Developer Reference for Intel® oneAPI Math Kernel Library for C
?gglse
Solves the linear equality-constrained least squares problem using a generalized RQ factorization.
Syntax
lapack_intLAPACKE_sgglse ( intmatrix_layout , lapack_intm , lapack_intn , lapack_intp , float*a , lapack_intlda , float*b , lapack_intldb , float*c , float*d , float*x );
lapack_intLAPACKE_dgglse ( intmatrix_layout , lapack_intm , lapack_intn , lapack_intp , double*a , lapack_intlda , double*b , lapack_intldb , double*c , double*d , double*x );
lapack_intLAPACKE_cgglse ( intmatrix_layout , lapack_intm , lapack_intn , lapack_intp , lapack_complex_float*a , lapack_intlda , lapack_complex_float*b , lapack_intldb , lapack_complex_float*c , lapack_complex_float*d , lapack_complex_float*x );
lapack_intLAPACKE_zgglse ( intmatrix_layout , lapack_intm , lapack_intn , lapack_intp , lapack_complex_double*a , lapack_intlda , lapack_complex_double*b , lapack_intldb , lapack_complex_double*c , lapack_complex_double*d , lapack_complex_double*x );
Include Files
mkl.h
Description
sgglse dgglse cgglse zgglse gglse
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 , work
-
REAL for sgglse DOUBLE PRECISION for dgglse COMPLEX for cgglse DOUBLE COMPLEX for zgglse . 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 .
The second dimension of a must be at least max(1, n ).
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 .
The second dimension of b must be at least max(1, n ).
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.
work is a workspace array, its dimension max(1, lwork) .
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 .
lwork
The size of the work array;
lwork≥ max(1, m+n+p) . If lwork = -1 , then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla . See Application Notes for the suggested value of lwork .
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
-
REAL for sgglse 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 .
- work(1)
-
If info = 0 , on exit, work(1) contains the minimum value of lwork required for optimum performance. Use this lwork for subsequent runs.
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.
LAPACK 95 Interface Notes
There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.
Application Notes
For optimum performance, use
lwork≥p + min(m, n) + max(m, n)*nb ,
where nb is an upper bound for the optimal blocksizes for ?geqrf , ?gerqf , ?ormqr / ?unmqr and ?ormrq / ?unmrq .
You may set lwork to -1. The routine returns immediately and provides the recommended workspace in the first element of the corresponding array ( work ). This operation is called a workspace query.
Note that if you set lwork to less than the minimal required value and not -1, the routine returns immediately with an error exit and does not provide any information on the recommended workspace.