Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?gglse

Solves the linear equality-constrained least squares problem using a generalized RQ factorization.

Syntax

lapack_int
LAPACKE_sgglse
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_int
p
,
float
*
a
,
lapack_int
lda
,
float
*
b
,
lapack_int
ldb
,
float
*
c
,
float
*
d
,
float
*
x
);
lapack_int
LAPACKE_dgglse
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_int
p
,
double
*
a
,
lapack_int
lda
,
double
*
b
,
lapack_int
ldb
,
double
*
c
,
double
*
d
,
double
*
x
);
lapack_int
LAPACKE_cgglse
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_int
p
,
lapack_complex_float
*
a
,
lapack_int
lda
,
lapack_complex_float
*
b
,
lapack_int
ldb
,
lapack_complex_float
*
c
,
lapack_complex_float
*
d
,
lapack_complex_float
*
x
);
lapack_int
LAPACKE_zgglse
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_int
p
,
lapack_complex_double
*
a
,
lapack_int
lda
,
lapack_complex_double
*
b
,
lapack_int
ldb
,
lapack_complex_double
*
c
,
lapack_complex_double
*
d
,
lapack_complex_double
*
x
);
Include Files
  • mkl.h
Description
The routine solves the linear equality-constrained least squares (LSE) problem:
minimize ||
c
 -
A
*
x
||
2
 subject to
B
*
x
 =
d
where
A
 is an
m
-by-
n
 matrix,
B
 is a
p
-by-
n
 matrix,
c
 is a given
m
-vector, and
d
 is a given
p
-vector. It is assumed that
p
≤
n
≤
m
+
p
, and
Equation
These conditions ensure that the LSE problem has a unique solution, which is obtained using a generalized
RQ
 factorization of the matrices
(
B
,
A
)
 given by
B=(0 R)*Q, A=Z*T*Q
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 of the matrix
A
 (
m
≥
 0
).
n
The number of columns of the matrices
A
 and
B
 (
n
≥
 0
).
p
The number of rows of the matrix
B
(
0
≤
p
≤
n
≤
m
+
p
)
.
a
,
b
,
c
,
d
Arrays:
a
(size max(1,
lda
*
n
) for column major layout and max(1,
lda
*
m
) for row major layout)
 contains the
m
-by-
n
 matrix
A
.
b
(size max(1,
ldb
*
n
) for column major layout and max(1,
ldb
*
p
) for row major layout)
 contains the
p
-by-
n
matrix
B
.
c
 size at least max(1,
m
), contains the right hand side vector for the least squares part of the LSE problem.
d
, size at least max(1,
p
), contains the right hand side vector for the constrained equation.
lda
The leading dimension of
a
; at least max(1,
m
)
for column major layout and max(1,
n
) for row major layout
.
ldb
The leading dimension of
b
; at least max(1,
p
)
for column major layout and max(1,
n
) for row major layout
.
Output Parameters
a
The elements on and above the diagonal contain the min(
m
,
n
)-by-
n
 upper trapezoidal matrix
T
 as returned by
?ggrqf
.
x
The solution of the LSE problem.
b
On exit, the upper right triangle contains the
p
-by-
p
 upper triangular matrix
R
 as returned by
?ggrqf
.
d
On exit,
d
 is destroyed.
c
On exit, the residual sum-of-squares for the solution is given by the sum of squares of elements
n
-
p
+1 to
m
 of vector
c
.
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.
If
info
 = 1
, the upper triangular factor
R
 associated with
B
 in the generalized RQ factorization of the pair
(
B
,
A
)
 is singular, so that
rank(
B
) <
p
; the least squares solution could not be computed.
If
info
 = 2
, the
(
n
-
p
)
-by-
(
n
-
p
)
 part of the upper trapezoidal factor
T
 associated with
A
 in the generalized RQ factorization of the pair
(
B
,
A
)
 is singular, so that
Equation
; the least squares solution could not be computed.

Product and Performance Information

1

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