.TH "SRC/DEPRECATED/sggsvp.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/DEPRECATED/sggsvp.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBsggsvp\fP (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola, tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, tau, work, info)"
.br
.RI "\fBSGGSVP\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine sggsvp (character jobu, character jobv, character jobq, integer m, integer p, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real tola, real tolb, integer k, integer l, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldq, * ) q, integer ldq, integer, dimension( * ) iwork, real, dimension( * ) tau, real, dimension( * ) work, integer info)"

.PP
\fBSGGSVP\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 This routine is deprecated and has been replaced by routine SGGSVP3\&.

 SGGSVP 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
 SGGSVD\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBU\fP 
.PP
.nf
          JOBU is CHARACTER*1
          = 'U':  Orthogonal matrix U is computed;
          = 'N':  U is not computed\&.
.fi
.PP
.br
\fIJOBV\fP 
.PP
.nf
          JOBV is CHARACTER*1
          = 'V':  Orthogonal matrix V is computed;
          = 'N':  V is not computed\&.
.fi
.PP
.br
\fIJOBQ\fP 
.PP
.nf
          JOBQ is CHARACTER*1
          = 'Q':  Orthogonal matrix Q is computed;
          = 'N':  Q is not computed\&.
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= 0\&.
.fi
.PP
.br
\fIP\fP 
.PP
.nf
          P is INTEGER
          The number of rows of the matrix B\&.  P >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrices A and B\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is REAL 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\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&. LDA >= max(1,M)\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is REAL array, dimension (LDB,N)
          On entry, the P-by-N matrix B\&.
          On exit, B contains the triangular matrix described in
          the Purpose section\&.
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of the array B\&. LDB >= max(1,P)\&.
.fi
.PP
.br
\fITOLA\fP 
.PP
.nf
          TOLA is REAL
.fi
.PP
.br
\fITOLB\fP 
.PP
.nf
          TOLB is REAL

          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\&.
.fi
.PP
.br
\fIK\fP 
.PP
.nf
          K is INTEGER
.fi
.PP
.br
\fIL\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIU\fP 
.PP
.nf
          U is REAL array, dimension (LDU,M)
          If JOBU = 'U', U contains the orthogonal matrix U\&.
          If JOBU = 'N', U is not referenced\&.
.fi
.PP
.br
\fILDU\fP 
.PP
.nf
          LDU is INTEGER
          The leading dimension of the array U\&. LDU >= max(1,M) if
          JOBU = 'U'; LDU >= 1 otherwise\&.
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is REAL array, dimension (LDV,P)
          If JOBV = 'V', V contains the orthogonal matrix V\&.
          If JOBV = 'N', V is not referenced\&.
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
          LDV is INTEGER
          The leading dimension of the array V\&. LDV >= max(1,P) if
          JOBV = 'V'; LDV >= 1 otherwise\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          Q is REAL array, dimension (LDQ,N)
          If JOBQ = 'Q', Q contains the orthogonal matrix Q\&.
          If JOBQ = 'N', Q is not referenced\&.
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
          LDQ is INTEGER
          The leading dimension of the array Q\&. LDQ >= max(1,N) if
          JOBQ = 'Q'; LDQ >= 1 otherwise\&.
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (N)
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is REAL array, dimension (N)
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (max(3*N,M,P))
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4
The subroutine uses LAPACK subroutine SGEQPF 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\&. 
.RE
.PP

.PP
Definition at line \fB253\fP of file \fBsggsvp\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.