Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?geqrt3

Recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Syntax

lapack_int
LAPACKE_sgeqrt3
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
float
*
a
,
lapack_int
lda
,
float
*
t
,
lapack_int
ldt
);
lapack_int
LAPACKE_dgeqrt3
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
double
*
a
,
lapack_int
lda
,
double
*
t
,
lapack_int
ldt
);
lapack_int
LAPACKE_cgeqrt3
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_complex_float
*
a
,
lapack_int
lda
,
lapack_complex_float
*
t
,
lapack_int
ldt
);
lapack_int
LAPACKE_zgeqrt3
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_complex_double
*
a
,
lapack_int
lda
,
lapack_complex_double
*
t
,
lapack_int
ldt
);
Include Files
  • mkl.h
Description
The strictly lower triangular matrix
V
 contains the elementary reflectors
H
(
i
) in the
i
th column below the diagonal. For example, if
m
=5 and
n
=3, the matrix
V
 is
Equation
where
v
i
 represents one of the vectors that define
H
(
i
). The vectors are returned in the lower part of triangular array
a
.
The 1s along the diagonal of
V
 are not stored in
a
.
The block reflector
H
 is then given by
H
 =
I
 -
V
*
T
*
V
T
 for real flavors, and
H
 =
I
 -
V
*
T
*
V
H
 for complex flavors,
where
V
T
 is the transpose and
V
H
is the conjugate transpose of
V
.
Input Parameters
m
The number of rows in the matrix
A
 (
m
 ≥
n
).
n
The number of columns in
A
 (
n
 ≥ 0).
a
Array, size
at least
max(1,
lda
*
n
)
 for column major and
max(1,
lda
*
m
)
 for row major layout
. Array
a
 contains the
m
-by-
n
 matrix
A
.
lda
The leading dimension of
a
; at least max(1,
m
)
for column major layout and max(1,
n
) for row major layout
.
ldt
The leading dimension of
t
; at least max(1,
n
).
Output Parameters
a
The elements on and above the diagonal of the array contain the
n
-by-
n
 upper triangular matrix
R
. The elements below the diagonal are the columns of
V
.
t
Array, size
ldt
 by
n
.
The
n
-by-
n
 upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector
T
. The elements below the diagonal are not used.
Return Values
This function returns a value
info
.
If
info
 = 0, the execution is successful.
If
info
 < 0 and
info
 =
-i
, the
i
th argument had an illegal value.
If
info
 = -1011
, memory allocation error occurred.

Product and Performance Information

1

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