Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • 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

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