[dipdip-dirty] Bessel transform for q=1,2, n=0,...,5, kappa=5 done

Former-commit-id: d60167f97f329540c617785aea4ec38fe364fddb

dipdip-dirty/lrhankel_recspace_dirty.c

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