quadrature_module_gbl Module Reference

Functions/Subroutines
subroutine, public	cfp_bfqad (f, t, bcoef, n, k, id, x1, x2, tol, quad, ierr, work)
subroutine, public	cfp_bsqad (f, t, bcoef, n, k, id, x1, x2, tol, quad, ierr, work)
subroutine, public	cfp_bfqro (f, t, bcoef, n, kk, id, x1, x2, tol, quad, ierr, work)

Detailed Description

Quadrature module

Contains routines for integration of a b-spline with an arbitrary user-defined function. The function is defined using the function_1d class. See function_integration module for details on how this is used.

Function/Subroutine Documentation

cfp_bfqad()

subroutine, public quadrature_module_gbl::cfp_bfqad	(	class(function_1d)	f,
		real(kind=cfp), dimension(:), intent(in)	t,
		real(kind=cfp), dimension(:), intent(in)	bcoef,
		integer	n,
		integer	k,
		integer	id,
		real(kind=cfp)	x1,
		real(kind=cfp)	x2,
		real(kind=cfp)	tol,
		real(kind=cfp)	quad,
		integer	ierr,
		real(kind=cfp), dimension(:)	work )

Purpose:

!>         Compute the integral of a product of a function and a
!>         derivative of a K-th order B-spline:
!> 

\[ \int_{x_{1}}^{x_{2}} dr B(r)f(r) \]

!>AUTHOR  Amos, D. E., (SNLA)
!>DESCRIPTION
!>
!>     Abstract    **** a double precision routine ****
!>
!>         cfp_bfqad computes the integral on (X1,X2) of a product of a
!>         function F and the ID-th derivative of a K-th order B-spline,
!>         using the B-representation (T,BCOEF,N,K).  (X1,X2) must be a
!>         subinterval of T(K) .LE. X .LE. T(N+1).  An integration rou-
!>         tine, DBSGQ8 (a modification of GAUS8), integrates the product
!>         on subintervals of (X1,X2) formed by included (distinct) knots
!>
!>         The maximum number of significant digits obtainable in
!>         DBSQAD is the smaller of 18 and the number of digits
!>         carried in double precision arithmetic.
!>
!>     Description of Arguments
!>         Input      F,T,BCOEF,X1,X2,TOL are double precision
!> 

Parameters

[in]	F	!> Function of one argument for the integrand BF(X)=F(X)*BVALU(T,BCOEF,N,K,ID,X,INBV,WORK) !>
[in]	T	!> Knot array of length N+K !>
[in]	BCOEF	!> Coefficient array of length N !>
[in]	N	!> Length of coefficient array !>
[in]	K	!> Order of B-spline, K .GE. 1 !>
[in]	ID	!> Order of the spline derivative, 0 .LE. ID .LE. K-1. ID=0 gives the spline function !>
[in]	X1,X2	!> End points of quadrature interval in T(K) .LE. X .LE. T(N+1) !>
[in]	TOL	!> Desired accuracy for the quadrature, suggest 10.*DTOL .LT. TOL .LE. .1 where DTOL is the maximum of 1.0D-18 and double precision unit roundoff for the machine = F1MACH(4) !>
[out]	QUAD	\( \int_{x_{1}}^{x_{2}} dr B(r)f(r) \) !> Integral of BF(X) on (X1,X2) !>
[out]	IERR	!> A status code !> IERR=1 normal return !> 2 some quadrature on (X1,X2) does not meet the requested tolerance. !>
[in,out]	WORK	!> Work vector of length 3*K !> !> !> Error Conditions !> Improper input is a fatal error !> Some quadrature fails to meet the requested tolerance !> !>***REFERENCES D. E. Amos, Quadrature subroutines for splines and !> B-splines, Report SAND79-1825, Sandia Laboratories, !> December 1979. !>***ROUTINES CALLED F1MACH, DBSGQ8, INTRV, XERMSG !>

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cfp_bfqro()

subroutine, public quadrature_module_gbl::cfp_bfqro	(	class(function_1d)	f,
		real(kind=cfp), dimension(:), intent(in)	t,
		real(kind=cfp), dimension(:), intent(in)	bcoef,
		integer	n,
		integer	kk,
		integer	id,
		real(kind=cfp)	x1,
		real(kind=cfp)	x2,
		real(kind=cfp)	tol,
		real(kind=cfp)	quad,
		integer	ierr,
		real(kind=cfp), dimension(:), intent(inout)	work )

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cfp_bsqad()

subroutine, public quadrature_module_gbl::cfp_bsqad	(	class(function_1d)	f,
		real(kind=cfp), dimension(:), intent(in)	t,
		real(kind=cfp), dimension(:), intent(in)	bcoef,
		integer	n,
		integer	k,
		integer	id,
		real(kind=cfp)	x1,
		real(kind=cfp)	x2,
		real(kind=cfp)	tol,
		real(kind=cfp)	quad,
		integer	ierr,
		real(kind=cfp), dimension(:)	work )

Purpose:

!>***BEGIN PROLOGUE  cfp_bsqad
!>***PURPOSE  Compute the integral of a product of a function and a square of the
!>            derivative of a K-th order B-spline.
!>***LIBRARY   SLATEC
!>***CATEGORY  H2A2A1, E3, K6
!>***TYPE      REAL(kind=cfp) (BFQAD-S, cfp_bsqad-D)
!>***KEYWORDS  INTEGRAL OF B-SPLINE, QUADRATURE
!>***AUTHOR  Amos, D. E., (SNLA)
!>***DESCRIPTION
!>
!>     Abstract    **** a double precision routine ****
!>
!>         cfp_bsqad computes the integral on (X1,X2) of a product of a
!>         function F and the ID-th derivative of a K-th order B-spline,
!>         using the B-representation (T,BCOEF,N,K).  (X1,X2) must be a
!>         subinterval of T(K) .LE. X .LE. T(N+1).  An integration rou-
!>         tine, DBSGQ8 (a modification of GAUS8), integrates the product
!>         on subintervals of (X1,X2) formed by included (distinct) knots
!>
!>         The maximum number of significant digits obtainable in
!>         DBSQAD is the smaller of 18 and the number of digits
!>         carried in double precision arithmetic.
!>
!>     Description of Arguments
!>         Input      F,T,BCOEF,X1,X2,TOL are double precision
!>           F      - function of one argument for the integrand BF(X)=F(X)*BVALU(T,BCOEF,N,K,ID,X,INBV,WORK)
!>           T      - knot array of length N+K
!>           BCOEF  - coefficient array of length N
!>           N      - length of coefficient array
!>           K      - order of B-spline, K .GE. 1
!>           ID     - order of the spline derivative, 0 .LE. ID .LE. K-1
!>                    ID=0 gives the spline function
!>           X1,X2  - end points of quadrature interval in
!>                    T(K) .LE. X .LE. T(N+1)
!>           TOL    - desired accuracy for the quadrature, suggest
!>                    10.*DTOL .LT. TOL .LE. .1 where DTOL is the maximum
!>                    of 1.0D-18 and double precision unit roundoff for
!>                    the machine = F1MACH(4)
!>
!>         Output     QUAD,WORK are double precision
!>           QUAD   - integral of BF(X) on (X1,X2)
!>           IERR   - a status code
!>                    IERR=1  normal return
!>                         2  some quadrature on (X1,X2) does not meet
!>                            the requested tolerance.
!>           WORK   - work vector of length 3*K
!>
!>     Error Conditions
!>         Improper input is a fatal error
!>         Some quadrature fails to meet the requested tolerance
!>
!>***REFERENCES  D. E. Amos, Quadrature subroutines for splines and
!>                 B-splines, Report SAND79-1825, Sandia Laboratories,
!>                 December 1979.
!>***ROUTINES CALLED  F1MACH, DBSGQ8, INTRV, XERMSG
!>***REVISION HISTORY  (YYMMDD)
!>   800901  DATE WRITTEN
!>   890531  Changed all specific intrinsics to generic.  (WRB)
!>   890531  REVISION DATE from Version 3.2
!>   891214  Prologue converted to Version 4.0 format.  (BAB)
!>   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
!>   900326  Removed duplicate information from DESCRIPTION section.
!>           (WRB)
!>   920501  Reformatted the REFERENCES section.  (WRB)
!>***END PROLOGUE  cfp_bsqad
!>
!> 

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