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## dggsvp3()

subroutine dggsvp3 | ( | character | jobu,
|  | character | jobv,
|  | character | jobq,
|  | integer | m,
|  | integer | p,
|  | integer | n,
|  | double precision, dimension( lda, * ) | a,
|  | integer | lda,
|  | double precision, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | double precision | tola,
|  | double precision | tolb,
|  | integer | k,
|  | integer | l,
|  | double precision, dimension( ldu, * ) | u,
|  | integer | ldu,
|  | double precision, dimension( ldv, * ) | v,
|  | integer | ldv,
|  | double precision, dimension( ldq, * ) | q,
|  | integer | ldq,
|  | integer, dimension( * ) | iwork,
|  | double precision, dimension( * ) | tau,
|  | double precision, dimension( * ) | work,
|  | integer | lwork,
|  | integer | info )

DGGSVP3

Download DGGSVP3 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> DGGSVP3 computes orthogonal matrices U, V and Q such that
      !>
      !>                    N-K-L  K    L
      !>  U**T*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
      !>                 L ( 0     0   A23 )
      !>             M-K-L ( 0     0    0  )
      !>
      !>                  N-K-L  K    L
      !>         =     K ( 0    A12  A13 )  if M-K-L < 0;
      !>             M-K ( 0     0   A23 )
      !>
      !>                  N-K-L  K    L
      !>  V**T*B*Q =   L ( 0     0   B13 )
      !>             P-L ( 0     0    0  )
      !>
      !> where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
      !> upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
      !> otherwise A23 is (M-K)-by-L upper trapezoidal.  K+L = the effective
      !> numerical rank of the (M+P)-by-N matrix (A**T,B**T)**T.
      !>
      !> This decomposition is the preprocessing step for computing the
      !> Generalized Singular Value Decomposition (GSVD), see subroutine
      !> DGGSVD3.
      !>

Parameters

  [in]

  JOBU

      !>          JOBU is CHARACTER*1
      !>          = 'U':  Orthogonal matrix U is computed;
      !>          = 'N':  U is not computed.
      !>

  [in]

  JOBV

      !>          JOBV is CHARACTER*1
      !>          = 'V':  Orthogonal matrix V is computed;
      !>          = 'N':  V is not computed.
      !>

  [in]

  JOBQ

      !>          JOBQ is CHARACTER*1
      !>          = 'Q':  Orthogonal matrix Q is computed;
      !>          = 'N':  Q is not computed.
      !>

  [in]

  M

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

  [in]

  P

      !>          P is INTEGER
      !>          The number of rows of the matrix B.  P >= 0.
      !>

  [in]

  N

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

  [in,out]

  A

      !>          A is DOUBLE PRECISION array, dimension (LDA,N)
      !>          On entry, the M-by-N matrix A.
      !>          On exit, A contains the triangular (or trapezoidal) matrix
      !>          described in the Purpose section.
      !>

  [in]

  LDA

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

  [in,out]

  B

      !>          B is DOUBLE PRECISION array, dimension (LDB,N)
      !>          On entry, the P-by-N matrix B.
      !>          On exit, B contains the triangular matrix described in
      !>          the Purpose section.
      !>

  [in]

  LDB

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

  [in]

  TOLA

      !>          TOLA is DOUBLE PRECISION
      !>

  [in]

  TOLB

      !>          TOLB is DOUBLE PRECISION
      !>
      !>          TOLA and TOLB are the thresholds to determine the effective
      !>          numerical rank of matrix B and a subblock of A. Generally,
      !>          they are set to
      !>             TOLA = MAX(M,N)*norm(A)*MACHEPS,
      !>             TOLB = MAX(P,N)*norm(B)*MACHEPS.
      !>          The size of TOLA and TOLB may affect the size of backward
      !>          errors of the decomposition.
      !>

  [out]

  K

      !>          K is INTEGER
      !>

  [out]

  L

      !>          L is INTEGER
      !>
      !>          On exit, K and L specify the dimension of the subblocks
      !>          described in Purpose section.
      !>          K + L = effective numerical rank of (A**T,B**T)**T.
      !>

  [out]

  U

      !>          U is DOUBLE PRECISION array, dimension (LDU,M)
      !>          If JOBU = 'U', U contains the orthogonal matrix U.
      !>          If JOBU = 'N', U is not referenced.
      !>

  [in]

  LDU

      !>          LDU is INTEGER
      !>          The leading dimension of the array U. LDU >= max(1,M) if
      !>          JOBU = 'U'; LDU >= 1 otherwise.
      !>

  [out]

  V

      !>          V is DOUBLE PRECISION array, dimension (LDV,P)
      !>          If JOBV = 'V', V contains the orthogonal matrix V.
      !>          If JOBV = 'N', V is not referenced.
      !>

  [in]

  LDV

      !>          LDV is INTEGER
      !>          The leading dimension of the array V. LDV >= max(1,P) if
      !>          JOBV = 'V'; LDV >= 1 otherwise.
      !>

  [out]

  Q

      !>          Q is DOUBLE PRECISION array, dimension (LDQ,N)
      !>          If JOBQ = 'Q', Q contains the orthogonal matrix Q.
      !>          If JOBQ = 'N', Q is not referenced.
      !>

  [in]

  LDQ

      !>          LDQ is INTEGER
      !>          The leading dimension of the array Q. LDQ >= max(1,N) if
      !>          JOBQ = 'Q'; LDQ >= 1 otherwise.
      !>

  [out]

  IWORK

      !>          IWORK is INTEGER array, dimension (N)
      !>

  [out]

  TAU

      !>          TAU is DOUBLE PRECISION array, dimension (N)
      !>

  [out]

  WORK

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

  [in]

  LWORK

      !>          LWORK is INTEGER
      !>          The dimension of the array WORK. LWORK >= 1.
      !>
      !>          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.
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>          = 0:  successful exit
      !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

Further Details:

      !>
      !>  The subroutine uses LAPACK subroutine DGEQP3 for the QR factorization
      !>  with column pivoting to detect the effective numerical rank of the
      !>  a matrix. It may be replaced by a better rank determination strategy.
      !>
      !>  DGGSVP3 replaces the deprecated subroutine DGGSVP.
      !>
      !>