Contents

# ?gglse

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

## Syntax

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
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
a
; at least max(1,
m
)
for column major layout and max(1,
n
) for row major layout
.
ldb
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
; 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.