Synaptic scaling balances learning in a spiking model of neocortex (Rowan & Neymotin 2013)

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Accession:147141
Learning in the brain requires complementary mechanisms: potentiation and activity-dependent homeostatic scaling. We introduce synaptic scaling to a biologically-realistic spiking model of neocortex which can learn changes in oscillatory rhythms using STDP, and show that scaling is necessary to balance both positive and negative changes in input from potentiation and atrophy. We discuss some of the issues that arise when considering synaptic scaling in such a model, and show that scaling regulates activity whilst allowing learning to remain unaltered.
Reference:
1 . Rowan MS,Neymotin SA (2013) Synaptic Scaling Balances Learning in a Spiking Model of Neocortex Adaptive and Natural Computing Algorithms, Tomassini M, Antonioni A, Daolio F, Buesser P, ed. pp.20
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Neocortex;
Cell Type(s): Neocortex V1 pyramidal corticothalamic L6 cell; Neocortex V1 pyramidal intratelencephalic L2-5 cell; Neocortex V1 interneuron basket PV cell; Neocortex fast spiking (FS) interneuron; Neocortex spiny stellate cell; Neocortex spiking regular (RS) neuron; Neocortex spiking low threshold (LTS) neuron; Abstract integrate-and-fire adaptive exponential (AdEx) neuron;
Channel(s):
Gap Junctions:
Receptor(s): GabaA; AMPA; NMDA;
Gene(s):
Transmitter(s): Gaba; Glutamate;
Simulation Environment: NEURON; Python;
Model Concept(s): Synaptic Plasticity; Long-term Synaptic Plasticity; Learning; STDP; Homeostasis;
Implementer(s): Lytton, William [billl at neurosim.downstate.edu]; Neymotin, Sam [samn at neurosim.downstate.edu]; Rowan, Mark [m.s.rowan at cs.bham.ac.uk];
Search NeuronDB for information about:  Neocortex V1 pyramidal corticothalamic L6 cell; Neocortex V1 pyramidal intratelencephalic L2-5 cell; Neocortex V1 interneuron basket PV cell; GabaA; AMPA; NMDA; Gaba; Glutamate;
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stdpscalingpaper
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alz.hoc
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basestdp.hoc *
batch.hoc *
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batchcommon
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clusterrun.sh
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// $Id: decmat.hoc,v 1.78 2011/07/11 05:58:31 samn Exp $ 
 
print "Loading decmat.hoc..."
 
//** mtriavg(mat,[mask]) - get average of elements in upper triangular part of matrix $o1
// mask is of same size as mat, has 0 for entries to skip
func mtriavg () { local i,j,s,c localobj mm,msk
  mm=$o1 s=c=0
  if(numarg()>1) { msk=$o2
    for i=0,mm.nrow-1 for j=i+1,mm.ncol-1 if(msk.x(i,j)) {
      s+=mm.x[i][j]
      c+=1
    }    
  } else {
    for i=0,mm.nrow-1 for j=i+1,mm.ncol-1 {
      s+=mm.x[i][j]
      c+=1
    }
  }
  if(c>0) return s/c else return 0
}

//** mltristd(mat,[mask]) - get stdev of elements in upper triangular part of matrix $o1
// mask is of same size as mat, has 0 for entries to skip
func mtristd () { local i,j,s,c,s2,tm localobj mm,msk
  mm=$o1 s=s2=c=0
  if(numarg()>1) { msk=$o2
    for i=0,mm.nrow-1 for j=i+1,mm.ncol-1 if(msk.x(i,j)) {
      s+=mm.x[i][j]
      s2+=mm.x[i][j]^2
      c+=1
    }
  } else {
    for i=0,mm.nrow-1 for j=i+1,mm.ncol-1 {
      s+=mm.x[i][j]
      s2+=mm.x[i][j]^2
      c+=1
    }
  }
  if(c>0) return sqrt(s2/c - (s/c)^2) else return 0
}

//** mltristd(mat,[mask]) - get std-error of elements in upper triangular part of matrix $o1
// mask is of same size as mat, has 0 for entries to skip
func mtristderr () { local i,j,s,c,s2,tm localobj mm,msk
  mm=$o1 s=s2=c=0
  if(numarg()>0) {
    msk=$o2
    for i=0,mm.nrow-1 for j=i+1,mm.ncol-1 if(msk.x(i,j)) {
      s+=mm.x[i][j]
      s2+=mm.x[i][j]^2
      c+=1
    }
  } else {
    for i=0,mm.nrow-1 for j=i+1,mm.ncol-1 {
      s+=mm.x[i][j]
      s2+=mm.x[i][j]^2
      c+=1
    }
  }
  if(c>0) return sqrt(s2/c - (s/c)^2)/sqrt(c) else return 0
}

//** vi2mi(ind[,COLS]) take index from vector and print out matrix indices using COLS 
obfunc vi2mi () { local x,co,r,c
  x=$1
  if (argtype(2)==0) co=$2 else co=COLS
  r=int(x/COLS) c=x%COLS
  if (verbose) print r,c
  return new Union(r,c)
}

//** symmclean(vec[,COLS]) remove redundant entries from vector representing a symm matrix
proc vimiclean() {print "Use symmclean() statt vimiclean()"}
func symmclean () { local ix,dg,cols,ii,n,flag localobj v1
  v1=$o1 
  if (argtype(2)==0) cols=$2 else cols=COLS
  if (argtype(3)==0) flag=$3 else flag=0 // flag gets rid of the diagonal as well
  for ii=0,v1.size-1 { ix=v1.x[ii]
    dg=(n=int(ix/(cols+1)))*(cols+1)
    if (ix<dg || ix>=dg+(cols-n)) v1.x[ii]=-1
    if (flag && ix==dg) v1.x[ii]=-1
  }
  v1.where(">",-1)
  return v1.size
}

//** msqdif(m1,m2) - get matrix with elements squared difference of m1-m2
obfunc msqdif () { local i,j localobj m1,m2,md
  m1=$o1 m2=$o2
  md=new Matrix(m1.nrow,m1.ncol)
  for i=0,m1.nrow-1 for j=0,m1.ncol-1 md.x[i][j]=(m1.x[i][j]-m2.x[i][j])^2
  return md
}

//** mthresh(mat,th) - get matrix with mat elements thresholded : values < t set to 0, >= t to 1
obfunc mthresh () { local i,j,t localobj mi,mo
  mi=$o1 t=$2
  mo=new Matrix(mi.nrow,mi.ncol)
  for i=0,mo.nrow-1 for j=0,mo.ncol-1 if(mi.x[i][j]>=t) mo.x[i][j]=1 else mo.x[i][j]=0
  return mo
}

//** mdif(m1,m2) - get matrix with elements difference of m1-m2
obfunc mdif () { local i,j localobj m1,m2,md
  m1=$o1 m2=$o2
  md=new Matrix(m1.nrow,m1.ncol)
  for i=0,m1.nrow-1 for j=0,m1.ncol-1 md.x[i][j]=(m1.x[i][j]-m2.x[i][j])
  return md
}

//** getttmat(nqs,[column-name]) - uses NQS $o1 to make time-time correlation matrix
//optional $s2 , otherwise default column-name = 'vc'.
//column $s2 must be .odec with Vector objects
obfunc getttmat () { local i,j,inc,szm localobj mc,nq,v1,v2,str,lc
  {nq=$o1    str=new String()}
  if(numarg()>1)str.s=$s2 else str.s="vc"
  {szm=nq.v.size()  mc=new Matrix(szm,szm)  lc=new List()}
  for i=0,szm-1 lc.append(nq.get(str.s,i).o)
  for i=0,szm-1 {
    mc.x(i,i)=1
    v1=lc.o(i) 
    for j=i+1,szm-1 {
      v2=lc.o(j) 
      mc.x(i,j)=mc.x(j,i)=v1.pcorrel(v2)
    }
  }
  return mc
}

//** svmat(matrix,path,[writesz,binary]) - save a matrix to file as ascii, each row on new line
//$o1==matrix, $s2==file path -- will overwrite!! , $3 = optional == 1 to include nrows,ncols
// writesz = write rows,cols . binary - use binary output format, this will write using vwrite
// and first two elements of written vector will have rows,cols (so writesz arg is ignored)
func svmat () { local pr,bin,a localobj m,f,myv1,myv2,mt
  {m=$o1 a=allocvecs(myv1,myv2) f=new File() f.wopen($s2)}
  if(!f.isopen()) {
    printf("svmat ERRA: couldnt open output file %s\n",$s2)
    return 0
  }
  if(numarg()>2)pr=$3 else pr=0
  if(numarg()>3)bin=$4 else bin=0
  if(bin) {
    mt=$o1.transpose()
    mt.to_vector(myv1)
    myv2.append($o1.ncol,$o1.nrow)
    myv2.append(myv1)
    myv2.vwrite(f)
  } else {
    if(pr) m.fprint(f) else m.fprint(0,f)
  }
  {f.close() dealloc(a)}
  return 1
}

//obfunc rdmat () { local pr localobj m,f
// m=$o1
// f=new File()
// f.wopen($s2)
// if(!f.isopen()) {
//   printf("svmat ERRA: couldnt open output file %s\n",$s2)
//   return 0
// }
// if(numarg()>2)pr=$3 else pr=0
// if(pr) m.fprint(f) else m.fprint(0,f)
// f.close()
// return 1
//}

//** matimagesc - display a matrix ($o1) in matlab using matimgsc program
// or a text file $s1 , $2 = min scale value , $3 = max scale value, $4 optional
// binary input flag
func matimagesc () { local x,binflag localobj str
  if(numarg()>3) binflag=$4 else binflag=1
  str=new String2()
  if(argtype(1)==2) {
    str.s=$s1
  } else {
    str.s="__tmp__mat__ml__.txt"
    if(!svmat($o1,str.s,1,binflag)) return 0
  }
  sprint(str.t,"/usr/site/nrniv/local/matlab/matimgsc %s %g %g %d",str.s,$2,$3,binflag)
  x = system(str.t)
  return x
}

//** pyimagesc - display a matrix ($o1) in python's matplotlib or a text file $s1
//opt:[$2=min scaling for colors, $3=max scaling for colors, [$s4=title,$s5=xlabel,$s6=ylabel]
func pyimagesc () { local i,minc,maxc localobj str,cmd,strout,strt,strl,fp
  str=new String2()
  strout=new String()//collect stdout from script
  if(argtype(1)==2) {
    str.s=$s1
  } else {
    str.s="__tmp__mat__py__.txt"
    if(!svmat($o1,str.s)) return 0
  }
  if(numarg()>1)minc=$2 else minc=-1
  if(numarg()>2)maxc=$3 else maxc=1  
  if(numarg()>3) { //write title,xlabel,ylabel for pyimgsc.py
    {strl=new String() strl.s="__tmp__str__py__.txt"    fp=new File()}
    fp.wopen(strl.s)
    if(!fp.isopen()){
      printf("pyimagesc ERRB: couldnt save tmp file %s\n",strl.s)
      return 0
    }
    for i=4,numarg() fp.printf("%s\n",$si)
    fp.close()
    sprint(str.t,"/u/samn/python/pyimgsc.py %s %g %g %s",str.s,minc,maxc,strl.s)
  } else {
    sprint(str.t,"/u/samn/python/pyimgsc.py %s %g %g",str.s,minc,maxc)
  }
  return system(str.t,strout.s)
}

//** matgcspks(vec1,vec2,samplingrate,pathin1,pathin2,pathout,pid])
// this function calls /usr/site/nrniv/local/matlab/callmatgcspks to send a signal to
// /usr/site/nrniv/local/matlab/matgcspks and run MZD's granger causality on spike trains
// this function returns an NQS with 1 row containing output
// vec1,vec2 are binned spike trains (spikes per time)
// returns a vector containing vec1->vec2,  vec2->vec1 granger causality
obfunc matgcspks () { local sampr,pid localobj vspks1,vspks2,fpin1,fpin2,fpout,str,vop,strin,strout
  if(numarg()==0) {printf("matgcspks(vec1,vec2,samplingrate)\nvec1,2 are binned spike trains\n") return nil}
  vspks1=$o1 vspks2=$o2 sampr=$3 vop=new Vector(2)
  fpin1=new File() fpin2=new File() fpout=new File() str=new String() strin=new String2() strout=new String()  
  {strin.s=$s4 strin.t=$s5 strout.s=$s6 pid=$7}
  {fpin1.wopen(strin.s) fpin2.wopen(strin.t)}
  if(!fpin1.isopen()) {printf("matgcspks ERRA: couldn't open %s for writing\n",strin.s)  return nil}
  if(!fpin2.isopen()) {printf("matgcspks ERRA: couldn't open %s for writing\n",strin.t)  return nil}
  {vspks1.vwrite(fpin1)  fpin1.close() vspks2.vwrite(fpin2)  fpin2.close()}
  sprint(str.s,"/usr/site/nrniv/local/matlab/callmatgcspks %d",pid)
  {printf("%s\n",str.s) system(str.s)}
  fpout.ropen(strout.s)
  while(!fpout.isopen()){
    printf("matgcspks ERRB: couldn't open %s for reading\n",strout.s)
    fpout.ropen(strout.s)
  }
  vop.vread(fpout)
  return vop
}

//** matspecgram(vec,samplingrate,maxfrequency,fftwinsz,[,dodraw,mincolor,maxcolor])
// if fftwinsz <= 0, matspecgram will pick a WINDOW size for STFT
obfunc matspecgram () { local a,sampr,maxfreq,dodraw,rows,cols,x,y,minc,maxc,fftwinsz\
                       localobj vin,fpin,fpout,str,vop,vof,nqo,strin,strout,vtmp,strd
  vin=$o1 sampr=$2 maxfreq=$3 fftwinsz=$4 fpin=new File() fpout=new File()
  str=new String() strin=new String() strout=new String() strd=new String()
  a=allocvecs(vtmp,vop,vof)  if(numarg()>4)dodraw=$5 else dodraw=1  
  if(!fpin.mktemp || !fpout.mktemp) {
    print "matspecgram ERR0: couldn't make temp files!"
    {dealloc(a) return nil}
  }  
  {strin.s=fpin.getname strout.s=fpout.getname strd.s="/usr/site/nrniv/local/matlab" fpin.wopen(strin.s)}
  if(!fpin.isopen()){printf("matspecgram ERRA: couldn't open %s for writing\n",strin.s) dealloc(a) return nil}
  {vin.vwrite(fpin)  fpin.close()}
  if(dodraw && numarg()>=7) {
    sprint(str.s,"%s/matspecgram %s %g %g %d %d %s %g %g",strd.s,strin.s,sampr,maxfreq,fftwinsz,dodraw,strout.s,$6,$7)
  } else {
    sprint(str.s,"%s/matspecgram %s %g %g %d %d %s",strd.s,strin.s,sampr,maxfreq,fftwinsz,dodraw,strout.s)
  }
  print str.s
  system(str.s)
  fpout.ropen(strout.s) 
  if(!fpout.isopen()){printf("matspecgram ERRB: couldn't open %s for reading\n",strout.s) dealloc(a) return nil}
  {vop.vread(fpout) vof.vread(fpout)}  
  {nqo=new NQS("f","pow")  nqo.odec("pow")}
  {rows=vof.size() cols=vop.size()/rows x=0}
  for y=0,rows-1 { vtmp.resize(0)
    vtmp.copy(vop,x,x+cols-1)
    nqo.append(vof.x(y),vtmp)
    x+=cols
  }
  {fpin.unlink() fpout.unlink()}
  {dealloc(a) return nqo}
}

//** matmodind(vec,samplingrate,lohz1,lohz2,hihz1,hihz2)
// this function calls /usr/site/nrniv/local/matlab/matmodindex to run Canolty's modulation index with Matlab
// returns an NQS with 1 row containing output
obfunc matmodind () { local a,sampr,lohz1,lohz2,hihz1,hihz2\
                       localobj vin,fpin,fpout,str,vop,nqo,strin,strout
  if(numarg()==0) {printf("matmodind(vec,samplingrate,lohz1,lohz2,hihz1,hihz2)\n") return nil}
  vin=$o1 sampr=$2 lohz1=$3 lohz2=$4 hihz1=$5 hihz2=$6
  fpin=new File() fpout=new File() str=new String() strin=new String() strout=new String()
  a=allocvecs(vop)
  if(!fpin.mktemp || !fpout.mktemp) {
    print "matmodind ERR0: couldn't make temp files!"
    {dealloc(a) return nil}
  }
  {strin.s=fpin.getname strout.s=fpout.getname}
  {fpin.wopen(strin.s)}
  if(!fpin.isopen()) {printf("matmodind ERRA: couldn't open %s for writing\n",strin.s) dealloc(a) return nil}
  {vin.vwrite(fpin)  fpin.close()}
  sprint(str.s,"/usr/site/nrniv/local/matlab/matmodindex %s %g %g %g %g %g %s",strin.s,sampr,lohz1,lohz2,hihz1,hihz2,strout.s)
  print str.s
  system(str.s)
  fpout.ropen(strout.s) 
  if(!fpout.isopen()){printf("matmodind ERRB: couldn't open %s for reading\n",strout.s) dealloc(a) return nil}
  {vop.vread(fpout) nqo=new NQS("modind","phase","lohz1","lohz2","hihz1","hihz2")}
  nqo.append(vop.x(0),vop.x(1),lohz1,lohz2,hihz1,hihz2)
  {dealloc(a) fpin.unlink() fpout.unlink()}
  return nqo
}

//** matpmtm(vec,samplingrate)
// this function calls /usr/site/nrniv/local/matlab/matpmtm to run multitaper power spectra using matlab, returns an nqs
obfunc matpmtm () { local a,sampr,rows,cols,x,y\
                       localobj vin,fpin,fpout,str,vop,vof,nqo,strin,strout
  if(numarg()==0) {printf("%s\n","matpmtm(vec,samplingrate)") return nil}
  vin=$o1 sampr=$2 fpin=new File() fpout=new File() str=new String() strin=new String() strout=new String()
  a=allocvecs(vop,vof)  
  if(!fpin.mktemp || !fpout.mktemp) {
    print "matpmtm ERR0: couldn't make temp files!"
    {dealloc(a) return nil}
  }
  {strin.s=fpin.getname strout.s=fpout.getname}
  {fpin.wopen(strin.s)}
  if(!fpin.isopen()) {printf("matpmtm ERRA: couldn't open %s for writing\n",strin.s) dealloc(a) return nil}
  {vin.vwrite(fpin)  fpin.close()}
  sprint(str.s,"/usr/site/nrniv/local/matlab/matpmtm %s %g %s",strin.s,sampr,strout.s)
  print str.s
  system(str.s)
  fpout.ropen(strout.s) 
  if(!fpout.isopen()){printf("matpmtm ERRB: couldn't open %s for reading\n",strout.s) dealloc(a) return nil}
  {vop.vread(fpout) vof.vread(fpout) nqo=new NQS("f","pow")}
  {nqo.v[0].copy(vof) nqo.v[1].copy(vop) dealloc(a) fpin.unlink() fpout.unlink()}
  return nqo
}

//** matfftpow(vec,samplingrate,maxfrequency,[dodraw,dosmooth,smoothwindowsz])
// this function calls /usr/site/nrniv/local/matlab/matfftpow to run power spectra using matlab, returns an nqs
// dosmooth controls whether to smooth output, is OFF by default
// smoothwindowsz controls size of running average smoothing of power spectra output
obfunc matfftpow () { local a,sampr,maxfreq,dodraw,rows,cols,x,y,dosmooth\
                       localobj vin,fpin,fpout,str,vop,vof,nqo,strin,strout
  if(numarg()==0) {printf("%s\n","matfftpow(vec,samplingrate,maxfrequency,[dodraw,dosmooth,smoothwindowsz])") return nil}
  vin=$o1 sampr=$2 maxfreq=$3 fpin=new File() fpout=new File() str=new String() strin=new String() strout=new String()
  a=allocvecs(vop,vof)  if(numarg()>3)dodraw=$4 else dodraw=1
  if(numarg()>4)dosmooth=$5 else dosmooth=0
  if(!fpin.mktemp || !fpout.mktemp) {
    print "matfftpow ERR0: couldn't make temp files!"
    {dealloc(a) return nil}
  }
  {strin.s=fpin.getname strout.s=fpout.getname}
  {fpin.wopen(strin.s)}
  if(!fpin.isopen()) {printf("matfftpow ERRA: couldn't open %s for writing\n",strin.s) dealloc(a) return nil}
  {vin.vwrite(fpin)  fpin.close()}
  if(numarg()>5) {
    sprint(str.s,"/usr/site/nrniv/local/matlab/matfftpow %s %g %d %d %s %d %d",strin.s,sampr,maxfreq,dodraw,strout.s,dosmooth,$6)
  } else sprint(str.s,"/usr/site/nrniv/local/matlab/matfftpow %s %g %d %d %s %d",strin.s,sampr,maxfreq,dodraw,strout.s,dosmooth)
  print str.s
  system(str.s)
  fpout.ropen(strout.s) 
  if(!fpout.isopen()){printf("matfftpow ERRB: couldn't open %s for reading\n",strout.s) dealloc(a) return nil}
  {vop.vread(fpout) vof.vread(fpout) nqo=new NQS("f","pow")}
  {nqo.v[0].copy(vof) nqo.v[1].copy(vop) dealloc(a) fpin.unlink() fpout.unlink()}
  return nqo
}

//** mathilbert(vec,samplingrate,minfrequency,maxfrequency)
obfunc mathilbert () { local a,sampr,minfreq,maxfreq\
                       localobj vin,fp,str,vfilt,vph,vamp,nqo,strin,strout
  vin=$o1 sampr=$2 minfreq=$3 maxfreq=$4 fp=new File() str=new String() strin=new String() strout=new String()
  a=allocvecs(vfilt,vph,vamp) 
  {sprint(strin.s,"__tmp__mat__hilbert__input__vec__.vec")  sprint(strout.s,"__tmp__mat__hilbert_output__vec__.vec")}
  {fp.wopen(strin.s)}
  if(!fp.isopen()) {
    printf("mathilbert ERRA: couldn't open %s for writing\n",strin.s)
    dealloc(a)
    return nil
  }
  {vin.vwrite(fp)  fp.close()}
  sprint(str.s,"/usr/site/nrniv/local/matlab/mathilbert %s %g %g %g %s",strin.s,sampr,minfreq,maxfreq,strout.s)
  print str.s
  system(str.s)
  fp.ropen(strout.s) 
  if(!fp.isopen()) {
    printf("mathilbert ERRB: couldn't open %s for reading\n",strout.s)
    dealloc(a)
    return nil
  }
  {vfilt.vread(fp) vph.vread(fp) vamp.vread(fp) nqo=new NQS("filt","phase","amp","t")}
  {nqo.v[0].copy(vfilt) nqo.v[1].copy(vph) nqo.v[2].copy(vamp)}
  {nqo.v[3].indgen(0,1e3*nqo.v[2].size/sampr,1e3/sampr)  nqo.v[3].resize(nqo.v[2].size)}
  dealloc(a)
  return nqo
}

//** matprincomp(input Matrix object)
// returns list with : eigenvectors as Vector, scores as Vector, eigenvalues as Vector, scores as Matrix
// scores has same size as $o1, eigenvectors is $o1.ncols^2, eigenvalues is $o1.ncols
// input matrix has rows as observations and columns as dimensions
obfunc matprincomp () { local i,j,k localobj mcin,fp,str,strin,strout,lsout,vcoeff,vscore,vlat,mscore
  mcin=$o1 fp=new File() str=new String() strin=new String() strout=new String() lsout=new List()
  {vcoeff=new Vector() vscore=new Vector() vlat=new Vector()}
  {sprint(strin.s,"__tmp__mat__princomp__input__mat__.txt")  sprint(strout.s,"__tmp__mat__princomp_output__vec__.vec")}
  if(!svmat(mcin,strin.s,1)) {
    printf("matprincomp ERRA: couldn't open %s for writing\n",strin.s)
    return nil
  }
  sprint(str.s,"/usr/site/nrniv/local/matlab/matprincomp %s %s",strin.s,strout.s)
  print str.s
  system(str.s)
  fp.ropen(strout.s) 
  if(!fp.isopen()) {
    printf("matprincomp ERRB: couldn't open %s for reading\n",strout.s)
    return nil
  }
  {vcoeff.vread(fp) vscore.vread(fp) vlat.vread(fp) fp.close()}
  mscore=new Matrix(mcin.nrow,mcin.ncol)
  mscore.from_vector(vscore) //reads it in in column major order
  {lsout.append(vcoeff) lsout.append(vscore) lsout.append(vlat) lsout.append(mscore)}
  return lsout
}

//** matmin(mat) - return min element of mat
func matmin () { local i,j,me,tmp localobj m
  m=$o1 
  me=m.getrow(0).min()
  for i=1,m.nrow-1 if((tmp=m.getrow(i).min)<me) me=tmp
  return me
}

//** matmax(mat) - return max element of mat
func matmax () { local i,j,me,tmp localobj m
  m=$o1 
  me=m.getrow(0).max()
  for i=1,m.nrow-1 if((tmp=m.getrow(i).max)>me) me=tmp
  return me
}

//** mlk(mat) - use vlk to print rows of matrix
// a matrix will have it's lower/smaller rows printed first:
//    1 2 3 
//    4 5 6 
//    7 8 9 
proc mlk () { local i localobj m
  m=$o1
  for i=0,m.nrow-1 vlk(m.getrow(i))
}

//** mateq(mat1,mat2) - return 1 iff matrix row Vectors are eq, 0 otherwise
func mateq () { local i localobj m1,m2
  m1=$o1 m2=$o2
  if(m1.nrow!=m2.nrow || m1.ncol!=m2.ncol) return 0
  for i=0,m1.nrow-1 if(m1.getrow(i).eq(m2.getrow(i))==0) return 0
  return 1
}

//** matavg - return average value in Matrix $o1
func matavg () { local i,s localobj m
  m=$o1
  if(m.nrow<1 || m.ncol<1) {
    printf("matavg ERRA: empty matrix!\n")
    return 0
  }
  s=0
  for i=0,m.nrow-1 s += m.getrow(i).sum()
  return s/(m.nrow*m.ncol)
}

//** avgmat(list of Matrix) - return Matrix that has its elements avg of elements in $o1 List
obfunc avgmat () { local sz,i localobj ma
  sz=$o1.count
  if(sz<1) return nil
  ma=new Matrix($o1.o(0).nrow,$o1.o(0).ncol)
  for i=0,sz-1 ma.add($o1.o(i))
  ma.muls(1.0/sz)
  return ma
}

//** stdmat(list of Matrix) - return Matrix that has its elements stdev of elements in $o1 List
obfunc stdmat () {  local sz,i,j,k localobj ms,ma
  sz=$o1.count
  if(sz<1) return nil
  ma=new Matrix($o1.o(0).nrow,$o1.o(0).ncol)
  ms=new Matrix($o1.o(0).nrow,$o1.o(0).ncol)
  for i=0,sz-1 for j=0,ma.nrow-1 for k=0,ma.ncol-1 {
    ms.x(j,k) += $o1.o(i).x(j,k)^2
    ma.x(j,k) += $o1.o(i).x(j,k)
  }
  ma.muls(1.0/sz)
  ms.muls(1.0/sz)  
  for j=0,ma.nrow-1 for k=0,ma.ncol-1 {
    ms.x(j,k) -= ma.x(j,k)^2
    if(ms.x(j,k) > 1e-9) ms.x(j,k) = sqrt(ms.x(j,k)) else ms.x(j,k) = 0
  }
  return ms
}

//** chgmat(list of before Matrices, list of after Matrices) - returns change in each entry in units of std-dev
obfunc chgmat () { local szbef,szaft,i,j,k localobj lbef,laft,mavg,mstd,lchg,mchg,mt
  lbef=$o1 laft=$o2
  szbef=lbef.count szaft=laft.count
  lchg=new List()
  mavg=avgmat(lbef)
  mstd=stdmat(lbef)
  mchg=new Matrix(mavg.nrow,mavg.ncol)
  for i=0,szaft-1 {
    mt=laft.o(i)
    for j=0,mt.nrow-1 for k=0,mt.ncol-1 {
      if(mstd.x(j,k)>1e-9) {
        mchg.x(j,k) += ( mt.x(j,k) - mavg.x(j,k) ) / mstd.x(j,k)
      } else if(szbef==1) {
        mchg.x(j,k) += ( mt.x(j,k) - mavg.x(j,k) ) 
      }
    }
  }
  return mchg
}

//** getlv(rows,cols) - make a List of Vectors as 2D array
//$1 == # of rows (vectors), $2 == # of cols (size of vectors)
obfunc getlv () { local idx,rows,cols localobj ls
  ls=new List()
  rows=$1 cols=$2
  for idx=0,rows-1 ls.append(new Vector(cols))
  return ls
}

//** vec2mat(vec,rows) - get a matrix from a vec -- row major order
obfunc vec2mat () { local i,j,k,rows,cols localobj vin,mout
  vin=$o1 rows=$2 cols=vin.size/rows mout=new Matrix(rows,cols) k=0
  for i=0,rows-1 for j=0,cols-1 {
    mout.x(i,j)=vin.x(k)
    k+=1
  }
  return mout
}

//** mat2vec(mat) - get a vec from a matrix -- row major order 
obfunc mat2vec () { local i,j,k,rows,cols localobj mat,vout
  mat=$o1 rows=mat.nrow cols=mat.ncol i=j=k=0 vout=new Vector(rows*cols)
  for i=0,rows-1 for j=0,cols-1 {
    vout.x(k)=mat.x(i,j)
    k+=1
  }
  return vout
}
//** mltmed(mat) - get median values from lower-triangular portion - lower triang. means smaller rows
// this matrix printed as (with printf or mlk):
//    1 2 3 
//    4 5 6 
//    7 8 9 
// will have mltmed of 3, since uses 2,3,6 from bottom of matrix to get median
func mltmed () { local i,j,a localobj m,vo
  a=allocvecs(vo) m=$o1
  for i=0,m.nrow-1 for j=i+1,m.ncol-1 vo.append(m.x(i,j))
  return vo.median()
}
//** mzerout(mat) - zero out everything >= diagonal
// a matrix printed as (with printf or mlk):
//    1 2 3 
//    4 5 6 
//    7 8 9 
// will end up as:
//    0 2 3 
//    0 0 6 
//    0 0 0 
proc mzerout () { local i,j,a localobj m,vo
  a=allocvecs(vo) m=$o1
  for i=0,m.nrow-1 for j=0,i m.x(i,j)=0
}
//** matsqsymm(matrix) - return 1 iff matrix is square and symmetric
func matsqsymm () { local i,j localobj mc
  mc=$o1  if(mc.nrow!=mc.ncol) return 0
  for i=0,mc.nrow-1 for j=i+1,mc.ncol-1 if(mc.x(i,j)!=mc.x(j,i)) return 0
  return 1
}
//** getsubmat(matrix,startx,endx,starty,endy) - copy subsection of matrix
// and return in new output matrix
obfunc getsubmat () { local x,y,startx,endx,starty,endy localobj m1,msub
  m1=$o1
  startx=$2 endx=$3 starty=$4 endy=$5
  msub=new Matrix(endy-starty+1,endx-startx+1)
  for y=starty,endy for x=startx,endx msub.x(y-starty,x-startx)=m1.x(y,x)
  return msub
}

Rowan MS,Neymotin SA (2013) Synaptic Scaling Balances Learning in a Spiking Model of Neocortex Adaptive and Natural Computing Algorithms, Tomassini M, Antonioni A, Daolio F, Buesser P, ed. pp.20

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