Developer Reference

Contents

gebrd (USM Version)

Reduces a general matrix to bidiagonal form. This routine belongs to the
oneapi::mkl::lapack
namespace.

Description

The routine reduces a general
m
-by-
n
matrix
A
to a bidiagonal matrix
B
by an orthogonal (unitary) transformation.
If
m≥n
, the reduction is given by
LaTex Math image.
where
B
1
is an
n
-by-
n
upper diagonal matrix,
Q
and
P
are orthogonal or, for a complex
A
, unitary matrices;
Q
1
consists of the first
n
columns of
Q
.
If
m < n
, the reduction is given by
A = Q*B*PH = Q*(B10)*PH = Q1*B1*P1H
,
where
B
1
is an
m
-by-
m
lower diagonal matrix,
Q
and
P
are orthogonal or, for a complex
A
, unitary matrices;
P
1
consists of the first
m
columns of
P
.
The routine does not form the matrices
Q
and
P
explicitly, but represents them as products of elementary reflectors. Routines are provided to work with the matrices
Q
and
P
in this representation:
If the matrix
A
is real,
If the matrix
A
is complex,

API

Syntax
namespace oneapi::mkl::lapack { cl::sycl::event gebrd(cl::sycl::queue &queue, std::int64_t m, std::int64_t n, T *a, std::int64_t lda, RealT *d, RealT *e, T *tauq, T *taup, T *scratchpad, std::int64_t scratchpad_size, const std::vector<cl::sycl::event> &events = {}) }
gebrd
(USM version) supports the following precisions and devices:
T
Devices supported
float
Host, CPU, GPU
double
Host, CPU, GPU
std::complex<float>
Host, CPU, GPU
std::complex<double>
Host, CPU, GPU
Input Parameters
queue
Device queue where calculations will be performed.
m
The number of rows in the matrix
A
(
0≤m
).
n
The number of columns in the matrix
A
(
0≤n
).
a
Pointer to matrix
A
. The second dimension of
a
must be at least
max(1, m)
.
lda
The leading dimension of
a
.
scratchpad
Pointer to scratchpad memory to be used by the 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 than the value returned by the gebrd_scratchpad_size function.
events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
a
If
m≥n
, the diagonal and first super-diagonal of a are overwritten by the upper bidiagonal matrix
B
. The elements below the diagonal, with the tauq, represent the orthogonal matrix
Q
as a product of elementary reflectors, and the elements above the first superdiagonal, with the taup, represent the orthogonal matrix
P
as a product of elementary reflectors.
If
m<n
, the diagonal and first sub-diagonal of a are overwritten by the lower bidiagonal matrix
B
. The elements below the first subdiagonal, with the tauq, represent the orthogonal matrix
Q
as a product of elementary reflectors, and the elements above the diagonal, with the taup, represent the orthogonal matrix
P
as a product of elementary reflectors.
d
Pointer to memory of size at least
max(1, min(m,n))
. Contains the diagonal elements of
B
.
e
Pointer to memory of size at least
max(1, min(m,n) - 1)
. Contains the off-diagonal elements of
B
.
tauq
Pointer to memory of size at least
max(1, min(m, n))
. The scalar factors of the elementary reflectors which represent the orthogonal or unitary matrix
Q
.
taup
Pointer to memory of size at least
max(1, min(m, n))
. The scalar factors of the elementary reflectors which represent the orthogonal or unitary matrix
P
.
Exceptions
Exception
Description
mkl::lapack::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 = -i
, the
i
-th parameter had an illegal value.
If
info
is equal to the value passed as scratchpad size, and detail() returns non zero, then the passed scratchpad has an insufficient size, and the required size should not be less than the value returned by the detail() method of the exception object.
Return Values
Output event to wait on to ensure computation is complete.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.