LALSimIMRSpinEOBInitialConditions.c File Reference

Prototypes
static REAL8	CalculateDotProduct (const REAL8 a[], const REAL8 b[])
	Calculates the dot product of two vectors. More...
static REAL8	CalculateCrossProduct (const INT4 i, const REAL8 a[], const REAL8 b[])
	calculates the ith component of the cross product of two vectors, where i is in the range 0-2. More...
static int	NormalizeVector (REAL8 a[])
	Normalizes the given vector. More...
static int	CalculateRotationMatrix (gsl_matrix *rotMatrix, gsl_matrix *rotInverse, REAL8 r[], REAL8 v[], REAL8 L[])
	Calculate the rotation matrix and its inverse. More...
static int	ApplyRotationMatrix (gsl_matrix *rotMatrix, REAL8 a[])
	Applies a rotation matrix to a given vector. More...
static int	SphericalToCartesian (REAL8 qCart[], REAL8 pCart[], const REAL8 qSph[], const REAL8 pSph[])
	Performs a co-ordinate transformation from spherical to Cartesian co-ordinates. More...
static int	CartesianToSpherical (REAL8 qSph[], REAL8 pSph[], const REAL8 qCart[], const REAL8 pCart[])
	Perform a co-ordinate transformation from Cartesian to spherical co-ordinates. More...
static int	XLALFindSphericalOrbit (const gsl_vector *x, void *params, gsl_vector *f)
	Root function for gsl root finders. More...
static double	GSLSpinHamiltonianDerivWrapperHybrid (double x, void *params)
	Wrapper for calculating specific derivative of the Hamiltonian in spherical co-ordinates, dH/dr, dH/dptheta and dH/dpphi. More...
static double	GSLSpinHamiltonianDerivWrapper (double x, void *params)
	Wrapper for calculating specific derivative of the Hamiltonian in spherical co-ordinates, dH/dr, dH/dptheta and dH/dpphi. More...
static REAL8	XLALCalculateSphHamiltonianDeriv2Hybrid (const int idx1, const int idx2, const REAL8 values[], SpinEOBParams *params)
static REAL8	XLALCalculateSphHamiltonianDeriv2 (const int idx1, const int idx2, const REAL8 values[], SpinEOBParams *params)
static int	XLALSimIMRSpinEOBInitialConditions (REAL8Vector *initConds, const REAL8 mass1, const REAL8 mass2, const REAL8 fMin, const REAL8 inc, const REAL8 spin1[], const REAL8 spin2[], SpinEOBParams *params, INT4 use_optimized_v2)
	Main function for calculating the spinning EOB initial conditions, following the quasi-spherical initial conditions described in Sec. More...

Go to the source code of this file.

Data Structures
struct	SEOBRootParams
	Structure consisting SEOBNR parameters that can be used by gsl root finders. More...

Macros
#define	_LALSIMIMRSPINEOBINITIALCONDITIONS_C

Macro Definition Documentation

_LALSIMIMRSPINEOBINITIALCONDITIONS_C

#define _LALSIMIMRSPINEOBINITIALCONDITIONS_C

Definition at line 21 of file LALSimIMRSpinEOBInitialConditions.c.

Function Documentation

CalculateDotProduct()

static REAL8 CalculateDotProduct ( const REAL8  a[], const REAL8  b[]  )

inlinestatic

Calculates the dot product of two vectors.

Definition at line 41 of file LALSimIMRSpinEOBInitialConditions.c.

CalculateCrossProduct()

static REAL8 CalculateCrossProduct ( const INT4  i, const REAL8  a[], const REAL8  b[]  )

inlinestatic

calculates the ith component of the cross product of two vectors, where i is in the range 0-2.

Definition at line 53 of file LALSimIMRSpinEOBInitialConditions.c.

NormalizeVector()

static int NormalizeVector ( REAL8  a[] )

inlinestatic

Normalizes the given vector.

Definition at line 64 of file LALSimIMRSpinEOBInitialConditions.c.

CalculateRotationMatrix()

static int CalculateRotationMatrix ( gsl_matrix *  rotMatrix, gsl_matrix *  rotInverse, REAL8  r[], REAL8  v[], REAL8  L[]  )

static

Calculate the rotation matrix and its inverse.

Rotate the ex-ey-ez frame to the r-v-L frame. This static function is called only by XLALSimIMRSpinEOBInitialConditions

a, b, g are the angles alpha, beta and gamma

Implement the Rotation Matrix following the "x-convention"

1. rotate about the z-axis by an angle a, rotation matrix Rz(a);
2. rotate about the former x-axis (now x') by an angle b, rotation matrix Rx(b);
3. rotate about the former z-axis (now z') by an algle g, rotation matrix Rz(g);

Parameters

rotMatrix	OUTPUT, rotation matrix
rotInverse	OUTPUT, rotation matrix inversed
r	position vector
v	velocity vector
L	orbital angular momentum

Definition at line 81 of file LALSimIMRSpinEOBInitialConditions.c.

ApplyRotationMatrix()

static int ApplyRotationMatrix ( gsl_matrix *  rotMatrix, REAL8  a[]  )

static

Applies a rotation matrix to a given vector.

Parameters

rotMatrix	rotation matrix
a	OUTPUT, vector rotated

Definition at line 170 of file LALSimIMRSpinEOBInitialConditions.c.

SphericalToCartesian()

static int SphericalToCartesian ( REAL8  qCart[], REAL8  pCart[], const REAL8  qSph[], const REAL8  pSph[]  )

static

Performs a co-ordinate transformation from spherical to Cartesian co-ordinates.

In the code from Tyson Littenberg, this was only applicable to the special theta=pi/2, phi=0 case. This special transformation is a static function called only by GSLSpinHamiltonianDerivWrapper and XLALSimIMRSpinEOBInitialConditions

Parameters

qCart	< OUTPUT, position vector in Cartesean coordinates
pCart	< OUTPUT, momentum vector in Cartesean coordinates
qSph	< position vector in spherical coordinates
pSph	< momentum vector in spherical coordinates

Definition at line 201 of file LALSimIMRSpinEOBInitialConditions.c.

CartesianToSpherical()

static int CartesianToSpherical ( REAL8  qSph[], REAL8  pSph[], const REAL8  qCart[], const REAL8  pCart[]  )

static

Perform a co-ordinate transformation from Cartesian to spherical co-ordinates.

In the code from Tyson Littenberg, this was only applicable to the special theta=pi/2, phi=0 case. This special transformation is a static function called only by XLALSimIMRSpinEOBInitialConditions

Parameters

qSph	< OUTPUT, position vector in spherical coordinates
pSph	< OUTPUT, momentum vector in Cartesean coordinates
qCart	< position vector in spherical coordinates
pCart	< momentum vector in Cartesean coordinates

Definition at line 245 of file LALSimIMRSpinEOBInitialConditions.c.

XLALFindSphericalOrbit()

static int XLALFindSphericalOrbit ( const gsl_vector *  x, void *  params, gsl_vector *  f  )

static

Root function for gsl root finders.

The gsl root finder with look for gsl_vector *x position in parameter space where the returned values in gsl_vector *f are zero. The functions on which we search for roots are: dH/dr, dH/dptheta and dH/dpphi-omega, namely, Eqs. 4.8 and 4.9 of Buonanno et al. PRD 74, 104005 (2006).

Parameters

x	< Parameters requested by gsl root finder
params	< Spin EOB parameters
f	< Function values for the given parameters

Definition at line 291 of file LALSimIMRSpinEOBInitialConditions.c.

GSLSpinHamiltonianDerivWrapperHybrid()

static double GSLSpinHamiltonianDerivWrapperHybrid ( double  x, void *  params  )

static

Wrapper for calculating specific derivative of the Hamiltonian in spherical co-ordinates, dH/dr, dH/dptheta and dH/dpphi.

It only works for the specific co-ord system we use here

Parameters

x	< Derivative at x
params	< Function parameters

Definition at line 360 of file LALSimIMRSpinEOBInitialConditions.c.

GSLSpinHamiltonianDerivWrapper()

static double GSLSpinHamiltonianDerivWrapper ( double  x, void *  params  )

static

Wrapper for calculating specific derivative of the Hamiltonian in spherical co-ordinates, dH/dr, dH/dptheta and dH/dpphi.

It only works for the specific co-ord system we use here

Parameters

x	< Derivative at x
params	< Function parameters

Definition at line 419 of file LALSimIMRSpinEOBInitialConditions.c.

XLALCalculateSphHamiltonianDeriv2Hybrid()

static REAL8 XLALCalculateSphHamiltonianDeriv2Hybrid ( const int  idx1, const int  idx2, const REAL8  values[], SpinEOBParams *  params  )

static

Parameters

idx1	< Derivative w.r.t. index 1
idx2	< Derivative w.r.t. index 2
values	< Dynamical variables in spherical coordinates
params	< Spin EOB Parameters

Definition at line 472 of file LALSimIMRSpinEOBInitialConditions.c.

XLALCalculateSphHamiltonianDeriv2()

static REAL8 XLALCalculateSphHamiltonianDeriv2 ( const int  idx1, const int  idx2, const REAL8  values[], SpinEOBParams *  params  )

static

Parameters

idx1	< Derivative w.r.t. index 1
idx2	< Derivative w.r.t. index 2
values	< Dynamical variables in spherical coordinates
params	< Spin EOB Parameters

Definition at line 509 of file LALSimIMRSpinEOBInitialConditions.c.

XLALSimIMRSpinEOBInitialConditions()

static int XLALSimIMRSpinEOBInitialConditions ( REAL8Vector *  initConds, const REAL8  mass1, const REAL8  mass2, const REAL8  fMin, const REAL8  inc, const REAL8  spin1[], const REAL8  spin2[], SpinEOBParams *  params, INT4  use_optimized_v2  )

static

Main function for calculating the spinning EOB initial conditions, following the quasi-spherical initial conditions described in Sec.

IV A of Buonanno, Chen & Damour PRD 74, 104005 (2006). All equation numbers in the comments of this function refer to this paper. Inputs are binary parameters (masses, spin vectors and inclination), EOB model parameters and initial frequency. Outputs are initial dynamical variables in a vector (x, y, z, px, py, pz, S1x, S1y, S1z, S2x, S2y, S2z). In the paper, the initial conditions are solved for a given initial radius, while in this function, they are solved for a given inital orbital frequency. This difference is reflected in solving Eq. (4.8). The calculation is done in 5 steps: STEP 1) Rotate to LNhat0 along z-axis and N0 along x-axis frame, where LNhat0 and N0 are initial normal to orbital plane and initial orbital separation; STEP 2) After rotation in STEP 1, in spherical coordinates, phi0 and theta0 are given directly in Eq. (4.7), r0, pr0, ptheta0 and pphi0 are obtained by solving Eqs. (4.8) and (4.9) (using gsl_multiroot_fsolver). At this step, we find initial conditions for a spherical orbit without radiation reaction. STEP 3) Rotate to L0 along z-axis and N0 along x-axis frame, where L0 is the initial orbital angular momentum and L0 is calculated using initial position and linear momentum obtained in STEP 2. STEP 4) In the L0-N0 frame, we calculate (dE/dr)|sph using Eq. (4.14), then initial dr/dt using Eq. (4.10), and finally pr0 using Eq. (4.15). STEP 5) Rotate back to the original inertial frame by inverting the rotation of STEP 3 and then inverting the rotation of STEP 1.

Parameters

initConds	< OUTPUT, Initial dynamical variables
mass1	< mass 1
mass2	< mass 2
fMin	< Initial frequency (given)
inc	< Inclination
spin1	< Initial spin vector 1
spin2	< Initial spin vector 2
params	< Spin EOB parameters
use_optimized_v2	< Use optimized v2?

Definition at line 595 of file LALSimIMRSpinEOBInitialConditions.c.