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 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141` `````` GNU Scientific Library – Reference Manual: CQUAD doubly-adaptive integration

CQUAD is a new doubly-adaptive general-purpose quadrature routine which can handle most types of singularities, non-numerical function values such as Inf or NaN, as well as some divergent integrals. It generally requires more function evaluations than the integration routines in QUADPACK, yet fails less often for difficult integrands.

The underlying algorithm uses a doubly-adaptive scheme in which Clenshaw-Curtis quadrature rules of increasing degree are used to compute the integral in each interval. The L_2-norm of the difference between the underlying interpolatory polynomials of two successive rules is used as an error estimate. The interval is subdivided if the difference between two successive rules is too large or a rule of maximum degree has been reached.

This function allocates a workspace sufficient to hold the data for n intervals. The number n is not the maximum number of intervals that will be evaluated. If the workspace is full, intervals with smaller error estimates will be discarded. A minimum of 3 intervals is required and for most functions, a workspace of size 100 is sufficient.