Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
Contents

?tzrzf

Reduces the upper trapezoidal matrix A to upper triangular form.

Syntax

lapack_int
LAPACKE_stzrzf
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
float
*
a
,
lapack_int
lda
,
float
*
tau
);
lapack_int
LAPACKE_dtzrzf
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
double
*
a
,
lapack_int
lda
,
double
*
tau
);
lapack_int
LAPACKE_ctzrzf
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_complex_float
*
a
,
lapack_int
lda
,
lapack_complex_float
*
tau
);
lapack_int
LAPACKE_ztzrzf
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_complex_double
*
a
,
lapack_int
lda
,
lapack_complex_double
*
tau
);
Include Files
  • mkl.h
Description
The routine reduces the
m
-by-
n
 (
m
≤
n
) real/complex upper trapezoidal matrix
A
 to upper triangular form by means of orthogonal/unitary transformations. The upper trapezoidal matrix
A
 = [
A
1
A
2] = [
A
1:
m
, 1:
m
,
A
1:
m
,
m
+1:
n
] is factored as
A
 = [
R
0
]*
Z
,
where
Z
 is an
n
-by-
n
 orthogonal/unitary matrix,
R
 is an
m
-by-
m
 upper triangular matrix, and
0
 is the
m
-by-(
n-m
) zero matrix.
The
?tzrzf
 routine replaces the deprecated
?tzrqf
 routine.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
m
The number of rows in the matrix
A
 (
m
≥
 0
).
n
The number of columns in
A
 (
n
≥
m
).
a
Array
a
 is of size max(1,
lda
*
n
) for column major layout and max(1,
lda
*
m
) for row major layout.
The leading
m
-by-
n
 upper trapezoidal part of the array
a
 contains the matrix
A
 to be factorized.
lda
The leading dimension of
a
; at least max(1,
m
)
for column major layout and max(1,
n
) for row major layout
.
Output Parameters
a
Overwritten on exit by the factorization data as follows:
the leading
m
-by-
m
 upper triangular part of
a
 contains the upper triangular matrix
R
, and elements
m
 +1 to
n
 of the first
m
 rows of
a
, with the array
tau
, represent the orthogonal matrix
Z
 as a product of
m
 elementary reflectors.
tau
Array, size at least max (1,
m
). Contains scalar factors of the elementary reflectors for the matrix
Z
.
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
 =
-i
, the
i
-th parameter had an illegal value.
Application Notes
The factorization is obtained by Householder's method. The
k
-th transformation matrix,
Z
(
k
), which is used to introduce zeros into the (
m
 -
k
 + 1)-th row of
A
, is given in the form
Equation
where for real flavors
Equation
and for complex flavors
Equation
tau
 is a scalar and
z
(
k
) is an
l
-element vector.
tau
 and
z
(
k
) are chosen to annihilate the elements of the
k-
th row of
A
2.
The scalar
tau
 is returned in the
k-
th element of
tau
 and the vector
u
(
k
) in the
k-
th row of
A
, such that the elements of
z
(
k
) are stored in
the last
m
 -
n
 elements of the
k
-th row of array
a
.
The elements of
R
 are returned in the upper triangular part of
A
.
The matrix
Z
 is given by
Z
 =
Z
(1)*
Z
(2)*...*
Z
(
m
)
.
Related routines include:
to apply matrix Q (for real matrices)
to apply matrix Q (for complex matrices).

Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804