qr#
Perform a QR decomposition.
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template<typename AType>
__MATX_INLINE__ auto matx::qr(const AType &A)# Perform QR decomposition on a matrix using housholders reflections.
If rank > 2, operations are batched.
- Template Parameters:
AType – Tensor or operator type for output of A input tensors.
- Parameters:
A – Input tensor or operator for tensor A input.
- Returns:
Operator to generate Q/R outputs
Note
This function is currently not supported with host-based executors (CPU), and performs a full QR decomposition of a tensor A with shape … x m x n, where Q is shaped … x m x m and R is shaped … x m x n.
Examples#
(mtie(Q, R) = qr(A)).run(exec);
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template<typename OpA>
__MATX_INLINE__ auto matx::qr_econ(const OpA &a)# Perform an economic QR decomposition on a matrix using cuSolver.
If rank > 2, operations are batched.
- Template Parameters:
OpA – Data type of input a tensor or operator
- Parameters:
a – Input tensor or operator of shape
... x m x n- Returns:
Operator that produces QR outputs.
Q - Of shape
... x m x min(m, n), the reduced orthonormal basis for the span of A.R - Upper triangular matrix of shape
... x min(m, n) x n.
Note
This function is currently not supported with host-based executors (CPU). It returns an economic QR decomposition, where Q/R are shaped m x k and k x n respectively, where k = min(m, n). This is useful when m >> n to save memory and computation time.
Examples#
(mtie(Q, R) = qr_econ(A)).run(exec);
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template<typename OpA>
__MATX_INLINE__ auto matx::qr_solver(const OpA &a)# Perform a QR decomposition on a matrix using cuSolver or a LAPACK host library.
If rank > 2, operations are batched.
- Template Parameters:
OpA – Data type of input a tensor or operator
- Parameters:
a – Input tensor or operator of shape
... x m x n- Returns:
Operator that produces R/householder vectors and tau tensor outputs.
Out - Of shape
... x m x n. The householder vectors are returned in the bottom half and R is returned in the top half.Tau - The scalar factors tau of shape
... x min(m, n).
Note
This function does not return Q explicitly as it only runs geqrf from LAPACK/cuSolver.
For full or economic Q/R, use qr or qr_econ on a CUDA executor.
Examples#
(mtie(Av, TauV) = qr_solver(Av)).run(this->exec);