mindspore.ops.orgqr

mindspore.ops.orgqr(input, input2)

Compute the first $N$ columns of a product of Householder matrices.

Usually used to calculate the explicit representation of the orthogonal matrix $Q$ returned by mindspore.ops.Geqrf.

Take the case of input without batch dimension as an example: Suppose input input is a matrix of size $(M,N)$ after householder transformation. When the diagonal of input is set to 1, every column of lower triangular in input is denoted as $w_j$ for $j$ for $j=1,\dots ,M$, this function returns the first $N$ columns of the matrix

$$H_1{H}_2\dots H_k\text{ with }{H}_j={\mathrm{I}}_M-{\tau }_j{w}_j{w}_j^{\mathrm{H}}$$

where ${\mathrm{I}}_M$ is the $M$-dimensional identity matrix. And when $w$ is complex, $w^{\mathrm{H}}$ is the conjugate transpose, otherwise the transpose. The output matrix is the same size as the input matrix input. $tau$ is corresponding to input2.

Parameters

• input (Tensor) – 2-D or 3-D input tensor, householder vectors, shape $(\ast ,M,N)$.

• input2 (Tensor) – 1-D or 2-D input tensor, householder reflection coefficients, shape $(\ast ,K)$, where K is less than or equal to N, indicating.

Returns

Tensor

Supported Platforms:

Ascend GPU CPU

Examples

>>> import mindspore
>>> input = mindspore.tensor([[-2.0, -1.0], [1.0, 2.0]])
>>> y, tau = mindspore.ops.geqrf(input)
>>> mindspore.ops.orgqr(y, tau)
Tensor(shape=[2, 2], dtype=Float32, value=
[[-8.94427061e-01,  4.47213590e-01],
 [ 4.47213590e-01,  8.94427180e-01]])