Collaboration diagram for [apu.h] APU Advanced Operations:

Functions
void	APUSpSmoothCovMatrix (uint16_t N, void pInput, uint16_t L, void pResult, uint16_t fb)
	APU accelerator for covariance matrix computation using spatial smoothing and forward-backward averaging (optional) More...

void	APUJacobiEVD (uint16_t N, void pInput, void pResultV, uint16_t maxIter, float minSum, float epsTol)
	APU accelerator for Jacobi Eigen-Decomposition (EVD) of Hermitian Matrix. More...

void	APUGaussJordanElim (uint16_t M, uint16_t N, void *pInput, float epsTol)
	APU accelerator for Gauss-Jordan Elimination of a rectable complex matrix. More...

void	APUConfigFft (uint16_t N, void *pX)
	Configure APU accelerator for Fast Fourier transform. More...

void	APUComputeFft (uint16_t N, void *pX)
	APU accelerator for Fast Fourier transform. More...

void	APUComputeIfft (uint16_t N, void *pX)
	APU accelerator for invert Fast Fourier transform. More...

void	APUUnitCircle (uint16_t N, uint16_t M, uint16_t phase, uint16_t conj, void *pResult)
	APU accelerator for generating points evenly distributed on unit circle. More...

void	APUVectorMaxMin (uint16_t N, void pInput, float thresh, uint16_t op, void pResult)
	APU accelerator for computing max/min of the real part of a vector and a real value scalar. More...

void	APUVectorR2C (uint16_t N, void pInputA, void pInputB, uint16_t op, void *pResult)
	APU accelerator for converting back and forth between real and complex numbers. More...

void	APUHermLo (uint16_t N, void pInput, void pResult)
	APU accelerator for converting Hermitian upper-triangular to lower-triangular. More...

Detailed Description

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Function Documentation

§ APUSpSmoothCovMatrix()

void APUSpSmoothCovMatrix	(	uint16_t	N,
		void *	pInput,
		uint16_t	L,
		void *	pResult,
		uint16_t	fb
	)

APU accelerator for covariance matrix computation using spatial smoothing and forward-backward averaging (optional)

Calculate covariance matrix with spatial smoothing and forward-backward averaging. Given a received signal length N, a smaller matrix (LxL) with L < N is created by averaging (N-L+1) overlapped covariance matrices. The spatially smoothed matrix can also be applied forward-backward averaging (optional).

Parameters

N	length of the received signal vector
pInput	a pointer to the base of the input vector, in APU memory
L	size of the output square covariance matrix
pResult	a pointer to the output covariance matrix, in APU memory
fb	forward-backward averaging (FBA) option APU_FBA_DISABLE : No FBA APU_FBA_ENABLE : Applying FBA on top of spatially smoothed matrix

Returns: None

References APU_API_COVMATRIX, and APU_GET_DATA_MEM_OFFSET.

§ APUJacobiEVD()

void APUJacobiEVD	(	uint16_t	N,
		void *	pInput,
		void *	pResultV,
		uint16_t	maxIter,
		float	minSum,
		float	epsTol
	)

APU accelerator for Jacobi Eigen-Decomposition (EVD) of Hermitian Matrix.

Calculate the eigenvalues and eigenvectors of a Hermitian matrix.

Defined as:

[V D] = eigen_decomposition(A), such that V' * A * V = D

in which, A[NxN] is Hermitian matrix, D[NxN] is a diagonal matrix of eigenvalues, and V[NxN] is a matrix whose columns are the corresponding eigenvectors

Note: Since A is the Hermitian matrix, eigenvalues are all real and positive numbers. In addition, in APU, the output eigenvalues are already sorted in descending order. To save memory, the input matrix A is updated by in-place rotation, resulting in diagonal matrix D

Parameters

N	size of the input/output square matrices
pInput	a pointer to the base of the input Hermitian matrix and the output diagonal matrix D, in APU memory.
pResultV	a pointer to output eigenvectors, in APU memory
maxIter	the maximum number of iterations (Jacobi sweeps), typically 3
minSum	threshold for early stopping condition (if summation of the off-diagonal values is smaller than this threshold)
epsTol	threshold for off-diagonal elements to be considered small enough

Returns: None

References APU_API_EIGEN, APU_GET_DATA_MEM_ABS, APU_GET_DATA_MEM_OFFSET, and APU_HEAP_ADDR.

§ APUGaussJordanElim()

void APUGaussJordanElim	(	uint16_t	M,
		uint16_t	N,
		void *	pInput,
		float	epsTol
	)

APU accelerator for Gauss-Jordan Elimination of a rectable complex matrix.

Reduce the input rectangle matrix A[MxN] to reduced echelon form using Gauss-Jordan Elimination.

Defined as:

C[MxN] = gauss_elimination(A[MxN])

in which, A[MxN] is input matrix, C[MxN] is the output matrix in reduced echelon form (in other words, C[M,1:M] is the identity matrix).

Note: Gauss-Jordan reduces the matrix to REDUCED echelon form (instead of echelon form with Gauss). In addition, to save memory, the input matrix A is overwritten by its reduced echelon form C using in-place transformation. If out-place ever needed, the input matrix must be copied before calling this function.

Deprecated:: Due to errata SYS_211, this function shall not be used. Instead, use the equivalent function provided in the driver: APULPF3_jacobiEVDDma()

Parameters

M	number of rows of input/output matrices
N	number of columns of input/output matrices (N >= M)
pInput	a pointer to the base of the input matrix and the output matrix, in APU memory
epsTol	threshold that smaller than it, a value considered zero

Returns: None

References APU_API_GAUSS, APU_GET_DATA_MEM_ABS, APU_GET_DATA_MEM_OFFSET, and APU_HEAP_ADDR.

§ APUConfigFft()

void APUConfigFft	(	uint16_t	N,
		void *	pX
	)

Configure APU accelerator for Fast Fourier transform.

Computes the Discrete Fourier transform (DFT) of a vector using a fast Fourier transform (FFT) algorithm.

Defined as:

Y = DFT(X, N)

in which, X is the input vector length N, Y is the DFT of X with same length.

Note: This is the config function, must be called BEFORE feeding input vector to the APU memory

Parameters

N	length of input/output vectors
pX	a pointer to the base of the input/output vector (since this is config, this pointer is just a placeholder), in APU memory

Returns: None

See also: APUComputeFft()

References APU_API_FFT, and APU_GET_DATA_MEM_OFFSET.

§ APUComputeFft()

void APUComputeFft	(	uint16_t	N,
		void *	pX
	)

APU accelerator for Fast Fourier transform.

Computes the Discrete Fourier transform (DFT) of a vector using a fast Fourier transform (FFT) algorithm.

Defined as:

Y = DFT(X, N)

in which, X is the input vector length N, Y is the DFT of X with same length.

Note: This is where the FFT computation happen. It should be called AFTER APUConfigFft(). In addition, to save memory, the input is overwritten by the output using in-place transformation. If out-place ever needed, the input vector must be copied before calling this function.

Parameters

N	length of input/output vectors
pX	a pointer to the base of the input/output vector, in APU memory

Returns: None

References APU_API_FFT, and APU_GET_DATA_MEM_OFFSET.

§ APUComputeIfft()

void APUComputeIfft	(	uint16_t	N,
		void *	pX
	)

APU accelerator for invert Fast Fourier transform.

Computes the invert Discrete Fourier transform (DFT) of a vector using a fast Fourier transform (FFT) algorithm.

Defined as:

Y = IFFT(X, N)

in which, X is the input vector length N, Y is the invert DFT of X with same length.

Note: This is where the IFFT computation happens. It should be called AFTER APUConfigFft(). In addition, to save memory, the input is overwritten by the output using in-place transformation. If out-place ever needed, the input vector must be copied before calling this function.

Deprecated:: Due to errata SYS_211, this function shall not be used. Instead, use the equivalent function provided in the driver: APULPF3_gaussJordanElimDma().

Parameters

N	length of input/output vectors
pX	a pointer to the base of the input/output vector, in APU memory

Returns: None

References APU_API_FFT, and APU_GET_DATA_MEM_OFFSET.

§ APUUnitCircle()

void APUUnitCircle	(	uint16_t	N,
		uint16_t	M,
		uint16_t	phase,
		uint16_t	conj,
		void *	pResult
	)

APU accelerator for generating points evenly distributed on unit circle.

APU generates a unit circle as follows: exp(-j*2*pi*(k*M+phase)/1024 * (-1)^(conj)) here k is iterated internally by the APU from 0 to N-1. The result is stored at pResult

k = 0:N-1 (Iterated internally)
M = 10-bit constant
phase = 10-bit constant
conj = 0 or 1

Parameters

N	number of points to be generated
M	constant M in k*M+phase
phase	constant phase in k*M+phase
conj	conj = 0 : Without conjugate the output conj = 1 : Conjugate output
pResult	a pointer to the output vector of points, in APU memory

Returns: None

References APU_API_UNITCIRC, and APU_GET_DATA_MEM_OFFSET.

§ APUVectorMaxMin()

void APUVectorMaxMin	(	uint16_t	N,
		void *	pInput,
		float	thresh,
		uint16_t	op,
		void *	pResult
	)

APU accelerator for computing max/min of the real part of a vector and a real value scalar.

When op is APU_OP_MAX the function is defined as:

Y = max(X, thresh) = [max(real(X[i]), thresh)] for i = 1:N

When op is APU_OP_MIN the function is defined as:

Y = min(X, thresh) = [min(real(X[i]), thresh)] for i = 1:N

in which, X and Y is the N-length complex vector, and thresh is a real scalar.

Deprecated:: Due to errata SYS_211, this function shall not be used. Instead, use the equivalent function provided in the driver: APULPF3_vectorMaxMinDma().

Parameters

N	length of input/output vectors
pInput	a pointer to the base of the input vector, in APU memory
thresh	a real value threshold to be compared against
op	select between max or min operators APU_OP_MAX APU_OP_MIN
pResult	a pointer to the output vector of points, in APU memory

Returns: None

References APU_API_MAXMIN, APU_GET_DATA_MEM_ABS, APU_GET_DATA_MEM_OFFSET, and APU_HEAP_ADDR.

§ APUVectorR2C()

void APUVectorR2C	(	uint16_t	N,
		void *	pInputA,
		void *	pInputB,
		uint16_t	op,
		void *	pResult
	)

APU accelerator for converting back and forth between real and complex numbers.

APU accelerator for converting back and forth between real and complex numbers for vectors.

Defined as:

Y = R2C(A, B) = [R2C(A[i], B[i])] for i = 1:N

in which, A, B and Y are N-length complex vectors.

Parameters

N	length of input/output vectors
pInputA	a pointer to the base of the input vector A, in APU memory
pInputB	a pointer to the base of the input vector B, in APU memory Note that when only vector A is used, this pInputB pointer is ignored and can be NULL.
pResult	a pointer to the base of the output vector Y, in APU memory
op	select among converters, must be one of: APU_OP_R2C APU_OP_R2CC APU_OP_R2CA APU_OP_R2CCA APU_OP_RA APU_OP_IMA APU_OP_ABS
pResult	a pointer to the output vector of points, in APU memory

Returns: None

References APU_API_R2C, and APU_GET_DATA_MEM_OFFSET.

§ APUHermLo()

void APUHermLo	(	uint16_t	N,
		void *	pInput,
		void *	pResult
	)

APU accelerator for converting Hermitian upper-triangular to lower-triangular.

APU accelerator for converting converting Hermitian upper-triangular to lower-triangular. To save memory, APU stores only upper-triangular elements of Hermitian matrix in column-major order. This function converts this format to lower-triangular, column-major order Hermitian.

Parameters

N	length of input/output vectors
pInput	a pointer to the base of the input vector, in APU memory
pResult	a pointer to the output vector of points, in APU memory

Returns: None

References APU_API_HERMLO, and APU_GET_DATA_MEM_OFFSET.

Functions

Detailed Description

Function Documentation

§ APUSpSmoothCovMatrix()

§ APUJacobiEVD()

§ APUGaussJordanElim()

§ APUConfigFft()

§ APUComputeFft()

§ APUComputeIfft()

§ APUUnitCircle()

§ APUVectorMaxMin()

§ APUVectorR2C()

§ APUHermLo()