QagsIntegration Type

Namespace: Altaxo.Calc.Integration
Assembly: AltaxoCore.Redist.dll
Base Type: IntegrationBase

Adaptive integration with singularities.

The presence of an integrable singularity in the integration region causes an adaptive routine to concentrate new subintervals around the singularity. As the subintervals decrease in size the successive approximations to the integral converge in a limiting fashion. This approach to the limit can be accelerated using an extrapolation procedure. The QAGS algorithm combines adaptive bisection with the Wynn epsilon-algorithm to speed up the integration of many types of integrable singularities.

Ref.: Gnu Scientific library reference manual ()

Constructors

Constructor Description

QagsIntegration()

Full Usage: QagsIntegration()

Creates an instance of this integration class with a default integration rule and default debug flag setting.

QagsIntegration(debug)

Full Usage: QagsIntegration(debug)

Parameters:
    debug : bool - Setting of the debug flag for this instance. If the integration fails or the specified accuracy is not reached, an exception is thrown if the debug flag is set to true. If set to false, the return value of the integration function will be set to the appropriate error code (an exception will be thrown then only for serious errors).

Creates an instance of this integration class with a default integration rule and specified debug flag setting.

debug : bool

Setting of the debug flag for this instance. If the integration fails or the specified accuracy is not reached, an exception is thrown if the debug flag is set to true. If set to false, the return value of the integration function will be set to the appropriate error code (an exception will be thrown then only for serious errors).

QagsIntegration(integrationRule, debug)

Full Usage: QagsIntegration(integrationRule, debug)

Parameters:
    integrationRule : gsl_integration_rule - Integration rule used for integration.
    debug : bool - Setting of the debug flag for this instance. If the integration fails or the specified accuracy is not reached, an exception is thrown if the debug flag is set to true. If set to false, the return value of the integration function will be set to the appropriate error code (an exception will be thrown then only for serious errors).

Creates an instance of this integration class with specified integration rule and specified debug flag setting.

integrationRule : gsl_integration_rule

Integration rule used for integration.

debug : bool

Setting of the debug flag for this instance. If the integration fails or the specified accuracy is not reached, an exception is thrown if the debug flag is set to true. If set to false, the return value of the integration function will be set to the appropriate error code (an exception will be thrown then only for serious errors).

Instance members

Instance member Description

this.Integrate

Full Usage: this.Integrate

Parameters:
    f : Func<float, float> - Function to integrate.
    a : float - Lower integration limit.
    b : float - Upper integration limit.
    epsabs : float - Specifies the expected absolute error of integration. Should be set to zero (0) if you specify a relative error.
    epsrel : float - Specifies the expected relative error of integration. Should be set to zero (0) if you specify an absolute error.
    limit : int - Maximum number of subintervals used for integration.
    integrationRule : gsl_integration_rule - Integration rule used for integration (only for this function call).
    debug : bool - Setting of the debug flag (only for this function call). If the integration fails or the specified accuracy is not reached, an exception is thrown if the debug flag is set to true. If set to false, the return value of the integration function will be set to the appropriate error code (an exception will be thrown then only for serious errors).
    result : byref<float> - On return, contains the integration result.
    abserr : byref<float> - On return, contains the absolute error of integration.

Returns: GSL_ERROR Null if successfull, otherwise the appropriate error code.

Adaptive integration with (unknown) singularities.

f : Func<float, float>

Function to integrate.

a : float

Lower integration limit.

b : float

Upper integration limit.

epsabs : float

Specifies the expected absolute error of integration. Should be set to zero (0) if you specify a relative error.

epsrel : float

Specifies the expected relative error of integration. Should be set to zero (0) if you specify an absolute error.

limit : int

Maximum number of subintervals used for integration.

integrationRule : gsl_integration_rule

Integration rule used for integration (only for this function call).

debug : bool

Setting of the debug flag (only for this function call). If the integration fails or the specified accuracy is not reached, an exception is thrown if the debug flag is set to true. If set to false, the return value of the integration function will be set to the appropriate error code (an exception will be thrown then only for serious errors).

result : byref<float>

On return, contains the integration result.

abserr : byref<float>

On return, contains the absolute error of integration.

Returns: GSL_ERROR

Null if successfull, otherwise the appropriate error code.

this.Integrate

Full Usage: this.Integrate

Parameters:
    f : Func<float, float> - Function to integrate.
    a : float - Lower integration limit.
    b : float - Upper integration limit.
    epsabs : float - Specifies the expected absolute error of integration. Should be set to zero (0) if you specify a relative error.
    epsrel : float - Specifies the expected relative error of integration. Should be set to zero (0) if you specify an absolute error.
    limit : int - Maximum number of subintervals used for integration.
    result : byref<float> - On return, contains the integration result.
    abserr : byref<float> - On return, contains the absolute error of integration.

Returns: GSL_ERROR Null if successfull, otherwise the appropriate error code.

Adaptive integration with (unknown) singularities using the integration rule and debug setting given in the constructor..

f : Func<float, float>

Function to integrate.

a : float

Lower integration limit.

b : float

Upper integration limit.

epsabs : float

Specifies the expected absolute error of integration. Should be set to zero (0) if you specify a relative error.

epsrel : float

Specifies the expected relative error of integration. Should be set to zero (0) if you specify an absolute error.

limit : int

Maximum number of subintervals used for integration.

result : byref<float>

On return, contains the integration result.

abserr : byref<float>

On return, contains the absolute error of integration.

Returns: GSL_ERROR

Null if successfull, otherwise the appropriate error code.

Static members

Static member Description

QagsIntegration.DefaultIntegrationRule

Full Usage: QagsIntegration.DefaultIntegrationRule

Returns: gsl_integration_rule

Returns the default integration rule used for this class.

Returns: gsl_integration_rule

QagsIntegration.Integration(f, a, b, epsabs, epsrel, limit, integrationRule, debug, result, abserr, tempStorage)

Full Usage: QagsIntegration.Integration(f, a, b, epsabs, epsrel, limit, integrationRule, debug, result, abserr, tempStorage)

Parameters:
    f : Func<float, float> - Function to integrate.
    a : float - Lower integration limit.
    b : float - Upper integration limit.
    epsabs : float - Specifies the expected absolute error of integration. Should be set to zero (0) if you specify a relative error.
    epsrel : float - Specifies the expected relative error of integration. Should be set to zero (0) if you specify an absolute error.
    limit : int - Maximum number of subintervals used for integration.
    integrationRule : gsl_integration_rule - Integration rule used for integration (only for this function call).
    debug : bool - Setting of the debug flag (only for this function call). If the integration fails or the specified accuracy is not reached, an exception is thrown if the debug flag is set to true. If set to false, the return value of the integration function will be set to the appropriate error code (an exception will be thrown then only for serious errors).
    result : byref<float> - On return, contains the integration result.
    abserr : byref<float> - On return, contains the absolute error of integration.
    tempStorage : byref<obj> - Provides a temporary storage object that you can reuse for repeating function calls.

Returns: GSL_ERROR Null if successfull, otherwise the appropriate error code.

Adaptive integration with (unknown) singularities.

f : Func<float, float>

Function to integrate.

a : float

Lower integration limit.

b : float

Upper integration limit.

epsabs : float

Specifies the expected absolute error of integration. Should be set to zero (0) if you specify a relative error.

epsrel : float

Specifies the expected relative error of integration. Should be set to zero (0) if you specify an absolute error.

limit : int

Maximum number of subintervals used for integration.

integrationRule : gsl_integration_rule

Integration rule used for integration (only for this function call).

debug : bool

Setting of the debug flag (only for this function call). If the integration fails or the specified accuracy is not reached, an exception is thrown if the debug flag is set to true. If set to false, the return value of the integration function will be set to the appropriate error code (an exception will be thrown then only for serious errors).

result : byref<float>

On return, contains the integration result.

abserr : byref<float>

On return, contains the absolute error of integration.

tempStorage : byref<obj>

Provides a temporary storage object that you can reuse for repeating function calls.

Returns: GSL_ERROR

Null if successfull, otherwise the appropriate error code.

QagsIntegration.Integration(f, a, b, epsabs, epsrel, limit, result, abserr, tempStorage)

Full Usage: QagsIntegration.Integration(f, a, b, epsabs, epsrel, limit, result, abserr, tempStorage)

Parameters:
    f : Func<float, float> - Function to integrate.
    a : float - Lower integration limit.
    b : float - Upper integration limit.
    epsabs : float - Specifies the expected absolute error of integration. Should be set to zero (0) if you specify a relative error.
    epsrel : float - Specifies the expected relative error of integration. Should be set to zero (0) if you specify an absolute error.
    limit : int - Maximum number of subintervals used for integration.
    result : byref<float> - On return, contains the integration result.
    abserr : byref<float> - On return, contains the absolute error of integration.
    tempStorage : byref<obj> - Provides a temporary storage object that you can reuse for repeating function calls.

Returns: GSL_ERROR Null if successfull, otherwise the appropriate error code.

Adaptive integration with (unknown) singularities.

f : Func<float, float>

Function to integrate.

a : float

Lower integration limit.

b : float

Upper integration limit.

epsabs : float

Specifies the expected absolute error of integration. Should be set to zero (0) if you specify a relative error.

epsrel : float

Specifies the expected relative error of integration. Should be set to zero (0) if you specify an absolute error.

limit : int

Maximum number of subintervals used for integration.

result : byref<float>

On return, contains the integration result.

abserr : byref<float>

On return, contains the absolute error of integration.

tempStorage : byref<obj>

Provides a temporary storage object that you can reuse for repeating function calls.

Returns: GSL_ERROR

Null if successfull, otherwise the appropriate error code.

QagsIntegration.Integration(f, a, b, epsabs, epsrel, limit, integrationRule, debug, result, abserr)

Full Usage: QagsIntegration.Integration(f, a, b, epsabs, epsrel, limit, integrationRule, debug, result, abserr)

Parameters:
    f : Func<float, float> - Function to integrate.
    a : float - Lower integration limit.
    b : float - Upper integration limit.
    epsabs : float - Specifies the expected absolute error of integration. Should be set to zero (0) if you specify a relative error.
    epsrel : float - Specifies the expected relative error of integration. Should be set to zero (0) if you specify an absolute error.
    limit : int - Maximum number of subintervals used for integration.
    integrationRule : gsl_integration_rule - Integration rule used for integration (only for this function call).
    debug : bool - Setting of the debug flag (only for this function call). If the integration fails or the specified accuracy is not reached, an exception is thrown if the debug flag is set to true. If set to false, the return value of the integration function will be set to the appropriate error code (an exception will be thrown then only for serious errors).
    result : byref<float> - On return, contains the integration result.
    abserr : byref<float> - On return, contains the absolute error of integration.

Returns: GSL_ERROR Null if successfull, otherwise the appropriate error code.

Adaptive integration with (unknown) singularities.

f : Func<float, float>

Function to integrate.

a : float

Lower integration limit.

b : float

Upper integration limit.

epsabs : float

Specifies the expected absolute error of integration. Should be set to zero (0) if you specify a relative error.

epsrel : float

Specifies the expected relative error of integration. Should be set to zero (0) if you specify an absolute error.

limit : int

Maximum number of subintervals used for integration.

integrationRule : gsl_integration_rule

Integration rule used for integration (only for this function call).

debug : bool

Setting of the debug flag (only for this function call). If the integration fails or the specified accuracy is not reached, an exception is thrown if the debug flag is set to true. If set to false, the return value of the integration function will be set to the appropriate error code (an exception will be thrown then only for serious errors).

result : byref<float>

On return, contains the integration result.

abserr : byref<float>

On return, contains the absolute error of integration.

Returns: GSL_ERROR

Null if successfull, otherwise the appropriate error code.

QagsIntegration.Integration(f, a, b, epsabs, epsrel, limit, result, abserr)

Full Usage: QagsIntegration.Integration(f, a, b, epsabs, epsrel, limit, result, abserr)

Parameters:
    f : Func<float, float> - Function to integrate.
    a : float - Lower integration limit.
    b : float - Upper integration limit.
    epsabs : float - Specifies the expected absolute error of integration. Should be set to zero (0) if you specify a relative error.
    epsrel : float - Specifies the expected relative error of integration. Should be set to zero (0) if you specify an absolute error.
    limit : int - Maximum number of subintervals used for integration.
    result : byref<float> - On return, contains the integration result.
    abserr : byref<float> - On return, contains the absolute error of integration.

Returns: GSL_ERROR Null if successfull, otherwise the appropriate error code.

Adaptive integration with (unknown) singularities.

f : Func<float, float>

Function to integrate.

a : float

Lower integration limit.

b : float

Upper integration limit.

epsabs : float

Specifies the expected absolute error of integration. Should be set to zero (0) if you specify a relative error.

epsrel : float

Specifies the expected relative error of integration. Should be set to zero (0) if you specify an absolute error.

limit : int

Maximum number of subintervals used for integration.

result : byref<float>

On return, contains the integration result.

abserr : byref<float>

On return, contains the absolute error of integration.

Returns: GSL_ERROR

Null if successfull, otherwise the appropriate error code.