public class Jacobi extends Elliptic
Modifier and Type | Method and Description |
---|---|
static de.jtem.mfc.field.Complex |
cn(de.jtem.mfc.field.Complex u,
de.jtem.mfc.field.Complex k)
Returns cn(u,k).
|
static void |
cn(de.jtem.mfc.field.Complex u,
de.jtem.mfc.field.Complex tau,
de.jtem.mfc.field.Complex[] thetaConstants,
de.jtem.mfc.field.Complex cnOfU)
Computes cn(u,k(τ)) for given latiuce paramter τ, and theta constants.
|
static double |
cn(double u,
double k)
Returns cn(u,k).
|
static de.jtem.mfc.field.Complex |
dn(de.jtem.mfc.field.Complex u,
de.jtem.mfc.field.Complex k)
Returns dn(u,k).
|
static void |
dn(de.jtem.mfc.field.Complex u,
de.jtem.mfc.field.Complex tau,
de.jtem.mfc.field.Complex[] thetaConstants,
de.jtem.mfc.field.Complex dnOfU)
Computes dn(u,k(τ)) for given latiuce paramter τ, and theta constants.
|
static double |
dn(double u,
double k)
Returns dn(u,k).
|
static de.jtem.mfc.field.Complex |
K_from_k(de.jtem.mfc.field.Complex k)
Returns quarter period K as function of the modulus k.
|
static void |
K_from_k(de.jtem.mfc.field.Complex k,
de.jtem.mfc.field.Complex K)
Computes quarter period K as function of the modulus k.
|
static de.jtem.mfc.field.Complex |
K_from_KPrime_and_tau(de.jtem.mfc.field.Complex KPrime,
de.jtem.mfc.field.Complex tau)
Returns quarter period K as function of
complementary quarter period K' and lattice parameter τ.
|
static void |
K_from_KPrime_and_tau(de.jtem.mfc.field.Complex KPrime,
de.jtem.mfc.field.Complex tau,
de.jtem.mfc.field.Complex K)
Computes quarter period K as function of
complementary quarter period K' and lattice parameter τ.
|
static de.jtem.mfc.field.Complex |
k_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants)
Returns modulus k as function of theta constants.
|
static de.jtem.mfc.field.Complex |
K_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants)
Returns quarter period K as function of theta constants.
|
static void |
k_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants,
de.jtem.mfc.field.Complex k)
Computes modulus k as function of theta constants
|
static void |
K_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants,
de.jtem.mfc.field.Complex K)
Computes quarter period K as function of theta constants.
|
static de.jtem.mfc.field.Complex |
KPrime_from_K_and_tau(de.jtem.mfc.field.Complex K,
de.jtem.mfc.field.Complex tau)
Returns complementary quarter period K' as function of
quarter period K and lattice parameter τ.
|
static void |
KPrime_from_K_and_tau(de.jtem.mfc.field.Complex K,
de.jtem.mfc.field.Complex tau,
de.jtem.mfc.field.Complex KPrime)
Computes complementary quarter period K' as function of
quarter period K and lattice parameter τ.
|
static de.jtem.mfc.field.Complex |
kPrime_from_k(de.jtem.mfc.field.Complex k)
Returns complementary modulus k' as function of the modulus.
|
static de.jtem.mfc.field.Complex |
KPrime_from_k(de.jtem.mfc.field.Complex k)
Returns complementary quarter Period K' as function of the modulus k.
|
static void |
kPrime_from_k(de.jtem.mfc.field.Complex k,
de.jtem.mfc.field.Complex kPrime)
Computes complementary modulus k' as function of the modulus.
|
static void |
KPrime_from_k(de.jtem.mfc.field.Complex k,
de.jtem.mfc.field.Complex KPrime)
Computes cmplementary quarter period K' as function of the modulus k.
|
static double |
kPrime_from_k(double k)
Returns complementary modulus k' as function of the modulus.
|
static de.jtem.mfc.field.Complex |
kPrime_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants)
Returns complementary modulus k' as function of theta constants.
|
static void |
kPrime_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants,
de.jtem.mfc.field.Complex kPrime)
Computes complementary modulus k' as function theta constants.
|
static de.jtem.mfc.field.Complex |
sn(de.jtem.mfc.field.Complex u,
de.jtem.mfc.field.Complex k)
Returns sn(u,k).
|
static void |
sn(de.jtem.mfc.field.Complex u,
de.jtem.mfc.field.Complex tau,
de.jtem.mfc.field.Complex[] thetaConstants,
de.jtem.mfc.field.Complex snOfU)
Computes sn(u,k(τ)) for given latiuce paramter τ, and theta constants.
|
static double |
sn(double u,
double k)
Returns sn(u,k).
|
static de.jtem.mfc.field.Complex |
tau_from_k(de.jtem.mfc.field.Complex k)
Computes lattice parameter τ as function of modulus k.
|
static void |
tau_from_k(de.jtem.mfc.field.Complex k,
de.jtem.mfc.field.Complex tau)
Computes lattice parameter τ as function of modulus k.
|
static de.jtem.mfc.field.Complex |
tauPrime_from_tau(de.jtem.mfc.field.Complex tau)
Returns complementary lattice paramter τ' = -1/τ for lattice
parameter τ.
|
static void |
tauPrime_from_tau(de.jtem.mfc.field.Complex tau,
de.jtem.mfc.field.Complex tauPrime)
Computes complementary lattice paramter τ' = -1/τ for lattice
parameter τ.
|
public static de.jtem.mfc.field.Complex cn(de.jtem.mfc.field.Complex u, de.jtem.mfc.field.Complex k)
cn(Complex,Complex,Complex[],Complex)
.u
- argumentk
- modulusElliptic.thetaConstants(Complex)
,
tau_from_k(Complex)
,
cn(Complex,Complex,Complex[],Complex)
public static void cn(de.jtem.mfc.field.Complex u, de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex[] thetaConstants, de.jtem.mfc.field.Complex cnOfU)
u
- argumenttau
- lattice parameterthetaConstants
- theta constantscnOfU
- sn(u,k(τ)) (on output)Elliptic.thetaConstants(Complex)
,
tau_from_k(Complex)
,
cn(Complex,Complex)
public static double cn(double u, double k)
cn(Complex,Complex,Complex[],Complex)
.u
- argumentk
- modulusElliptic.thetaConstants(Complex)
,
tau_from_k(Complex)
,
cn(Complex,Complex,Complex[],Complex)
,
cn(Complex,Complex)
public static de.jtem.mfc.field.Complex dn(de.jtem.mfc.field.Complex u, de.jtem.mfc.field.Complex k)
dn(Complex,Complex,Complex[],Complex)
.u
- argumentk
- modulusElliptic.thetaConstants(Complex)
,
tau_from_k(Complex)
,
dn(Complex,Complex,Complex[],Complex)
public static void dn(de.jtem.mfc.field.Complex u, de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex[] thetaConstants, de.jtem.mfc.field.Complex dnOfU)
u
- argumenttau
- lattice parameterthetaConstants
- theta constantsdnOfU
- sn(u,k(τ)) (on output)Elliptic.thetaConstants(Complex)
,
tau_from_k(Complex)
,
dn(Complex,Complex)
public static double dn(double u, double k)
dn(Complex,Complex,Complex[],Complex)
.u
- argumentk
- modulusElliptic.thetaConstants(Complex)
,
tau_from_k(Complex)
,
dn(Complex,Complex,Complex[],Complex)
,
dn(Complex,Complex)
public static de.jtem.mfc.field.Complex K_from_k(de.jtem.mfc.field.Complex k)
k
- moduluspublic static void K_from_k(de.jtem.mfc.field.Complex k, de.jtem.mfc.field.Complex K)
k
- modulusK
- quarter period K (on output)
#see K_from_k(Complex)public static de.jtem.mfc.field.Complex K_from_KPrime_and_tau(de.jtem.mfc.field.Complex KPrime, de.jtem.mfc.field.Complex tau)
KPrime
- complementary quarter periodtau
- lattice parameterK_from_KPrime_and_tau(Complex,Complex,Complex)
public static void K_from_KPrime_and_tau(de.jtem.mfc.field.Complex KPrime, de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex K)
KPrime
- complementary quarter periodtau
- lattice parameterK
- quarter period (on output)K_from_KPrime_and_tau(Complex,Complex)
public static de.jtem.mfc.field.Complex k_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants)
thetaConstants
- theta constantsElliptic.thetaConstants(Complex)
,
k_from_thetaConstants(Complex[],Complex)
public static de.jtem.mfc.field.Complex K_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants)
thetaConstants
- theta constantsElliptic.thetaConstants(Complex)
,
K_from_thetaConstants(Complex[],Complex)
public static void k_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants, de.jtem.mfc.field.Complex k)
thetaConstants
- theta constantsk
- modulus (on output)Elliptic.thetaConstants(Complex)
,
k_from_thetaConstants(Complex[])
public static void K_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants, de.jtem.mfc.field.Complex K)
thetaConstants
- theta constantsK
- quarter period (on output)Elliptic.thetaConstants(Complex)
,
K_from_thetaConstants(Complex[])
public static de.jtem.mfc.field.Complex KPrime_from_K_and_tau(de.jtem.mfc.field.Complex K, de.jtem.mfc.field.Complex tau)
K
- quarter periodtau
- lattice parameterKPrime_from_K_and_tau(Complex,Complex,Complex)
public static void KPrime_from_K_and_tau(de.jtem.mfc.field.Complex K, de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex KPrime)
K
- quarter periodtau
- lattice parameterKPrime
- complementary quarter period (on output)KPrime_from_K_and_tau(Complex,Complex)
public static de.jtem.mfc.field.Complex kPrime_from_k(de.jtem.mfc.field.Complex k)
k
- moduluskPrime_from_k(Complex,Complex)
public static de.jtem.mfc.field.Complex KPrime_from_k(de.jtem.mfc.field.Complex k)
k
- modulusKPrime_from_k(Complex,Complex)
public static void kPrime_from_k(de.jtem.mfc.field.Complex k, de.jtem.mfc.field.Complex kPrime)
k
- moduluskPrime
- complementary modulus k'= sqrt( 1-k*k ) (on output)kPrime_from_k(Complex)
public static void KPrime_from_k(de.jtem.mfc.field.Complex k, de.jtem.mfc.field.Complex KPrime)
k
- modulusKPrime
- complementary quarter period K' (on output)KPrime_from_k(Complex)
public static double kPrime_from_k(double k)
k
- moduluskPrime_from_k(Complex,Complex)
public static de.jtem.mfc.field.Complex kPrime_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants)
thetaConstants
- theta constantsElliptic.thetaConstants(Complex)
,
kPrime_from_thetaConstants(Complex[],Complex)
public static void kPrime_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants, de.jtem.mfc.field.Complex kPrime)
thetaConstants
- theta constantskPrime
- complementary modulus k' (on output)Elliptic.thetaConstants(Complex)
,
kPrime_from_thetaConstants(Complex[])
public static de.jtem.mfc.field.Complex sn(de.jtem.mfc.field.Complex u, de.jtem.mfc.field.Complex k)
sn(Complex,Complex,Complex[],Complex)
.u
- argumentk
- modulusElliptic.thetaConstants(Complex)
,
tau_from_k(Complex)
,
sn(Complex,Complex,Complex[],Complex)
,
sn(double,double)
public static void sn(de.jtem.mfc.field.Complex u, de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex[] thetaConstants, de.jtem.mfc.field.Complex snOfU)
u
- argumenttau
- lattice parameterthetaConstants
- theta constantssnOfU
- sn(u,k(τ)) (on output)Elliptic.thetaConstants(Complex)
,
tau_from_k(Complex)
,
sn(Complex,Complex)
,
sn(double,double)
public static double sn(double u, double k)
sn(Complex,Complex,Complex[],Complex)
.u
- argumentk
- modulusElliptic.thetaConstants(Complex)
,
tau_from_k(Complex)
,
sn(Complex,Complex,Complex[],Complex)
,
sn(Complex,Complex)
public static de.jtem.mfc.field.Complex tau_from_k(de.jtem.mfc.field.Complex k)
k
- modulustau_from_k(Complex,Complex)
public static void tau_from_k(de.jtem.mfc.field.Complex k, de.jtem.mfc.field.Complex tau)
k
- modulustau
- lattice paramter τtau_from_k(Complex)
public static de.jtem.mfc.field.Complex tauPrime_from_tau(de.jtem.mfc.field.Complex tau)
tau
- lattice paramter τtauPrime_from_tau(Complex,Complex)
public static void tauPrime_from_tau(de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex tauPrime)
tau
- lattice paramter τtauPrime
- complementary lattice paramter τ'(on output)tauPrime_from_tau(Complex)