Gyoto
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Geometrically thin disk read from a set of FITS files. More...
#include <GyotoDynamicalDisk.h>
Public Types | |
typedef Gyoto::SmartPointer< Gyoto::SmartPointee > | Subcontractor_t(Gyoto::FactoryMessenger *) |
A subcontractor builds an object upon order from the Factory. More... | |
Public Member Functions | |
virtual Property const * | getProperties () const |
Get list of properties. More... | |
DynamicalDisk () | |
Standard constructor. | |
DynamicalDisk (const DynamicalDisk &) | |
Copy constructor. | |
virtual DynamicalDisk * | clone () const |
Cloner. | |
virtual | ~DynamicalDisk () |
Destructor. | |
std::string | file () const |
void | file (std::string const &fname) |
void | tinit (double t) |
double | tinit () const |
void | dt (double t) |
double | dt () const |
virtual double | emission (double nu_em, double dsem, double c_ph[8], double c_obj[8]=NULL) const |
Specific intensity Iν More... | |
void | getVelocity (double const pos[4], double vel[4]) |
Get fluid 4-velocity at point. More... | |
double const * | getVelocity () const |
Get PatternDisk::velocity_. | |
bool | spectralEmission () const |
void | spectralEmission (bool t) |
double | risco () const |
void | risco (double r) |
virtual double | emission (double, double, double *, double) const |
virtual void | emission (double Inu[], double nu_em[], size_t nbnu, double dsem, double coord_ph[8], double coord_obj[8]=NULL) const |
Specific intensity Iν for several values of νem More... | |
void | metric (SmartPointer< Metric::Generic > gg) |
Insures metric is KerrBL or alike. | |
virtual SmartPointer< Metric::Generic > | metric () const |
Get the Metric gg_. | |
void | fillProperty (Gyoto::FactoryMessenger *fmp, Property const &p) const |
Output a single Property to XML. More... | |
virtual void | innerRadius (double) |
Set rin_. | |
virtual double | innerRadius () const |
Get rin_. | |
virtual double | innerRadius (std::string const &) const |
Get rin_. | |
virtual void | innerRadius (double, std::string const &) |
Set rin_. | |
virtual void | outerRadius (double) |
Set rout_. | |
virtual double | outerRadius () const |
Get rout_. | |
virtual double | outerRadius (std::string const &) const |
Get rout_. | |
virtual void | outerRadius (double, std::string const &) |
Set rout_. | |
virtual void | patternVelocity (double) |
Set PatternDisk::Omega_. More... | |
virtual double | patternVelocity () const |
Get PatternDisk::Omega_. | |
void | setEmission (double *pattern) |
Set PatternDisk::emission_. More... | |
void | setVelocity (double *pattern) |
Set PatternDisk::velocity__. More... | |
void | radius (double *pattern) |
Set PatternDisk::radius_. More... | |
virtual void | copyIntensity (double const *const pattern=NULL, size_t const naxes[3]=NULL) |
Set PatternDisk::emission_. More... | |
virtual double const * | getIntensity () const |
Get PatternDisk::emission_. | |
virtual void | getIntensityNaxes (size_t naxes[3]) const |
Get PatternDisk::nnu_, PatternDisk::nphi_, and PatternDisk::nr_. | |
virtual void | copyOpacity (double const *const pattern=NULL, size_t const naxes[3]=NULL) |
Set PatternDisk::opacity_. More... | |
virtual double const * | opacity () const |
Get PatternDisk::opacity_. | |
virtual void | copyVelocity (double const *const pattern=NULL, size_t const naxes[2]=NULL) |
Set PatternDisk::velocity_. More... | |
virtual void | copyGridRadius (double const *const pattern=NULL, size_t nr=0) |
Set PatternDisk::radius_. More... | |
virtual double const * | getGridRadius () const |
Get PatternDisk::radius_. | |
virtual void | repeatPhi (size_t n) |
Set PatternDisk::repeat_phi_. | |
virtual size_t | repeatPhi () const |
Get PatternDisk::repeat_phi_. | |
virtual void | nu0 (double freq) |
Set PatternDisk::nu0_. | |
virtual double | nu0 () const |
Get PatternDisk::nu0_. | |
virtual void | dnu (double dfreq) |
Set PatternDisk::dnu_. | |
virtual double | dnu () const |
Get PatternDisk::dnu_. | |
void | phimin (double phimin) |
Set PatternDisk::phimin_. | |
double | phimin () const |
Get PatternDisk::phimin_. | |
void | phimax (double phimax) |
Set PatternDisk::phimax_. | |
double | phimax () const |
Get PatternDisk::phimax_. | |
virtual double | transmission (double nu_em, double dsem, double coord[8]) const |
Transmission: exp( αν * dsem ) More... | |
virtual double | thickness () const |
Get thickness_. | |
virtual double | thickness (std::string const &) const |
Get thickness_. | |
virtual void | thickness (double) |
Set thickness_. | |
virtual void | thickness (double, std::string const &) |
Set thickness_. | |
virtual int | dir () const |
Get dir_. | |
virtual void | dir (int) |
Set dir_. | |
virtual bool | corotating () const |
virtual void | corotating (bool t) |
Get dir_==1. | |
virtual double | operator() (double const coord[]) |
Set dir_=t?1:-1. More... | |
virtual double | projectedRadius (double const coord[]) const |
Projected radius of position coord on the equatorial plane. | |
virtual double | sphericalPhi (double const coord[]) const |
Longitude. | |
virtual int | Impact (Gyoto::Photon *ph, size_t index, Astrobj::Properties *data=NULL) |
Does a photon at these coordinates impact the object? More... | |
virtual double | rMax () |
Get maximal distance from center of coordinate system. More... | |
virtual double | rMax () const |
Get maximal distance from center of coordinate system. | |
virtual double | rMax (std::string const &unit) |
Get rmax_ is specified unit. More... | |
virtual double | rMax (std::string const &unit) const |
Get rmax_ is specified unit. | |
virtual void | rMax (double val) |
Set maximal distance from center of coordinate system. More... | |
virtual void | rMax (double val, std::string const &unit) |
Set maximal distance from center of coordinate system. More... | |
virtual double | deltaMax (double coord[8]) |
Get max step constraint for adaptive integration. More... | |
const std::string | kind () const |
Get the kind of the Astrobj (e.g. "Star") | |
void | opticallyThin (bool flag) |
Set whether the object is optically thin. More... | |
bool | opticallyThin () const |
Query whether object is optically thin. More... | |
void | radiativeQ (bool flag) |
bool | radiativeQ () const |
virtual void | radiativeQ (double Inu[], double Taunu[], double nu_em[], size_t nbnu, double dsem, double coord_ph[8], double coord_obj[8]=NULL) const |
void | redshift (bool flag) |
bool | redshift () const |
virtual Gyoto::Quantity_t | getDefaultQuantities () |
Which quantities to compute if know was requested. More... | |
virtual void | setParameters (FactoryMessenger *fmp) |
Main loop in Subcontractor_t function. More... | |
virtual void | setParameters (Gyoto::FactoryMessenger *fmp) |
Main loop for parsing Properties from XML description. More... | |
virtual void | processHitQuantities (Photon *ph, double *coord_ph_hit, double *coord_obj_hit, double dt, Astrobj::Properties *data) const |
Fills Astrobj::Properties. More... | |
virtual double | integrateEmission (double nu1, double nu2, double dsem, double c_ph[8], double c_obj[8]=NULL) const |
∫ν1ν2 Iν dν (or jν) More... | |
virtual void | integrateEmission (double *I, double const *boundaries, size_t const *chaninds, size_t nbnu, double dsem, double *cph, double *co) const |
∫ν1ν2 Iν dν (or jν) More... | |
void | incRefCount () |
Increment the reference counter. Warning: Don't mess with the counter. | |
int | decRefCount () |
Decrement the reference counter and return current value. Warning: Don't mess with the counter. | |
int | getRefCount () |
Get the current number of references. | |
void | set (Property const &p, Value val) |
Set Value of a Property. | |
void | set (Property const &p, Value val, std::string const &unit) |
Set Value (expressed in unit) of a Property. | |
void | set (std::string const &pname, Value val) |
Set Value of a Property. | |
void | set (std::string const &pname, Value val, std::string const &unit) |
Set Value (expressed in unit) of a Property. | |
Value | get (Property const &p) const |
Get Value of a Property. | |
Value | get (std::string const &pname) const |
Get Value of a Property. | |
Value | get (Property const &p, std::string const &unit) const |
Get Value of a Property, converted to unit. | |
Value | get (std::string const &pname, std::string const &unit) const |
Get Value of a Property, converted to unit. | |
Property const * | property (std::string const pname) const |
Find property by name. More... | |
virtual void | fillElement (Gyoto::FactoryMessenger *fmp) const |
Fill the XML element for this Object. More... | |
virtual int | setParameter (std::string name, std::string content, std::string unit) |
Set parameter by name. More... | |
virtual void | setParameter (Gyoto::Property const &p, std::string const &name, std::string const &content, std::string const &unit) |
Set parameter by Property (and name) More... | |
Static Public Attributes | |
static GYOTO_OBJECT Property const | properties [] |
Protected Member Functions | |
void | copyQuantities (int iq) |
Set underlying PatternDisk pointers to a specific date slice. More... | |
void | getIndices (size_t i[3], double const co[4], double nu=0.) const |
Get emission_ cell corresponding to position co[4]. | |
Protected Attributes | |
SmartPointer< Spectrum::BlackBody > | spectrumBB_ |
emission law More... | |
double | rin_ |
disk inner radius in geometrical units | |
double | rout_ |
disk outer radius in geometrical units | |
double | thickness_ |
disk thickness More... | |
int | dir_ |
1 for corotating (default), -1 for counterrotating. | |
SmartPointer< Gyoto::Metric::Generic > | gg_ |
The Metric in this end of the Universe. | |
double | rmax_ |
Maximum distance to the center of the coordinate system [geometrical units]. More... | |
bool | flag_radtransf_ |
1 if radiative transfer inside Astrobj, else 0 | |
int | radiativeq_ |
1 to use the new radiativeQ function (under dvp) | |
int | noredshift_ |
1 to impose redshift factor g = 1 | |
std::string | kind_ |
The "kind" that is output in the XML entity. More... | |
Private Attributes | |
char * | dirname_ |
FITS files directory. | |
double | tinit_ |
date of the first FITS file | |
double | dt_ |
Time increment between two FITS (assumed constant) | |
int | nb_times_ |
Number of dates. | |
double ** | emission_array_ |
Array of PatternDisk::emission_ arrays. | |
double ** | opacity_array_ |
Array of PatternDisk::opacity_ arrays. | |
double ** | velocity_array_ |
Array of PatternDisk::velocity_ arrays. | |
double ** | radius_array_ |
Array of PatternDisk::radius_ arrays. More... | |
double * | dnu_array_ |
Array of PatternDisk::dnu_ values. | |
double * | nu0_array_ |
Array of PatternDisk::nu0_ values. | |
size_t * | nnu_array_ |
Array of PatternDisk::nu1_ values. | |
double * | dphi_array_ |
Array of PatternDisk::dphi_ values. | |
size_t * | nphi_array_ |
Array of PatternDisk::nphi_ values. | |
double * | dr_array_ |
Array of PatternDisk::dr_ values. | |
size_t * | nr_array_ |
Array of PatternDisk::nr_ values. | |
Friends | |
class | Gyoto::SmartPointer< Gyoto::Astrobj::DynamicalDisk > |
Geometrically thin disk read from a set of FITS files.
This class describes a PatternDiskBB that evolves dynamically. It is described by a set of FITS files.
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inherited |
A subcontractor builds an object upon order from the Factory.
Various classes need to provide a subcontractor to be able to instanciate themselves upon order from the Factory. A subcontractor is a function (often a static member function) which accepts a pointer to a FactoryMessenger as unique parameter, communicates with the Factory using this messenger to read an XML description of the object to build, and returns this objet. SmartPointee::Subcontractor_t* is just generic enough a typedef to cast to and from other subcontractor types: Astrobj::Subcontractor_t, Metric::Subcontractor_t, Spectrum::Subcontractor_t. A subcontractor needs to be registered using the relevant Register() function: Astrobj::Register(), Metric::Register(), Spectrum::Register().
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virtualinherited |
Set PatternDisk::radius_.
PatternDisk::radius_ is first freed if not NULL and set to NULL.
If pattern is not NULL, PatternDisk::emission_ must have been set previously with matching dimensions. PatternDisk::radius_ is then reallocated, and pattern is copied into radius_.
pattern | Array to copy as radius_. May be NULL in which case radius_ is simply deallocated and set to NULL. |
nr | size of radius array. |
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virtualinherited |
PatternDisk::emission_ is freed if not NULL, reallocated, and pattern is copied into emission_.
If PatternDisk::opacity_, PatternDisk::velocity_ or PatternDisk::radius_ have been set previously with mismatching sizes, they are deallocated too.
Finally, PatternDisk::nnu_, PatternDisk::nphi_, and PatternDisk::nr_ are set according to naxes.
pattern | Array to copy as emission_. May be NULL in which case emission_ is simply deallocated and set to NULL. |
naxes | { nnu_, nphi_, nr_ }. |
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virtualinherited |
PatternDisk::opacity_ is first freed if not NULL and set to NULL.
If pattern is not NULL, PatternDisk::emission_ must have been set previously with matching dimensions. PatternDisk::opacity_ is then reallocated, and pattern is copied into opacity_.
pattern | Array to copy as opacity_. May be NULL in which case opacity_ is simply deallocated and set to NULL. |
naxes | { nnu_, nphi_, nr_ }. |
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protected |
Set underlying PatternDisk pointers to a specific date slice.
iq | Index of the date slice. |
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virtualinherited |
PatternDisk::velocity_ is first freed if not NULL and set to NULL.
If pattern is not NULL, PatternDisk::emission_ must have been set previously with matching dimensions. PatternDisk::velocity_ is then reallocated, and pattern is copied into velocity_.
pattern | Array to copy as velocity_. May be NULL in which case velocity_ is simply deallocated and set to NULL. |
naxes | { nphi_, nr_ }. |
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virtualinherited |
Get max step constraint for adaptive integration.
[in] | coord | position |
Reimplemented in Gyoto::Astrobj::Complex.
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virtual |
Specific intensity Iν
Called by the default implementation for processHitQuantities().
emission() computes the intensity Iν emitted by the small volume of length dsem, in the emitter's frame. It should take self-absorption along dsem into account.
Reminder :
The equation used for radiative transfer (without absorption) is:
d(Iν/ν3)/dλ = (jν/ν2) [*]
where λ is the integration parameter along the null geodesic.
NB: Let us consider a particular observer, with ν being the frequency measured by this observer, and ds being the proper distance (as measured by the observer) that the photon travels as it moves from λ to λ+dλ along its geodesic. Then it can be shown that:
dλ = ds/ν
This shows that Eq. [*] is homogeneous.
The default implementation returns 1. if optically thick and dsem if optically thin. It allows for a quick implementation of your object for visualization purposes.
nu_em | Frequency at emission [Hz] |
dsem | length over which to integrate inside the object [geometrical units] |
coord_ph | Photon coordinate |
coord_obj | Emitter coordinate at current photon position |
Reimplemented from Gyoto::Astrobj::PatternDisk.
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virtualinherited |
Specific intensity Iν for several values of νem
Called by the default implementation for processHitQuantities().
emission() computes the intensity Iν emitted by the small volume of length dsem. It should take self-absorption along dsem into account.
Same as emission(double nu_em, double dsem, double coord_ph[8], double coord_obj[8]=NULL) const looping on several values of nu_em.
Inu[nbnu] | Output (must be set to a previously allocated array of doubles) |
nu_em[nbnu] | Frequencies at emission |
nbnu | Size of Inu[] and nu_em[] |
dsem | Length over which to integrate inside the object |
coord_ph | Photon coordinate |
coord_obj | Emitter coordinate at current photon position |
Reimplemented in Gyoto::Astrobj::PolishDoughnut.
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virtualinherited |
Fill the XML element for this Object.
The base implementation simply calls fillProperty() for each Property defined for the Object.
Derived classes should avoid overriding fillElement(). It may make sense occasionally, e.g. to make sure that the metric is output first.
To customize how a given Property is rendered, it is better to override fillProperty().
If this method is overridden, the implementation should in general call fillElement() on the direct base.
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virtualinherited |
Output a single Property to XML.
The base implementation decides what to do based on the p.type. The format matches how setParameters() an setParameter() would interpret the XML descition.
Overriding this method should be avoided, but makes sense in some cases (for instance Screen::fillProperty() selects a different unit for Distance based on its magnitude, so that stellar sizes are expressed in solar radii while smaller sizes can be expressed in meters and larger sizes in parsecs).
Overriding implementation should fall-back on calling the implementation in the direct parent class:
Reimplemented from Gyoto::Object.
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virtualinherited |
Which quantities to compute if know was requested.
Return a Gyoto::Quantity_t suitable as input to Gyoto::Scenery::setRequestedQuantities() to set de default quantities to compute for this object. The default of these defaults GYOTO_QUANTITY_INTENSITY.
Reimplemented in Gyoto::Astrobj::PageThorneDisk.
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virtual |
Get list of properties.
This method is declared automatically by the GYOTO_OBJECT macro and defined automatically by the GYOTO_PROPERTY_END macro.
Reimplemented from Gyoto::Astrobj::PatternDiskBB.
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virtual |
Get fluid 4-velocity at point.
Fill vel with the 4-vector velocity of the fluid at 4-position pos. getVelocity() should work at some distance from the equatorial plane. The default implementation calls Metric::Generic::circularVelocity().
[in] | pos | 4-position at which to compute velocity; |
[out] | vel | 4-velocity at pos. |
Reimplemented from Gyoto::Astrobj::PatternDisk.
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virtualinherited |
Does a photon at these coordinates impact the object?
Impact() checks whether a Photon impacts the object between two integration steps of the photon's trajectory (those two steps are photon->getCoord(index, coord1) and photon->getCoord(index+1, coord2)). Impact returns 1 if the photon impacts the object between these two steps, else 0. In many cases of geometrically thick obects, the implementation Astrobj::Standard::Impact() will be fine.
Impact will call Generic::processHitQuantities() (which is virtual and may be re-implemented) to compute observable properties on demand: if the data pointer is non-NULL, the object will look in it for pointers to properties which apply to its kind. If a pointer to a property known to this object is present, then the property is computed and store at the pointed-to address. For instance, all objects know the "intensity" property. If data->intensity != NULL, the instensity is computed and stored in *data->intensity.
If data is non-NULL and only in this case, processHitQuantities() will also call ph->transmit() to update the transmissions of the Photon (see Photon::transmit(size_t, double)). This must not be done if data is NULL (see Astrobj::Complex::Impact() for an explanation).
ph | Gyoto::Photon aimed at the object; |
index | Index of the last photon step; |
data | Pointer to a structure to hold the observables at impact. |
Implements Gyoto::Astrobj::Generic.
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virtualinherited |
∫ν1ν2 Iν dν (or jν)
Compute the integral of emission() from ν1 to ν2. The default implementation is a numerical integrator which works well enough and is reasonably fast if emission() is a smooth function (i.e. no emission or absorption lines). If possible, it is wise to implement an analytical solution. It is used by processHitQuantities to compute the "BinSpectrum" quantity which is the most physical: it is the only quantity that can be actually measured directly by a real-life instrument.
Reimplemented in Gyoto::Astrobj::UniformSphere, and Gyoto::Astrobj::Torus.
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virtualinherited |
∫ν1ν2 Iν dν (or jν)
Like double integrateEmission(double nu1, double nu2, double dsem, double c_ph[8], double c_obj[8]) const for each Spectrometer channel.
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virtualinherited |
Set dir_=t?1:-1.
A function which changes sign on the equatorial plane.theta-pi/2 or z
Implements Gyoto::Functor::Double_constDoubleArray.
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inherited |
Set whether the object is optically thin.
Set flag indicating that radiative transfer should be integrated, i.e. the object is to be considered optically thin.
flag | 1 if optically thin, 0 if optically thick. |
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inherited |
Query whether object is optically thin.
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virtualinherited |
Set PatternDisk::Omega_.
Unit: radians per geometrical unit time.
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virtualinherited |
Fills Astrobj::Properties.
processHitQuantities fills the requested data in Impact. To use it, you need to call it in the Impact() method for your object in case of hit. It will fill Redshift, Intensity, Spectrum, BinSpectrum and update the Photon's transmission by calling Photon::transmit(), only if data==NULL.
You can overload it for your Astrobj. The generic implementation calls emission(), integrateEmission() and transmission() below.
Reimplemented in Gyoto::Astrobj::UniformSphere, and Gyoto::Astrobj::PageThorneDisk.
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inherited |
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inherited |
Set PatternDisk::radius_.
The pointer is copied directly, not the array content.
This is a low-level function. Beware that:
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virtualinherited |
Get maximal distance from center of coordinate system.
Get maximal distance from center of coordinate system at which a Photon may hit the object.
Child classes may use the rmax_ member to cache this value, if its current value is DBL_MAX.
It can also be set using rMax().
Reimplemented in Gyoto::Astrobj::Star, Gyoto::Astrobj::Torus, and Gyoto::Astrobj::FixedStar.
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virtualinherited |
Get rmax_ is specified unit.
Call rMax() and convert result to unit.
unit | string |
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virtualinherited |
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virtualinherited |
Set maximal distance from center of coordinate system.
Call Generic::rMax(double val) after converting val from unit to geometrical units.
val | rmax_ expressed in unit "unit"; |
unit | string... |
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inherited |
The pointer is copied directly, not the array content.
This is a low-level function. Beware that:
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virtualinherited |
Set parameter by name.
This function is used when parsing an XML description, if no Property of this name is found. Overriding implementation should fall-back on calling the direct's parent implementation:
name | XML name of the parameter (XML entity). This may have a path component, e.g. "Astrobj::Radius", in which case a property named "Astrobj" will be sought in the current object, and setParameter will be called recusrively on this Astrobj with Radius as name. |
content | string representation of the value |
unit | string representation of the unit |
Reimplemented in Gyoto::Astrobj::Star, and Gyoto::Metric::RotStar3_1.
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virtualinherited |
Set parameter by Property (and name)
This function is used when parsing an XML description, if Property (p) of this name is found (i.e. either p.name or p.name_false is equal to name). Implementation should fall-back on calling the direct's parent implementation:
p | Property that matches name (p.name == name or p.name_false == name) |
name | XML name of the parameter (XML entity) |
content | string representation of the value |
unit | string representation of the unit |
Reimplemented in Gyoto::Astrobj::PolishDoughnut.
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virtualinherited |
Main loop for parsing Properties from XML description.
This function queries the FactoryMessenger for elements to parse, and tries to matche each element to a Property to set it accordingly.
Any class that tries to be buildable from XML must supply a subcontractor (for base classes such as Metric, Astrobj, Spectrum and Spectrometer, it is done as a template that must be specialized for each class).
This subcontractor typically looks somewhat like this:
Although this is discouraged, it is possible to override the following functions to customize how XML entities are parsed: - setParameters() if low-level access to the FactoryMessenger is required; - setParameter(std::string name, std::string content, std::string unit) to interpret an entity that does not match a Property (e.g. alternative name); - setParameter(Gyoto::Property const &p, std::string const &name, std::string const &content, std::string const &unit) to change how a Property is interpreted.
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virtualinherited |
Main loop in Subcontractor_t function.
The Subcontractor_t function for each Astrobj kind should look somewhat like this (templated as Gyoto::Astrobj::Subcontractor<MyKind>):
Each object kind should implement setParameter(string name, string content, string unit) to interpret the individual XML elements. setParameters() can be overloaded in case the specific Astrobj class needs low level access to the FactoryMessenger. See UniformSphere::setParameters().
Reimplemented in Gyoto::Astrobj::Star, and Gyoto::Astrobj::Complex.
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inherited |
Set PatternDisk::velocity__.
The pointer is copied directly, not the array content.
This is a low-level function. Beware that:
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virtualinherited |
Transmission: exp( αν * dsem )
transmission() computes the transmission of this fluid element or 0 if optically thick. The default implementation returns 1. (no attenuation) if optically thin, 0. if optically thick.
nuem | frequency in the fluid's frame |
coord | Photon coordinate |
dsem | geometrical length in geometrical units |
Reimplemented from Gyoto::Astrobj::Generic.
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protectedinherited |
The "kind" that is output in the XML entity.
E.g. for an Astrobj, fillElement() will ensure
is written.
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private |
Array of PatternDisk::radius_ arrays.
radius vector
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protectedinherited |
Maximum distance to the center of the coordinate system [geometrical units].
Maximum distance from the center of the coordinate system at which a photon may hit the object. Child classes may compute a decent value for rmax_ at any time if rmax_ is DBL_MAX. External classes (Photons in particular) must use rMax() to access this information.
rmax_ is in geometrical units.
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protectedinherited |
emission law
disk black body
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protectedinherited |
disk thickness
Geometrical thickness in geometrical units. Used only in the optically thin regime (flag_radtransf_==1). Should be << rin_. Default: 1e-3.