SECTION I. User-callable Routines Category H. Differentiation, integration

```         H1.  Numerical differentiation
H2.  Quadrature (numerical evaluation of definite integrals)

H1.  Numerical differentiation

CHFDV-S   Evaluate a cubic polynomial given in Hermite form and its
DCHFDV-D  first derivative at an array of points.  While designed for
use by PCHFD, it may be useful directly as an evaluator
for a piecewise cubic Hermite function in applications,
such as graphing, where the interval is known in advance.
If only function values are required, use CHFEV instead.

PCHFD-S   Evaluate a piecewise cubic Hermite function and its first
DPCHFD-D  derivative at an array of points.  May be used by itself
for Hermite interpolation, or as an evaluator for PCHIM
or PCHIC.  If only function values are required, use

H2.  Quadrature (numerical evaluation of definite integrals)

QPDOC-A   Documentation for QUADPACK, a package of subprograms for
automatic evaluation of one-dimensional definite integrals.

H2A.  One-dimensional integrals
H2A1.  Finite interval (general integrand)
H2A1A.  Integrand available via user-defined procedure
H2A1A1.  Automatic (user need only specify required accuracy)

GAUS8-S   Integrate a real function of one variable over a finite
DGAUS8-D  interval using an adaptive 8-point Legendre-Gauss
algorithm.  Intended primarily for high accuracy
integration or integration of smooth functions.

QAG-S     The routine calculates an approximation result to a given
DQAG-D    definite integral I = integral of F over (A,B),
hopefully satisfying following claim for accuracy
ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

QAGE-S    The routine calculates an approximation result to a given
DQAGE-D   definite integral   I = Integral of F over (A,B),
hopefully satisfying following claim for accuracy
ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QAGS-S    The routine calculates an approximation result to a given
DQAGS-D   Definite integral  I = Integral of F over (A,B),
Hopefully satisfying following claim for accuracy
ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QAGSE-S   The routine calculates an approximation result to a given
DQAGSE-D  definite integral I = Integral of F over (A,B),
hopefully satisfying following claim for accuracy
ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QNC79-S   Integrate a function using a 7-point adaptive Newton-Cotes

QNG-S     The routine calculates an approximation result to a
DQNG-D    given definite integral I = integral of F over (A,B),
hopefully satisfying following claim for accuracy
ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

H2A1A2.  Nonautomatic

QK15-S    To compute I = Integral of F over (A,B), with error
DQK15-D                  estimate
J = integral of ABS(F) over (A,B)

QK21-S    To compute I = Integral of F over (A,B), with error
DQK21-D                  estimate
J = Integral of ABS(F) over (A,B)

QK31-S    To compute I = Integral of F over (A,B) with error
DQK31-D                  estimate
J = Integral of ABS(F) over (A,B)

QK41-S    To compute I = Integral of F over (A,B), with error
DQK41-D                  estimate
J = Integral of ABS(F) over (A,B)

QK51-S    To compute I = Integral of F over (A,B) with error
DQK51-D                  estimate
J = Integral of ABS(F) over (A,B)

QK61-S    To compute I = Integral of F over (A,B) with error
DQK61-D                  estimate
J = Integral of ABS(F) over (A,B)

H2A1B.  Integrand available only on grid
H2A1B2.  Nonautomatic

AVINT-S   Integrate a function tabulated at arbitrarily spaced
DAVINT-D  abscissas using overlapping parabolas.

PCHIA-S   Evaluate the definite integral of a piecewise cubic
DPCHIA-D  Hermite function over an arbitrary interval.

PCHID-S   Evaluate the definite integral of a piecewise cubic
DPCHID-D  Hermite function over an interval whose endpoints are data
points.

H2A2.  Finite interval (specific or special type integrand including weight
functions, oscillating and singular integrands, principal value
integrals, splines, etc.)
H2A2A.  Integrand available via user-defined procedure
H2A2A1.  Automatic (user need only specify required accuracy)

BFQAD-S   Compute the integral of a product of a function and a

BSQAD-S   Compute the integral of a K-th order B-spline using the

PFQAD-S   Compute the integral on (X1,X2) of a product of a function
DPFQAD-D  F and the ID-th derivative of a B-spline,
(PP-representation).

PPQAD-S   Compute the integral on (X1,X2) of a K-th order B-spline
DPPQAD-D  using the piecewise polynomial (PP) representation.

QAGP-S    The routine calculates an approximation result to a given
DQAGP-D   definite integral I = Integral of F over (A,B),
hopefully satisfying following claim for accuracy
break points of the integration interval, where local
difficulties of the integrand may occur(e.g. SINGULARITIES,
DISCONTINUITIES), are provided by the user.

QAGPE-S   Approximate a given definite integral I = Integral of F
DQAGPE-D  over (A,B), hopefully satisfying the accuracy claim:
ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
Break points of the integration interval, where local
difficulties of the integrand may occur (e.g. singularities
or discontinuities) are provided by the user.

QAWC-S    The routine calculates an approximation result to a
DQAWC-D   Cauchy principal value I = INTEGRAL of F*W over (A,B)
(W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
following claim for accuracy
ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

QAWCE-S   The routine calculates an approximation result to a
DQAWCE-D  CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)
(W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying
following claim for accuracy
ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

QAWO-S    Calculate an approximation to a given definite integral
DQAWO-D    I = Integral of F(X)*W(X) over (A,B), where
W(X) = COS(OMEGA*X)
or W(X) = SIN(OMEGA*X),
hopefully satisfying the following claim for accuracy
ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QAWOE-S   Calculate an approximation to a given definite integral
DQAWOE-D     I = Integral of F(X)*W(X) over (A,B), where
W(X) = COS(OMEGA*X)
or W(X) = SIN(OMEGA*X),
hopefully satisfying the following claim for accuracy
ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QAWS-S    The routine calculates an approximation result to a given
DQAWS-D   definite integral I = Integral of F*W over (A,B),
(where W shows a singular behaviour at the end points
see parameter INTEGR).
Hopefully satisfying following claim for accuracy
ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QAWSE-S   The routine calculates an approximation result to a given
DQAWSE-D  definite integral I = Integral of F*W over (A,B),
(where W shows a singular behaviour at the end points,
see parameter INTEGR).
Hopefully satisfying following claim for accuracy
ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QMOMO-S   This routine computes modified Chebyshev moments.  The K-th
DQMOMO-D  modified Chebyshev moment is defined as the integral over
(-1,1) of W(X)*T(K,X), where T(K,X) is the Chebyshev
polynomial of degree K.

H2A2A2.  Nonautomatic

QC25C-S   To compute I = Integral of F*W over (A,B) with
DQC25C-D  error estimate, where W(X) = 1/(X-C)

QC25F-S   To compute the integral I=Integral of F(X) over (A,B)
DQC25F-D  Where W(X) = COS(OMEGA*X) Or (WX)=SIN(OMEGA*X)
and to compute J=Integral of ABS(F) over (A,B). For small
value of OMEGA or small intervals (A,B) 15-point GAUSS-
KRONROD Rule used. Otherwise generalized CLENSHAW-CURTIS us

QC25S-S   To compute I = Integral of F*W over (BL,BR), with error
DQC25S-D  estimate, where the weight function W has a singular
behaviour of ALGEBRAICO-LOGARITHMIC type at the points
A and/or B. (BL,BR) is a part of (A,B).

QK15W-S   To compute I = Integral of F*W over (A,B), with error
DQK15W-D                 estimate
J = Integral of ABS(F*W) over (A,B)

H2A3.  Semi-infinite interval (including e**(-x) weight function)
H2A3A.  Integrand available via user-defined procedure
H2A3A1.  Automatic (user need only specify required accuracy)

QAGI-S    The routine calculates an approximation result to a given
DQAGI-D   INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
OR I = Integral of F over (-INFINITY,BOUND)
OR I = Integral of F over (-INFINITY,+INFINITY)
Hopefully satisfying following claim for accuracy
ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QAGIE-S   The routine calculates an approximation result to a given
DQAGIE-D  integral   I = Integral of F over (BOUND,+INFINITY)
or I = Integral of F over (-INFINITY,BOUND)
or I = Integral of F over (-INFINITY,+INFINITY),
hopefully satisfying following claim for accuracy
ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

QAWF-S    The routine calculates an approximation result to a given
DQAWF-D   Fourier integral
I = Integral of F(X)*W(X) over (A,INFINITY)
where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).
Hopefully satisfying following claim for accuracy
ABS(I-RESULT).LE.EPSABS.

QAWFE-S   The routine calculates an approximation result to a
DQAWFE-D  given Fourier integral
I = Integral of F(X)*W(X) over (A,INFINITY)
where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X),
hopefully satisfying following claim for accuracy
ABS(I-RESULT).LE.EPSABS.

H2A3A2.  Nonautomatic

QK15I-S   The original (infinite integration range is mapped
DQK15I-D  onto the interval (0,1) and (A,B) is a part of (0,1).
it is the purpose to compute
I = Integral of transformed integrand over (A,B),
J = Integral of ABS(Transformed Integrand) over (A,B).

H2A4.  Infinite interval (including e**(-x**2)) weight function)
H2A4A.  Integrand available via user-defined procedure
H2A4A1.  Automatic (user need only specify required accuracy)

QAGI-S    The routine calculates an approximation result to a given
DQAGI-D   INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
OR I = Integral of F over (-INFINITY,BOUND)
OR I = Integral of F over (-INFINITY,+INFINITY)
Hopefully satisfying following claim for accuracy
ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

QAGIE-S   The routine calculates an approximation result to a given
DQAGIE-D  integral   I = Integral of F over (BOUND,+INFINITY)
or I = Integral of F over (-INFINITY,BOUND)
or I = Integral of F over (-INFINITY,+INFINITY),
hopefully satisfying following claim for accuracy
ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

H2A4A2.  Nonautomatic

QK15I-S   The original (infinite integration range is mapped
DQK15I-D  onto the interval (0,1) and (A,B) is a part of (0,1).
it is the purpose to compute
I = Integral of transformed integrand over (A,B),
J = Integral of ABS(Transformed Integrand) over (A,B).
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