Texas Instruments TI-89 Tip List page 209

xl
yl
zmat
x
y
The z-values are passed as a 3x3 matrix only because that is a convenient way for the user to enter
the z-values, directly as they appear in a printed table.
The first two when() functions scale x and y to u and v as shown in [7]. The last line of the function
calculates and returns the interpolation result. The augment(augment(...))
to a single-column vector, to perform the matrix multiplication in [10]. The coefficient solution vector is
converted to a list, so that the built-in list multiplication can be used to find each term of the sum in [11].
As an example, suppose that we want to interpolate with this table at x = 0.27 and y = 0.55:
So we have
xl = {.1, .2, .3}
yl = {.4, .5, .6}
.1692 .2571 .3616
zmat =
.1987 .2860 .3894
.2474 .3335 .4350
x = 0.27
y = 0.55
and the call to do the interpolation looks like
intrpz9({.1,.2,.3},{.4,.5,.6},[.1692,.2571,.3616;.1987,.286,.3894;.2474,.3335,
.435],0.27,0.55)
which returns 0.3664.
This program, intrp9ui(), provides a user interface for intrpz9().
intrp9ui()
Prgm
©UI for intrpz9()
©calls math\intrpz9, util\rq2v, util\rq3v
©calls util\copyto_h by Samuel Stearly
©31mar01/dburkett@infinet.com
local x123,y123,zz1,zz2,zz3,xy,res,xl,yl,zmat,x,y,z,inhome,errdisp
©Error message display program
define errdisp(msg)=Prgm
dialog
Three-element list of the table x-coordinates {x1,x2,x3}
Three-element list of the table y-coordinates {y1,y2,y3}
3x3 matrix of the table z-values
The x-value at which to interpolate
The y-value at which to interpolate
0.4
0.1 0.1692
0.2 0.1987
0.3 0.2474
T
convertst the 3x3 z-matrix
0.5 0.6
0.2571 0.3616
0.2860 0.3894
0.3335 0.4350
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