DSPLIB_svd

Introduction

Kernel for calculating Singular Value Decomposition (SVD).

• This kernel factorizes a given input matrix \(A\) into two orthogonal matrices \(U\) and \(V\), and a 1-D array \(D\) consisting of real non-negative singular values in descending order such that

  \begin{eqnarray*} A = U \times \Sigma \times V^{T} \qquad where\;&(1)&V^{T}\;is\;transpose\;of\;V.\\ &(2)& \Sigma \;is\;a\;diagonal\;matrix\;with\;main\;diagonal\;D. \end{eqnarray*}

• \(U\) and \(V\) are orthogonal matrices such that

  \begin{eqnarray*} \hspace{-2em} \hspace{-2em} \hspace{-2em} \hspace{-2em} \hspace{-2em} U \times U^{T} = V \times V^{T} = I \qquad where\;I\;is\;Identity\;matrix\\. \end{eqnarray*}

• The kernel supports REDUCED FORM and FULL FORM generation. Refer DSPLIB_svdInitArgs::enableReducedForm
• For a given input matrix \(A\) of shape (M, N)
  1. If FULL FORM: The output matrix \(U\) is of shape (M, M) and \(V\) is of shape (N, N)
  2. If REDUCED FORM: The output matrix \(U\) is of shape (M, K) and \(V\) is of shape (N, K) where K is minimum of M,N.

Data Structures
struct	DSPLIB_svdInitArgs
	Structure containing the parameters to initialize the kernel. More...

Functions
int32_t	DSPLIB_svd_getHandleSize (DSPLIB_svdInitArgs *pKerInitArgs)
	This is a query function to calculate the size of internal handle. More...
DSPLIB_STATUS	DSPLIB_svd_init_checkParams (DSPLIB_kernelHandle handle, const DSPLIB_bufParams2D_t *bufParamsA, const DSPLIB_bufParams2D_t *bufParamsU, const DSPLIB_bufParams2D_t *bufParamsV, const DSPLIB_bufParams1D_t *bufParamsDiag, const DSPLIB_bufParams1D_t *bufParamsSuperDiag, const DSPLIB_svdInitArgs *pKerInitArgs)
	This function checks the validity of the parameters passed to DSPLIB_svd_init function. This function is called with the same parameters as the DSPLIB_svd_init, and this function must be called before the DSPLIB_svd_init is called. More...
DSPLIB_STATUS	DSPLIB_svd_init (DSPLIB_kernelHandle handle, const DSPLIB_bufParams2D_t *bufParamsA, const DSPLIB_bufParams2D_t *bufParamsU, const DSPLIB_bufParams2D_t *bufParamsV, const DSPLIB_bufParams1D_t *bufParamsDiag, const DSPLIB_bufParams1D_t *bufParamsSuperDiag, const DSPLIB_svdInitArgs *pKerInitArgs)
	This function should be called before the DSPLIB_svd_exec function is called. This function takes care of any one-time operations such as setting up the configuration of required hardware resources such as the streaming engine and streaming address generator. The results of these operations are stored in the handle. More...
DSPLIB_STATUS	DSPLIB_svd_exec_checkParams (DSPLIB_kernelHandle handle, const void *restrict pA, const void *restrict pU, const void *restrict pV, const void *restrict pDiag, const void *restrict pSuperDiag, const void *restrict pU1, const void *restrict pV1, const void *restrict pScratch)
	This function checks the validity of the parameters passed to DSPLIB_svd_exec function. This function is called with the same parameters as the DSPLIB_svd_exec, and this function must be called before the DSPLIB_svd_exec is called. More...
DSPLIB_STATUS	DSPLIB_svd_exec (DSPLIB_kernelHandle handle, void *restrict pA, void *restrict pU, void *restrict pV, void *restrict pDiag, void *restrict pSuperDiag, void *restrict pU1, void *restrict pV1, void *restrict pScratch)
	This function is the main kernel compute function. More...

Function Documentation

DSPLIB_svd_getHandleSize()

int32_t DSPLIB_svd_getHandleSize

(

DSPLIB_svdInitArgs *

pKerInitArgs

)

This is a query function to calculate the size of internal handle.

Parameters

[in]

pKerInitArgs

: Pointer to structure holding init parameters

Returns

Size of the buffer in bytes

Remarks

Application is expected to allocate buffer of the requested size and provide it as input to other functions requiring it.

Definition at line 25 of file DSPLIB_svd.cpp.

DSPLIB_svd_init_checkParams()

DSPLIB_STATUS DSPLIB_svd_init_checkParams	(	DSPLIB_kernelHandle	handle,
		const DSPLIB_bufParams2D_t *	bufParamsA,
		const DSPLIB_bufParams2D_t *	bufParamsU,
		const DSPLIB_bufParams2D_t *	bufParamsV,
		const DSPLIB_bufParams1D_t *	bufParamsDiag,
		const DSPLIB_bufParams1D_t *	bufParamsSuperDiag,
		const DSPLIB_svdInitArgs *	pKerInitArgs
	)

This function checks the validity of the parameters passed to DSPLIB_svd_init function. This function is called with the same parameters as the DSPLIB_svd_init, and this function must be called before the DSPLIB_svd_init is called.

Parameters

[in]	handle	: Active handle to the kernel
[in]	bufParamsA	: Pointer to the structure containing dimensional information of input buffer A
[out]	bufParamsU	: Pointer to the structure containing dimensional information of output buffer U
[out]	bufParamsV	: Pointer to the structure containing dimensional information of output buffer V
[out]	bufParamsDiag	: Pointer to the structure containing dimensional information of output buffer Diag
[out]	bufParamsSuperDiag	: Pointer to the structure containing dimensional information of output buffer SuperDiag
[in]	pKerInitArgs	: Pointer to the structure holding init parameters

Returns

Status value indicating success or failure. Refer to DSPLIB_STATUS.

Remarks

None

Definition at line 34 of file DSPLIB_svd.cpp.

DSPLIB_svd_init()

DSPLIB_STATUS DSPLIB_svd_init	(	DSPLIB_kernelHandle	handle,
		const DSPLIB_bufParams2D_t *	bufParamsA,
		const DSPLIB_bufParams2D_t *	bufParamsU,
		const DSPLIB_bufParams2D_t *	bufParamsV,
		const DSPLIB_bufParams1D_t *	bufParamsDiag,
		const DSPLIB_bufParams1D_t *	bufParamsSuperDiag,
		const DSPLIB_svdInitArgs *	pKerInitArgs
	)

This function should be called before the DSPLIB_svd_exec function is called. This function takes care of any one-time operations such as setting up the configuration of required hardware resources such as the streaming engine and streaming address generator. The results of these operations are stored in the handle.

Parameters

[in]	handle	: Active handle to the kernel
[in]	bufParamsA	: Pointer to the structure containing dimensional information of input buffer A
[out]	bufParamsU	: Pointer to the structure containing dimensional information of output buffer U
[out]	bufParamsV	: Pointer to the structure containing dimensional information of output buffer V
[out]	bufParamsDiag	: Pointer to the structure containing dimensional information of output buffer Diag
[out]	bufParamsSuperDiag	: Pointer to the structure containing dimensional information of output buffer SuperDiag
[in]	pKerInitArgs	: Pointer to the structure holding init parameters

Returns

Status value indicating success or failure. Refer to DSPLIB_STATUS.

Remarks

Application is expected to provide a valid handle.

Definition at line 104 of file DSPLIB_svd.cpp.

DSPLIB_svd_exec_checkParams()

DSPLIB_STATUS DSPLIB_svd_exec_checkParams	(	DSPLIB_kernelHandle	handle,
		const void *restrict	pA,
		const void *restrict	pU,
		const void *restrict	pV,
		const void *restrict	pDiag,
		const void *restrict	pSuperDiag,
		const void *restrict	pU1,
		const void *restrict	pV1,
		const void *restrict	pScratch
	)

This function checks the validity of the parameters passed to DSPLIB_svd_exec function. This function is called with the same parameters as the DSPLIB_svd_exec, and this function must be called before the DSPLIB_svd_exec is called.

Parameters

[in]	handle	: Active handle to the kernel
[in]	pA	: Pointer to the input buffer pA
[out]	pU	: Pointer to the output buffer pU
[out]	pV	: Pointer to the output buffer pV
[out]	pDiag	: Pointer to the output buffer pDiag
[out]	pSuperDiag	: Pointer to the output buffer pSuperDiag
[in]	pU1	: Pointer to the intermediate transpose buffer pU1
[in]	pV1	: Pointer to the intermediate transpose buffer pV1
[out]	pScratch	: Pointer to the intermediate scratch buffer pScratch

Returns

Status value indicating success or failure. Refer to DSPLIB_STATUS.

Remarks

None

Definition at line 78 of file DSPLIB_svd.cpp.

DSPLIB_svd_exec()

DSPLIB_STATUS DSPLIB_svd_exec	(	DSPLIB_kernelHandle	handle,
		void *restrict	pA,
		void *restrict	pU,
		void *restrict	pV,
		void *restrict	pDiag,
		void *restrict	pSuperDiag,
		void *restrict	pU1,
		void *restrict	pV1,
		void *restrict	pScratch
	)

This function is the main kernel compute function.

Please refer to details under DSPLIB_svd_exec

Parameters

[in]	handle	: Active handle to the kernel
[in]	pA	: Pointer to the input buffer pA
[out]	pU	: Pointer to the output buffer pU
[out]	pV	: Pointer to the output buffer pV
[out]	pDiag	: Pointer to the output buffer pDiag
[out]	pSuperDiag	: Pointer to the output buffer pSuperDiag
[in]	pU1	: Pointer to the intermediate transpose buffer pU1
[in]	pV1	: Pointer to the intermediate transpose buffer pV1
[out]	pScratch	: Pointer to the intermediate scratch buffer pScratch

Memory Requirements

Buffer	dimY	dimX	Comments
pA	M	N	Input Matrix
pU	max(M,N)	max(M,N)	Output Matrix
pV	N	N	Output Matrix
pDiag	1	min(M,N)	Output Vector
pSuperDiag	1	min(M,N)	Intermediate Vector
pU1	max(M,N)	max(M,N)	Scratch buffer to store transpose of U
pV1	N	N	Scratch buffer to store transpose of V
pScratch	4	max(M,N)	Scratch buffer to store coefficient calculations, sorting singular values etc.

Returns

Status value indicating success or failure. Refer to DSPLIB_STATUS.

Assumptions: - None

Performance Considerations:

For best performance,

• The input and output data buffers are expected to be in L2 memory
• The buffer pointers are assumed to be 64-byte aligned
• Ensure that the starting point of adjacent rows in a 2-D matrix are allocated from different banks in L2 memory with the help of memory padding.
  

Remarks

Before calling this function, application is expected to call DSPLIB_svd_init and DSPLIB_svd_exec_checkParams functions. This ensures resource configuration and error checks are done only once for several invocations of this function.

Definition at line 164 of file DSPLIB_svd.cpp.