kopia lustrzana https://github.com/Dsplib/libdspl-2.0
111 wiersze
2.8 KiB
Plaintext
111 wiersze
2.8 KiB
Plaintext
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/*! *****************************************************************************
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\ingroup SPEC_MATH_TRANSCEND
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\fn int cheby_poly1(double* x, int n, int ord, double* y)
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\brief Chebyshev polynomial of the first kind order `ord`
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Function calculates Chebyshev polynomial \f$ C_ord(x)\f$ of the first kind
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order `ord` for the real vector `x` (length `n`) by recurrent equation:
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\f[
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C_ord(x) = 2 x C_{ord-1}(x) - C_{ord-2}(x),
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\f]
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where \f$ C_0(x) = 1 \f$, \f$ C_1(x) = x\f$
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\param[in] x
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Pointer to the real argument vector `x`. \n
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Vector size is `[n x 1]`. \n \n
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\param[in] n
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Size of vectors `x` and `y`. \n \n
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\param[in] ord
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Chebyshev polynomial order. \n \n
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\param[out] y
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Pointer to the Chebyshev polynomial values, corresponds to the argument `x`. \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` if Chebyshev polynomial is calculated successfully. \n
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Else \ref ERROR_CODE_GROUP "code error". \n
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Example:
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\include cheby_poly1_test.c
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\n \n
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Text files will be created in `dat` directory: \n
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<pre>
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cheby_poly1_ord1.txt
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cheby_poly1_ord2.txt
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cheby_poly1_ord3.txt
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cheby_poly1_ord4.txt
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</pre>
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GNUPLOT package will create Chebyshev polynomials plot from saved text-files:
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\image html cheby_poly1.png
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GNUPLOT script is follow:
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\include cheby_poly1.plt
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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_TRANSCEND
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\fn int cheby_poly2(double* x, int n, int ord, double* y)
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\brief Chebyshev polynomial of the second kind order `ord`
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Function calculates Chebyshev polynomial \f$ U_ord(x)\f$ of the first kind
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order `ord` for the real vector `x` (length `n`) by recurrent equation:
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\f[
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U_ord(x) = 2 x U_{ord-1}(x) - U_{ord-2}(x),
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\f]
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where \f$ U_0(x) = 1 \f$, \f$ U_1(x) = 2x\f$
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\param[in] x
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Pointer to the real argument vector `x`. \n
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Vector size is `[n x 1]`. \n \n
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\param[in] n
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Size of vectors `x` and `y`. \n \n
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\param[in] ord
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Chebyshev polynomial order. \n \n
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\param[out] y
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Pointer to the Chebyshev polynomial values, corresponds to the argument `x`. \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` if Chebyshev polynomial is calculated successfully. \n
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Else \ref ERROR_CODE_GROUP "code error". \n
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Example:
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\include cheby_poly2_test.c
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\n \n
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Text files will be created in `dat` directory: \n
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<pre>
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cheby_poly2_ord1.txt
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cheby_poly2_ord2.txt
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cheby_poly2_ord3.txt
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cheby_poly2_ord4.txt
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</pre>
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GNUPLOT package will create Chebyshev polynomials plot from saved text-files:
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\image html cheby_poly2.png
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GNUPLOT script is follow:
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\include cheby_poly2.plt
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\author Sergey Bakhurin www.dsplib.org
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****************************************************************************** */ |