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[doc] Move Maxima scripts for geodesics to doc/other/maxima/geod.mac
This commit is contained in:
Adeel Ahmad
parent
a10815366a
commit
df0cafdd19
232
doc/other/maxima/geod.mac
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232
doc/other/maxima/geod.mac
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/*
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Compute the series expansions for the ellipsoidal geodesic problem.
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Copyright (c) Charles Karney (2009-2015) <charles@karney.com> and
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licensed under the MIT/X11 License. For more information, see
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https://geographiclib.sourceforge.io
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References:
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Charles F. F. Karney,
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Algorithms for geodesics, J. Geodesy 87, 43-55 (2013),
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https://doi.org/10.1007/s00190-012-0578-z
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Addenda: https://geographiclib.sourceforge.io/geod-addenda.html
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The code below contains minor modifications to conform with
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Boost Geometry style guidelines.
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To run the code, start Maxima and enter
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load("geod.mac")$
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*/
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taylordepth:5$
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ataylor(expr,var,ord):=expand(ratdisrep(taylor(expr,var,0,ord)))$
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jtaylor(expr,var1,var2,ord):=block([zz],expand(subst([zz=1],
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ratdisrep(taylor(subst([var1=zz*var1,var2=zz*var2],expr),zz,0,ord)))))$
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computeI1(maxpow):=block([sintegrand,sintegrandexp,s,sigma,tau1,k2,eps],
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sintegrand:sqrt(1+k2*sin(sigma)^2),
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sintegrandexp:ataylor(
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(1-eps)*subst([k2=4*eps/(1-eps)^2],sintegrand),
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eps,maxpow),
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s:trigreduce(integrate(sintegrandexp,sigma)),
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s:s-subst(sigma=0,s),
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A1:expand(subst(sigma=2*%pi,s)/(2*%pi)),
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tau1:ataylor(s/A1,eps,maxpow),
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for i:1 thru maxpow do C1[i]:coeff(tau1,sin(2*i*sigma)),
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if expand(tau1-sigma-sum(C1[i]*sin(2*i*sigma),i,1,maxpow)) # 0
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then error("left over terms in B1"),
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A1:A1/(1-eps),
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'done)$
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codeA1(maxpow):=block([tab2:" ",tab3:" "],
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print("// The scale factor A1-1 = mean value of (d/dsigma)I1 - 1
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static inline CT evaluate_series_A1(CT eps) {
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CT eps2 = math::sqr(eps);
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CT t;
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switch (SeriesOrder/2) {"),
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for n:0 thru entier(maxpow/2) do block([
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q:horner(ataylor(subst([eps=sqrt(eps2)],A1*(1-eps)-1),eps2,n)),
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linel:1200],
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print(concat(tab2,"case ",string(n),":")),
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print(concat(tab3,"t = ",string(q),";")),
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print(concat(tab3,"break;"))),
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print(" }
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return (t + eps) / (1 - eps);
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}"),
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'done)$
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computeI2(maxpow):=block([sintegrand,sintegrandexp,s,sigma,tau1,k2,eps],
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sintegrand:1/sqrt(1+k2*sin(sigma)^2),
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sintegrandexp:ataylor(
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(1+eps)*subst([k2=4*eps/(1-eps)^2],sintegrand),
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eps,maxpow),
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s:trigreduce(integrate(sintegrandexp,sigma)),
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s:s-subst(sigma=0,s),
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A2:expand(subst(sigma=2*%pi,s)/(2*%pi)),
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tau1:ataylor(s/A2,eps,maxpow),
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for i:1 thru maxpow do C2[i]:coeff(tau1,sin(2*i*sigma)),
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if expand(tau1-sigma-sum(C2[i]*sin(2*i*sigma),i,1,maxpow)) # 0
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then error("left over terms in B2"),
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A2:A2/(1+eps),
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'done)$
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codeA2(maxpow):=block([tab2:" ",tab3:" "],
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print("// The scale factor A2-1 = mean value of (d/dsigma)I2 - 1
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CT evaluate_series_A2(CT const& eps)
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{
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CT const eps2 = math::sqr(eps);
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CT t;
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switch (SeriesOrder/2) {"),
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for n:0 thru entier(maxpow/2) do block([
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q:horner(ataylor(subst([eps=sqrt(eps2)],A2*(1+eps)-1),eps2,n)),
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linel:1200],
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print(concat(tab2,"case ",string(n),":")),
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print(concat(tab3,"t = ",string(q),";")),
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print(concat(tab3,"break;"))),
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print(" }
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return (t - eps) / (1 + eps);
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}"),
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'done)$
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computeI3(maxpow):=block([int,intexp,dlam,eta,del,eps,nu,f,z,n],
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maxpow:maxpow-1,
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int:subst([k2=4*eps/(1-eps)^2],
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(2-f)/(1+(1-f)*sqrt(1+k2*sin(sigma)^2))),
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int:subst([f=2*n/(1+n)],int),
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intexp:jtaylor(int,n,eps,maxpow),
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dlam:trigreduce(integrate(intexp,sigma)),
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dlam:dlam-subst(sigma=0,dlam),
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A3:expand(subst(sigma=2*%pi,dlam)/(2*%pi)),
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eta:jtaylor(dlam/A3,n,eps,maxpow),
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A3:jtaylor(A3,n,eps,maxpow),
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for i:1 thru maxpow do C3[i]:coeff(eta,sin(2*i*sigma)),
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if expand(eta-sigma-sum(C3[i]*sin(2*i*sigma),i,1,maxpow)) # 0
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then error("left over terms in B3"),
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'done)$
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codeA3(maxpow):=block([tab2:" ",tab3:" "],
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print("// The scale factor A3 = mean value of (d/dsigma)I3
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static inline void evaluate_series_A3(CT const& n, CT c[])
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{
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switch (SeriesOrder) {"),
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for nn:0 thru maxpow do block(
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[q:if nn=0 then 0 else
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jtaylor(subst([n=n],A3),n,eps,nn-1),
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linel:1200],
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print(concat(tab2,"case ",string(nn),":")),
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for i : 0 thru nn-1 do
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print(concat(tab3,"c[",i,"] = ",
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string(horner(coeff(q,eps,i))),";")),
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print(concat(tab3,"break;"))),
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print(" }
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}"),
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'done)$
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codeC1(maxpow):=block([tab2:" ",tab3:" "],
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print("// The coefficients C1[l] in the Fourier expansion of B1
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static inline evaluate_coeffs_C1(CT eps, CT c[]) {
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CT eps2 = math::sqr(eps);
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CT d = eps;
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switch (SeriesOrder) {"),
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for n:0 thru maxpow do (
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print(concat(tab2,"case ",string(n),":")),
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for m:1 thru n do block([q:d*horner(
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subst([eps=sqrt(eps2)],ataylor(C1[m],eps,n)/eps^m)),
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linel:1200],
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if m>1 then print(concat(tab3,"d *= eps;")),
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print(concat(tab3,"c[",string(m),"] = ",string(q),";"))),
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print(concat(tab3,"break;"))),
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print(" }
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}"),
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'done)$
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revertI1(maxpow):=block([tau,eps,tauacc:1,sigacc:0],
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for n:1 thru maxpow do (
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tauacc:trigreduce(ataylor(
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-sum(C1[j]*sin(2*j*tau),j,1,maxpow-n+1)*tauacc/n,
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eps,maxpow)),
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sigacc:sigacc+expand(diff(tauacc,tau,n-1))),
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for i:1 thru maxpow do C1p[i]:coeff(sigacc,sin(2*i*tau)),
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if expand(sigacc-sum(C1p[i]*sin(2*i*tau),i,1,maxpow)) # 0
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then error("left over terms in B1p"),
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'done)$
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codeC1p(maxpow):=block([tab2:" ",tab3:" "],
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print("// The coefficients C1p[l] in the Fourier expansion of B1p
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static inline evaluate_coeffs_C1p(CT eps, CT c[])
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{
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CT const eps2 = math::sqr(eps);
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CT d = eps;
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switch (SeriesOrder) {"),
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for n:0 thru maxpow do (
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print(concat(tab2,"case ",string(n),":")),
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for m:1 thru n do block([q:d*horner(
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subst([eps=sqrt(eps2)],ataylor(C1p[m],eps,n)/eps^m)),
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linel:1200],
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if m>1 then print(concat(tab3,"d *= eps;")),
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print(concat(tab3,"c[",string(m),"] = ",string(q),";"))),
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print(concat(tab3,"break;"))),
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print(" }
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}"),
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'done)$
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codeC2(maxpow):=block([tab2:" ",tab3:" "],
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print("// The coefficients C2[l] in the Fourier expansion of B2
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static inline void evaluate_coeffs_C2(CT const& eps, CT c[])
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{
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CT const eps2 = math::sqr(eps);
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CT d = eps;
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switch (SeriesOrder) {"),
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for n:0 thru maxpow do (
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print(concat(tab2,"case ",string(n),":")),
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for m:1 thru n do block([q:d*horner(
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subst([eps=sqrt(eps2)],ataylor(C2[m],eps,n)/eps^m)),
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linel:1200],
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if m>1 then print(concat(tab3,"d *= eps;")),
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print(concat(tab3,"c[",string(m),"] = ",string(q),";"))),
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print(concat(tab3,"break;"))),
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print(" }
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}"),
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'done)$
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codeC3(maxpow):=block([tab2:" ",tab3:" "],
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print("// The coefficients C3[l] in the Fourier expansion of B3
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static inline void evaluate_coeffs_C3(CT const& n, CT c[])
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{
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const CT n2 = math::sqr(n);
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switch (SeriesOrder) {"),
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for nn:0 thru maxpow do block([c],
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print(concat(tab2,"case ",string(nn),":")),
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c:0,
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for m:1 thru nn-1 do block(
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[q:if nn = 0 then 0 else
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jtaylor(subst([n=n],C3[m]),_n,eps,nn-1),
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linel:1200],
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for j:m thru nn-1 do (
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print(concat(tab3,"c[",c,"] = ",
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string(horner(coeff(q,eps,j))),";")),
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c:c+1)
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),
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print(concat(tab3,"break;"))),
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print(" }
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}"),
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'done)$
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maxpow:8$
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computeI1(maxpow)$
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computeI2(maxpow)$
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computeI3(maxpow)$
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revertI1(maxpow)$
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codeA1(maxpow)$
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codeA2(maxpow)$
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codeA3(maxpow)$
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codeC1(maxpow)$
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codeC2(maxpow)$
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codeC3(maxpow)$
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codeC1p(maxpow)$
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@ -30,51 +30,8 @@ namespace boost { namespace geometry { namespace series_expansion {
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The expansion above is performed in Maxima, a Computer Algebra System.
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The C++ code (that yields the function evaluate_series_A1 below) is
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generated by the following Maxima script and is based on script:
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http://geographiclib.sourceforge.net/html/geod.mac
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// Maxima script begin
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taylordepth:5$
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ataylor(expr,var,ord):=expand(ratdisrep(taylor(expr,var,0,ord)))$
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jtaylor(expr,var1,var2,ord):=block([zz],expand(subst([zz=1],
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ratdisrep(taylor(subst([var1=zz*var1,var2=zz*var2],expr),zz,0,ord)))))$
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computeI1(maxpow):=block([sintegrand,sintegrandexp,s,sigma,tau1,k2,eps],
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sintegrand:sqrt(1+k2*sin(sigma)^2),
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sintegrandexp:ataylor(
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(1-eps)*subst([k2=4*eps/(1-eps)^2],sintegrand),
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eps,maxpow),
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s:trigreduce(integrate(sintegrandexp,sigma)),
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s:s-subst(sigma=0,s),
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A1:expand(subst(sigma=2*%pi,s)/(2*%pi)),
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tau1:ataylor(s/A1,eps,maxpow),
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for i:1 thru maxpow do C1[i]:coeff(tau1,sin(2*i*sigma)),
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if expand(tau1-sigma-sum(C1[i]*sin(2*i*sigma),i,1,maxpow)) # 0
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then error("left over terms in B1"),
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A1:A1/(1-eps),
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'done)$
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codeA1(maxpow):=block([tab2:" ",tab3:" "],
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print("// The scale factor A1-1 = mean value of (d/dsigma)I1 - 1
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static inline CT evaluate_series_A1(CT eps) {
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CT eps2 = math::sqr(eps);
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CT t;
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switch (SeriesOrder/2) {"),
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for n:0 thru entier(maxpow/2) do block([
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q:horner(ataylor(subst([eps=sqrt(eps2)],A1*(1-eps)-1),eps2,n)),
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linel:1200],
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print(concat(tab2,"case ",string(n),":")),
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print(concat(tab3,"t = ",string(q),";")),
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print(concat(tab3,"break;"))),
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print(" }
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return (t + eps) / (1 - eps);
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}"),
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'done)$
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maxpow:8$
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computeI1(maxpow)$
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codeA1(maxpow)$
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// Maxima script end
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generated by the following Maxima script:
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geometry/doc/other/maxima/geod.mac
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To replace each number x by CT(x) the following
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script can be used:
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@ -123,52 +80,8 @@ namespace boost { namespace geometry { namespace series_expansion {
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The expansion above is performed in Maxima, a Computer Algebra System.
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The C++ code (that yields the function evaluate_series_A2 below) is
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generated by the following Maxima script and is based on script:
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http://geographiclib.sourceforge.net/html/geod.mac
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// Maxima script begin
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computeI2(maxpow):=block([sintegrand,sintegrandexp,s,sigma,tau1,k2,eps],
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sintegrand:1/sqrt(1+k2*sin(sigma)^2),
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sintegrandexp:ataylor(
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(1+eps)*subst([k2=4*eps/(1-eps)^2],sintegrand),
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eps,maxpow),
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s:trigreduce(integrate(sintegrandexp,sigma)),
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s:s-subst(sigma=0,s),
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A2:expand(subst(sigma=2*%pi,s)/(2*%pi)),
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tau1:ataylor(s/A2,eps,maxpow),
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for i:1 thru maxpow do C2[i]:coeff(tau1,sin(2*i*sigma)),
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if expand(tau1-sigma-sum(C2[i]*sin(2*i*sigma),i,1,maxpow)) # 0
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then error("left over terms in B2"),
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A2:A2/(1+eps),
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'done)$
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codeA2(maxpow):=block([tab2:" ",tab3:" "],
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print("// The scale factor A2-1 = mean value of (d/dsigma)I2 - 1
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CT evaluate_series_A2(CT const& eps)
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{
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CT const eps2 = math::sqr(eps);
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CT t;
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switch (SeriesOrder/2) {"),
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for n:0 thru entier(maxpow/2) do block([
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q:horner(ataylor(subst([eps=sqrt(eps2)],A2*(1+eps)-1),eps2,n)),
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linel:1200],
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print(concat(tab2,"case ",string(n),":")),
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print(concat(tab3,"t = ",string(q),";")),
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print(concat(tab3,"break;"))),
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print(" }
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return (t - eps) / (1 + eps);
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}"),
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'done)$
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maxpow:8$
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computeI2(maxpow)$
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codeA2(maxpow)$
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// Maxima script end
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To replace each number x by CT(x) the following
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script can be used:
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sed -e 's/[0-9]\+/CT(&)/g; s/\[CT/\[/g; s/)\]/\]/g;
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s/case\sCT(/case /g; s/):/:/g; s/epsCT(2)/eps2/g;'
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generated by the following Maxima script:
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geometry/doc/other/maxima/geod.mac
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*/
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template <typename CT, std::size_t SeriesOrder>
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CT evaluate_series_A2(CT const& eps)
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@ -212,53 +125,8 @@ namespace boost { namespace geometry { namespace series_expansion {
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The expansion above is performed in Maxima, a Computer Algebra System.
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The C++ code (that yields the function evaluate_coeffs_A3 below) is
|
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generated by the following Maxima script and is based on script:
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http://geographiclib.sourceforge.net/html/geod.mac
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// Maxima script begin
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computeI3(maxpow):=block([int,intexp,dlam,eta,del,eps,nu,f,z,n],
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maxpow:maxpow-1,
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int:subst([k2=4*eps/(1-eps)^2],
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(2-f)/(1+(1-f)*sqrt(1+k2*sin(sigma)^2))),
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int:subst([f=2*n/(1+n)],int),
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intexp:jtaylor(int,n,eps,maxpow),
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dlam:trigreduce(integrate(intexp,sigma)),
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dlam:dlam-subst(sigma=0,dlam),
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A3:expand(subst(sigma=2*%pi,dlam)/(2*%pi)),
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eta:jtaylor(dlam/A3,n,eps,maxpow),
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A3:jtaylor(A3,n,eps,maxpow),
|
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for i:1 thru maxpow do C3[i]:coeff(eta,sin(2*i*sigma)),
|
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if expand(eta-sigma-sum(C3[i]*sin(2*i*sigma),i,1,maxpow)) # 0
|
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then error("left over terms in B3"),
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'done)$
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codeA3(maxpow):=block([tab2:" ",tab3:" "],
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print("// The scale factor A3 = mean value of (d/dsigma)I3
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static inline void evaluate_series_A3(CT const& n, CT c[])
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{
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switch (SeriesOrder) {"),
|
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for nn:0 thru maxpow do block(
|
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[q:if nn=0 then 0 else
|
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jtaylor(subst([n=n],A3),n,eps,nn-1),
|
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linel:1200],
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print(concat(tab2,"case ",string(nn),":")),
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for i : 0 thru nn-1 do
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print(concat(tab3,"c[",i,"] = ",
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string(horner(coeff(q,eps,i))),";")),
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print(concat(tab3,"break;"))),
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print(" }
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}"),
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'done)$
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maxpow:8$
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||||
computeI3(maxpow)$
|
||||
codeA3(maxpow)$
|
||||
// Maxima script end
|
||||
|
||||
To replace each number x by CT(x) the following
|
||||
script can be used:
|
||||
sed -e 's/[0-9]\+/CT(&)/g; s/\[CT(/\[/g; s/)\]/\]/g;
|
||||
s/case\sCT(/case /g; s/):/:/g'
|
||||
generated by the following Maxima script:
|
||||
geometry/doc/other/maxima/geod.mac
|
||||
*/
|
||||
// TODO: this produces different results that geographiclib
|
||||
template <typename CT, std::size_t SeriesOrder>
|
||||
@ -327,38 +195,8 @@ namespace boost { namespace geometry { namespace series_expansion {
|
||||
|
||||
The expansion below is performed in Maxima, a Computer Algebra System.
|
||||
The C++ code (that yields the function evaluate_coeffs_C1 below) is
|
||||
generated by the following Maxima script and is based on script:
|
||||
http://geographiclib.sourceforge.net/html/geod.mac
|
||||
|
||||
// Maxima script begin
|
||||
codeC1(maxpow):=block([tab2:" ",tab3:" "],
|
||||
print("// The coefficients C1[l] in the Fourier expansion of B1
|
||||
static inline evaluate_coeffs_C1(CT eps, CT c[]) {
|
||||
CT eps2 = math::sqr(eps);
|
||||
CT d = eps;
|
||||
switch (SeriesOrder) {"),
|
||||
for n:0 thru maxpow do (
|
||||
print(concat(tab2,"case ",string(n),":")),
|
||||
for m:1 thru n do block([q:d*horner(
|
||||
subst([eps=sqrt(eps2)],ataylor(C1[m],eps,n)/eps^m)),
|
||||
linel:1200],
|
||||
if m>1 then print(concat(tab3,"d *= eps;")),
|
||||
print(concat(tab3,"c[",string(m),"] = ",string(q),";"))),
|
||||
print(concat(tab3,"break;"))),
|
||||
print(" }
|
||||
}"),
|
||||
'done)$
|
||||
|
||||
maxpow:8$
|
||||
computeI1(maxpow)$
|
||||
codeC1(maxpow)$
|
||||
// Maxima script end
|
||||
|
||||
To replace each number x by CT(x) the following
|
||||
script can be used:
|
||||
sed -e 's/[0-9]\+/CT(&)/g; s/\[CT(/\[/g; s/)\]/\]/g;
|
||||
s/case\sCT(/case /g; s/):/:/g; s/epsCT(2)/eps2/g;
|
||||
s/eps(CT(2))/eps2/g;'
|
||||
generated by the following Maxima script:
|
||||
geometry/doc/other/maxima/geod.mac
|
||||
*/
|
||||
template <typename CT, std::size_t SeriesOrder>
|
||||
static inline void evaluate_coeffs_C1(CT eps, CT c[])
|
||||
@ -456,51 +294,8 @@ namespace boost { namespace geometry { namespace series_expansion {
|
||||
|
||||
The expansion below is performed in Maxima, a Computer Algebra System.
|
||||
The C++ code (that yields the function evaluate_coeffs_C1p below) is
|
||||
generated by the following Maxima script and is based on script:
|
||||
http://geographiclib.sourceforge.net/html/geod.mac
|
||||
|
||||
// Maxima script begin
|
||||
revertI1(maxpow):=block([tau,eps,tauacc:1,sigacc:0],
|
||||
for n:1 thru maxpow do (
|
||||
tauacc:trigreduce(ataylor(
|
||||
-sum(C1[j]*sin(2*j*tau),j,1,maxpow-n+1)*tauacc/n,
|
||||
eps,maxpow)),
|
||||
sigacc:sigacc+expand(diff(tauacc,tau,n-1))),
|
||||
for i:1 thru maxpow do C1p[i]:coeff(sigacc,sin(2*i*tau)),
|
||||
if expand(sigacc-sum(C1p[i]*sin(2*i*tau),i,1,maxpow)) # 0
|
||||
then error("left over terms in B1p"),
|
||||
'done)$
|
||||
|
||||
codeC1p(maxpow):=block([tab2:" ",tab3:" "],
|
||||
print("// The coefficients C1p[l] in the Fourier expansion of B1p
|
||||
static inline evaluate_coeffs_C1p(CT eps, CT c[])
|
||||
{
|
||||
CT const eps2 = math::sqr(eps);
|
||||
CT d = eps;
|
||||
switch (SeriesOrder) {"),
|
||||
for n:0 thru maxpow do (
|
||||
print(concat(tab2,"case ",string(n),":")),
|
||||
for m:1 thru n do block([q:d*horner(
|
||||
subst([eps=sqrt(eps2)],ataylor(C1p[m],eps,n)/eps^m)),
|
||||
linel:1200],
|
||||
if m>1 then print(concat(tab3,"d *= eps;")),
|
||||
print(concat(tab3,"c[",string(m),"] = ",string(q),";"))),
|
||||
print(concat(tab3,"break;"))),
|
||||
print(" }
|
||||
}"),
|
||||
'done)$
|
||||
|
||||
maxpow:8$
|
||||
computeI1(maxpow)$
|
||||
revertI1(maxpow)$
|
||||
codeC1p(maxpow)$
|
||||
// Maxima script end
|
||||
|
||||
To replace each number x by CT(x) the following
|
||||
script can be used:
|
||||
sed -e 's/[0-9]\+/CT(&)/g; s/\[CT(/\[/g; s/)\]/\]/g;
|
||||
s/case\sCT(/case /g; s/):/:/g; s/epsCT(2)/eps2/g;
|
||||
s/eps(CT(2))/eps2/g;'
|
||||
generated by the following Maxima script:
|
||||
geometry/doc/other/maxima/geod.mac
|
||||
*/
|
||||
template <typename CT, std::size_t SeriesOrder>
|
||||
static inline void evaluate_coeffs_C1p(CT eps, CT c[])
|
||||
@ -598,39 +393,8 @@ namespace boost { namespace geometry { namespace series_expansion {
|
||||
|
||||
The expansion below is performed in Maxima, a Computer Algebra System.
|
||||
The C++ code (that yields the function evaluate_coeffs_C2 below) is
|
||||
generated by the following Maxima script and is based on script:
|
||||
http://geographiclib.sourceforge.net/html/geod.mac
|
||||
|
||||
// Maxima script begin
|
||||
codeC2(maxpow):=block([tab2:" ",tab3:" "],
|
||||
print("// The coefficients C2[l] in the Fourier expansion of B2
|
||||
static inline void evaluate_coeffs_C2(CT const& eps, CT c[])
|
||||
{
|
||||
CT const eps2 = math::sqr(eps);
|
||||
CT d = eps;
|
||||
switch (SeriesOrder) {"),
|
||||
for n:0 thru maxpow do (
|
||||
print(concat(tab2,"case ",string(n),":")),
|
||||
for m:1 thru n do block([q:d*horner(
|
||||
subst([eps=sqrt(eps2)],ataylor(C2[m],eps,n)/eps^m)),
|
||||
linel:1200],
|
||||
if m>1 then print(concat(tab3,"d *= eps;")),
|
||||
print(concat(tab3,"c[",string(m),"] = ",string(q),";"))),
|
||||
print(concat(tab3,"break;"))),
|
||||
print(" }
|
||||
}"),
|
||||
'done)$
|
||||
|
||||
maxpow:8$
|
||||
computeI2(maxpow)$
|
||||
codeC2(maxpow)$
|
||||
// Maxima script end
|
||||
|
||||
To replace each number x by CT(x) the following
|
||||
script can be used:
|
||||
sed -e 's/[0-9]\+/CT(&)/g; s/\[CT(/\[/g; s/)\]/\]/g;
|
||||
s/case\sCT(/case /g; s/):/:/g; s/epsCT(2)/eps2/g;
|
||||
s/eps(CT(2))/eps2/g;'
|
||||
generated by the following Maxima script:
|
||||
geometry/doc/other/maxima/geod.mac
|
||||
*/
|
||||
template <typename CT, std::size_t SeriesOrder>
|
||||
static inline void evaluate_coeffs_C2(CT const& eps, CT c[])
|
||||
@ -728,43 +492,8 @@ namespace boost { namespace geometry { namespace series_expansion {
|
||||
|
||||
The expansion below is performed in Maxima, a Computer Algebra System.
|
||||
The C++ code (that yields the function evaluate_coeffs_C3 below) is
|
||||
generated by the following Maxima script and is based on script:
|
||||
http://geographiclib.sourceforge.net/html/geod.mac
|
||||
|
||||
// Maxima script begin
|
||||
codeC3(maxpow):=block([tab2:" ",tab3:" "],
|
||||
print("// The coefficients C3[l] in the Fourier expansion of B3
|
||||
static inline void evaluate_coeffs_C3(CT const& n, CT c[])
|
||||
{
|
||||
const CT n2 = math::sqr(n);
|
||||
switch (SeriesOrder) {"),
|
||||
for nn:0 thru maxpow do block([c],
|
||||
print(concat(tab2,"case ",string(nn),":")),
|
||||
c:0,
|
||||
for m:1 thru nn-1 do block(
|
||||
[q:if nn = 0 then 0 else
|
||||
jtaylor(subst([n=n],C3[m]),_n,eps,nn-1),
|
||||
linel:1200],
|
||||
for j:m thru nn-1 do (
|
||||
print(concat(tab3,"c[",c,"] = ",
|
||||
string(horner(coeff(q,eps,j))),";")),
|
||||
c:c+1)
|
||||
),
|
||||
print(concat(tab3,"break;"))),
|
||||
print(" }
|
||||
}"),
|
||||
'done)$
|
||||
|
||||
maxpow:8$
|
||||
computeI3(maxpow)$
|
||||
codeC3(maxpow)$
|
||||
// Maxima script end
|
||||
|
||||
To replace each number x by CT(x) the following
|
||||
script can be used:
|
||||
sed -e 's/[0-9]\+/CT(&)/g; s/\[CT(/\[/g; s/)\]/\]/g;
|
||||
s/case\sCT(/case /g; s/):/:/g; s/epsCT(2)/eps2/g;
|
||||
s/eps(CT(2))/eps2/g;'
|
||||
generated by the following Maxima script:
|
||||
geometry/doc/other/maxima/geod.mac
|
||||
*/
|
||||
template <typename CT, int SeriesOrder>
|
||||
void evaluate_coeffs_C3x(CT const& n, CT c[], const CT coeff[])
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user