Algorithm 912: A Module for Calculating Cylindrical Functions of Complex Order and Complex Argument
Algorithm 912: A Module for Calculating Cylindrical Functions of Complex Order and Complex Argument
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DOI：
10.1145/1916461.1916471
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发表时间：
2011-02
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通讯作者：
M. Kodama
中科院分区：
文献类型：
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作者：
M. Kodama
本算法提供了用于计算柱面函数Jv(Z)、Yv(Z)、Hv(1)(Z)和Hv(2)(Z)的模块，其中阶数v是复数且复变量z满足−πz≤π。该算法是用Fortran 90编写的，使用用户的Fortran系统接受其种类类型参数的任何内在数据类型的实数和复数来计算函数。函数的计算方法有级数展开法和数值积分法两种。Wronskian测试在区域|Re v|≤60、|Im v|≤60、|Re z|≤300、|Im z|≤300中的4,100,625个伪随机测试点上以双精度检验由该算法计算的函数值。测试结果表明，两种Wronskian的误差均小于6.42×10−-14。
The present algorithm provides a module for calculating the cylindrical functions Jv(z), Yv(z), Hv(1)(z), and Hv(2)(z), where the order v is complex and the complex argument z satisfies −π z ≤ π. The algorithm is written in Fortran 90 and calculates the functions using real and complex numbers of any intrinsic data type whose kind type parameter the user’s Fortran system accepts. The methods of calculating the functions are based on two kinds of series expansions and numerical integration. Wronskian tests examine the functional values computed by this algorithm with double precision at 4,100,625 pseudorandom test points in the region |Re v| ≤ 60, |Im v| ≤ 60, |Re z| ≤ 300, |Im z| ≤ 300. From the results of the tests, we find that the errors of two kinds of Wronskians are less than 6.42 × 10−14.