Re: Speeding up code
- To: mathgroup at smc.vnet.net
- Subject: [mg100432] Re: Speeding up code
- From: dh <dh at metrohm.com>
- Date: Wed, 3 Jun 2009 05:28:26 -0400 (EDT)
- References: <h02vo6$8ek$1@smc.vnet.net>
Hi Alexander,
see below, Daniel
borisov at sas.upenn.edu wrote:
> Hello all,
>
>
> I need some advise on speeding up code. Here is a section that is executed more
> than 100000 times during my simulations. Currently it takes about 0.06s per
> execution which is about 80% of the total time for the simulation. The
> subsection MITime itself takes 0.03s out of those 0.06s. All variables not
> defined in this section are predefined. Anyone have suggestions?
>
> MDTime = First[
> Timing[
> yps = Table[(ys[[i]] + ys[[i - 1]])/2, {i, 2, ngrid}];
this can be written: yps= Differences[ys]/2
> yms = Table[(ys[[i]] - ys[[i - 1]]), {i, 2, ngrid}];
> ups = Table[(us[[i]] + us[[i - 1]])/2, {i, 2, ngrid}];
> ums = Table[(us[[i]] - us[[i - 1]]), {i, 2, ngrid}];
> Etus = Table[rrms[[i]]*Exp[-ups[[i]]], {i, 1, ngrid - 1}];
> (*Etu2s=Table[Exp[-ups[[i]]/2],{i,1,ngrid-1}];*)
>
> SqEts = Table[
> rrpms[[i]]*sqrrs[[i]]*Exp[-ups[[i]]/2]*acubed*rba, {i, 1,
> ngrid - 1}];
this can be written: SqEts= rrpms sqrrs Exp[-ups/2] acubed rba
> ElemEIEI = Table[N[SqEts[[i]]/4, Precis], {i, ngrid - 1}];
> ElemOIOI = Table[N[-Etus[[i]]/2, Precis], {i, ngrid - 1}];
> ElemOIOI1 =
> Table[N[yps[[i]]*Etus[[i]]/2, Precis], {i, ngrid - 1}];
> Es[[ngrid*nvar]] = N[Exp[us[[ngrid]]] - rrs[[ngrid]], Precis];
> Es[[1]] = Exp[us[[1]]] - rrs[[1]]*ys[[1]];
> For[i = 1, i <= ngrid - 1, i++,
> Es[[nvar*i]] = N[yms[[i]] + Yds[[i]] - SqEts[[i]], Precis];
> Es[[nvar*i + 1]] = N[ums[[i]] - yps[[i]]*Etus[[i]], Precis];
> ];
the loop can be written:
Es[[nvar Range[ngrid-1]]]= N[yms + Yds - SqEts, Precis]
Es[[nvar Range[ngrid-1]+1]]= N[ums - yps Etus, Precis]
> (* Table of rules used to create the Sms matrix*)
>
> MITime = First[
> Timing[
> DataSAP = Join[
> Table[{nvar*i, nvar*(i - 1) + 1} -> N[-1., Precis], {i,
> ngrid - 1}],
this can be written:
Thread[Transpose[{nvar*Range[ngrid-1], nvar*(Range[ngrid-1] - 1) + 1}]
-> N[-1., Precis]]
> Table[{nvar*i, nvar*(i - 1) + 2} -> ElemEIEI[[i]], {i,
> ngrid - 1}],
this can be written:
Thread[Transpose[{nvar*Range[ngrid-1], nvar*(Range[ngrid-1] - 1) + 1}]
-> ElemEIEI]
> Table[{nvar*i, nvar*(i - 1) + 3} -> N[1., Precis], {i,
> ngrid - 1}],
> Table[{nvar*i, nvar*(i - 1) + 4} -> ElemEIEI[[i]], {i,
> ngrid - 1}],
> Table[{nvar*i + 1, nvar*(i - 1) + 1} -> ElemOIOI[[i]], {i,
> ngrid - 1}],
> Table[{nvar*i + 1, nvar*(i - 1) + 2} ->
> ElemOIOI1[[i]] - 1., {i, ngrid - 1}],
> Table[{nvar*i + 1, nvar*(i - 1) + 3} -> ElemOIOI[[i]], {i,
> ngrid - 1}],
> Table[{nvar*i + 1, nvar*(i - 1) + 4} ->
> ElemOIOI1[[i]] + 1., {i, ngrid - 1}]]
> ]
> ];
> DataSA = Prepend[DataSAP, {1, 2} -> N[Exp[us[[1]]], Precis]];
> DataSA =
> Prepend[DataSA, {nvg, nvg} -> N[Exp[us[[ngrid]]], Precis]];
> DataSA = Prepend[DataSA, {1, 1} -> N[-rrs[[1]], Precis]];
> Sms = SparseArray[DataSA];
> ]
> ];
>
>
>
> Best regards
> Alexander
>