/* file mbe5batch.mac 
   Jan. 2009 version.
   Maxima ver. 5.17.1,
   run with batch(mbe5batch); */
   
" this is mbe5batch.mac batch
  file: shows plots from Ch. 5,
     Maxima by Example. "$
  
(load(draw),load(qdraw))$

ratprint:false$


" 5.1 Quick Plots for Explicit Functions: ex(...) .
    does not include eps and jpg file examples:
    
    enter c; to continue "$
    
readonly(" ")$

qdraw( ex( [x,x^2,x^3],x,-3,3 ) )$

qdraw( ex([x,x^2,x^3],x,-3,3 ),yr(-2,2) )$ 

qdraw(ex([x,x^2,x^3],x,-3,3 ),yr(-2,2), lw(6))$

qdraw( ex( [x,x^2,x^3],x,-3,3 ),yr(-2,2),lw(6),key(bottom) )$

qdraw( ex( [x,x^2,x^3],x,-3,3 ),yr(-2,2),
                 lw(6),key(bottom), cut(grid, xyaxes) )$
                 
qdraw( ex( [x,x^2,x^3],x,-3,3 ),yr(-2,2),
                 lw(6), cut( all ) )$


qdraw( ex([x,x^2,x^3],x,-3,3 ),yr(-2,2),lw(6),
              key(bottom),pts( [ [-1,-1],[0,0],[1,1] ] ) )$

qdraw( ex( [x,x^2,x^3],x,-3,3 ),yr(-2,2), lw(6),key(bottom), 
              pts([ [-1,-1],[0,0],[1,1] ],ps(2),pc(magenta) ) )$
      
qdraw( ex( [x,x^2,x^3],x,-3,3 ),yr(-2,2), lw(6),key(bottom), 
           pts([ [-1,-1],[0,0],[1,1] ],ps(2),pc(magenta),pk("intersections") ) )$
           
qdraw( yr(-2,2),lw(6), ex( [x,x^2,x^3],x,-3,3 ),
              key(bottom), ex(sin(3*x)*exp(x/3),x,-3,3),
              pts([ [-1,-1],[0,0],[1,1] ]) )$
              
       
"5.2 Quick Plots for Implicit Functions: imp(...):

      enter c; to continue"$

readonly(" ")$    

qdraw( imp( sin(2*x)*cos(y)=0.4,x,-3,3,y,-3,3 ) ,
             cut(key) )$
             
qdraw( imp( [sin(2*x)*cos(y)=0.4,
             sin(2*x)*cos(y)=0.7,
             sin(2*x)*cos(y)=0.9] ,x,-3,3,y,-3,3 ) ,
             cut(key) )$
             
g : sin(2*x)*cos(y)$

             
qdraw( imp( [g = 0.4,g = 0.7,g = 0.9] ,x,-4.2,4.2,y,-3,3 ) ,
             cut(key) )$
             


"5.3 Contour Plots with contour(...):

       enter c; to continue"$

readonly(" ")$

qdraw( contour(g, x,-4.2,4.2, y,-3,3, cvals(0.4,0.7,0.9) ) )$

qdraw( contour(g,x,-4.2,4.2,y,-3,3,cvals(0.4,0.7,0.9),
        lw(2),lc(brown) ), ipgrid(15) )$
        
qdraw( contour(g,x,-4.2,4.2,y,-3,3,crange(4,0.2,0.9),
        lw(2),lc(brown) ), ipgrid(15)  )$
        
qdraw( contour(sin(x)*sin(y),x,-2,2,y,-2,2,crange(4,0.2,0.9),
              lw(3),lc(blue),add(xyaxes) ), ipgrid(15) )$
              

" 5.4 Density Plots with qdensity(...):

       enter c; to continue"$

readonly(" ")$

qdensity(x*y,[x,0,1,0.2],[y,0,1,0.2] )$

qdensity(x*y,[x,0,1,0.2],[y,0,1,0.2],
                 palette(gray) )$
                 
qdensity(x*y,[x,0,1,0.2],[y,0,1,0.2],
                 palette(color) )$                 
                 
                 
qdensity(x*y,[x,0,1,0.05],[y,0,1,0.05] )$

qdensity(sin(x)*sin(y),[x,-2,2,0.05],[y,-2,2,0.05] )$


" 5.5 Explicit Plots with Greater Control: ex1(...):

        enter c; to continue"$

readonly(" ")$

qdraw( xr(-1.4,2.8),yr(-1,2),
        ex1(x^2,x,-2,2,lw(5),lc(brown),lk("X^2")),
        ex1(2*x-1,x,-2,2,lw(2),lc(blue),lk("TANGENT")),
        ex1(-x/2 + 3/2,x,-2,2,lw(2),lc(magenta),lk("NORMAL") ) ,
         pts( [ [1,1] ],ps(2),pc(red) ) )$
         
qdraw( ex1(bessel_j(0,x),x,0,20,lc(red),lw(6),lk("bessel_j ( 0, x)") ),
          ex1(bessel_j(1,x),x,0,20,lc(blue),lw(5),lk("bessel_j ( 1, x)")),
          ex1(bessel_j(2,x),x,0,20,lc(brown),lw(4),lk("bessel_j ( 2, x)") ),
          ex1(bessel_j(3,x),x,0,20,lc(green),lw(3),lk("bessel_j ( 3, x)") ) )$
          
qdraw( ex1(bessel_j(0, sqrt(x)),x,0,50 ,lc(blue),
              lw(7),lk("J0( sqrt(x) )") ) , 
         line(0,0,50,0,lc(red),lw(2) ) )$
         
" 5.6 Explicit Plots with ex1(...) and Log Scaled Axes:

         enter c; to continue"$

readonly(" ")$

g : x*exp(-x)$

qdraw( ex1( log(g),x,0.001,10, lc(red) ),yr(-8,0)  )$

qdraw( ex1(g, x, 0.001,10,lc(red) ),
                 yr(0.0001, 1), log(y) )$
                 
qdraw( ex1(g, x, 0.001,10,lc(red),lw(7) ),
                 yr(0,0.4), log(x) )$
                 
qdraw( ex1(g, x, 0.001,10,lc(red) ),
                  yr(0.0001,1), log(xy) )$
                  
" 5.7 Data Plots with Error Bars: pts(...) and errorbars(...),
               this section needs fit1.dat and fit2.dat:
               
                 enter c; to continue"$
               
readonly(" ")$
               
plist : read_nested_list("fit1.dat");

qdraw( pts(plist) )$

qdraw( pts(plist, ps(2)), xr(0,12),yr(0,15) )$

qdraw( pts(plist,pc(blue),pk("fit1"), ps(2)), xr(0,12),yr(0,15),
          key(bottom), errorbars( plist, 1) )$
          
qdraw( pts(plist,pc(blue),pk("fit1"), ps(2)), xr(0,12),yr(0,15),
          key(bottom), errorbars( plist, 1, lw(3),lc(red) )  )$
          
dyl : [0.2,0.3,0.5,1.5,0.8,1,1.4,1.8,2,2]$

map(length,[plist,dyl] );

qdraw( pts(plist,pc(blue),pk("fit1"), ps(2)), xr(0,12),yr(0,15),
          key(bottom), errorbars( plist, dyl, lw(3),lc(red) )  )$
          
display2d:false$

pmatrix : apply( 'matrix, plist );

load(lsquares);

soln : (lsquares_estimates(pmatrix,[x,y],y=a*x+b,
                   [a,b]), float(%%) );
                   
[a,b] : (fpprintprec:5, map( 'rhs, soln[1] ) )$

[a,b];

qdraw( pts(plist,pc(blue),pk("fit1"), ps(2)), xr(0,12),yr(0,15),
          key(bottom), errorbars( plist, dyl, lw(3),lc(red) ),
         ex1( a*x + b,x,0,12, lc(brown),lk("linear fit") )  )$
         
printfile("fit2.dat");

p2list: read_nested_list("fit2.dat");

qdraw( pts(plist,pc(blue),pk("fit1"), ps(2)), xr(0,12),yr(0,15),
          key(bottom), errorbars( plist, dyl, lw(3),lc(red) ),
         ex1( a*x + b,x,0,12, lc(brown),lk("linear fit 1") ),
         pts(p2list, pc(magenta),pk("fit2"),ps(2)),
         errorbars( p2list,0.5,lw(3) ) )$
         

" 5.8 Implicit Plots with Greater Control: imp1(...):

         enter c; to continue"$

readonly(" ")$

eqn1 : 5*x^2 + 4*x*y + 8*y^2 - 16*x + 8*y - 16 = 0$

eqn2 : y+1 = 2*(x-2)$

eqn3 : y+1 = -(x-2)/2$

qdraw( imp1(eqn1,x,-2,6.4,y,-4,2,lc(red),lw(6),lk("ELLIPSE")),
              imp1(eqn2,x,-2,6.4,y,-4,2,lc(blue),lw(4),lk("ROT X AXIS")),
              imp1(eqn3,x,-2,6.4,y,-4,2,lc(brown),lw(4),lk("ROT Y AXIS") ),
          pts([ [2,-1] ],ps(2),pc(magenta),pk("TRANSLATED ORIGIN") ) )$
          
qdraw( imp1(y^3=x^2,x,-3,3,y,-1,3,lw(10),lc(dark-blue)) )$

" 5.9 Parametric Plots with para(...):

           enter c; to continue"$

readonly(" ")$

qdraw(xr(-1.5,2),yr(-2,2), 
         para(sin(t),sin(2*t),t,0,2*%pi ) ,
         pts( [ [sin(%pi/8),sin(%pi/4)] ],ps(2),pc(blue),pk("t = pi/8")),
         pts( [ [1,0] ],ps(2),pc(red),pk("t = pi/2")) )$
         
qdraw(xr(-3,4),yr(-1,40), para(2*cos(u),u^2,u,0,2*%pi) ,
         pts([ [2,0] ],ps(2),pc(blue),pk("u = 0")),
         pts( [ [0,(%pi/2)^2] ],ps(2), pc(red), pk("u = pi/2")),
         pts([ [-2,%pi^2]],ps(2),pc(green),pk("u = pi")),
         pts( [[0,(3*%pi/2)^2]],ps(2),pc(magenta),pk("u = 3*pi/2")) )$
         

" 5.10 Polar Plots with polar(...):

          enter c; to continue"$

readonly(" ")$

qdraw( polar(10/t,t,1,3*%pi,lc(brown),lw(5)),nticks(200),
            xr(-4,6),yr(-3,9),key(bottom) ,
       pts( [[10*cos(1),10*sin(1)]],ps(3),pc(red),pk("t = 1 rad")),         
     pts([[5*cos(2),5*sin(2)]],ps(3),pc(blue),pk("t = 2 rad") ),
              line(0,0,5*cos(2),5*sin(2)) )$
              

               
" 5.11 Geometric Figures: line(...), needs doplot1.mac:

             enter c; to continue"$
              
readonly(" ")$

qdraw( line(0,0,1,1) )$

qdraw( line(0,0,1,1,lc(blue),lw(6),lk("radius") ),
              xr(0,2),yr(0,2),key(bottom),
              pts([ [1,1] ] ,pc(red),pk("point")) )$
              
" series of vertical colored lines "$


load(doplot1)$

doplot1(20)$

" 5.12 Geometric Figures: rect(...):

           enter c; to continue"$

readonly(" ")$

qdraw( xr(-1,2),yr(-1,2),rect(0,0,1,1) )$

qdraw( xr(-1,2),yr(-1,2),
            rect(0,0,1,1,lw(5),lc(brown),fill(khaki) ) )$
            
qdraw( xr(-3,3),yr(-3,3), rect( -2.5,-2.5,2.5,2.5,lw(4),lc(blue) ),
         rect( -2,-2,2,2,lw(4),lc(red) ),
         rect( -1.5,-1.5,1.5,1.5,lw(4),lc(green) ),
         rect( -1,-1,1,1,lw(4),lc(brown) ),
         rect( -.5,-.5,.5,.5,lw(4),lc(magenta) ),
           cut(all) )$
           
" 5.13 Geometric Figures: poly(...), needs file doplot2.mac:

            enter c; to continue"$
             
readonly(" ")$

qdraw( xr(-2,2),yr(-1,2),cut(all),
            poly([ [-1,-1],[1,-1], [2,2] ]  ) )$
            

" eighteen triangles in color "$

load(doplot2)$

doplot2()$

" 5.14 Geometric Figures: circle(...) and ellipse(...):

            enter c; to continue"$

readonly(" ")$
             
qdraw( xr(-2, 2), yr(-2, 2), circle( 0, 0, 1 ) )$

qdraw(xr(-2.1,2.1),yr(-1.5,1.5),cut(all),
            circle(0,0,1,lw(5),lc(brown),fill(khaki) ),
              line(-1.5,-1.5,1.5,1.5,lw(8), lc(red) ),
                key(bottom) )$
                
qdraw(xr(-2.1,2.1),yr(-1.5,1.5),cut(all),
            line(-1.5,-1.5,1.5,1.5,lw(8),lc(red) ),
            circle(0,0,1,lw(8),lc(brown),fill(khaki) ),
                key(bottom) )$

qdraw( xr(-4.2,4.2),yr(-3,3),
         ellipse(0,0,3,2,90,270) )$
			
qdraw( xr(-5.6,5.6),yr(-4,4),ex1(x,x,-4,4,lc(blue),lw(5)),
                  ex1(4*cos(x),x,-4,4,lc(red),lw(5) ),
         ellipse(0,0,3,1,90,270,lc(brown),lw(5),fill(khaki)) ,
             cut(all) )$
             

" 5.15 Geometric Figures: vector(..):

           enter c; to continue"$

readonly(" ")$

qdraw( xr(-2,2), yr(-2,2), vector( [-1,-1], [2,2] ) )$ 

qdraw(xr(-2,2),yr(-2,2),
           vector([-1,-1],[2,2],lw(5),lc(brown),lk("vec 1")),
            key(bottom) )$
            
qdraw(xr(-2,2),yr(-2,2),
           vector([0,0],[1,1],lw(5),lc(blue),lk("vec 1"),
                  ht(e),hb(t),ha(45) ), key(bottom) )$

qdraw(xr(-2.8,2.8),yr(-2,2),
           vector([0,0],[1,1],lw(5),lc(blue),lk("vec 1"),
                       ht(e),hb(t),ha(45) ),
           vector([0,0],[-1,-1],lw(5),lc(red),lk("vec 2")),
            key(bottom) )$

" 5.16 Geometric Figures: arrowhead(..):

             enter c; to continue"$

readonly(" ")$

qdraw(xr(-2.8,2.8),yr(-2,2),
            arrowhead(1.5,0,180,.3),arrowhead(0,1,270,.3),
            arrowhead(-1.5,0,0,.3),arrowhead(0,-1,90,.3) )$
            

" 5.17.3 Using Windows Fonts with the Gnuplot Console Window:
           As described in the text, right click the graphics window
           icon in the upper left hand corner, choose Options,
           Choose Font, and in the fonts panel, choose Graecall font
           from the left panel, choose "regular" from the middle
           panel, and choose size 36 from the right panel, and
           then click "ok".  The "q" will be converted to
           the Greek lower case theta.

           enter c; to continue"$

readonly(" ")$

qdraw(xr(0,2.8),yr(0,2),
             line(0,0,2.8,0),
             line(0,0,2,2,lc(blue),lw(5) ),
           ellipse(0,0,1,1,0,45 ),
           arrowhead(0.707,0.707,135,0.15),
            label(["q",1,0.4]), cut(all) )$
            

            
" 5.18 Even More with more(...):
         The Windows console version not as powerful as 
         the eps version shown in the text, but for what it's worth:

          enter c; to continue"$
            

readonly(" ")$

            
qdraw(  ex([x,x^2,x^3],x,-2,2),
          more(xlabel = "X AXIS", title="intersections of x, x^2, x^3" ),
		   cut(key), vector([-1,5],[-0.4,-2.7],lc(red),hl(0.1) ),
               label(["x^2",-0.9,6]),
               vector([-1.2,-6],[-0.5,0],lc(turquoise),lw(5)),
               label( ["x^3", -1,-5.5] ),
              pts( [[-1,-1],[0,0],[1,1]],ps(2),pc(magenta) ) )$