V5.2 or 5.1 slower than v.5.0 for NIntegrate ?
- To: mathgroup at smc.vnet.net
- Subject: [mg61055] V5.2 or 5.1 slower than v.5.0 for NIntegrate ?
- From: "Toshiyuki \(Toshi\) Meshii" <meshii at mech.fukui-u.ac.jp>
- Date: Sun, 9 Oct 2005 01:35:03 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hello I found out that NIntegrate applied for a function with a singurality point might become slow by upgrading from v5.0 to 5.1 or 5.2. Here are some results. Xeon-2.8GHz, ram 1024MB, winxp64 $B!!!!!!!!(Bv5.0$B!!!!!!!!(B v5.1$B!!!!!!(B v5.2 $B!!(B 362.31 sec 1006.48sec 1042.14 sec P4-3.0GHzHT, ram 512MB, winxppro $B!!!!!!!!(Bv5.0$B!!!!!!!!!!!!(B v5.1 $B!!(B 385.16 sec 963.81 sec Does someone have any idea about this inconvenience? The benchmark time is the CPU time for calculating Kcyl in the below. -Toshi -------------------------- \!\(\* RowBox[{"\n", \( \), "\[IndentingNewLine]", RowBox[{\(Ri\ := \ 1000\ ri\ ; \ Ro\ := \ 1000\ ro\ ; W = Ro - Ri; \ Rm\ = \ \((Ri\ + Ro)\)\ / 2; w = ro - ri; rm = \((ri + ro)\)/2;\), "\[IndentingNewLine]", "\n", \( \), "\n", \ \(<< c:\\meshii\\Mathematica\\weight3.m;\), "\[IndentingNewLine]", "\n", "\n", RowBox[{ RowBox[{\(Kcyl[t_, $B&N(B_]\), ":=", RowBox[{"Module", "[", RowBox[{\({T, Tavg, Mt, Z = W\^2/6, Ftfer, Kfer, sin = Sin[H\ $B&B(B], cos = Cos[H\ $B&B(B], sinh = Sinh[H\ $B&B(B], cosh = Cosh[H\ $B&B(B], F1N, d$B&W(B = d$B&W(Bf[$B&N(B], c1 = Ri/W, X, F2N, \ $B&W(B = \ \ $B&W(Bf[$B&N(B], KNn, F1t, F2t, Ktn, Knl, d$B&K(B = \ $B&$&K(B[$B&N(B], Fm = \(\@\($B&P(B\ $B&N(B\ W\)\) FM[$B&N(B], EYt = \ \(EY\ $B&A(B\)\/\(1 - $B&M(B\), DYb = DY\ $B&B(B\ }\), ",", "\[IndentingNewLine]", \( (*\ u[\ r\ m, \ t\ sec]\ = \ T[r] $B$NDj5A(B, \ $B&$(BT = 1\ K*) \), "\[IndentingNewLine]", RowBox[{\(T[r_] = u[r, t]\), ";", "\[IndentingNewLine]", "\[IndentingNewLine]", \( (*$BJ?6Q29EY(B\ Tavg[t] $B!$G.JQ7AAjEv%b!<%a%s%H(BMt[t] $B$NDj5A(B*) \), "\[IndentingNewLine]", \(Tavg = \ 2\/\((\ ro\^2 - ri\^2)\)\ NIntegrate[Evaluate[r\ T[r]], \ {r, ri, ro}]\), \ ";", "\[IndentingNewLine]", \(Mt = \ EYt\ \(10\^6\) \ \((NIntegrate[Evaluate[T[r]\ \((rm\ - \ r)\)], {r, ri, ro}]\ )\)\), ";", "\n", "\[IndentingNewLine]", \( \ (*\($B@~7A29EYJ,I[AjEvJ,$N7W;;(B\ Kfer\ = \ Kfe\ + \ Kr\ \(( $B9bB.%"%k%4%j%:%`(B\)\)\($B!K(B\)*) \), "\n", "\n", \(Ftfer = \((2\ DYb\ \((cos - cosh - sin\ sinh)\)\ d$B&K(B)\)/\((\((sin + sinh + DYb\ \((\(-2\) + cos + cosh)\)\ d$B&K(B)\)\ \((\(- cos\) + cosh + DYb\ \((sin + sinh)\)\ d$B&K(B)\))\)\), "; ", "\[IndentingNewLine]", \(Kfer = \ Ftfer\ \((\(-Mt\)\/Z\ Fm)\)\), ";", "\n", "\n", \( (*\($BHs@~7A29EYJ,I[AjEvJ,$N7W;;(B\ Knl\ \ from\ Ktn\ and\ KNn\ \(($B9bB.%"%k%4%j%:%`(B\)\)\($B!K(B\)*) \), "\[IndentingNewLine]", \(vnn[X_]\ = \ vn[X, $B&N(B]\), ";", "\[IndentingNewLine]", \(F1N = \ d$B&W(B\ \ NIntegrate[\ Evaluate[\(( c1\ + \ X)\)\ \ vnn[X]], \ {X, 0, $B&N(B}]\), " ", ";", "\n", "\[IndentingNewLine]", \(dvnn[X_]\ = \ dvn[X, $B&N(B]\), ";", "\[ IndentingNewLine]", RowBox[{"F2N", "=", " ", RowBox[{"$B&W(B", " ", RowBox[{"NIntegrate", "[", RowBox[{\(Evaluate[\((c1\ + \ X)\)\ \ dvnn[X]]\), ",", " ", \({X, 0, $B&N(B}\), ",", "\n", "\t\t ", \(MinRecursion -> 3\), ", ", "\n", " ", \(MaxRecursion\ -> \ 10\), ",", "\n", "\t\t \ ", \(SingularityDepth\ -> \ 10\), ",", "\n", "\t\t \ ", RowBox[{"MaxPoints", "->", StyleBox[ RowBox[{ StyleBox["1", FontColor->RGBColor[1, 0, 0]], "00000"}]]}]}], \ "]"}]}]}], ";", "\n", "\[IndentingNewLine]", \(KNn = \ \ Tavg\ \((\ F1N + F2N)\)\), ";", "\[IndentingNewLine]", "\[IndentingNewLine]", \(F1t = \ \ \ d$B&W(B\ NIntegrate[\ \ Evaluate[\((c1\ + \ X)\)\ T[ri + w\ X]\ vnn[X]], \ {X, 0, $B&N(B}]\), " ", ";", "\[IndentingNewLine]", "\n", RowBox[{"F2t", "=", " ", RowBox[{"$B&W(B", " ", RowBox[{"NIntegrate", "[", RowBox[{\(Evaluate[\((c1\ + \ X)\)\ \ T[ri + w\ X]\ dvnn[X]]\), ",", " ", \({X, 0, $B&N(B}\), ",", "\n ", "\t\t ", \(MinRecursion -> 3\), ",", "\n", " ", \(MaxRecursion\ -> \ 10\), ",", "\n", "\t\t ", (SingularityDepth\ -> \ \ 10\), ",", "\n", "\t\t ", RowBox[{"MaxPoints", "->", StyleBox[ RowBox[{ StyleBox["1", FontColor->RGBColor[1, 0, 0]], " 00000"}]]}]}], "]"}]}]}], " ", ";", "\ \[IndentingNewLine]", "\n", \(Ktn = \ F1t + F2t\), ";", "\n", \(Knl = \ EYt \(\(\(\ \)\(W\)\)\/\((Ri\ /\ W + $B&N(B)\)\) 2 \ \((\(-Ktn\)\ + \ KNn)\)/\ \((\ $B&W(B\ Fm)\)\), ";", " ", "\[IndentingNewLine]", \( (*$B:G=*7W;;(B*) \), "\[IndentingNewLine]", \($B&$(BT \((Knl + Kfer)\)\)}]}], "]"}]}], ";"}]}]}]\) ---------------------------------------------------------------