Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

?gbbrd

Reduces a general band matrix to bidiagonal form.

Syntax

lapack_int LAPACKE_sgbbrd
(
int
matrix_layout
,
char
vect
,
lapack_int
m
,
lapack_int
n
,
lapack_int
ncc
,
lapack_int
kl
,
lapack_int
ku
,
float*
ab
,
lapack_int
ldab
,
float*
d
,
float*
e
,
float*
q
,
lapack_int
ldq
,
float*
pt
,
lapack_int
ldpt
,
float*
c
,
lapack_int
ldc
);
lapack_int LAPACKE_dgbbrd
(
int
matrix_layout
,
char
vect
,
lapack_int
m
,
lapack_int
n
,
lapack_int
ncc
,
lapack_int
kl
,
lapack_int
ku
,
double*
ab
,
lapack_int
ldab
,
double*
d
,
double*
e
,
double*
q
,
lapack_int
ldq
,
double*
pt
,
lapack_int
ldpt
,
double*
c
,
lapack_int
ldc
);
lapack_int LAPACKE_cgbbrd
(
int
matrix_layout
,
char
vect
,
lapack_int
m
,
lapack_int
n
,
lapack_int
ncc
,
lapack_int
kl
,
lapack_int
ku
,
lapack_complex_float*
ab
,
lapack_int
ldab
,
float*
d
,
float*
e
,
lapack_complex_float*
q
,
lapack_int
ldq
,
lapack_complex_float*
pt
,
lapack_int
ldpt
,
lapack_complex_float*
c
,
lapack_int
ldc
);
lapack_int LAPACKE_zgbbrd
(
int
matrix_layout
,
char
vect
,
lapack_int
m
,
lapack_int
n
,
lapack_int
ncc
,
lapack_int
kl
,
lapack_int
ku
,
lapack_complex_double*
ab
,
lapack_int
ldab
,
double*
d
,
double*
e
,
lapack_complex_double*
q
,
lapack_int
ldq
,
lapack_complex_double*
pt
,
lapack_int
ldpt
,
lapack_complex_double*
c
,
lapack_int
ldc
);
Include Files
  • mkl.h
Description
The routine reduces an
m
-by-
n
 band matrix
A
 to upper bidiagonal matrix
B
:
A
 =
Q*B*P
H
. Here the matrices
Q
 and
P
 are orthogonal (for real
A
) or unitary (for complex
A
). They are determined as products of Givens rotation matrices, and may be formed explicitly by the routine if required. The routine can also update a matrix
C
 as follows:
C
 =
Q
H
*C
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
vect
Must be
'N'
 or
'Q'
 or
'P'
 or
'B'
.
If
vect
 =
'N'
, neither
Q
 nor
P
H
 is generated.
If
vect
 =
'Q'
, the routine generates the matrix
Q
.
If
vect
 =
'P'
, the routine generates the matrix
P
H
.
If
vect
 =
'B'
, the routine generates both
Q
 and
P
H
.
m
The number of rows in the matrix
A
 (
m
≥
 0
).
n
The number of columns in
A
 (
n
≥
 0
).
ncc
The number of columns in
C
 (
ncc
≥
 0
).
kl
The number of sub-diagonals within the band of
A
 (
kl
≥
 0
).
ku
The number of super-diagonals within the band of
A
 (
ku
≥
 0
).
ab
,
c
Arrays:
ab
(size max(1,
ldab
*
n
) for column major layout and max(1,
ldab
*
m
) for row major layout)
 contains the matrix
A
 in band storage (see Matrix Storage Schemes).
c
(size max(1,
ldc
*
ncc
) for column major layout and max(1,
ldc
*
m
) for row major layout)
 contains an
m
-by-
ncc
 matrix
C
.
If
ncc
 = 0
, the array
c
 is not referenced.
ldab
The leading dimension of the array
ab
 (
ldab
≥
kl
 +
ku
 + 1
).
ldpt
The leading dimension of the output array
pt
.
ldpt
≥
 max(1,
n
)
 if
vect
 =
'P'
 or
'B'
,
ldpt
≥
 1
 otherwise.
ldc
The leading dimension of the array
c
.
ldc
≥
 max(1,
m
)
 if
ncc
 > 0
;
ldc
≥
 1
 if
ncc
 = 0
.
Output Parameters
ab
Overwritten by values generated during the reduction.
d
Array, size at least max(1, min(
m
,
n
)). Contains the diagonal elements of the matrix
B
.
e
Array, size at least
max(1, min(
m
,
n
) - 1)
.
Contains the off-diagonal elements of
B
.
q
,
pt
Arrays:
q
size max(1,
ldq
*
m
)
 contains the output
m
-by-
m
 matrix
Q
.
p
size max(1,
ldpt
*
n
)
 contains the output
n
-by-
n
 matrix
P
T
.
c
Overwritten by the product
Q
H
*
C
.
c
 is not referenced if
ncc
 = 0.
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 computed matrices
Q
,
B
, and
P
 satisfy
Q*B*P
H
 =
A
 +
E
, where
||
E
||
2
 =
c
(
n
)
ε
 ||
A
||
2
,
c
(
n
)
 is a modestly increasing function of
n
, and
ε
 is the machine precision.
If
m
 =
n
, the total number of floating-point operations for real flavors is approximately the sum of:
6*
n
2
*(
kl
 +
ku
)
 if
vect
 =
'N'
 and
ncc
 = 0
,
3*
n
2
*
ncc
*(
kl
 +
ku
 - 1)/(
kl
 +
ku
)
 if
C
 is updated, and
3*
n
3
*(
kl
 +
ku
 - 1)/(
kl
 +
ku
)
 if either
Q
 or
P
H
 is generated (double this if both).
To estimate the number of operations for complex flavors, use the same formulas with the coefficients 20 and 10 (instead of 6 and 3).

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