Factorization: LU, QR, Cholesky, singular values, eigenvalues, Hessenberg

LU Decomposition done in place. More...

Device pointer interface: lu Decomposition
See also Linear Algebra Parameters [out] d_piv Array of the pivot indices. Size: min(m, n) [out] d_U The upper triangular matrix. Size: size(min(m,n), n) [in,out] d_L If d_U isn't NULL, d_L (Size: (m, n)) contains lower triangular matrix. If d_U is NULL, d_L (First m x min(m,n) elements) contain the packed version of lu decomposition. [in] m number of rows in the input [in] n number of columns in the input [in] batch Number of tiles of input being handled.
afError	af_lu_S (int *d_piv, float *d_U, float *d_L, unsigned m, unsigned n, unsigned batch)
	lu Decomposition on single precision data. No DLA license required. More...
afError	af_lu_C (int *d_piv, cfloat *d_U, cfloat *d_L, unsigned m, unsigned n, unsigned batch)
	lu Decomposition on single precision, complex data. DLA license required. More...
afError	af_lu_D (int *d_piv, double *d_U, double *d_L, unsigned m, unsigned n, unsigned batch)
	lu Decomposition on double precision data. DLA license required. More...
afError	af_lu_Z (int *d_piv, cdouble *d_U, cdouble *d_L, unsigned m, unsigned n, unsigned batch)
	lu Decomposition on double precision, complex data. DLA license required. More...

Device pointer interface: qr decomposition
See also Linear Algebra Parameters [out] d_tau Vector on device containing scalar factors. Size: min(m, n). [out] d_R The upper triangular matrix. Size: (k, n) [in,out] d_Q If d_R isn't NULL, d_Q contains orthogonal matrix. Size: (m, k) if d_R is NULL, d_Q contains the packed version of qr decomposition. Size: (m, n) [in] m number of rows in the input [in] n number of columns in the input [in] k number of columns to be calculated in the orthogonal matrix. [in] batch Number of tiles of input being handled.
afError	af_qr_S (float *d_tau, float *d_R, float *d_Q, unsigned m, unsigned n, unsigned k, unsigned batch)
	qr decomposition on single precision data. More...
afError	af_qr_C (cfloat *d_tau, cfloat *d_R, cfloat *d_Q, unsigned m, unsigned n, unsigned k, unsigned batch)
	qr decomposition on single precision, complex data. DLA license required. More...
afError	af_qr_D (double *d_tau, double *d_R, double *d_Q, unsigned m, unsigned n, unsigned k, unsigned batch)
	qr decomposition on double precision data. DLA license required. More...
afError	af_qr_Z (cdouble *d_tau, cdouble *d_R, cdouble *d_Q, unsigned m, unsigned n, unsigned k, unsigned batch)
	qr decomposition on double precision, complex data. DLA license required. More...

Device pointer interface: Cholesky decomposition
See also Linear Algebra Parameters [out] d_R Matrix of Size: (n, n). [in] n Width of the input matrix d_A. [in] d_A Input square matrix of width n. [in] is_upper Flag to specify the format out the required output. d_R is upper triangular if is_upper is true. d_R is lower triangular if is_upper is false. [in] batch Number of tiles of input being handled.
afError	af_cholesky_S (float *d_R, unsigned *info, unsigned n, const float *d_A, bool is_upper, unsigned batch)
	Cholesky decomposition, single precision data. No DLA license required. More...
afError	af_cholesky_C (cfloat *d_R, unsigned *info, unsigned n, const cfloat *d_A, bool is_upper, unsigned batch)
	Cholesky decomposition, single precision complex data. DLA license required. More...
afError	af_cholesky_D (double *d_R, unsigned *info, unsigned n, const double *d_A, bool is_upper, unsigned batch)
	Cholesky decomposition, double precision data. DLA license required. More...
afError	af_cholesky_Z (cdouble *d_R, unsigned *info, unsigned n, const cdouble *d_A, bool is_upper, unsigned batch)
	Cholesky decomposition, double precision, complex data. DLA license required. More...

Device pointer interface: Hessenberg Matrix
See also Linear Algebra Parameters [out] d_H Hessenberg matrix of input d_A [out] d_Q Unitary matrix such that d_A = d_Q * d_H * d_Q' [in] n Width of the input matrix d_A. [in] d_A Input square matrix of width n. [in] batch Number of tiles of input being handled.
afError	af_hessenberg_S (float *d_H, float *d_Q, unsigned n, const float *d_A, unsigned batch)
	Find the hessenberg matrix on single precision data. More...
afError	af_hessenberg_C (cfloat *d_H, cfloat *d_Q, unsigned n, const cfloat *d_A, unsigned batch)
	Find the hessenberg matrix on single precision complex data. More...
afError	af_hessenberg_D (double *d_H, double *d_Q, unsigned n, const double *d_A, unsigned batch)
	Find the hessenberg matrix on double precision data. More...
afError	af_hessenberg_Z (cdouble *d_H, cdouble *d_Q, unsigned n, const cdouble *d_A, unsigned batch)
	Find the hessenberg matrix on double precision complex data. More...

Device pointer interface: Eigen vectors and Eigen values
See also Linear Algebra Parameters [out] d_Val The output containing the eigen values of d_A. For real inputs, this is allocated internally based on the resulting complexity of output and is_imag indicates complexity, e.g. real-valued hermitial matrices produce real-valued eigen values while non-hermitian produce complex-valued eigen values. [out] d_Vec The output containing the eigen vectors of d_A, or NULL if this is to be ignored (faster). For real inputs, this is allocated internally based on complexity of output and is_imag indicates complexity. For complex inputs, caller allocates. Pass NULL to avoid computing eigen vectors (faster). [out] is_imag The output format specifier for real inputs. If is_imag is true, the outputs are stored as cfloat or (cdouble). If is_imag is false, the outputs are stored as float (or double). [in] n Width of the input matrix d_A. [in] d_A Input square matrix of width n. [in] is_diag Specifier of d_Val data structure. If is_diag is true, d_Val is a diagonal matrix. if is_diag is false, d_Val is a vector. is_diag can not be false if d_Vec is not NULL [in] batch Number of tiles of input being handled.
afError	af_eigen_S (void **d_Val, void **d_Vec, bool *is_imag, unsigned n, const float *d_A, bool is_diag, unsigned batch)
	Eigen value decomposition of single precision input. More...
afError	af_eigen_D (void **d_Val, void **d_Vec, bool *is_imag, unsigned n, const double *d_A, bool is_diag, unsigned batch)
	Eigen value decomposition of single precision complex input. More...
afError	af_eigen_C (void **d_Val, cfloat *d_Vec, bool *is_imag, unsigned n, const cfloat *d_A, bool is_diag, unsigned batch)
	Eigen value decomposition of double precision input. More...
afError	af_eigen_Z (void **d_Val, cdouble *d_Vec, bool *is_imag, unsigned n, const cdouble *d_A, bool is_diag, unsigned batch)
	Eigen value decomposition of double precision complex input. More...

Device pointer interface: Singular value decomposition
See also Linear Algebra Parameters [out] d_S The output containing the singular of the input. if is_diag is false, d_S is a vector. if is_diag is true , d_S is a diagonal matrix. d_A = d_U * d_S * d_V' [out] d_U Left unitary Matrix [out] d_V Right unitary Matrix [in] jobU Can be one of 'A', 'O', 'S', 'N' similar to lapack [in] jobV Can be one of 'A', 'O', 'S', 'N' similar to lapack [in] m Number of rows in the input. [in] n Number of columns in the input [in] d_A The input matrix. [in] m_ Number of rows required in the output. [in] n_ Number of columns required in the output. [in] is_diag Data structure specifier of input d_S. is_diag can not be false if d_U or d_V are not NULL [in] batch Number of tiles of input being handled.
afError	af_svd_S (float *d_S, float *d_U, float *d_V, char jobU, char jobV, unsigned m, unsigned n, const float *d_A, unsigned m_, unsigned n_, bool is_diag, unsigned batch)
	Singular value decomposition on single precision input DLA license not required. More...
afError	af_svd_C (float *d_S, cfloat *d_U, cfloat *d_V, char jobU, char jobV, unsigned m, unsigned n, const cfloat *d_A, unsigned m_, unsigned n_, bool is_diag, unsigned batch)
	Singular value decomposition on single precision complex input DLA license required. More...
afError	af_svd_D (double *d_S, double *d_U, double *d_V, char jobU, char jobV, unsigned m, unsigned n, const double *d_A, unsigned m_, unsigned n_, bool is_diag, unsigned batch)
	Singular value decomposition on double precision input DLA license not required. More...
afError	af_svd_Z (double *d_S, cdouble *d_U, cdouble *d_V, char jobU, char jobV, unsigned m, unsigned n, const cdouble *d_A, unsigned m_, unsigned n_, bool is_diag, unsigned batch)
	Singular value decomposition on double precision complex input DLA license not required. More...

Detailed Description

LU Decomposition done in place.

Singular values of a matrix.

Eigen values and eigen vectors of an input matrix.

Hessenberg Matrix.

Cholesky Decomposition.

QR Decomposition done in place.

Double-precision or complex input requires ArrayFire Pro.

Requires ArrayFire Pro.

Function Documentation

afError af_lu_S	(	int *	d_piv,
		float *	d_U,
		float *	d_L,
		unsigned	m,
		unsigned	n,
		unsigned	batch
	)

lu Decomposition on single precision data. No DLA license required.

afError af_lu_C	(	int *	d_piv,
		cfloat *	d_U,
		cfloat *	d_L,
		unsigned	m,
		unsigned	n,
		unsigned	batch
	)

lu Decomposition on single precision, complex data. DLA license required.

afError af_lu_D	(	int *	d_piv,
		double *	d_U,
		double *	d_L,
		unsigned	m,
		unsigned	n,
		unsigned	batch
	)

lu Decomposition on double precision data. DLA license required.

afError af_lu_Z	(	int *	d_piv,
		cdouble *	d_U,
		cdouble *	d_L,
		unsigned	m,
		unsigned	n,
		unsigned	batch
	)

lu Decomposition on double precision, complex data. DLA license required.

afError af_qr_S	(	float *	d_tau,
		float *	d_R,
		float *	d_Q,
		unsigned	m,
		unsigned	n,
		unsigned	k,
		unsigned	batch
	)

qr decomposition on single precision data.

if d_R is NULL, DLA license not required, else required.

afError af_qr_C	(	cfloat *	d_tau,
		cfloat *	d_R,
		cfloat *	d_Q,
		unsigned	m,
		unsigned	n,
		unsigned	k,
		unsigned	batch
	)

qr decomposition on single precision, complex data. DLA license required.

afError af_qr_D	(	double *	d_tau,
		double *	d_R,
		double *	d_Q,
		unsigned	m,
		unsigned	n,
		unsigned	k,
		unsigned	batch
	)

qr decomposition on double precision data. DLA license required.

afError af_qr_Z	(	cdouble *	d_tau,
		cdouble *	d_R,
		cdouble *	d_Q,
		unsigned	m,
		unsigned	n,
		unsigned	k,
		unsigned	batch
	)

qr decomposition on double precision, complex data. DLA license required.

afError af_cholesky_S	(	float *	d_R,
		unsigned *	info,
		unsigned	n,
		const float *	d_A,
		bool	is_upper,
		unsigned	batch
	)

Cholesky decomposition, single precision data. No DLA license required.

afError af_cholesky_C	(	cfloat *	d_R,
		unsigned *	info,
		unsigned	n,
		const cfloat *	d_A,
		bool	is_upper,
		unsigned	batch
	)

Cholesky decomposition, single precision complex data. DLA license required.

afError af_cholesky_D	(	double *	d_R,
		unsigned *	info,
		unsigned	n,
		const double *	d_A,
		bool	is_upper,
		unsigned	batch
	)

Cholesky decomposition, double precision data. DLA license required.

afError af_cholesky_Z	(	cdouble *	d_R,
		unsigned *	info,
		unsigned	n,
		const cdouble *	d_A,
		bool	is_upper,
		unsigned	batch
	)

Cholesky decomposition, double precision, complex data. DLA license required.

afError af_hessenberg_S	(	float *	d_H,
		float *	d_Q,
		unsigned	n,
		const float *	d_A,
		unsigned	batch
	)

Find the hessenberg matrix on single precision data.

DLA license required.

afError af_hessenberg_C	(	cfloat *	d_H,
		cfloat *	d_Q,
		unsigned	n,
		const cfloat *	d_A,
		unsigned	batch
	)

Find the hessenberg matrix on single precision complex data.

DLA license required.

afError af_hessenberg_D	(	double *	d_H,
		double *	d_Q,
		unsigned	n,
		const double *	d_A,
		unsigned	batch
	)

Find the hessenberg matrix on double precision data.

DLA license required.

afError af_hessenberg_Z	(	cdouble *	d_H,
		cdouble *	d_Q,
		unsigned	n,
		const cdouble *	d_A,
		unsigned	batch
	)

Find the hessenberg matrix on double precision complex data.

DLA license required.

afError af_eigen_S	(	void **	d_Val,
		void **	d_Vec,
		bool *	is_imag,
		unsigned	n,
		const float *	d_A,
		bool	is_diag,
		unsigned	batch
	)

Eigen value decomposition of single precision input.

DLA license is required.

afError af_eigen_D	(	void **	d_Val,
		void **	d_Vec,
		bool *	is_imag,
		unsigned	n,
		const double *	d_A,
		bool	is_diag,
		unsigned	batch
	)

Eigen value decomposition of single precision complex input.

DLA license is required.

afError af_eigen_C	(	void **	d_Val,
		cfloat *	d_Vec,
		bool *	is_imag,
		unsigned	n,
		const cfloat *	d_A,
		bool	is_diag,
		unsigned	batch
	)

Eigen value decomposition of double precision input.

DLA license is required.

afError af_eigen_Z	(	void **	d_Val,
		cdouble *	d_Vec,
		bool *	is_imag,
		unsigned	n,
		const cdouble *	d_A,
		bool	is_diag,
		unsigned	batch
	)

Eigen value decomposition of double precision complex input.

DLA license is required.

afError af_svd_S	(	float *	d_S,
		float *	d_U,
		float *	d_V,
		char	jobU,
		char	jobV,
		unsigned	m,
		unsigned	n,
		const float *	d_A,
		unsigned	m_,
		unsigned	n_,
		bool	is_diag,
		unsigned	batch
	)

Singular value decomposition on single precision input DLA license not required.

afError af_svd_C	(	float *	d_S,
		cfloat *	d_U,
		cfloat *	d_V,
		char	jobU,
		char	jobV,
		unsigned	m,
		unsigned	n,
		const cfloat *	d_A,
		unsigned	m_,
		unsigned	n_,
		bool	is_diag,
		unsigned	batch
	)

Singular value decomposition on single precision complex input DLA license required.

afError af_svd_D	(	double *	d_S,
		double *	d_U,
		double *	d_V,
		char	jobU,
		char	jobV,
		unsigned	m,
		unsigned	n,
		const double *	d_A,
		unsigned	m_,
		unsigned	n_,
		bool	is_diag,
		unsigned	batch
	)

Singular value decomposition on double precision input DLA license not required.

afError af_svd_Z	(	double *	d_S,
		cdouble *	d_U,
		cdouble *	d_V,
		char	jobU,
		char	jobV,
		unsigned	m,
		unsigned	n,
		const cdouble *	d_A,
		unsigned	m_,
		unsigned	n_,
		bool	is_diag,
		unsigned	batch
	)

Singular value decomposition on double precision complex input DLA license not required.