addone(n, ncpu, c)
					c = 0
				}else{
//printf("leave as is, use next cpu c=%d n=%d\n", c, n)
					n = addone(n, ncpu, c)
					c = 0
				}
			}else{ //safe to split
				// fill up n
				cpu.x[j1] = n
				sp = splitxlist.object(j1)
				si = splitixlist.object(j1)
				sb = splitbrlist.object(j1)
				k = sp.indwhere(">=", climit - c)
				if (k == -1) k = sp.size-1
				if (k > 1 && c + sp.x[k] > climit*margin) k -= 1
				if (c + sp.x[k] > climit*margin) {
//printf("leave as is, use next cpu c=%d n=%d\n", c, n)
					n = addone(n, ncpu, c)
					c = 0
					continue
				}
				allocated.x[j1] = 1
				// should check if k-1 is better split point
				splitcplx.x[j1] = sp.x[k]
				splitindex.x[j1] = si.x[k]
				splitbres.x[j1] = sb.x[k]
//printf("safe split j=%d j1=%d cold=%d cmax=%d sp=%d cnew=%d remain=%d n=%d k=%d\n",\
//j, j1, c, cmax, sp.x[k], c+sp.x[k], cmax-sp.x[k], n, k)
				c += sp.x[k]
				n = addone(n, ncpu, c)
				c = cmax - sp.x[k]
			}
		}
	}
	if (c > 0) {
		cplx.append(c)
	}
objref cvec, splitxlist, splitixlist, cpu, splitcplx, splitindex, allocated, sorted, sp, si
objref splitbrlist, splitbres, sb
//printf("trial %d ncpu=%d max=%g avg=%g min=%g %d\n", $2, cplx.size, cplx.max, cplx.mean, cplx.min, cplx.min_ind)
	return cplx.size
}

//greedy(i, j, c, climit, margin, &j2, &k)
func greedy() {local i, i1, k, c, climit, margin, rest, remain, max, min \
  localobj sp
	c = $3
	climit = $4
	margin = $5
	rest = climit*margin
	remain = rest - c
	max = rest + remain
	min = 2*climit - c
	for i = $1, $2 {
		i1 = sorted.x[i]
		if (allocated.x[i1]) { continue }
		if (max < cvec.x[i1]) { continue }
		if (min > cvec.x[i1]) { continue }
		sp = splitxlist.object(i1)
		k = sp.indwhere(">=", climit - c)
		if ( sp.x[k] <= remain && cvec.x[i1] - sp.x[k] <= rest) {
			$&6 = i1
			$&7 = k
			return 1
		}
	}
	return 0
}

func addone() {local n
	cplx.append($3)
	n = $1 + 1
	if (n >= $2) {
//		printf("Warning, increasing the cpu index past %d\n", $2)
	}
	return n
}

proc read_load_balance_info() {local i, n, h, g, si, sx, sb, cx, myid  localobj f
	myid = $2
	f = new File()
	if (!f.ropen($s1)) {
		execerror("could not open", $s1)
	}
	n = f.scanvar()
	host = new Vector()
	gid = new Vector()
	splitx = new Vector()
	spliti = new Vector()
	splitb = new Vector()
	unsplitx = new Vector()
	for i=0, n-1 {
		h = f.scanvar()
		g = f.scanvar()
		si = f.scanvar()
		sb = f.scanvar()
		sx = f.scanvar()
		cx = f.scanvar()
		if (h == myid) {
			host.append(h)
			gid.append(g)
			spliti.append(si)
			splitb.append(sb)
			splitx.append(sx)
			unsplitx.append(cx)
		}else if (h == (myid - 1) && sx > -1) {
			host.append(h)
			gid.append(g)
			spliti.append(si)
			splitb.append(sb)
			splitx.append(sx)
			unsplitx.append(cx)
		}
	}
	f.close()
}

// here we split a cell at the soma and at one other point (to form
// a short backbone) so that the maximum size piece is as small as
// possible. Return the index of the section which we will split
// at the 1 end.

// enhanced to try to split consistent with the optional second arg value for
// maximum complexity

// 12/24/2006 try again. several issues were revealed in the experience
// with the first implementation. Need to divide into possibly many pieces,
// not just 3 and each piece has to be < some max complexity.
// Do not worry about adjacent backbone sizes since we plan on enhancing
// ParallelContext.multisplit to solve exactly anyway. Sometimes branches
// are at several locations on soma. Generally the user will coalesce these
// and the problem will go away. But if not...
// Usually choose a split point at the
// largest branch, but the collection of (smaller) branches at the other point
// may total > cmax. If the collections of branches at both points that do
// not include our largest branch is still > cmax then we are forced to
// have two split points in the soma.
// With respect to returning a result, originally we used a String but that
// is getting out of hand so switch to Vector with a suitable format where
// the information is not too difficult to extract for use by mssel, msdiv,
// and pmetis. Format is
// gid
// total complexity
// how many split points, may be 0 if cell is not split
// for the first split point, the number of subtrees
//    Note, the first subtree of the first split point is assumed to contain
//    the soma (parent). Therefore the sum of all the subtree complexities
//    is the same as the total complexity.
// for the first subtree: complexity, number of children, ids of children
// ...

iterator children() {local i   localobj p
	p = srlist.object($1)
	for i=0, p.nchild - 1  p.child[i] {
		$&2 = cm(.0001)
		iterator_statement
	}
}

func x2iseg() { local x
	if ($1 <= 0) { return -1 }
	if ($1 >= 1) { return $2 }
	return $1*$2 - .5	
}

// args: gid, cmax, result Vector
// return number of pieces
func multisplit() {local i, x, ilargest, cmax, c \
 localobj root, cc, xcon
	npiece = 1
	cbk_soma = 0
	cmax = $2
	$o3.resize(0)
	$o3.append($1)
	compute_roots()
if (0 && $1 == 79) {
printf("compute_roots\n")
for i=0, roots_complex_.size-1 {
printf("  %d %d %g %g\n", i, parent_vec_.x[i], sec_complex_.x[i], roots_complex_.x[i])
}
}
	$o3.append(roots_complex_.x[0])
	$o3.append(0) // update later if we do, in fact, split
	// maybe the cell is small enough that we do not have to split at all
	if (roots_complex_.x[0] < cmax) {
		return npiece
	}
	// cannot split if only one section
	if (roots_complex_.size < 2) {
		return npiece
	}
	// map from section to srlist index
	save_capac()
	root = srlist.object(0)
	for sections(&i) { cm(.0001) = i }

	// what is the pattern of connection at the soma
	// this helps us determine the best sid0 split point
	xcon = new Vector()
	root.sec for (x) xcon.append(x)
	cc = new Vector(xcon.size) // complexity of child trees
	for children(0, &i) {
		x = x2iseg(parent_connection(), root.sec.nseg) + 1
		c = roots_complex_.x[i]
		cc.x[x] += c
	}
	// First splitpoint is on the soma. That is a mistake if
	// the soma has only one branch...
	// The first split subtree contains the soma.
	// It must also contain the complexity of other branches
	// at different locations (if they are not also at a split point).
	// on the soma.
	// The soma cannot have more than two split points.
	// The first is the maximum cc.
	// The second is the next largest if it is larger than the
	// max.
	c = sec_complex_.x[0]
	cx_piece_indices = new Vector()
	bb_piece_cx = new Vector()
	
	if ((c + cc.sum - cc.max) < cmax) { // one split point at max point
		c += cc.sum - cc.max // everything except max subtree
		$o3.x[2] += 1
		ms_split($o3, 0, xcon.x[cc.max_ind], c, cmax)
	}else{ // two split points on soma
		i = cc.max_ind
		c += cc.sum - cc.max
		cc.x[i] = 0
		c -= cc.max // everything except max and next max subtree
		$o3.x[2] += 1
		ms_split($o3, 0, xcon.x[i], c, cmax)
		if (cc.max > 0) { //another split point on soma
			$o3.x[2] += 1
			ms_split($o3, 0, xcon.x[cc.max_ind], 0, cmax)
		}
	}
	// Note: if the root split point (contains the soma complexity) has
	// a child piece count of $o3.x[3] == 1, then that split point does
	// not have to be used.
	if ($o3.x[3] == 1) {
		$o3.x[4] -= cbk_soma
	}
	restore_capac()
	// the total complexity needs to be increased because of the extra
	// zero area nodes. It is also increased by multisplit
	// piece overhead and the someday perhaps the overhead of the reduced tree.
//$o3.x[0] = npiece + 1000*cx_piece_indices.size
	$o3.x[1] += m_complex_[0].x[0] * (cx_piece_indices.size - 1)
	for i = 1, cx_piece_indices.size-1 {
		$o3.x[cx_piece_indices.x[i]] += m_complex_[0].x[0]
	}
	$o3.x[1] += bb_piece_cx.sum
	for i=1, cx_piece_indices.size-1 {
		$o3.x[cx_piece_indices.x[i]] += bb_piece_cx.x[i]
	}
	return npiece - 1
}

// split at srlist.object($2).sec($3)
// $o1 is result vector to append
// $4 is extra complexity to be added to first subtree (for soma, otherwise 0)
// $5 is max complexity of a subtree
// return value is the total complexity of the subtree (includes complexity
//  of that portion which was recursively split away.)
func ms_split() {local i, j, cbk, ctotal, nsubtree_index, cx_index, nchild_index, c \
    localobj cx, is, sort
	cx = new Vector()  is = cx.c
	for children($2, &i) if ($3 == parent_connection()) {
		is.append(i)
		cx.append(roots_complex_.x[i])
	}
	if (cx.size == 0) {
srlist.object($2).sec printf("No children of %s(%g)\n", secname(), $3)
execerror("LoadBalance failure:")
	}
	sort = cx.c.sortindex
	is.index(sort)
	cx.index(sort)
	cx.x[0] += $4 // add to smallest
	ctotal = cx.sum

	nsubtree_index = $o1.size $o1.append(1) // number of subtrees
	cx_index = $o1.size $o1.append(cx.x[0]) // subtree complexity
	cx_piece_indices.append(cx_index)
	bb_piece_cx.append(0)
	nchild_index = $o1.size $o1.append(1) // number of children in subtree
	$o1.append(is.x[0])
	for i=1, is.size-1 {
		if ($o1.x[cx_index] + cx.x[i] < $5) {
			$o1.x[cx_index] += cx.x[i]
			$o1.x[nchild_index] += 1
		}else{
			$o1.x[nsubtree_index] += 1
			cx_index = $o1.size $o1.append(cx.x[i])
			nchild_index = $o1.size $o1.append(1)
		}
		$o1.append(is.x[i])
	}
	// some of the individuals may be large and need to be split themselves
	// so the complexity added above may need to be updated
	cx_index = nsubtree_index + 1
	for i = 0, $o1.x[nsubtree_index] - 1 {
		if ($o1.x[cx_index] > $5) { // needs splitting
    if (cansplit(srlist, $o1, cx_index+2)) {
//    if (srlist.object($o1.x[cx_index+2]).nchild > 0 ) {
			j = ms_getsplit($o1.x[cx_index+2], $5)
			$o1.x[2] += 1
			c = ms_split($o1, j, 1, 0, $5)
			$o1.x[cx_index] -= c
			// but now this subtree has a backbone so there
			// is extra complexity proportional to the number
			// of segments on the backbone. Count from (j,1) to
			// ($2,$3)
			if (backbone_cx_) {
				cbk = backbone_cx_ * cnt_bb_seg($2, $3, j, 1)
				if ($2 == 0) {
					// in case we do not in fact split
					// cbk_soma = cbk
				}
		bb_piece_cx.x[cx_piece_indices.indwhere("==", cx_index)] += cbk
			}
    }else{
//	printf("Piece %d with complexity %g cannot be split\n", cx_index, $o1.x[cx_index])
    }
		}
		if (i < $o1.x[nsubtree_index] - 1) {
			cx_index += 2 + $o1.x[cx_index + 1]
			cx_piece_indices.append(cx_index)
			bb_piece_cx.append(0)
		}
	}
	npiece += $o1.x[nsubtree_index]
	
	return ctotal
}

//    if (cansplit(srlist, $o1, cx_index+2)) { replaces
//    if (srlist.object($o1.x[cx_index+2]).nchild > 0 ) {
func cansplit() {local i, b, x  localobj sr
	sr = $o1.o($o2.x[$3])
//	sr.sec print "cansplit ", secname(), " ", $3
	if (sr.nchild == 0) { return 0 }
	b = 0
	for i=0, sr.nchild -1 sr.child[i] {
		x = parent_connection()
		if (x == 0 || x == 1) {
			b = 1
		}
	}
	return b
}

func cnt_bb_seg() {local i, j, ns, xp
	ns = 0
	// all segs until reach the first section
	for (i = $3; i != $1; i = j) {
		srlist.object(i).sec {
			ns += nseg + 1 // include the 0 area node
			xp = parent_connection()
		}
		srlist.object(i).parent {
			j = cm(.0001)
		}
	}
	// only the segs in first section from $2 to ...
	srlist.object($1).sec { j = (nseg*abs($2-xp)) + 1 }
	ns += j
//	srlist.object($3).sec printf("%d segments from %s(%g) to ", ns, secname(), $4)
//	srlist.object($1).sec printf("%s(%g)\n", secname(), $2)
	return ns
}

// return a split parent index descending from srlist.object($1)
// so the backbone is < $2
// The only problem is that one or more of the children at the
// split point should be allowed to be part of the parent backbone

func ms_getsplit() {local i, id, idold, c, ctotal, clargest, ilargest
	id = $1
	idold = $1
	ctotal = roots_complex_.x[id]
	c = ctotal
	while (ctotal - c < $2 && c > $2) {
		c = 0
		clargest = 0
		for children(id, &i) {
			c += roots_complex_.x[i]	
			if (roots_complex_.x[i] > clargest) {
				clargest = roots_complex_.x[i]
				ilargest = i
			}
		}
		if (ctotal - c > $2) { break }
		idold = id
		id = ilargest
	}
	return idold
}

endtemplate LoadBalance
