/*               COPYRIGHT NOTICE

Copyright (C) 2014, 2015 Edwin L. (Ted) Woollett
http://www.csulb.edu/~woollett

k1util.mac is a utility file associated with Ch. 1 of
Computational Physics with Maxima or R, Numerical
Differentiation, Quadrature, and Roots.
 See  cp1.pdf for more info.

This program is free software; you can redistribute
it and/or modify it under the terms of the
GNU General Public License as published by
the Free Software Foundation; either version 2 
of the License, or (at your option) any later version. 

This program is distributed in the hope that it
will be useful, but WITHOUT ANY WARRANTY;
without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the 
GNU General Public License for more details at
http://www.gnu.org/copyleft/gpl.html
*/



fll(x) := [first(x),last(x),length(x)]$

head(mylist) :=
block([numL,nleft:6],
    numL : length(mylist),
    rest (mylist, -(numL - nleft)))$
    
tail(mylist) :=
block([numL,nleft:6],
    numL : length(mylist),
    rest (mylist, numL - nleft))$
    
take(%aL,%nn) := (map(lambda([x],part(x,%nn)), %aL))$


merge(list1,list2) := (flatten ( cons(list1, list2) ) )$

/*
(%i21) aa : [a1,a2,a3]$
(%i22) bb : [b1,b2,b3]$    
(%i25) merge(aa,bb);
(%o25) [a1,a2,a3,b1,b2,b3]
*/

/*  print(" merge(list1, list2) ")$  
    print(" fll(mylist), head(mylist), tail(mylist), take(mylist,mm) ")$
*/

/*
example using fll and take:

SHO WITH UNIT PERIOD

fll, head, tail, and take are loaded by maxima-init.mac
and are in k1util.mac

SHO WITH UNIT PERIOD

(%i13) pts : rk([vx,-4*%pi^2*x],[x,vx],[1,0],[t,0,1,0.01])$

(%i15) fll(pts);
(%o15) [[0.0,1.0,0.0],[1.0,0.99999995729235,5.1201813129342355E-6],101]

list of times:

(%i16) tL : take(pts,1)$
(%i17) fll(tL);
(%o17) [0.0,1.0,101]
---------------
plot of x(t) vs. t:

list of positions:

(%i18) xL : take(pts,2)$
(%i19) fll(xL);
(%o19) [1.0,0.99999995729235,101]
(%i20) plot2d([discrete,tL,xL],[x,0,1],[xlabel,"T"],[ylabel,"X"])$
(%i21) plot2d([discrete,tL,xL],[x,0,1],[xlabel,"T"],[ylabel,"X"],
          [style,[lines,3]])$
		 
---------------------
plot of vx(t) vs. t:

list of velocities:
		  
(%i22) vxL : take(pts,3)$
(%i23) fll(vxL);
(%o23) [0.0,5.1201813129342355E-6,101]
(%i24) plot2d([discrete,tL,vxL],[x,0,1],[xlabel,"T"],[ylabel,"Vx"],
            [style,[lines,3]])$

-------------------------------------
*/

/*  make_pts(x1,y1,xf,yf,N), an example of Maxima
    list arithmetic methods and use of makelist,
    fills in intermediate points along a straight line
    between (x1,y1) and (xf,yf), and returns the list
    [xL,yL].
    N = number of intervals, N+1 = number of points  */
    

make_pts(x1,y1,%xf,%yf,N):=
block([h, slope, %xL,%yL, numer], numer:true,   
   h : (%xf - x1)/N,
   slope : (%yf-y1)/(%xf-x1),
   %xL : makelist(x,x,x1,%xf,h),
   %yL :  y1 + slope*(%xL - x1),
   [ %xL, %yL ])$    

/*
(%i7) make_pts(0,0,4,4,8);
(%o7) [[0,0.5,1.0,1.5,2.0,2.5,3.0,3.5,4.0],[0,0.5,1.0,1.5,2.0,2.5,3.0,3.5,
                                            4.0]]
*/

/*   find_x( x_list, y_list )
    given two equal length lists, a x_list and a list
   of the corresponding y values, y_list, find the
   value of x corresponding to the minimum value of y. */


which_min(aL) :=
block([amin,j,jval:0,numer ],numer:true,
    amin:lmin(aL),
    for j thru length(aL) do 
       if is(equal(aL[j], amin)) then (
	         jval : j,
		       return()),
		jval)$
		
/*		
(%i2) xL : makelist(x,x,1,10);
(%o2) [1,2,3,4,5,6,7,8,9,10]
(%i3) which_min(xL);
(%o3) 1
*/

find_x(xL,yL) := (xL[which_min(yL)])$