kopia lustrzana https://github.com/Dsplib/libdspl-2.0
419 wiersze
10 KiB
Plaintext
419 wiersze
10 KiB
Plaintext
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/*! ****************************************************************************
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\ingroup SPEC_MATH_ELLIP_GROUP
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\fn int ellip_acd(double* w, int n, double k, double* u)
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\brief Inverse Jacobi elliptic function \f$ u = \textrm{cd}^{-1}(w, k)\f$
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of the real vector argument
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Function calculates inverse Jacobi elliptic function
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\f$ u = \textrm{cd}^{-1}(w, k)\f$ of the real vector `w`. \n
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\param[in] w
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Pointer to the argument vector \f$ w \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\param[in] n
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Size of vector `w`. \n
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\param[in] k
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Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter,
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which values can be from 0 to 1. \n \n
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\param[out] u
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Pointer to the vector of inverse Jacobi elliptic function
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\f$ u = \textrm{cd}^{-1}(w, k)\f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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\author Sergey Bakhurin www.dsplib.org
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***************************************************************************** */
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/*! ****************************************************************************
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\ingroup SPEC_MATH_ELLIP_GROUP
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\fn int ellip_acd_cmplx(complex_t* w, int n, double k, complex_t* u)
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\brief Inverse Jacobi elliptic function \f$ u = \textrm{cd}^{-1}(w, k)\f$
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of complex vector argument
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Function calculates inverse Jacobi elliptic function
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\f$ u = \textrm{cd}^{-1}(w, k)\f$ of complex vector `w`. \n
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\param[in] w
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Pointer to the argument vector \f$ w \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\param[in] n
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Size of vector `w`. \n
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\param[in] k
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Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter,
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which values can be from 0 to 1. \n \n
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\param[out] u
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Pointer to the vector of inverse Jacobi elliptic function
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\f$ u = \textrm{cd}^{-1}(w, k)\f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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\author Sergey Bakhurin www.dsplib.org
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***************************************************************************** */
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/*! ****************************************************************************
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\ingroup SPEC_MATH_ELLIP_GROUP
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\fn int ellip_asn(double* w, int n, double k, double* u)
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\brief Inverse Jacobi elliptic function \f$ u = \textrm{sn}^{-1}(w, k)\f$
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of real vector argument
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Function calculates inverse Jacobi elliptic function
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\f$ u = \textrm{sn}^{-1}(w, k)\f$ of real vector `w`. \n
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\param[in] w
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Pointer to the argument vector \f$ w \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\param[in] n
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Size of vector `w`. \n
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\param[in] k
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Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter,
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which values can be from 0 to 1. \n \n
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\param[out] u
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Pointer to the vector of inverse Jacobi elliptic function
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\f$ u = \textrm{sn}^{-1}(w, k)\f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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\author Sergey Bakhurin www.dsplib.org
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***************************************************************************** */
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/*! ****************************************************************************
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\ingroup SPEC_MATH_ELLIP_GROUP
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\fn int ellip_asn_cmplx(complex_t* w, int n, double k, complex_t* u)
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\brief Inverse Jacobi elliptic function \f$ u = \textrm{sn}^{-1}(w, k)\f$
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of complex vector argument
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Function calculates inverse Jacobi elliptic function
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\f$ u = \textrm{sn}^{-1}(w, k)\f$ of complex vector `w`. \n
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\param[in] w
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Pointer to the argument vector \f$ w \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\param[in] n
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Size of vector `w`. \n
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\param[in] k
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Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter,
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which values can be from 0 to 1. \n \n
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\param[out] u
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Pointer to the vector of inverse Jacobi elliptic function
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\f$ u = \textrm{sn}^{-1}(w, k)\f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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\author Sergey Bakhurin www.dsplib.org
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***************************************************************************** */
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/*! ****************************************************************************
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\ingroup SPEC_MATH_ELLIP_GROUP
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\fn int ellip_cd(double* u, int n, double k, double* y)
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\brief Jacobi elliptic function \f$ y = \textrm{cd}(u K(k), k)\f$
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of real vector argument
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Function calculates Jacobi elliptic function
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\f$ y = \textrm{cd}(u K(k), k)\f$ of real vector `u` and
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elliptical modulus `k`. \n
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\param[in] u
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Pointer to the argument vector \f$ u \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\param[in] n
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Size of vector `u`. \n
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\param[in] k
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Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter,
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which values can be from 0 to 1. \n \n
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\param[out] y
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Pointer to the vector of Jacobi elliptic function
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\f$ y = \textrm{cd}(u K(k), k)\f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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\author Sergey Bakhurin www.dsplib.org
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***************************************************************************** */
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/*! ****************************************************************************
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\ingroup SPEC_MATH_ELLIP_GROUP
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\fn int ellip_cd_cmplx(complex_t* u, int n, double k, complex_t* y)
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\brief Jacobi elliptic function \f$ y = \textrm{cd}(u K(k), k)\f$
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of complex vector argument
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Function calculates Jacobi elliptic function
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\f$ y = \textrm{cd}(u K(k), k)\f$ of complex vector `u` and
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elliptical modulus `k`. \n
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\param[in] u
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Pointer to the argument vector \f$ u \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\param[in] n
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Size of vector `u`. \n
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\param[in] k
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Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter,
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which values can be from 0 to 1. \n \n
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\param[out] y
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Pointer to the vector of Jacobi elliptic function
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\f$ y = \textrm{cd}(u K(k), k)\f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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\author Sergey Bakhurin www.dsplib.org
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***************************************************************************** */
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/*! ****************************************************************************
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\ingroup SPEC_MATH_ELLIP_GROUP
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\fn int ellip_landen(double k, int n, double* y)
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\brief Function calculates complete elliptical integral
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coefficients \f$ k_i \f$
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Complete elliptical integral \f$ K(k) \f$ can be described as:
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\f[
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K(k) = \frac{\pi}{2} \prod_{i = 1}^{\infty}(1+k_i),
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\f]
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here \f$ k_i \f$ -- coefficients which calculated
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iterative from \f$ k_0 = k\f$:
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\f[
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k_i =
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\left(
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\frac{k_{i-1}}
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{
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1+\sqrt{1-k_{i-1}^2}
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}
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\right)^2
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\f]
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This function calculates `n` fist coefficients \f$ k_i \f$, which can
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be used for Complete elliptical integral.
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\param[in] k
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Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter, which values can be from 0 to 1. \n \n
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\param[in] n
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Number of \f$ k_i \f$ which need to calculate. \n
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Parameter `n` is size of output vector `y`. \n
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\param[out] y
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pointer to the real vector which keep \f$ k_i \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` -- successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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Example:
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\include ellip_landen_test.c
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Result:
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\verbatim
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i k[i]
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1 4.625e-01
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2 6.009e-02
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3 9.042e-04
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4 2.044e-07
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5 1.044e-14
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6 2.727e-29
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7 1.859e-58
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8 8.640e-117
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9 1.866e-233
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10 0.000e+00
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11 0.000e+00
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12 0.000e+00
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13 0.000e+00
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\endverbatim
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\note Complete elliptical integral converges enough fast
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if modulus \f$ k<1 \f$. There are 10 to 20 coefficients \f$ k_i \f$
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are sufficient for practical applications
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to ensure complete elliptic integral precision within EPS.
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\author Sergey Bakhurin www.dsplib.org
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***************************************************************************** */
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/*! ****************************************************************************
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\ingroup SPEC_MATH_ELLIP_GROUP
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\fn int ellip_sn(double* u, int n, double k, double* y)
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\brief Jacobi elliptic function \f$ y = \textrm{sn}(u K(k), k)\f$
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of real vector argument
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Function calculates Jacobi elliptic function
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\f$ y = \textrm{sn}(u K(k), k)\f$ of real vector `u` and
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elliptical modulus `k`. \n
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\param[in] u
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Pointer to the argument vector \f$ u \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\param[in] n
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Size of vector `u`. \n
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\param[in] k
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Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter,
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which values can be from 0 to 1. \n \n
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\param[out] y
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Pointer to the vector of Jacobi elliptic function
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\f$ y = \textrm{sn}(u K(k), k)\f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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\author Sergey Bakhurin www.dsplib.org
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***************************************************************************** */
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/*! ****************************************************************************
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\ingroup SPEC_MATH_ELLIP_GROUP
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\fn int ellip_sn_cmplx(complex_t* u, int n, double k, complex_t* y)
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\brief Jacobi elliptic function \f$ y = \textrm{sn}(u K(k), k)\f$ of complex vector argument
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Function calculates Jacobi elliptic function
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\f$ y = \textrm{sn}(u K(k), k)\f$ of complex vector `u` and
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elliptical modulus `k`. \n
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\param[in] u
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Pointer to the argument vector \f$ u \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\param[in] n
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Size of vector `u`. \n
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\param[in] k
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Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter,
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which values can be from 0 to 1. \n \n
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\param[out] y
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Pointer to the vector of Jacobi elliptic function
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\f$ y = \textrm{sn}(u K(k), k)\f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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\author Sergey Bakhurin www.dsplib.org
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***************************************************************************** */
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