Functions/Subroutines | |
| subroutine, public | gl_expand_A_B (x, w, n, x_AB, w_AB, A, B) |
| Takes the Gauss-Legendre rule for the interval [0,1] and expands it for the given interval [A,B]. More... | |
| recursive real(kind=cfp) function, public | quad1d (f, A, B, eps, Qest) |
| Adaptive 1D quadrature based on Gauss-Legendre rule. More... | |
| recursive real(kind=cfp) function, public | quad2d (f, Ax, Bx, Ay, By, eps, Qest) |
| Adaptive 2D quadrature on rectangle based on Gauss-Kronrod rule. The algorithm is based on that of Romanowski published in Int. J. Q. Chem. More... | |
| real(kind=cfp) function, public | gl2d (f, Ax, Bx, Ay, By) |
| 2D Quadrature on rectangle using the Gauss-Kronrod rule of order 8. The meaning of the input variables is identical to quad2d input parameters. More... | |
| subroutine, public | DQAGS (F, A, B, EPSABS, EPSREL, RESULT, ABSERR, NEVAL, IER, LIMIT, LENW, LAST, IWORK, WORK) |
| ***BEGIN PROLOGUE DQAGS ***PURPOSE The routine calculates an approximation result to a 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)). ***LIBRARY SLATEC (QUADPACK) ***CATEGORY H2A1A1 ***TYPE real(kind=cfp) (QAGS-S, DQAGS-D) ***KEYWORDS AUTOMATIC INTEGRATOR, END POINT SINGULARITIES, EXTRAPOLATION, GENERAL-PURPOSE, GLOBALLY ADAPTIVE, QUADPACK, QUADRATURE ***AUTHOR Piessens, Robert Applied Mathematics and Programming Division K. U. Leuven de Doncker, Elise Applied Mathematics and Programming Division K. U. Leuven ***DESCRIPTION More... | |
| subroutine, public | DQELG (N, EPSTAB, RESULT, ABSERR, RES3LA, NRES) |
| ***BEGIN PROLOGUE DQELG ***SUBSIDIARY ***PURPOSE The routine determines the limit of a given sequence of approximations, by means of the Epsilon algorithm of P.Wynn. An estimate of the absolute error is also given. The condensed Epsilon table is computed. Only those elements needed for the computation of the next diagonal are preserved. ***LIBRARY SLATEC ***TYPE real(kind=cfp) (QELG-S, DQELG-D) ***KEYWORDS CONVERGENCE ACCELERATION, EPSILON ALGORITHM, EXTRAPOLATION ***AUTHOR Piessens, Robert Applied Mathematics and Programming Division K. U. Leuven de Doncker, Elise Applied Mathematics and Programming Division K. U. Leuven ***DESCRIPTION More... | |
| subroutine | DQK21 (F, A, B, RESULT, ABSERR, RESABS, RESASC) |
| ***BEGIN PROLOGUE DQK21 ***PURPOSE To compute I = Integral of F over (A,B), with error estimate J = Integral of ABS(F) over (A,B) ***LIBRARY SLATEC (QUADPACK) ***CATEGORY H2A1A2 ***TYPE real(kind=cfp) (QK21-S, DQK21-D) ***KEYWORDS 21-POINT GAUSS-KRONROD RULES, QUADPACK, QUADRATURE ***AUTHOR Piessens, Robert Applied Mathematics and Programming Division K. U. Leuven de Doncker, Elise Applied Mathematics and Programming Division K. U. Leuven ***DESCRIPTION More... | |
Variables | |
| integer, parameter, public | n_7 = 7 |
| Order of the Gauss-Legendre quadrature to which the x_7 and w_7 arrays correspond. More... | |
| real(kind=cfp), dimension(2 *n_7+1), parameter, public | w_7 = (/0.015376620998058634177314196788602209_cfp,0.035183023744054062354633708225333669_cfp,0.05357961023358596750593477334293465_cfp,0.06978533896307715722390239725551416_cfp,0.08313460290849696677660043024060441_cfp,0.09308050000778110551340028093321141_cfp,0.09921574266355578822805916322191966_cfp,0.10128912096278063644031009998375966_cfp,0.09921574266355578822805916322191966_cfp,0.09308050000778110551340028093321141_cfp,0.08313460290849696677660043024060441_cfp,0.06978533896307715722390239725551416_cfp,0.05357961023358596750593477334293465_cfp,0.035183023744054062354633708225333669_cfp,0.015376620998058634177314196788602209_cfp/) |
| Weights for the Gauss-Legendre quadrature of order 7 on interval [0,1]. More... | |
| real(kind=cfp), dimension(2 *n_7+1), parameter, public | x_7 = (/0.0060037409897572857552171407066937094_cfp,0.031363303799647047846120526144895264_cfp,0.075896708294786391899675839612891574_cfp,0.13779113431991497629190697269303100_cfp,0.21451391369573057623138663137304468_cfp,0.30292432646121831505139631450947727_cfp,0.39940295300128273884968584830270190_cfp,0.50000000000000000000000000000000000_cfp,0.60059704699871726115031415169729810_cfp,0.69707567353878168494860368549052273_cfp,0.78548608630426942376861336862695532_cfp,0.86220886568008502370809302730696900_cfp,0.92410329170521360810032416038710843_cfp,0.96863669620035295215387947385510474_cfp,0.99399625901024271424478285929330629_cfp/) |
| Abscissas for the Gauss-Legendre quadrature of order 7 on interval [0,1]. More... | |
| integer, parameter, public | n_10 = 10 |
| Order of the Gauss-Legendre quadrature to which the x_10 and w_10 arrays correspond. More... | |
| real(kind=cfp), dimension(2 *n_10+1), parameter, public | x_10 = (/0.0031239146898052498698789820310295354_cfp,0.016386580716846852841688892546152419_cfp,0.039950332924799585604906433142515553_cfp,0.073318317708341358176374680706216165_cfp,0.11578001826216104569206107434688598_cfp,0.16643059790129384034701666500483042_cfp,0.22419058205639009647049060163784336_cfp,0.28782893989628060821316555572810597_cfp,0.35598934159879945169960374196769984_cfp,0.42721907291955245453148450883065683_cfp,0.50000000000000000000000000000000000_cfp,0.57278092708044754546851549116934317_cfp,0.64401065840120054830039625803230016_cfp,0.71217106010371939178683444427189403_cfp,0.77580941794360990352950939836215664_cfp,0.83356940209870615965298333499516958_cfp,0.88421998173783895430793892565311402_cfp,0.92668168229165864182362531929378384_cfp,0.96004966707520041439509356685748445_cfp,0.98361341928315314715831110745384758_cfp,0.99687608531019475013012101796897046_cfp/) |
| Abscissas for the Gauss-Legendre quadrature of order 10 on interval [0,1]. More... | |
| real(kind=cfp), dimension(2 *n_10+1), parameter, public | w_10 = (/0.008008614128887166662112308429235508_cfp,0.018476894885426246899975334149664833_cfp,0.028567212713428604141817913236223979_cfp,0.038050056814189651008525826650091590_cfp,0.046722211728016930776644870556966044_cfp,0.05439864958357418883173728903505282_cfp,0.06091570802686426709768358856286680_cfp,0.06613446931666873089052628724838780_cfp,0.06994369739553657736106671193379156_cfp,0.07226220199498502953191358327687627_cfp,0.07304056682484521359599257384168559_cfp,0.07226220199498502953191358327687627_cfp,0.06994369739553657736106671193379156_cfp,0.06613446931666873089052628724838780_cfp,0.06091570802686426709768358856286680_cfp,0.05439864958357418883173728903505282_cfp,0.046722211728016930776644870556966044_cfp,0.038050056814189651008525826650091590_cfp,0.028567212713428604141817913236223979_cfp,0.018476894885426246899975334149664833_cfp,0.008008614128887166662112308429235508_cfp/) |
| Weights for the Gauss-Legendre quadrature of order 10 on interval [0,1]. More... | |
Function/Subroutine Documentation
◆ DQAGS()
| subroutine, public general_quadrature_gbl::DQAGS | ( | class(function_1d) | F, |
| real(kind=cfp) | A, | ||
| real(kind=cfp) | B, | ||
| real(kind=cfp) | EPSABS, | ||
| real(kind=cfp) | EPSREL, | ||
| real(kind=cfp) | RESULT, | ||
| real(kind=cfp) | ABSERR, | ||
| integer | NEVAL, | ||
| integer | IER, | ||
| integer | LIMIT, | ||
| integer | LENW, | ||
| integer | LAST, | ||
| integer, dimension(*) | IWORK, | ||
| real(kind=cfp), dimension(*) | WORK | ||
| ) |
***BEGIN PROLOGUE DQAGS ***PURPOSE The routine calculates an approximation result to a 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)). ***LIBRARY SLATEC (QUADPACK) ***CATEGORY H2A1A1 ***TYPE real(kind=cfp) (QAGS-S, DQAGS-D) ***KEYWORDS AUTOMATIC INTEGRATOR, END POINT SINGULARITIES, EXTRAPOLATION, GENERAL-PURPOSE, GLOBALLY ADAPTIVE, QUADPACK, QUADRATURE ***AUTHOR Piessens, Robert Applied Mathematics and Programming Division K. U. Leuven de Doncker, Elise Applied Mathematics and Programming Division K. U. Leuven ***DESCRIPTION
Computation of a definite integral
Standard fortran subroutine
Double precision version
PARAMETERS
ON ENTRY
F - class(function_1d)
Function whose method 'eval' defines the integrand
Function F(X).
A - Double precision
Lower limit of integration
B - Double precision
Upper limit of integration
EPSABS - Double precision
Absolute accuracy requested
EPSREL - Double precision
Relative accuracy requested
If EPSABS.LE.0
And EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28),
The routine will end with IER = 6.
ON RETURN
RESULT - Double precision
Approximation to the integral
ABSERR - Double precision
Estimate of the modulus of the absolute error,
which should equal or exceed ABS(I-RESULT)
NEVAL - Integer
Number of integrand evaluations
IER - Integer
IER = 0 Normal and reliable termination of the
routine. It is assumed that the requested
accuracy has been achieved.
IER.GT.0 Abnormal termination of the routine
The estimates for integral and error are
less reliable. It is assumed that the
requested accuracy has not been achieved.
ERROR MESSAGES
IER = 1 Maximum number of subdivisions allowed
has been achieved. One can allow more sub-
divisions by increasing the value of LIMIT
(and taking the according dimension
adjustments into account. However, if
this yields no improvement it is advised
to analyze the integrand in order to
determine the integration difficulties. If
the position of a local difficulty can be
determined (E.G. SINGULARITY,
DISCONTINUITY WITHIN THE INTERVAL) one
will probably gain from splitting up the
interval at this point and calling the
integrator on the subranges. If possible,
an appropriate special-purpose integrator
should be used, which is designed for
handling the type of difficulty involved.
= 2 The occurrence of roundoff error is detec-
ted, which prevents the requested
tolerance from being achieved.
The error may be under-estimated.
= 3 Extremely bad integrand behaviour
occurs at some points of the integration
interval.
= 4 The algorithm does not converge.
Roundoff error is detected in the
Extrapolation table. It is presumed that
the requested tolerance cannot be
achieved, and that the returned result is
the best which can be obtained.
= 5 The integral is probably divergent, or
slowly convergent. It must be noted that
divergence can occur with any other value
of IER.
= 6 The input is invalid, because
(EPSABS.LE.0 AND
EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28)
OR LIMIT.LT.1 OR LENW.LT.LIMIT*4.
RESULT, ABSERR, NEVAL, LAST are set to
zero. Except when LIMIT or LENW is
invalid, IWORK(1), WORK(LIMIT*2+1) and
WORK(LIMIT*3+1) are set to zero, WORK(1)
is set to A and WORK(LIMIT+1) TO B.
DIMENSIONING PARAMETERS
LIMIT - Integer
DIMENSIONING PARAMETER FOR IWORK
LIMIT determines the maximum number of subintervals
in the partition of the given integration interval
(A,B), LIMIT.GE.1.
IF LIMIT.LT.1, the routine will end with IER = 6.
LENW - Integer
DIMENSIONING PARAMETER FOR WORK
LENW must be at least LIMIT*4.
If LENW.LT.LIMIT*4, the routine will end
with IER = 6.
LAST - Integer
On return, LAST equals the number of subintervals
produced in the subdivision process, determines the
number of significant elements actually in the WORK
Arrays.
WORK ARRAYS
IWORK - Integer
Vector of dimension at least LIMIT, the first K
elements of which contain pointers
to the error estimates over the subintervals
such that WORK(LIMIT*3+IWORK(1)),... ,
WORK(LIMIT*3+IWORK(K)) form a decreasing
sequence, with K = LAST IF LAST.LE.(LIMIT/2+2),
and K = LIMIT+1-LAST otherwise
WORK - Double precision
Vector of dimension at least LENW
on return
WORK(1), ..., WORK(LAST) contain the left
end-points of the subintervals in the
partition of (A,B),
WORK(LIMIT+1), ..., WORK(LIMIT+LAST) contain
the right end-points,
WORK(LIMIT*2+1), ..., WORK(LIMIT*2+LAST) contain
the integral approximations over the subintervals,
WORK(LIMIT*3+1), ..., WORK(LIMIT*3+LAST)
contain the error estimates.
***REFERENCES (NONE) ***ROUTINES CALLED DQAGSE, XERMSG ***REVISION HISTORY (YYMMDD) 800101 DATE WRITTEN 890831 Modified array declarations. (WRB) 890831 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) ***END PROLOGUE DQAGS
◆ DQELG()
| subroutine, public general_quadrature_gbl::DQELG | ( | integer | N, |
| real(kind=cfp), dimension(max_epstab) | EPSTAB, | ||
| real(kind=cfp) | RESULT, | ||
| real(kind=cfp) | ABSERR, | ||
| real(kind=cfp), dimension(3) | RES3LA, | ||
| integer | NRES | ||
| ) |
***BEGIN PROLOGUE DQELG ***SUBSIDIARY ***PURPOSE The routine determines the limit of a given sequence of approximations, by means of the Epsilon algorithm of P.Wynn. An estimate of the absolute error is also given. The condensed Epsilon table is computed. Only those elements needed for the computation of the next diagonal are preserved. ***LIBRARY SLATEC ***TYPE real(kind=cfp) (QELG-S, DQELG-D) ***KEYWORDS CONVERGENCE ACCELERATION, EPSILON ALGORITHM, EXTRAPOLATION ***AUTHOR Piessens, Robert Applied Mathematics and Programming Division K. U. Leuven de Doncker, Elise Applied Mathematics and Programming Division K. U. Leuven ***DESCRIPTION
Epsilon algorithm
Standard fortran subroutine
Double precision version
PARAMETERS
N - Integer
EPSTAB(N) contains the new element in the
first column of the epsilon table.
EPSTAB - Double precision
Vector of dimension 52 containing the elements
of the two lower diagonals of the triangular
epsilon table. The elements are numbered
starting at the right-hand corner of the
triangle.
RESULT - Double precision
Resulting approximation to the integral
ABSERR - Double precision
Estimate of the absolute error computed from
RESULT and the 3 previous results
RES3LA - Double precision
Vector of dimension 3 containing the last 3
results
NRES - Integer
Number of calls to the routine
(should be zero at first call)
***SEE ALSO DQAGIE, DQAGOE, DQAGPE, DQAGSE ***ROUTINES CALLED F1MACH ***REVISION HISTORY (YYMMDD) 800101 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) 900328 Added TYPE section. (WRB) ***END PROLOGUE DQELG
LIST OF MAJOR VARIABLES
-----------------------
E0 - THE 4 ELEMENTS ON WHICH THE COMPUTATION OF A NEW
E1 ELEMENT IN THE EPSILON TABLE IS BASED
E2
E3 E0
E3 E1 NEW
E2
NEWELM - NUMBER OF ELEMENTS TO BE COMPUTED IN THE NEW
DIAGONAL
ERROR - ERROR = ABS(E1-E0)+ABS(E2-E1)+ABS(NEW-E2)
RESULT - THE ELEMENT IN THE NEW DIAGONAL WITH LEAST VALUE
OF ERROR
MACHINE DEPENDENT CONSTANTS
---------------------------
EPMACH IS THE LARGEST RELATIVE SPACING.
OFLOW IS THE LARGEST POSITIVE MAGNITUDE.
LIMEXP IS THE MAXIMUM NUMBER OF ELEMENTS THE EPSILON
TABLE CAN CONTAIN. IF THIS NUMBER IS REACHED, THE UPPER
DIAGONAL OF THE EPSILON TABLE IS DELETED.
◆ DQK21()
| subroutine general_quadrature_gbl::DQK21 | ( | class(function_1d) | F, |
| real(kind=cfp) | A, | ||
| real(kind=cfp) | B, | ||
| real(kind=cfp) | RESULT, | ||
| real(kind=cfp) | ABSERR, | ||
| real(kind=cfp) | RESABS, | ||
| real(kind=cfp) | RESASC | ||
| ) |
***BEGIN PROLOGUE DQK21 ***PURPOSE To compute I = Integral of F over (A,B), with error estimate J = Integral of ABS(F) over (A,B) ***LIBRARY SLATEC (QUADPACK) ***CATEGORY H2A1A2 ***TYPE real(kind=cfp) (QK21-S, DQK21-D) ***KEYWORDS 21-POINT GAUSS-KRONROD RULES, QUADPACK, QUADRATURE ***AUTHOR Piessens, Robert Applied Mathematics and Programming Division K. U. Leuven de Doncker, Elise Applied Mathematics and Programming Division K. U. Leuven ***DESCRIPTION
Integration rules
Standard fortran subroutine
Double precision version
PARAMETERS
ON ENTRY
F - class(function_1d)
Function whose method 'eval' defines the integrand
Function F(X).
A - Double precision
Lower limit of integration
B - Double precision
Upper limit of integration
ON RETURN
RESULT - Double precision
Approximation to the integral I
RESULT is computed by applying the 21-POINT
KRONROD RULE (RESK) obtained by optimal addition
of abscissae to the 10-POINT GAUSS RULE (RESG).
ABSERR - Double precision
Estimate of the modulus of the absolute error,
which should not exceed ABS(I-RESULT)
RESABS - Double precision
Approximation to the integral J
RESASC - Double precision
Approximation to the integral of ABS(F-I/(B-A))
over (A,B)
***REFERENCES (NONE) ***ROUTINES CALLED F1MACH ***REVISION HISTORY (YYMMDD) 800101 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) ***END PROLOGUE DQK21
THE ABSCISSAE AND WEIGHTS ARE GIVEN FOR THE INTERVAL (-1,1).
BECAUSE OF SYMMETRY ONLY THE POSITIVE ABSCISSAE AND THEIR
CORRESPONDING WEIGHTS ARE GIVEN.
XGK - ABSCISSAE OF THE 21-POINT KRONROD RULE
XGK(2), XGK(4), ... ABSCISSAE OF THE 10-POINT
GAUSS RULE
XGK(1), XGK(3), ... ABSCISSAE WHICH ARE OPTIMALLY
ADDED TO THE 10-POINT GAUSS RULE
WGK - WEIGHTS OF THE 21-POINT KRONROD RULE
WG - WEIGHTS OF THE 10-POINT GAUSS RULE
GAUSS QUADRATURE WEIGHTS AND KRONROD QUADRATURE ABSCISSAE AND WEIGHTS AS EVALUATED WITH 80 DECIMAL DIGIT ARITHMETIC BY L. W. FULLERTON, BELL LABS, NOV. 1981.
LIST OF MAJOR VARIABLES
-----------------------
CENTR - MID POINT OF THE INTERVAL
HLGTH - HALF-LENGTH OF THE INTERVAL
ABSC - ABSCISSA
FVAL* - FUNCTION VALUE
RESG - RESULT OF THE 10-POINT GAUSS FORMULA
RESK - RESULT OF THE 21-POINT KRONROD FORMULA
RESKH - APPROXIMATION TO THE MEAN VALUE OF F OVER (A,B),
I.E. TO I/(B-A)
MACHINE DEPENDENT CONSTANTS
---------------------------
EPMACH IS THE LARGEST RELATIVE SPACING.
UFLOW IS THE SMALLEST POSITIVE MAGNITUDE.
◆ gl2d()
| real(kind=cfp) function, public general_quadrature_gbl::gl2d | ( | class(function_2d) | f, |
| real(kind=cfp), intent(in) | Ax, | ||
| real(kind=cfp), intent(in) | Bx, | ||
| real(kind=cfp), intent(in) | Ay, | ||
| real(kind=cfp), intent(in) | By | ||
| ) |
2D Quadrature on rectangle using the Gauss-Kronrod rule of order 8. The meaning of the input variables is identical to quad2d input parameters.
◆ gl_expand_A_B()
| subroutine, public general_quadrature_gbl::gl_expand_A_B | ( | real(kind=cfp), dimension(2*n+1), intent(in) | x, |
| real(kind=cfp), dimension(2*n+1), intent(in) | w, | ||
| integer, intent(in) | n, | ||
| real(kind=cfp), dimension(2*n+1), intent(out) | x_AB, | ||
| real(kind=cfp), dimension(2*n+1), intent(out) | w_AB, | ||
| real(kind=cfp), intent(in) | A, | ||
| real(kind=cfp), intent(in) | B | ||
| ) |
Takes the Gauss-Legendre rule for the interval [0,1] and expands it for the given interval [A,B].
◆ quad1d()
| recursive real(kind=cfp) function, public general_quadrature_gbl::quad1d | ( | class(function_1d) | f, |
| real(kind=cfp), intent(in) | A, | ||
| real(kind=cfp), intent(in) | B, | ||
| real(kind=cfp), intent(in) | eps, | ||
| real(kind=cfp), intent(in), optional | Qest | ||
| ) |
Adaptive 1D quadrature based on Gauss-Legendre rule.
- Parameters
-
[in] f The 1D function to be integrated. [in] A Interval start. [in] B Interval end. [in] eps Required relative precision for the integral. [in] Qest Optional: an estimate of the integral over the interval as obtained by a call to gl1d.
◆ quad2d()
| recursive real(kind=cfp) function, public general_quadrature_gbl::quad2d | ( | class(function_2d) | f, |
| real(kind=cfp), intent(in) | Ax, | ||
| real(kind=cfp), intent(in) | Bx, | ||
| real(kind=cfp), intent(in) | Ay, | ||
| real(kind=cfp), intent(in) | By, | ||
| real(kind=cfp), intent(in) | eps, | ||
| real(kind=cfp), intent(in), optional | Qest | ||
| ) |
Adaptive 2D quadrature on rectangle based on Gauss-Kronrod rule. The algorithm is based on that of Romanowski published in Int. J. Q. Chem.
- Parameters
-
[in] f The 2D function to be integrated. [in] Ax Rectangle X-coordinate start. [in] Bx Rectangle X-coordinate end. [in] Ay Rectangle Y-coordinate start. [in] By Rectangle Y-coordinate end. [in] eps Required relative precision for the integral. [in] Qest Optional: an estimate of the integral over the specified rectangle as obtained by a call to gl2d. Note that the estimate must be obtained using gl2d for the algorithm to proceed correctly since it relies on the fixed-point G-K quadrature to calculate integrals on the sub-rectangles.
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Variable Documentation
◆ n_10
| integer, parameter, public general_quadrature_gbl::n_10 = 10 |
Order of the Gauss-Legendre quadrature to which the x_10 and w_10 arrays correspond.
◆ n_7
| integer, parameter, public general_quadrature_gbl::n_7 = 7 |
Order of the Gauss-Legendre quadrature to which the x_7 and w_7 arrays correspond.
◆ w_10
| real(kind=cfp), dimension(2*n_10+1), parameter, public general_quadrature_gbl::w_10 = (/0.008008614128887166662112308429235508_cfp,0.018476894885426246899975334149664833_cfp,0.028567212713428604141817913236223979_cfp,0.038050056814189651008525826650091590_cfp,0.046722211728016930776644870556966044_cfp,0.05439864958357418883173728903505282_cfp,0.06091570802686426709768358856286680_cfp,0.06613446931666873089052628724838780_cfp,0.06994369739553657736106671193379156_cfp,0.07226220199498502953191358327687627_cfp,0.07304056682484521359599257384168559_cfp,0.07226220199498502953191358327687627_cfp,0.06994369739553657736106671193379156_cfp,0.06613446931666873089052628724838780_cfp,0.06091570802686426709768358856286680_cfp,0.05439864958357418883173728903505282_cfp,0.046722211728016930776644870556966044_cfp,0.038050056814189651008525826650091590_cfp,0.028567212713428604141817913236223979_cfp,0.018476894885426246899975334149664833_cfp,0.008008614128887166662112308429235508_cfp/) |
Weights for the Gauss-Legendre quadrature of order 10 on interval [0,1].
◆ w_7
| real(kind=cfp), dimension(2*n_7+1), parameter, public general_quadrature_gbl::w_7 = (/0.015376620998058634177314196788602209_cfp,0.035183023744054062354633708225333669_cfp,0.05357961023358596750593477334293465_cfp,0.06978533896307715722390239725551416_cfp,0.08313460290849696677660043024060441_cfp,0.09308050000778110551340028093321141_cfp,0.09921574266355578822805916322191966_cfp,0.10128912096278063644031009998375966_cfp,0.09921574266355578822805916322191966_cfp,0.09308050000778110551340028093321141_cfp,0.08313460290849696677660043024060441_cfp,0.06978533896307715722390239725551416_cfp,0.05357961023358596750593477334293465_cfp,0.035183023744054062354633708225333669_cfp,0.015376620998058634177314196788602209_cfp/) |
Weights for the Gauss-Legendre quadrature of order 7 on interval [0,1].
◆ x_10
| real(kind=cfp), dimension(2*n_10+1), parameter, public general_quadrature_gbl::x_10 = (/0.0031239146898052498698789820310295354_cfp,0.016386580716846852841688892546152419_cfp,0.039950332924799585604906433142515553_cfp,0.073318317708341358176374680706216165_cfp,0.11578001826216104569206107434688598_cfp,0.16643059790129384034701666500483042_cfp,0.22419058205639009647049060163784336_cfp,0.28782893989628060821316555572810597_cfp,0.35598934159879945169960374196769984_cfp,0.42721907291955245453148450883065683_cfp,0.50000000000000000000000000000000000_cfp,0.57278092708044754546851549116934317_cfp,0.64401065840120054830039625803230016_cfp,0.71217106010371939178683444427189403_cfp,0.77580941794360990352950939836215664_cfp,0.83356940209870615965298333499516958_cfp,0.88421998173783895430793892565311402_cfp,0.92668168229165864182362531929378384_cfp,0.96004966707520041439509356685748445_cfp,0.98361341928315314715831110745384758_cfp,0.99687608531019475013012101796897046_cfp/) |
Abscissas for the Gauss-Legendre quadrature of order 10 on interval [0,1].
◆ x_7
| real(kind=cfp), dimension(2*n_7+1), parameter, public general_quadrature_gbl::x_7 = (/0.0060037409897572857552171407066937094_cfp,0.031363303799647047846120526144895264_cfp,0.075896708294786391899675839612891574_cfp,0.13779113431991497629190697269303100_cfp,0.21451391369573057623138663137304468_cfp,0.30292432646121831505139631450947727_cfp,0.39940295300128273884968584830270190_cfp,0.50000000000000000000000000000000000_cfp,0.60059704699871726115031415169729810_cfp,0.69707567353878168494860368549052273_cfp,0.78548608630426942376861336862695532_cfp,0.86220886568008502370809302730696900_cfp,0.92410329170521360810032416038710843_cfp,0.96863669620035295215387947385510474_cfp,0.99399625901024271424478285929330629_cfp/) |
Abscissas for the Gauss-Legendre quadrature of order 7 on interval [0,1].
