spap2.m

演示matlab曲线拟和与插直的基本方法

% SPAP2   僗僾儔僀儞嵟彫擇忔嬤帡
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% SPAP2(KNOTS,K,X,Y) 偼丄愡揰楍 KNOTS 傪傕偮 K師偺僗僾儔僀儞偵傛偭偰丄
% 僨乕僞 X, Y 傊偺 f 偺嵟彫擇忔嬤帡偺B-宆傪弌椡偟傑偡丅
% 僨乕僞僒僀僩 X(j) 偱偺僗僾儔僀儞嬤帡偼丄j=1:length(X) 偲偟偨偲偒偺
% 僨乕僞抣 Y(:,j) 傪梌偊傑偡丅
% 僨乕僞抣偼丄僗僇儔丄儀僋僩儖丄峴楍丄傑偨偼N師尦攝楍偱偡丅
% 摨偠僒僀僩偺僨乕僞揰偼丄偦傟傜偺暯嬒偵傛偭偰抲偒姺偊傜傟傑偡丅
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% f 偼丄
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% (*)                Y = f(X)
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% 偵懳偟偰丄擇忔暯嬒偺堄枴偱(偡側傢偪丄壓幃傪嵟彫壔偡傞)愡揰楍 KNOTS 傪
% 傕偮K師偺僗僾儔僀儞偱偡丅
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% (**)   sum_j W(j) |Y(:,j) - f(X(j))|^2 ,
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% 偙偙偱丄W = ones(size(X)) 偱偡丅僆僾僔儑儞堷悢丄偡側傢偪丄(**)傪嵟彫壔
% 偡傞K師偺愡揰 KNOTS 傪傕偭偨僗僾儔僀儞 f 傪弌椡偡傞 
% SPAP2(KNOTS,K,X,Y,W) 傪巊偭偰懠偺廳傒傪巜掕偡傞偙偲傕偱偒傑偡丅
% 僨僼僅儖僩偺 W = ones(size(X)) 傛傝傕傛偄慖戰偲偟偰丄暋崌戜宍懃偺廳傒 
% dx = diff(X(:)) 偲側傞 W = ([dx;0]+[0;dx]).'/2 偑揔愗偱偡(X 偼丄尩枾偵
% 憹壛偡傞傕偺偲壖掕偟傑偡)丅
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% 僨乕僞僒僀僩偑Schoenberg-Whitney忦審
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% (***)   KNOTS(j) < X(j) < KNOTS(j+K) ,
%                             j=1:length(X)=length(KNOTS)-K ,
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% 傪枮偨偡(懡廳搙 K 偺愡揰偵偍偄偰摍娫妘偱偁傞)偲偒丄f 偼丄(***)偺師悢傪
% 尩枾偵枮偨偡儐僯乕僋側僗僾儔僀儞偱偡丅X 偺偄偔傜偐偺晹暘楍偵懳偟偰
% (***)傪枮偨偝側偄応崌丄僗僾儔僀儞偼弌椡偝傟傑偣傫丅
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% 梌偊傜傟偨僨乕僞僒僀僩偵懳偟偰丄偦偺傛偆側愡揰楍傪梌偊傞偺偼擄偟偄偐傕
% 偟傟側偄偨傔丄惓偺惍悢偲偟偰 KNOTS 傪巜掕偡傞偙偲偑壜擻偱偡丅偦偺応崌丄
% 壜擻偱偁傟偽丄X 偺偁傞晹暘楍偵懳偟偰 (***) 傪枮偨偡愡揰楍偑梌偊傜傟丄
% KNOTS 懡崁幃嬫暘偐傜峔惉偝傟傞僗僾儔僀儞傪弌椡偟傑偡丅
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% Y 偑峴楍丄傑偨偼傛傝堦斒揑偵丄[d1,...,ds,n] 偺N師尦攝楍偺応崌丄
% Y(:,...,:,j) 偼丄X(j) 偱嬤帡偝傟偨抣偱丄寢壥偺僗僾儔僀儞偼丄[d1,...,ds]
% 屄偺抣偵懳墳偟傑偡丅偙偺応崌丄岆嵎婎弨 (**) 撪偺幃 |Y(:,j) - f(X(j))|^2 
% 偼丄Y(:,j)-f(X(j)) 偺偡傋偰偺梫慺 d1*...*ds 偺擇忔榓傪堄枴偟傑偡丅
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% 僌儕僢僪壔偝傟偨僨乕僞傪嬤帡偡傞偙偲傕壜擻偱偡丅
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% SPAP2( {KNOTS1,...,KNOTSm}, [K1,...,Km], {X1,...,Xm}, Y ) 偼丄慻傒崌傢
% 偣師悢 Ki 偱丄i=1,...,m 偵偮偄偰丄i斣栚偺曄悢偺愡揰楍 KNOTSi 傪傕偮
% m曄悢僥儞僜儖愊僗僾儔僀儞傪弌椡偟傑偡丅偙傟偵懳偟偰偼丄偡傋偰偺 
% i := (i1,...,im) 偱(応崌偵傛偭偰偼廳傒晅偒)擇忔暯嬒偺堄枴偱
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% Y(:,...,:,i1,...,im) = f(X1(i1),...,Xm(im))  
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% 偑惉傝棫偪傑偡丅
% 儀僋僩儖抣偺丄峏偵偼N師尦偺抣偺僨乕僞傊偺嬤帡偺壜擻惈偵拲栚偟傑偡丅
% 1曄悢偺応崌偲堎側傝丄僼傿僢僩偝傟傞僨乕僞偑僗僇儔抣側傜偽丄擖椡攝楍 
% Y 偼m師尦偵偡傞偙偲偑偱偒傑偡丅偙偺偲偒丄(廳傒晅偒)擇忔暯嬒偺堄枴偱丄
% 偮偓偺傛偆偵側傝傑偡丅
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% 偡傋偰偺 i := (i1,...,im) 偱
% Y(i1,...,im) = f(X1(i1),...,Xm(im)),  
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% 椺戣 1:
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%      spap2(augknt(x([1 end]),2),2,x,y);
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% 偼丄僨乕僞 x,y 偺嵟彫擇忔捈慄嬤帡傪梌偊丄偡傋偰偺僒僀僩 x(j) 偑嬫娫 
% [x(1) .. x(end)] 撪偵偁傞偲壖掕偟傑偡丅堦曽丄
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%      spap2(1,2,x,y);
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% 偼丄忦審側偟偱偙傟傪幚峴偟傑偡丅偦偟偰丄忦審偑偁傞応崌丄
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%      w = ones(size(x)); w([1 end]) = 100;
%      spap2(1,2,x,y,w);
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% 偼丄偦偺僼傿僢僥傿儞僌偑側傞傋偔嵟弶偲嵟屻偺僨乕僞揰偱嬤偔側傞傛偆偵
% 嬤帡偟傑偡丅
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% 椺戣 2: 僗僥乕僩儊儞僩
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%      x = -2:.2:2; y=-1:.25:1; [xx, yy] = ndgrid(x,y); 
%      z = exp(-(xx.^2+yy.^2)); 
%      sp = spap2({augknt([-2:2],3),2},[3 4],{x,y},z);
%      fnplt(sp)
% 
% 偼丄2曄悢娭悢偵嬤帡傪峴偭偨恾傪嶌惉偟傑偡丅
% 偙偙偱 NDGRID 偺戙傢傝偵 MESHGRID 傪巊梡偡傞偲丄僄儔乕偵側傝傑偡丅
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% 嶲峫 SPAPI, SPAPS.


%   Copyright 1987-2004 C. de Boor and The MathWorks, Inc.