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geqrf_batch (Group Version)
Computes the batch of QR factorizations of a batch of general m-by-n matrices. This routine belongs to the oneapi::mkl::lapack namespace.
Description
The routine forms the QiRi factorizations of a general m-by-n matrix Ai, iϵ{1...batch_size}, where batch_size is a sum of all parameter group sizes as provided with the group_sizes array. No pivoting is performed during factorization.
The routine does not form the matrix Qi explicitly. Instead, Qi is represented as a product of min(m, n) elementary reflectors. Routines are provided to work with Qi in this representation.
Total number of problems to solve, batch_size, is a sum of sizes of all of the groups of parameters as provided by group_sizesarray.
API
Syntax
namespace oneapi::mkl::lapack {
sycl::event geqrf_batch(sycl::queue &queue,
std::int64_t *m,
std::int64_t *n,
T **a,
std::int64_t *lda,
T **tau,
std::int64_t group_count,
std::int64_t *group_sizes,
T *scratchpad,
std::int64_t scratchpad_size,
const std::vector<sycl::event> &events = {})
}
This function supports the following precisions and devices:
T |
Devices supported |
|---|---|
float |
CPU and GPU |
double |
CPU and GPU |
std::complex<float> |
CPU and GPU |
std::complex<double> |
CPU and GPU |
Input Parameters
- queue
-
Device queue where calculations will be performed.
- m
-
Array of group_count parameters mg parameters.
Each of mg specifies the number of rows in the matrices Ai from array a, belonging to group g (mg ≥ 0).
- n
-
Array of group_count parameters ng parameters.
Each of ng specifies the number of columns in the matrices Ai from array a, belonging to group g (ng ≥ 0).
- a
-
Array of batch_size pointers to input matrices Ai, each being of size ldag*ng (g is an index of group to which Ai belongs).
- lda
-
Array of group_countldag parameters, each representing the leading dimensions of input matrices Ai, from array a, belonging to group g (ldag ≥ max(1, mg)).
- group_count
-
Specifies the number of groups of parameters. Must be at least 0.
- group_sizes
-
Array of group_count integers. Array element with index g specifies the number of problems to solve for each of the groups of parameters g. So the total number of problems to solve, batch_size, is a sum of all parameter group sizes.
- scratchpad
-
Scratchpad memory to be used by routine for storing intermediate results.
- scratchpad_size
-
Size of scratchpad memory as a number of floating point elements of type T. Size should not be less then the value returned by geqrf_batch_scratchpad_size (Group Version).
- events
-
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
- a
-
Matrices pointed to by array a are overwritten by the factorization data as follows:
The elements on and above the diagonal of Ai contain the min(mg,mng)-by-ng upper trapezoidal matrices Ri (Ri is upper triangular if mg ≥ ng); the elements below the diagonal, with the array taui, present the orthogonal matrix Qi as a product of min(mg,ng) elementary reflectors.
Here, g is an index of parameters group corresponding to i-th decomposition.
- tau
-
Array of pointers to store taui, each of size min(mg,ng), containing scalars that define elementary reflectors for the matrices Qi in its decomposition in a product of elementary reflectors.
Here, g is an index of parameters group corresponding to i-th decomposition.
Exceptions
Exception |
Description |
|---|---|
mkl::lapack::batch_exception |
This exception is thrown when problems occur during calculations. You can obtain the info code of the problem using the info() method of the exception object: If info = -n, the n-th parameter had an illegal value. If info equals the value passed as scratchpad size, and detail() returns non-zero, then the passed scratchpad is of insufficient size, and the required size should be not less then value returned by the detail() method of the exception object. |
Return Values
Output event to wait on to ensure computation is complete.