gglse(3)

NAME
gglse - gglse: equality-constrained least squares

SYNOPSIS

  Functions
subroutine cgglse (m, n, p, a, lda, b, ldb, c, d, x, work, lwork, info)
CGGLSE solves overdetermined or underdetermined systems for OTHER matrices
subroutine dgglse (m, n, p, a, lda, b, ldb, c, d, x, work, lwork, info)
DGGLSE solves overdetermined or underdetermined systems for OTHER matrices
subroutine sgglse (m, n, p, a, lda, b, ldb, c, d, x, work, lwork, info)
SGGLSE solves overdetermined or underdetermined systems for OTHER matrices
subroutine zgglse (m, n, p, a, lda, b, ldb, c, d, x, work, lwork, info)
ZGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Detailed Description

Function Documentation

  subroutine cgglse (integer m, integer n, integer p, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) c, complex, dimension( * ) d, complex, dimension( * ) x, complex, dimension( * ) work, integer lwork, integer info)

CGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Purpose:

     CGGLSE 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
              rank(B) = P and  rank( (A) ) = N.
                                   ( (B) )
     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.

Parameters
    M

              M is INTEGER
              The number of rows of the matrix A.  M >= 0.

    N

              N is INTEGER
              The number of columns of the matrices A and B. N >= 0.

    P

              P is INTEGER
              The number of rows of the matrix B. 0 <= P <= N <= M+P.

    A

              A is COMPLEX array, dimension (LDA,N)
              On entry, the M-by-N matrix A.
              On exit, the elements on and above the diagonal of the array
              contain the min(M,N)-by-N upper trapezoidal matrix T.

    LDA

              LDA is INTEGER
              The leading dimension of the array A. LDA >= max(1,M).

    B

              B is COMPLEX array, dimension (LDB,N)
              On entry, the P-by-N matrix B.
              On exit, the upper triangle of the subarray B(1:P,N-P+1:N)
              contains the P-by-P upper triangular matrix R.

    LDB

              LDB is INTEGER
              The leading dimension of the array B. LDB >= max(1,P).

    C

              C is COMPLEX array, dimension (M)
              On entry, C contains the right hand side vector for the
              least squares part of the LSE problem.
              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.

    D

              D is COMPLEX array, dimension (P)
              On entry, D contains the right hand side vector for the
              constrained equation.
              On exit, D is destroyed.

    X

              X is COMPLEX array, dimension (N)
              On exit, X is the solution of the LSE problem.

    WORK

              WORK is COMPLEX array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK. LWORK >= max(1,M+N+P).
              For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB,
              where NB is an upper bound for the optimal blocksizes for
              CGEQRF, CGERQF, CUNMQR and CUNMRQ.
              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.

    INFO

              INFO is INTEGER
              = 0:  successful exit.
              < 0:  if INFO = -i, the i-th argument had an illegal value.
              = 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.
              = 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
                    rank( (A) ) < N; the least squares solution could not
                        ( (B) )
                    be computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 178 of file cgglse.f.

  subroutine dgglse (integer m, integer n, integer p, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) c, double precision, dimension( * ) d, double precision, dimension( * ) x, double precision, dimension( * ) work, integer lwork, integer info)

DGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Purpose:

     DGGLSE 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
              rank(B) = P and  rank( (A) ) = N.
                                   ( (B) )
     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.

Parameters
    M

              M is INTEGER
              The number of rows of the matrix A.  M >= 0.

    N

              N is INTEGER
              The number of columns of the matrices A and B. N >= 0.

    P

              P is INTEGER
              The number of rows of the matrix B. 0 <= P <= N <= M+P.

    A

              A is DOUBLE PRECISION array, dimension (LDA,N)
              On entry, the M-by-N matrix A.
              On exit, the elements on and above the diagonal of the array
              contain the min(M,N)-by-N upper trapezoidal matrix T.

    LDA

              LDA is INTEGER
              The leading dimension of the array A. LDA >= max(1,M).

    B

              B is DOUBLE PRECISION array, dimension (LDB,N)
              On entry, the P-by-N matrix B.
              On exit, the upper triangle of the subarray B(1:P,N-P+1:N)
              contains the P-by-P upper triangular matrix R.

    LDB

              LDB is INTEGER
              The leading dimension of the array B. LDB >= max(1,P).

    C

              C is DOUBLE PRECISION array, dimension (M)
              On entry, C contains the right hand side vector for the
              least squares part of the LSE problem.
              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.

    D

              D is DOUBLE PRECISION array, dimension (P)
              On entry, D contains the right hand side vector for the
              constrained equation.
              On exit, D is destroyed.

    X

              X is DOUBLE PRECISION array, dimension (N)
              On exit, X is the solution of the LSE problem.

    WORK

              WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK. LWORK >= max(1,M+N+P).
              For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB,
              where NB is an upper bound for the optimal blocksizes for
              DGEQRF, SGERQF, DORMQR and SORMRQ.
              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.

    INFO

              INFO is INTEGER
              = 0:  successful exit.
              < 0:  if INFO = -i, the i-th argument had an illegal value.
              = 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.
              = 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
                    rank( (A) ) < N; the least squares solution could not
                        ( (B) )
                    be computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 178 of file dgglse.f.

  subroutine sgglse (integer m, integer n, integer p, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) c, real, dimension( * ) d, real, dimension( * ) x, real, dimension( * ) work, integer lwork, integer info)

SGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Purpose:

     SGGLSE 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
              rank(B) = P and  rank( (A) ) = N.
                                   ( (B) )
     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.

Parameters
    M

              M is INTEGER
              The number of rows of the matrix A.  M >= 0.

    N

              N is INTEGER
              The number of columns of the matrices A and B. N >= 0.

    P

              P is INTEGER
              The number of rows of the matrix B. 0 <= P <= N <= M+P.

    A

              A is REAL array, dimension (LDA,N)
              On entry, the M-by-N matrix A.
              On exit, the elements on and above the diagonal of the array
              contain the min(M,N)-by-N upper trapezoidal matrix T.

    LDA

              LDA is INTEGER
              The leading dimension of the array A. LDA >= max(1,M).

    B

              B is REAL array, dimension (LDB,N)
              On entry, the P-by-N matrix B.
              On exit, the upper triangle of the subarray B(1:P,N-P+1:N)
              contains the P-by-P upper triangular matrix R.

    LDB

              LDB is INTEGER
              The leading dimension of the array B. LDB >= max(1,P).

    C

              C is REAL array, dimension (M)
              On entry, C contains the right hand side vector for the
              least squares part of the LSE problem.
              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.

    D

              D is REAL array, dimension (P)
              On entry, D contains the right hand side vector for the
              constrained equation.
              On exit, D is destroyed.

    X

              X is REAL array, dimension (N)
              On exit, X is the solution of the LSE problem.

    WORK

              WORK is REAL array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK. LWORK >= max(1,M+N+P).
              For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB,
              where NB is an upper bound for the optimal blocksizes for
              SGEQRF, SGERQF, SORMQR and SORMRQ.
              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.

    INFO

              INFO is INTEGER
              = 0:  successful exit.
              < 0:  if INFO = -i, the i-th argument had an illegal value.
              = 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.
              = 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
                    rank( (A) ) < N; the least squares solution could not
                        ( (B) )
                    be computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 178 of file sgglse.f.

  subroutine zgglse (integer m, integer n, integer p, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) c, complex*16, dimension( * ) d, complex*16, dimension( * ) x, complex*16, dimension( * ) work, integer lwork, integer info)

ZGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Purpose:

     ZGGLSE 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
              rank(B) = P and  rank( (A) ) = N.
                                   ( (B) )
     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.

Parameters
    M

              M is INTEGER
              The number of rows of the matrix A.  M >= 0.

    N

              N is INTEGER
              The number of columns of the matrices A and B. N >= 0.

    P

              P is INTEGER
              The number of rows of the matrix B. 0 <= P <= N <= M+P.

    A

              A is COMPLEX*16 array, dimension (LDA,N)
              On entry, the M-by-N matrix A.
              On exit, the elements on and above the diagonal of the array
              contain the min(M,N)-by-N upper trapezoidal matrix T.

    LDA

              LDA is INTEGER
              The leading dimension of the array A. LDA >= max(1,M).

    B

              B is COMPLEX*16 array, dimension (LDB,N)
              On entry, the P-by-N matrix B.
              On exit, the upper triangle of the subarray B(1:P,N-P+1:N)
              contains the P-by-P upper triangular matrix R.

    LDB

              LDB is INTEGER
              The leading dimension of the array B. LDB >= max(1,P).

    C

              C is COMPLEX*16 array, dimension (M)
              On entry, C contains the right hand side vector for the
              least squares part of the LSE problem.
              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.

    D

              D is COMPLEX*16 array, dimension (P)
              On entry, D contains the right hand side vector for the
              constrained equation.
              On exit, D is destroyed.

    X

              X is COMPLEX*16 array, dimension (N)
              On exit, X is the solution of the LSE problem.

    WORK

              WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK. LWORK >= max(1,M+N+P).
              For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB,
              where NB is an upper bound for the optimal blocksizes for
              ZGEQRF, CGERQF, ZUNMQR and CUNMRQ.
              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.

    INFO

              INFO is INTEGER
              = 0:  successful exit.
              < 0:  if INFO = -i, the i-th argument had an illegal value.
              = 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.
              = 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
                    rank( (A) ) < N; the least squares solution could not
                        ( (B) )
                    be computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 178 of file zgglse.f.

Author

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