qr

qr#

Perform a QR decomposition.

Added in version 0.6.0.

Note

The mtie assignment forms of qr, qr_econ, and qr_solver use the normal non-JIT solver path. CUDA JIT fusion is available through lazy projection members such as qr(A).Q, qr(A).R, qr_econ(A).Q, qr_econ(A).R, qr_solver(A).Out, and qr_solver(A).Tau when -DMATX_EN_MATHDX=ON is enabled and the runtime shape/type is supported by cuSolverDx. Projection JIT currently supports ranks 2 through 4 and float, double, complex<float>, and complex<double> inputs. The full qr projection path is limited to square matrices to preserve its full Q/R output contract. qr_econ(A).Q JIT fusion is currently limited to non-wide matrices where m >= n; qr_econ(A).R and qr_solver projections support rectangular matrices when cuSolverDx supports the shape.

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);

Projection Examples#

Lazy Q and R projections can be used directly with other operators. This example is included from the ProjectionAPI unit test in QR2.cu.

auto op = qr(A);
(QR = matmul(op.Q, op.R)).run(exec);
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);

Projection Examples#

The economic Q and R projections have shapes ... x m x k and ... x k x n, so they can be multiplied to reconstruct the original input. This example is included from the ProjectionAPI unit test in QREcon.cu.

auto op = qr_econ(A);
(QR = matmul(op.Q, op.R)).run(exec);
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);

Projection Examples#

qr_solver exposes the raw Out factor storage and Tau Householder coefficients. This example is included from the CuSolverDxSingleMatrixQRSolverProjectionJIT unit test.

auto op = qr_solver(A);
(Combined = op.Out + clone<2>(op.Tau, {rows, matxKeepDim})).run(exec);
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