[dipdip-dirty] Bessel transform for q=1,2, n=0,...,5, kappa=5 done
Former-commit-id: d60167f97f329540c617785aea4ec38fe364fddb
This commit is contained in:
Marek Nečada
parent
b68c394819
commit
fecdc07a37
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@ -5,11 +5,36 @@
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#define SQ(x) ((x)*(x))
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#define MAXQM 1
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#define MAXN 2
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#define MAXN 5
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#define MAXKAPPA 5
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#define FF (-1)
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#define P4(x) (((x)*(x))*((x)*(x)))
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#define KAPPA5SUM(form) (\
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(form(0, 1)) \
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- 5*(form(1, 1)) \
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+10*(form(2, 1)) \
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-10*(form(3, 1)) \
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+ 5*(form(4, 1)) \
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- (form(5, 1)) \
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)
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#define KAPPA5SUMFF(form) (\
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(form(0, (-1))) \
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- 5*(form(1, 1)) \
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+10*(form(2, 1)) \
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-10*(form(3, 1)) \
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+ 5*(form(4, 1)) \
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- (form(5, 1)) \
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)
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#define LRHANKELDEF(fname) complex double fname(double c, double k0, double k, \
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const complex double *a, const complex double *b, const complex double *d, \
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const complex double *e, const complex double *ash)
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typedef complex double (*lrhankelspec)(double, double, double,
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const complex double *,
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const complex double *,
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@ -50,6 +75,35 @@ complex double fk5q1n3l(double c, double k0, double k,
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+ d[5]*(kk3+4*a[5]*a[5])
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)/(k0*k*k*k);
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}
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complex double fk5q1n4l(double c, double k0, double k,
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const complex double *a, const complex double *b, const complex double *d, const complex double *e, const complex double *ash) {
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double kk8 = k*k*8, kkkk = P4(k); // Není lepší pow?
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return (
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+ FF*e[0]*(kkkk + kk8*a[0]*a[0] + 8*P4(a[0]))
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- 5*e[1]*(kkkk + kk8*a[1]*a[1] + 8*P4(a[1]))
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+ 10*e[2]*(kkkk + kk8*a[2]*a[2] + 8*P4(a[2]))
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- 10*e[3]*(kkkk + kk8*a[3]*a[3] + 8*P4(a[3]))
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+ 5*e[4]*(kkkk + kk8*a[4]*a[4] + 8*P4(a[4]))
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- e[5]*(kkkk + kk8*a[5]*a[5] + 8*P4(a[5]))
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)/(k0*kkkk);
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}
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#define FORMK5Q1N5(i,ff) (d[i]*(kkkk*(-5*ff+b[i])-ff*kk20*a[i]*a[i]-ff*16*P4(a[i])))
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LRHANKELDEF(fk5q1n5l){
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double kk20 = k*k*20, kkkk = P4(k);
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return (
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KAPPA5SUMFF(FORMK5Q1N5)
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)/(k0*kkkk*k);
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}
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LRHANKELDEF(fk5q1n5s){
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double kk20 = k*k*20, kkkk = P4(k);
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return (
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KAPPA5SUM(FORMK5Q1N5)
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)/(k0*kkkk*k);
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}
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#undef FORMK5Q1N5
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complex double fk5q2n0(double c, double k0, double k,
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const complex double *a, const complex double *b, const complex double *d, const complex double *e, const complex double *ash) {
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return (
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@ -82,6 +136,7 @@ complex double fk5q2n2l(double c, double k0, double k,
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) / (k*k*k0*k0);
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}
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#if 0
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complex double fk5q3n0l(double c, double k0, double k,
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const complex double *a, const complex double *b, const complex double *d, const complex double *e, const complex double *ash) { // FIXME
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return ( /* FIXME */
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@ -93,7 +148,7 @@ complex double fk5q3n0l(double c, double k0, double k,
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+ k*b[5] + a[5] * ash[5]
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)/(k0*k0*k0);
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}
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#endif
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complex double fk5q1n0s(double c, double k0, double k,
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const complex double *a, const complex double *b, const complex double *d, const complex double *e, const complex double *ash) {
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@ -127,6 +182,18 @@ complex double fk5q1n3s(double c, double k0, double k,
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+ d[5]*(kk3+4*a[5]*a[5])
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)/(k0*k*k*k);
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}
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complex double fk5q1n4s(double c, double k0, double k,
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const complex double *a, const complex double *b, const complex double *d, const complex double *e, const complex double *ash) {
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double kk8 = k*k*8, kkkk = P4(k); // Není lepší pow?
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return (
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+ e[0]*(kkkk + kk8*a[0]*a[0] + 8*P4(a[0]))
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- 5*e[1]*(kkkk + kk8*a[1]*a[1] + 8*P4(a[1]))
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+ 10*e[2]*(kkkk + kk8*a[2]*a[2] + 8*P4(a[2]))
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- 10*e[3]*(kkkk + kk8*a[3]*a[3] + 8*P4(a[3]))
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+ 5*e[4]*(kkkk + kk8*a[4]*a[4] + 8*P4(a[4]))
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- e[5]*(kkkk + kk8*a[5]*a[5] + 8*P4(a[5]))
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)/(k0*kkkk);
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}
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const lrhankelspec fk5q2n0s = fk5q2n0, fk5q2n0l = fk5q2n0;
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@ -151,24 +218,74 @@ complex double fk5q2n2s(double c, double k0, double k,
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) / (k*k*k0*k0);
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}
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#define FORMK5Q2N3(i,ff) (ff*a[i]*b[i]*(kk + 4*a[i]*a[i]))
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LRHANKELDEF(fk5q2n3l){
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double kk = k*k;
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return (
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KAPPA5SUMFF(FORMK5Q2N3)
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)/(3*k0*k0*kk*k);
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}
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LRHANKELDEF(fk5q2n3s){
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double kk = k*k;
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return (
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KAPPA5SUM(FORMK5Q2N3)
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)/(3*k0*k0*kk*k);
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}
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#undef FORMK5Q2N3
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#define FORMK5Q2N4(i,ff) (-ff*b[i]*a[i]*a[i]*(kk+2*a[i]*a[i]))
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LRHANKELDEF(fk5q2n4l){
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double kk = k*k;
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return (
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KAPPA5SUMFF(FORMK5Q2N4)
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)/(k0*k0*kk*kk);
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}
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LRHANKELDEF(fk5q2n4s){
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double kk = k*k;
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return (
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KAPPA5SUM(FORMK5Q2N4)
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)/(k0*k0*kk*kk);
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}
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#undef FORMK5Q2N4
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#define FORMK5Q2N5(i,ff) (ff*a[i]*b[i]*(kkkk+12*kk*(a[i]*a[i])+16*P4(a[i])) )
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LRHANKELDEF(fk5q2n5l){
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double kk = k*k;
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double kkkk = kk * kk;
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return (
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KAPPA5SUMFF(FORMK5Q2N5)
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+16*120*P4(c)*c // Stirling S2(5,5) is no longer zero
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)/(5*k0*k0*kkkk*k);
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}
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LRHANKELDEF(fk5q2n5s){
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double kk = k*k;
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double kkkk = kk * kk;
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return (
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KAPPA5SUM(FORMK5Q2N5)
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+16*120*P4(c)*c // Stirling S2(5,5) is no longer zero
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)/(5*k0*k0*kkkk*k);
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}
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#undef FORMK5Q2N5
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static lrhankelspec transfuns_f[MAXKAPPA+1][MAXQM+1][MAXN+1] = {
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{{NULL,NULL,NULL},{NULL,NULL,NULL}},
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{{NULL,NULL,NULL},{NULL,NULL,NULL}},
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{{NULL,NULL,NULL},{NULL,NULL,NULL}},
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{{NULL,NULL,NULL},{NULL,NULL,NULL}},
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{{NULL,NULL,NULL},{NULL,NULL,NULL}},
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{{fk5q1n0l,fk5q1n1l,fk5q1n2l},{fk5q2n0,fk5q2n1l,fk5q2n2l}}
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{{NULL,NULL,NULL,NULL,NULL,NULL},{NULL,NULL,NULL,NULL,NULL,NULL}},
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{{NULL,NULL,NULL,NULL,NULL,NULL},{NULL,NULL,NULL,NULL,NULL,NULL}},
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{{NULL,NULL,NULL,NULL,NULL,NULL},{NULL,NULL,NULL,NULL,NULL,NULL}},
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{{NULL,NULL,NULL,NULL,NULL,NULL},{NULL,NULL,NULL,NULL,NULL,NULL}},
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{{NULL,NULL,NULL,NULL,NULL,NULL},{NULL,NULL,NULL,NULL,NULL,NULL}},
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{{fk5q1n0l,fk5q1n1l,fk5q1n2l,fk5q1n3l,fk5q1n4l,fk5q1n5l},{fk5q2n0,fk5q2n1l,fk5q2n2l,fk5q2n3l,fk5q2n4l,fk5q2n5l}}
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};
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static lrhankelspec transfuns_n[MAXKAPPA+1][MAXQM+1][MAXN+1] = {
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{{NULL,NULL,NULL},{NULL,NULL,NULL}},
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{{NULL,NULL,NULL},{NULL,NULL,NULL}},
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{{NULL,NULL,NULL},{NULL,NULL,NULL}},
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{{NULL,NULL,NULL},{NULL,NULL,NULL}},
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{{NULL,NULL,NULL},{NULL,NULL,NULL}},
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{{fk5q1n0s,fk5q1n1s,fk5q1n2s},{fk5q2n0,fk5q2n1s,fk5q2n2s}}
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{{NULL,NULL,NULL,NULL,NULL,NULL},{NULL,NULL,NULL,NULL,NULL,NULL}},
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{{NULL,NULL,NULL,NULL,NULL,NULL},{NULL,NULL,NULL,NULL,NULL,NULL}},
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{{NULL,NULL,NULL,NULL,NULL,NULL},{NULL,NULL,NULL,NULL,NULL,NULL}},
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{{NULL,NULL,NULL,NULL,NULL,NULL},{NULL,NULL,NULL,NULL,NULL,NULL}},
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{{NULL,NULL,NULL,NULL,NULL,NULL},{NULL,NULL,NULL,NULL,NULL,NULL}},
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{{fk5q1n0s,fk5q1n1s,fk5q1n2s,fk5q1n3s,fk5q1n4s,fk5q1n5s},{fk5q2n0,fk5q2n1s,fk5q2n2s,fk5q2n3s,fk5q2n4s,fk5q2n5s}}
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};
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void lrhankel_recpart_fill(complex double *target,
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size_t maxn, size_t lrk_cutoff,
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complex double *hct,
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@ -204,12 +321,12 @@ int main() {
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ash[sigma] = casinh(a[sigma]/k);
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}
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for (size_t qm = 0; qm <= MAXQM; ++qm)
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for (size_t n = 0; n <= MAXN; ++n)
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if (/*!*/((qm==1)&&(n==0))){ // not skip q==2, n=0 for now
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for (size_t n = 0; n <= MAXN; ++n) {
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//if (/*!*/((qm==1)&&(n==0))){ // not skip q==2, n=0 for now
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// complex double fun(double c, double k0, double k, ccd *a, ccd *b, ccd *d, ccd *e)
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complex double result =
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//transfuns_f[kappa][qm][n](c,k0,k,a,b,d,e,ash);
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fk5q1n3l(c,k0,k,a,b,d,e,ash);
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fk5q2n5l(c,k0,k,a,b,d,e,ash);
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printf("%.16e %.16e ", creal(result), cimag(result));
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}
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printf("\n");
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