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sggsvp (3)
  • >> sggsvp (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         sggsvp - compute orthogonal matrices U, V and  Q  such  that
         N-K-L K L  U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
    
    SYNOPSIS
         SUBROUTINE SGGSVP( JOBU, JOBV, JOBQ, M, P,  N,  A,  LDA,  B,
                   LDB,  TOLA,  TOLB,  K,  L, U, LDU, V, LDV, Q, LDQ,
                   IWORK, TAU, WORK, INFO )
    
         CHARACTER JOBQ, JOBU, JOBV
    
         INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P
    
         REAL TOLA, TOLB
    
         INTEGER IWORK( * )
    
         REAL A( LDA, * ), B( LDB, * ), Q( LDQ, * ),  TAU(  *  ),  U(
                   LDU, * ), V( LDV, * ), WORK( * )
    
    
    
         #include <sunperf.h>
    
         void sggsvp(char jobu, char jobv, char jobq, int m,  int  p,
                   int  n,  float  *sa,  int lda, float *sb, int ldb,
                   float tola, float tolb, int *k, int *l, float *su,
                   int  ldu,  float  *v,  int ldv, float *q, int ldq,
                   float *tau, int *info) ;
    
    PURPOSE
         SGGSVP computes orthogonal matrices U, V and Q such that
                       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'*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  non-
         singular 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',B')'.  Z' denotes the transpose of Z.
    
         This decomposition is the preprocessing step  for  computing
         the  Generalized  Singular  Value  Decomposition (GSVD), see
         subroutine SGGSVD.
    
    ARGUMENTS
         JOBU      (input) CHARACTER*1
                   = 'U':  Orthogonal matrix U is computed;
                   = 'N':  U is not computed.
    
         JOBV      (input) CHARACTER*1
                   = 'V':  Orthogonal matrix V is computed;
                   = 'N':  V is not computed.
    
         JOBQ      (input) CHARACTER*1
                   = 'Q':  Orthogonal matrix Q is computed;
                   = 'N':  Q is not computed.
    
         M         (input) INTEGER
                   The number of rows of the matrix A.  M >= 0.
    
         P         (input) INTEGER
                   The number of rows of the matrix B.  P >= 0.
    
         N         (input) INTEGER
                   The number of columns of the matrices A and B.   N
                   >= 0.
    
         A         (input/output) REAL array, dimension (LDA,N)
                   On entry, the M-by-N matrix A.  On  exit,  A  con-
                   tains   the  triangular  (or  trapezoidal)  matrix
                   described in the Purpose section.
    
         LDA       (input) INTEGER
                   The leading dimension  of  the  array  A.  LDA  >=
                   max(1,M).
    
         B         (input/output) REAL array, dimension (LDB,N)
                   On entry, the P-by-N matrix B.  On  exit,  B  con-
                   tains  the triangular matrix described in the Pur-
                   pose section.
    
         LDB       (input) INTEGER
                   The leading dimension  of  the  array  B.  LDB  >=
                   max(1,P).
    
         TOLA      (input) REAL
                   TOLB    (input) REAL TOLA and TOLB are the  thres-
                   holds 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.
    
         K         (output) INTEGER
                   L       (output) INTEGER On exit, K and L  specify
                   the  dimension  of the subblocks described in Pur-
                   pose.   K  +  L  =  effective  numerical  rank  of
                   (A',B')'.
    
         U         (output) REAL array, dimension (LDU,M)
                   If JOBU = 'U', U contains the orthogonal matrix U.
                   If JOBU = 'N', U is not referenced.
    
         LDU       (input) INTEGER
                   The leading dimension  of  the  array  U.  LDU  >=
                   max(1,M) if JOBU = 'U'; LDU >= 1 otherwise.
    
         V         (output) REAL array, dimension (LDV,M)
                   If JOBV = 'V', V contains the orthogonal matrix V.
                   If JOBV = 'N', V is not referenced.
    
         LDV       (input) INTEGER
                   The leading dimension  of  the  array  V.  LDV  >=
                   max(1,P) if JOBV = 'V'; LDV >= 1 otherwise.
    
         Q         (output) REAL array, dimension (LDQ,N)
                   If JOBQ = 'Q', Q contains the orthogonal matrix Q.
                   If JOBQ = 'N', Q is not referenced.
    
         LDQ       (input) INTEGER
                   The leading dimension  of  the  array  Q.  LDQ  >=
                   max(1,N) if JOBQ = 'Q'; LDQ >= 1 otherwise.
    
         IWORK     (workspace) INTEGER array, dimension (N)
    
         TAU       (workspace) REAL array, dimension (N)
    
         WORK      (workspace) REAL array, dimension (max(3*N,M,P))
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value.
    
    FURTHER DETAILS
         The subroutine uses LAPACK subroutine SGEQPF for the QR fac-
         torization  with  column  pivoting  to  detect the effective
         numerical rank of the a matrix. It  may  be  replaced  by  a
         better rank determination strategy.
    
    
    
    


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