spcol.m

演示matlab曲线拟和与插直的基本方法

% SPCOL B-僗僾儔僀儞慖揰峴楍
%
% COLLOC = SPCOL(KNOTS,K,TAU) 偼丄峴楍
%
%      [ D^m(i)B_j(TAU(i)) : i=1:length(TAU), j=1:length(KNOTS)-K ] ,
%
% 偱偡丅偙偙偱丄D^m(i)B_j 偼 B_j 偺m(i)師旝暘丄B_j 偼丄愡揰楍 KNOTS 偵
% 懳偡傞師悢 K 偺j斣栚偺B-僗僾儔僀儞丄TAU 偼僒僀僩偺楍偱偡丅KNOTS 偲 
% TAU 偼丄嫟偵旕尭彮偱偁傞偲壖掕偟傑偡丅
% 偝傜偵丄m(i) 偼丄惍悢 #{ j<i : TAU(j) = TAU(i) }丄懄偪 TAU 偵偍偗傞 
% TAU(i) 偺椵愊懡廳搙偱偡丅
%
% 偙傟偼丄COLLOC 偺戞j楍偑丄楍 KNOTS 偵懳偡傞師悢 K 偺B-僗僾儔僀儞偺
% j斣栚丄偡側傢偪丄愡揰傪 KNOTS(j:j+K) 偲偡傞B-僗僾儔僀儞偺儀僋僩儖 
% TAU 偺偡傋偰偺梫慺偵偍偗傞抣偲丄偙偲偵傛傞偲旝暘傪娷傓偙偲傪堄枴偟傑偡丅
% COLLOC 偺i斣栚偺峴偼丄偙傟傜偺B-僗僾儔僀儞偡傋偰偺m(i)師旝暘偺 TAU(i) 
% 偱偺抣傪娷傒傑偡丅偙偙偱丄m(i) 偼丄TAU(i) 偵摍偟偄 TAU 偺慜偺梫慺偺悢
% 偱偡丅
%
% 椺戣:
%  tau = [0,0,0,1,1,2];          % 廬偭偰丄m 偼 [0,1,2,0,1,0] 偵摍偟偔
%                                % 側傝傑偡丅
%  k = 3; knots = augknt(0:2,k); % 廬偭偰丄knots 偼 [0,0,0,1,2,2,2] 偵
%  colloc = spcol(knots,k,tau)   % 摍偟偔側傝傑偡丅
%
% 偙偙偱丄COLLOC(:,j)  偺6偮偺梫慺偑娷傓偺偼丄0偱偺 B_j 偺抣偲丄1師丄
% 2師旝暘丄偦傟偐傜丄1偱偺 B_j 偺抣偲1師旝暘丄嵟屻偵2偱偺 B_j 偺抣偱偡丅
% 偙偙偱 B_j 偼丄愡揰楍 knots 偵懳偡傞k師偺B-僗僾儔僀儞偺j斣栚偱丄偨偲
% 偊偽丄B_2 偼丄knots 傪 B_j 傪 0,0,1,2 偲偡傞B-僗僾儔僀儞偱偡丅
%
% 巜掕偟偨抣偲丄応崌偵傛偭偰偼丄巜掕偟偨僒僀僩偱偺偄偔偮偐偺旝暘傪傕偮
% 僗僾儔僀儞傪嶌惉偡傞偨傔偵 COLLOC 傪巊梡偡傞偙偲偑偱偒傑偡丅
% 
% 椺戣:
%      a = -pi; b = pi;  tau = [a a a 0 b b]; k = 5;
%      knots = augknt([a,0,b],k);
%      sp = spmak(knots, ( spcol(knots,k,tau) \ ...
%          [sin(a);cos(a);-sin(a);sin(0);sin(b);cos(b)] ).' )
%
% 偼丄0偱偪傚偆偳1偮偺撪晹愡揰傪傕偮嬫娫 [a,b] 忋偱偺2師偺僗僾儔僀儞傪
% 梌偊傑偡丅偙偺僗僾儔僀儞偼 a,0,b 偵偍偄偰丄惓尫娭悢傪曗娫偟丄傑偨丄a 偵
% 偍偄偰1師偍傛傃2師旝暘傪丄偦偟偰 b 偵偍偄偰1師旝暘傪堦抳偝偣傑偡丅
%
% COLLOC = SPCOL(KNOTS,K,TAU,ARG1,ARG2,...) 偼丄僆僾僔儑儞偺堷悢 ARG1, 
% ARG2, ... 偵埶懚偡傞丄摨偠偐偁傞偄偼娭楢偡傞峴楍傪梌偊傑偡丅
%
% 僆僾僔儑儞堷悢偺1偮偑 'slvblk' 偺応崌丄COLLOC 偼丄SLVBLK 偱昁梫偲偝傟傞
% (僗僾儔僀儞偵懳偟偰巜掕偝傟偨)傎傏僽儘僢僋懳妏側宍幃偱偡丅
%
% 僆僾僔儑儞堷悢偺1偮偑 'sparse' 偺応崌丄COLLOC 偼丄僗僷乕僗峴楍偱偡丅
%
% 僆僾僔儑儞堷悢偺1偮偑 'noderiv' 偺応崌丄懡廳搙偼柍帇偝傟傑偡丅偡側傢偪丄
% 偡傋偰偺 i 偵懳偟偰 m(i) = 0 偱偡丅
%
% B-僗僾儔僀儞偺慟壔幃偼丄峴楍偺梫慺傪惗惉偡傞偨傔偵巊梡偝傟傑偡丅
%
% 椺戣:
%      t = [0,1,1,3,4,6,6,6]; x = linspace(t(1),t(end),101); 
%      c = spcol(t,3,x); plot(x,c)
%
% 偼丄梌偊傜傟偨愡揰楍 t 偵懳偟偰j斣栚偺2師偺B-僗僾儔僀儞偺抣偺揔愗側楍傪
% c(:,j) 偵惗惉偡傞偨傔偵 SPCOL 傪巊梡偟傑偡丅
%
% 嶲峫 SLVBLK, SPARSE, SPAPI, SPAP2, BSPLINE.


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