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[Maxima-commits] [git] Maxima CAS branch rtoy-odepack-m4math-update-examples created. branch-5_48-base-173-g25ecbac0d
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From: rtoy <rt...@us...> - 2025-09-03 22:13:59
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The branch, rtoy-odepack-m4math-update-examples has been created
at 25ecbac0d49fa658dbbdb1f84dc8f440f92a1155 (commit)
- Log -----------------------------------------------------------------
commit 25ecbac0d49fa658dbbdb1f84dc8f440f92a1155
Author: Raymond Toy <toy...@gm...>
Date: Wed Sep 3 15:13:35 2025 -0700
Ignore odepack.texi
It's generated from odepack.texi.m4 now.
diff --git a/doc/info/.gitignore b/doc/info/.gitignore
index f5260f67d..e3a99709a 100644
--- a/doc/info/.gitignore
+++ b/doc/info/.gitignore
@@ -25,6 +25,7 @@ MathFunctions.texi
Numerical.texi
Special.texi
distrib.texi
+odepack.texi
orthopoly.texi
zeilberger.texi
trigtools.texi
commit f053771ccddf36028086b97bdb8cf7bc51135c39
Author: Raymond Toy <toy...@gm...>
Date: Wed Sep 3 15:11:21 2025 -0700
Add TeX formulas and code blocks to generate the examples
There's a bit of duplication in the examples because each code block
is independent of the others, so we need to copy some initialization
code into each block. This also means some of the text had to be
rephrased a bit.
diff --git a/doc/info/odepack.texi.m4 b/doc/info/odepack.texi.m4
index 051b6a442..1c6ccda34 100644
--- a/doc/info/odepack.texi.m4
+++ b/doc/info/odepack.texi.m4
@@ -41,6 +41,16 @@ Of the eight variants of the solver, Maxima currently only has an
interface to @code{dlsode}.
Let's say we have this system of equations to solve:
+m4_displaymath(
+<<<
+\eqalign{
+f_1 &= -0.04 y_1 + 10^4 y_2 y_3 \cr
+f_3 &= 3\times 10^7 y_2^2 \cr
+{dy_1 \over dt} &= f_1 \cr
+{dy_2 \over dt} &= -f_1 - f_3 \cr
+{dy_3 \over dt} &= f_3 \cr
+}>>>,
+<<<
@example
f1 = -.04d0*y1 + 1d4*y2*y3
f3 = 3d7*y2*y2
@@ -48,29 +58,70 @@ Let's say we have this system of equations to solve:
dy2/dt = -f1 - f3
dy3/dt = f3
@end example
-The independent variable is @math{t}; the dependent variables are @math{y1}, @math{y2},
-and @math{y3},
+>>>)
+
+The independent variable is @math{t}; the dependent variables are
+m4_mathcomma(y_1)
+m4_mathcomma(y_2)
+and
+m4_mathdot(y_3)
To start the solution, set up the differential equations to solved:
-@example
-load("dlsode");
-f1: -.04d0*y1 + 1d4*y2*y3$
-f3: 3d7*y2*y2$
-f2: -f1 - f3$
-fex: [f1, f2, f3];
+@c ===beg===
+@c load("dlsode")$
+@c f1: -.04d0*y1 + 1d4*y2*y3$
+@c f3: 3d7*y2*y2$
+@c f2: -f1 - f3$
+@c fex: [f1, f2, f3];
+@c ===end===
+@example maxima
+(%i1) load("dlsode")$
+(%i2) f1: -.04d0*y1 + 1d4*y2*y3$
+(%i3) f3: 3d7*y2*y2$
+(%i4) f2: -f1 - f3$
+@group
+(%i5) fex: [f1, f2, f3];
+(%o5) [10000.0 y2 y3 - 0.04 y1,
+ 2 2
+ - 10000.0 y2 y3 - 3.0e7 y2 + 0.04 y1, 3.0e7 y2 ]
+@end group
@end example
Initialize the solver, where we have selected method 21:
-@example
+@c ===beg===
+@c load("dlsode")$
+@c f1: -.04d0*y1 + 1d4*y2*y3$
+@c f3: 3d7*y2*y2$
+@c f2: -f1 - f3$
+@c fex: [f1, f2, f3];
+@c state : dlsode_init(fex, ['t,y1,y2,y3], 21);
+@c ===end===
+@example maxima
+(%i1) load("dlsode")$
+(%i2) f1: -.04d0*y1 + 1d4*y2*y3$
+(%i3) f3: 3d7*y2*y2$
+(%i4) f2: -f1 - f3$
+@group
+(%i5) fex: [f1, f2, f3];
+(%o5) [10000.0 y2 y3 - 0.04 y1,
+ 2 2
+ - 10000.0 y2 y3 - 3.0e7 y2 + 0.04 y1, 3.0e7 y2 ]
+@end group
+@group
(%i6) state : dlsode_init(fex, ['t,y1,y2,y3], 21);
-(%o6) [[f, #<Function "LAMBDA ($T $Y1 $Y2 $Y3)" @{49DAC061@}>],
-[vars, [t, y1, y2, y3]], [mf, 21], [neq, 3], [lrw, 58], [liw, 23], [rwork, @{Li\
-sp Array: #(0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
- 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
- 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
+(%o6) [[f, #<Function "LAMBDA ($T $Y1 $Y2 $Y3)" @{6177C099@}>],
+[vars, [t, y1, y2, y3]], [mf, 21], [neq, 3], [lrw, 58],
+[liw, 23], [rwork, @{Lisp Array: #(0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.\
+0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
+ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0\
+.0 0.0 0.0 0.0
+ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0\
+.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0)@}],
-[iwork, @{Lisp Array: #(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)@}],
-[fjac, #<Function "LAMBDA ($T $Y1 $Y2 $Y3)" @{49D52AC9@}>]]
+[iwork,
+@{Lisp Array: #(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)@}],
+[fjac, #<Function "LAMBDA ($T $Y1 $Y2 $Y3)" @{616B2099@}>]]
+@end group
@end example
The arrays rwork and iwork carry state between calls to
@mref{dlsode_step}, so they should not be modified by the user. In
@@ -80,31 +131,72 @@ Now that the algorithm has been initialized we can compute solutions
to the differential equation, using the @var{state} returned above.
For this example, we want to compute the solution at times
-@code{0.4*10^k} for @math{k} from 0 to 11, with the initial values of 1, 0, 0
-for the dependent variables and with a relative tolerance of 1d-4 and
-absolute tolerances of 1e-6, 1e-10, and 1d-6 for the dependent
+m4_math(0.4\times 10^k,
+@code{0.4*10^k})
+for @math{k} from 0 to 11, with the initial values of 1, 0, 0
+for the dependent variables and with a relative tolerance of
+m4_math(10^{-4}, 1e-4)
+and
+absolute tolerances of
+m4_mathcomma(10^{-6}, 1e-6)
+m4_mathcomma(10^{-10}, 1e-10)
+and
+m4_math(10^{-6}, 1e-6)
+for the dependent
variables.
-Then
-@example
-y: [1d0, 0d0, 0d0];
-t: 0d0;
-rtol : 1d-4;
-atol: [1d-6, 1d-10, 1d-6];
-istate: 1;
-t:0d0;
-tout:.4d0;
-
-for k : 1 thru 12 do
+Then, putting everything together
+@c ===beg===
+@c load("dlsode")$
+@c f1: -.04d0*y1 + 1d4*y2*y3$
+@c f3: 3d7*y2*y2$
+@c f2: -f1 - f3$
+@c fex: [f1, f2, f3];
+@c state : dlsode_init(fex, ['t,y1,y2,y3], 21)$
+@c y: [1d0, 0d0, 0d0]$
+@c t: 0d0$
+@c rtol : 1d-4$
+@c atol: [1d-6, 1d-10, 1d-6]$
+@c istate: 1$
+@c t:0d0$
+@c tout:.4d0$
+@c
+@c for k : 1 thru 12 do
+@c block([],
+@c result: dlsode_step(y, t, tout, rtol, atol, istate, state),
+@c printf(true, "At t = ~12,4,2e y = ~{~14,6,2e~}~%", result[1], result[2]),
+@c istate : result[3],
+@c tout : tout * 10);
+@c ===end===
+@example maxima
+(%i1) load("dlsode")$
+(%i2) f1: -.04d0*y1 + 1d4*y2*y3$
+(%i3) f3: 3d7*y2*y2$
+(%i4) f2: -f1 - f3$
+@group
+(%i5) fex: [f1, f2, f3];
+(%o5) [10000.0 y2 y3 - 0.04 y1,
+ 2 2
+ - 10000.0 y2 y3 - 3.0e7 y2 + 0.04 y1, 3.0e7 y2 ]
+@end group
+(%i6) state : dlsode_init(fex, ['t,y1,y2,y3], 21)$
+(%i7) y: [1d0, 0d0, 0d0]$
+(%i8) t: 0d0$
+(%i9) rtol : 1d-4$
+(%i10) atol: [1d-6, 1d-10, 1d-6]$
+(%i11) istate: 1$
+(%i12) t:0d0$
+@group
+(%i13) tout:.4d0$
+
+@end group
+@group
+(%i14) for k : 1 thru 12 do
block([],
result: dlsode_step(y, t, tout, rtol, atol, istate, state),
printf(true, "At t = ~12,4,2e y = ~@{~14,6,2e~@}~%", result[1], result[2]),
istate : result[3],
tout : tout * 10);
-@end example
-
-This produces the output:
-@example
At t = 4.0000e-01 y = 9.851726e-01 3.386406e-05 1.479357e-02
At t = 4.0000e+00 y = 9.055142e-01 2.240418e-05 9.446344e-02
At t = 4.0000e+01 y = 7.158050e-01 9.184616e-06 2.841858e-01
@@ -117,9 +209,10 @@ At t = 4.0000e+07 y = 5.306413e-05 2.122677e-10 9.999469e-01
At t = 4.0000e+08 y = 5.494530e-06 2.197824e-11 9.999945e-01
At t = 4.0000e+09 y = 5.129458e-07 2.051784e-12 9.999995e-01
At t = 4.0000e+10 y = -7.170563e-08 -2.868225e-13 1.000000e+00
+(%o14) done
+@end group
@end example
-
@node Functions and Variables for odepack, , Getting Started with ODEPACK, Package odepack
@section Functions and Variables for odepack
commit 8a86e987d94ae36964c6a53b8c0ba0c325a9a3df
Author: Raymond Toy <toy...@gm...>
Date: Wed Sep 3 14:30:21 2025 -0700
Rename odepack.texi to odepack.texi.m4
In preparation for adding some nice TeX formulas.
diff --git a/doc/info/odepack.texi b/doc/info/odepack.texi.m4
similarity index 100%
rename from doc/info/odepack.texi
rename to doc/info/odepack.texi.m4
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