Jacobian matrix calculation

Functions
STOASTLIB void	GenerateJacobian (const Raster *raster, const QMMesh *mesh, const CCompRowMatrix &mvec, const CVector *dphi, const CVector *aphi, DataScale dscale, RDenseMatrix &J)
	Generate Jacobian matrix of forward operator (complex case) More...
STOASTLIB void	GenerateJacobian (const Raster *raster, const QMMesh *mesh, const CVector *dphi, const CVector *aphi, const CVector *proj, DataScale dscale, RDenseMatrix &J)
	Generate Jacobian matrix of forward operator (complex case) More...
STOASTLIB void	GenerateJacobian_cw (const Raster *raster, const QMMesh *mesh, const RVector *dphi, const RVector *aphi, RDenseMatrix *Jmua=NULL, RDenseMatrix *Jkap=NULL)
	Generate raw Jacobian matrix for CW intensity data (real case) More...
STOASTLIB void	GenerateJacobian_cw (const Raster *raster, const QMMesh *mesh, const RCompRowMatrix &mvec, const RVector *dphi, const RVector *aphi, DataScale dscale, RDenseMatrix *Jmua=NULL, RDenseMatrix *Jkap=NULL)
	Generate Jacobian matrix for CW intensity data (real case). More...
STOASTLIB void	GenerateJacobian_cw (const Raster *raster, const QMMesh *mesh, const RVector *dphi, const RVector *aphi, const RVector *proj, DataScale dscale, RDenseMatrix *Jmua=NULL, RDenseMatrix *Jkap=NULL)
	Generate mua Jacobian matrix for CW intensity data (real case). More...
STOASTLIB void	GenerateJacobian (const Raster *raster, const QMMesh *mesh, const CCompRowMatrix &mvec, const CVector *dphi, const CVector *aphi, DataScale dscale, RDenseMatrixMPI &Jmod, RDenseMatrixMPI &Jarg)
	Generate Jacobian matrix of forward operator (complex case) More...
STOASTLIB void	GenerateJacobian (const Raster *raster, const QMMesh *mesh, const CVector *dphi, const CVector *aphi, const CVector *proj, DataScale dscale, RDenseMatrixMPI &Jmod, RDenseMatrixMPI &Jarg)
	Generate Jacobian matrix of forward operator (complex case) More...
STOASTLIB void	GenerateJacobian_cw_mua (const Raster *raster, const QMMesh *mesh, const RCompRowMatrix &mvec, const RVector *dphi, const RVector *aphi, DataScale dscale, RDenseMatrixMPI &J)
	Generate Jacobian matrix for CW intensity data (real case). More...

Detailed Description

This section contains functions that calculate the Jacobian matrix for the frequency-domain diffusion equation, in terms of absorption and diffusion coefficient, and either for real and imaginary parts of the complex data, or for log amplitude and phase.

Function Documentation

STOASTLIB void GenerateJacobian	(	const Raster *	raster,
		const QMMesh *	mesh,
		const CCompRowMatrix &	mvec,
		const CVector *	dphi,
		const CVector *	aphi,
		DataScale	dscale,
		RDenseMatrixMPI &	Jmod,
		RDenseMatrixMPI &	Jarg
	)

Generate Jacobian matrix of forward operator (complex case)

Parameters

raster	solution basis mapper, or NULL to generate the Jacobian directly on the forward mesh
mesh	FEM forward mesh
mvec	measurement vectors (rows of sparse matrix)
dphi	array of forward fields
aphi	array of adjoint fields
dscale	data scaling flag (lin/log)
Jmod	Jacobian (log amplitude block)
Jarg	Jacobian (phase block)

Note

This version generates the boundary projection values on the fly from mvec, if required (i.e. if using log data).

STOASTLIB void GenerateJacobian	(	const Raster *	raster,
		const QMMesh *	mesh,
		const CCompRowMatrix &	mvec,
		const CVector *	dphi,
		const CVector *	aphi,
		DataScale	dscale,
		RDenseMatrix &	J
	)

Generate Jacobian matrix of forward operator (complex case)

Parameters

raster	solution basis mapper, or NULL to generate the Jacobian directly on the forward mesh
mesh	FEM forward mesh
mvec	measurement vectors (rows of sparse matrix)
dphi	array of forward fields
aphi	array of adjoint fields
dscale	data scaling flag (lin/log)
J	Jacobian
elbasis	(only used if raster==0) If true, returned Jacobian is generated for piecewise constant element basis rather than shape function basis

Note

This version generates the boundary projection values on the fly from mvec, if required (i.e. if using log data).

STOASTLIB void GenerateJacobian	(	const Raster *	raster,
		const QMMesh *	mesh,
		const CVector *	dphi,
		const CVector *	aphi,
		const CVector *	proj,
		DataScale	dscale,
		RDenseMatrixMPI &	Jmod,
		RDenseMatrixMPI &	Jarg
	)

Generate Jacobian matrix of forward operator (complex case)

Parameters

raster	solution basis mapper, or NULL to generate the Jacobian directly on the forward mesh
mesh	FEM forward mesh
mvec	measurement vectors (rows of sparse matrix)
dphi	array of forward fields
aphi	array of adjoint fields
dscale	data scaling flag (lin/log)
Jmod	Jacobian (log amplitude block)
Jarg	Jacobian (phase block)

Note

This version passes the boundary projection values as input arguments.

STOASTLIB void GenerateJacobian	(	const Raster *	raster,
		const QMMesh *	mesh,
		const CVector *	dphi,
		const CVector *	aphi,
		const CVector *	proj,
		DataScale	dscale,
		RDenseMatrix &	J
	)

Generate Jacobian matrix of forward operator (complex case)

Parameters

raster	solution basis mapper, or NULL to generate the Jacobian directly on the forward mesh
mesh	FEM forward mesh
dphi	array of forward fields
aphi	array of adjoint fields
dscale	data scaling flag (lin/log)
J	Jacobian
elbasis	(only used if raster==0) If true, returned Jacobian is generated for piecewise constant element basis rather than shape function basis

Note

This version passes the boundary projection values as input arguments.

STOASTLIB void GenerateJacobian_cw	(	const Raster *	raster,
		const QMMesh *	mesh,
		const RVector *	dphi,
		const RVector *	aphi,
		RDenseMatrix *	Jmua = NULL,
		RDenseMatrix *	Jkap = NULL
	)

Generate raw Jacobian matrix for CW intensity data (real case)

Parameters

[in]	raster	solution basis mapper, or NULL to generate the Jacobian directly on the forward mesh
[in]	mesh	FEM forward mesh
[in]	dphi	array of direct fields
[in]	aphi	array of adjoint fields
[out]	Jmua	pointer to Jacobian matrix (absorption component), or NULL if not required
[out]	Jkap	pointer to Jacobian matrix (diffusion component), or NULL if not required

Note

This version performs no data or parameter scaling or mapping to logarithmic values. It calculates dy/dx, where y are boundary cw intensity data, and x is mua (absorption) and/or kappa (diffusion).

If Jmua == NULL or Jkap == NULL, then the corresponding component is not calculated.

STOASTLIB void GenerateJacobian_cw	(	const Raster *	raster,
		const QMMesh *	mesh,
		const RCompRowMatrix &	mvec,
		const RVector *	dphi,
		const RVector *	aphi,
		DataScale	dscale,
		RDenseMatrix *	Jmua = NULL,
		RDenseMatrix *	Jkap = NULL
	)

Generate Jacobian matrix for CW intensity data (real case).

Parameters

[in]	raster	solution basis mapper, or NULL to generate the Jacobian directly on the forward mesh
[in]	mesh	FEM forward mesh
[in]	mvec	measurement vectors (rows of sparse matrix)
[in]	dphi	array of forward fields
[in]	aphi	array of adjoint fields
[in]	dscale	data scaling flag (lin/log)
[out]	Jmua	Jacobian matrix (absorption component)
[out]	Jkap	Jacobian matrix (diffusion component)

Note

This version generates the boundary projection values on the fly from mvec, if required (i.e. if using log data).

If Jmua == NULL or Jkap == NULL, then the corresponding component is not calculated.

If dscale == DATA_LOG, then the Jacobian is calculated in terms of logarithmic amplitude (d log y)/dx.

STOASTLIB void GenerateJacobian_cw	(	const Raster *	raster,
		const QMMesh *	mesh,
		const RVector *	dphi,
		const RVector *	aphi,
		const RVector *	proj,
		DataScale	dscale,
		RDenseMatrix *	Jmua = NULL,
		RDenseMatrix *	Jkap = NULL
	)

Generate mua Jacobian matrix for CW intensity data (real case).

Parameters

[in]	raster	solution basis mapper, or NULL to generate the Jacobian directly on the forward mesh
[in]	mesh	FEM forward mesh
[in]	dphi	array of forward fields
[in]	aphi	array of adjoint fields
[in]	dscale	data scaling flag (lin/log)
[out]	Jmua	Jacobian matrix (absorption component)
[out]	Jkap	Jacobian matrix (diffusion component)

Note

This version passes the boundary projection values as input arguments.

If Jmua == NULL or Jkap == NULL, then the corresponding component is not calculated.

If dscale == DATA_LOG, then the Jacobian is calculated in terms of logarithmic amplitude (d log y)/dx.

STOASTLIB void GenerateJacobian_cw_mua	(	const Raster *	raster,
		const QMMesh *	mesh,
		const RCompRowMatrix &	mvec,
		const RVector *	dphi,
		const RVector *	aphi,
		DataScale	dscale,
		RDenseMatrixMPI &	J
	)

Generate Jacobian matrix for CW intensity data (real case).

Parameters

raster	solution basis mapper, or NULL to generate the Jacobian directly on the forward mesh
mesh	FEM forward mesh
mvec	measurement vectors (rows of sparse matrix)
dphi	array of forward fields
aphi	array of adjoint fields
dscale	data scaling flag (lin/log)
J	Jacobian

Note

This version generates the boundary projection values on the fly from mvec, if required (i.e. if using log data).