.TH "bdsdc" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
bdsdc \- bdsdc: bidiagonal SVD, divide and conquer
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBdbdsdc\fP (uplo, compq, n, d, e, u, ldu, vt, ldvt, q, iq, work, iwork, info)"
.br
.RI "\fBDBDSDC\fP "
.ti -1c
.RI "subroutine \fBsbdsdc\fP (uplo, compq, n, d, e, u, ldu, vt, ldvt, q, iq, work, iwork, info)"
.br
.RI "\fBSBDSDC\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine dbdsdc (character uplo, character compq, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldvt, * ) vt, integer ldvt, double precision, dimension( * ) q, integer, dimension( * ) iq, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)"

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

.PP
.nf
 DBDSDC computes the singular value decomposition (SVD) of a real
 N-by-N (upper or lower) bidiagonal matrix B:  B = U * S * VT,
 using a divide and conquer method, where S is a diagonal matrix
 with non-negative diagonal elements (the singular values of B), and
 U and VT are orthogonal matrices of left and right singular vectors,
 respectively\&. DBDSDC can be used to compute all singular values,
 and optionally, singular vectors or singular vectors in compact form\&.

 The code currently calls DLASDQ if singular values only are desired\&.
 However, it can be slightly modified to compute singular values
 using the divide and conquer method\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  B is upper bidiagonal\&.
          = 'L':  B is lower bidiagonal\&.
.fi
.PP
.br
\fICOMPQ\fP 
.PP
.nf
          COMPQ is CHARACTER*1
          Specifies whether singular vectors are to be computed
          as follows:
          = 'N':  Compute singular values only;
          = 'P':  Compute singular values and compute singular
                  vectors in compact form;
          = 'I':  Compute singular values and singular vectors\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix B\&.  N >= 0\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          On entry, the n diagonal elements of the bidiagonal matrix B\&.
          On exit, if INFO=0, the singular values of B\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is DOUBLE PRECISION array, dimension (N-1)
          On entry, the elements of E contain the offdiagonal
          elements of the bidiagonal matrix whose SVD is desired\&.
          On exit, E has been destroyed\&.
.fi
.PP
.br
\fIU\fP 
.PP
.nf
          U is DOUBLE PRECISION array, dimension (LDU,N)
          If  COMPQ = 'I', then:
             On exit, if INFO = 0, U contains the left singular vectors
             of the bidiagonal matrix\&.
          For other values of COMPQ, U is not referenced\&.
.fi
.PP
.br
\fILDU\fP 
.PP
.nf
          LDU is INTEGER
          The leading dimension of the array U\&.  LDU >= 1\&.
          If singular vectors are desired, then LDU >= max( 1, N )\&.
.fi
.PP
.br
\fIVT\fP 
.PP
.nf
          VT is DOUBLE PRECISION array, dimension (LDVT,N)
          If  COMPQ = 'I', then:
             On exit, if INFO = 0, VT**T contains the right singular
             vectors of the bidiagonal matrix\&.
          For other values of COMPQ, VT is not referenced\&.
.fi
.PP
.br
\fILDVT\fP 
.PP
.nf
          LDVT is INTEGER
          The leading dimension of the array VT\&.  LDVT >= 1\&.
          If singular vectors are desired, then LDVT >= max( 1, N )\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          Q is DOUBLE PRECISION array, dimension (LDQ)
          If  COMPQ = 'P', then:
             On exit, if INFO = 0, Q and IQ contain the left
             and right singular vectors in a compact form,
             requiring O(N log N) space instead of 2*N**2\&.
             In particular, Q contains all the DOUBLE PRECISION data in
             LDQ >= N*(11 + 2*SMLSIZ + 8*INT(LOG_2(N/(SMLSIZ+1))))
             words of memory, where SMLSIZ is returned by ILAENV and
             is equal to the maximum size of the subproblems at the
             bottom of the computation tree (usually about 25)\&.
          For other values of COMPQ, Q is not referenced\&.
.fi
.PP
.br
\fIIQ\fP 
.PP
.nf
          IQ is INTEGER array, dimension (LDIQ)
          If  COMPQ = 'P', then:
             On exit, if INFO = 0, Q and IQ contain the left
             and right singular vectors in a compact form,
             requiring O(N log N) space instead of 2*N**2\&.
             In particular, IQ contains all INTEGER data in
             LDIQ >= N*(3 + 3*INT(LOG_2(N/(SMLSIZ+1))))
             words of memory, where SMLSIZ is returned by ILAENV and
             is equal to the maximum size of the subproblems at the
             bottom of the computation tree (usually about 25)\&.
          For other values of COMPQ, IQ is not referenced\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          If COMPQ = 'N' then LWORK >= (4 * N)\&.
          If COMPQ = 'P' then LWORK >= (6 * N)\&.
          If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N)\&.
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (8*N)
.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\&.
          > 0:  The algorithm failed to compute a singular value\&.
                The update process of divide and conquer failed\&.
.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
\fBContributors:\fP
.RS 4
Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA 
.RE
.PP

.PP
Definition at line \fB196\fP of file \fBdbdsdc\&.f\fP\&.
.SS "subroutine sbdsdc (character uplo, character compq, integer n, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( * ) q, integer, dimension( * ) iq, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)"

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

.PP
.nf
 SBDSDC computes the singular value decomposition (SVD) of a real
 N-by-N (upper or lower) bidiagonal matrix B:  B = U * S * VT,
 using a divide and conquer method, where S is a diagonal matrix
 with non-negative diagonal elements (the singular values of B), and
 U and VT are orthogonal matrices of left and right singular vectors,
 respectively\&. SBDSDC can be used to compute all singular values,
 and optionally, singular vectors or singular vectors in compact form\&.

 The code currently calls SLASDQ if singular values only are desired\&.
 However, it can be slightly modified to compute singular values
 using the divide and conquer method\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  B is upper bidiagonal\&.
          = 'L':  B is lower bidiagonal\&.
.fi
.PP
.br
\fICOMPQ\fP 
.PP
.nf
          COMPQ is CHARACTER*1
          Specifies whether singular vectors are to be computed
          as follows:
          = 'N':  Compute singular values only;
          = 'P':  Compute singular values and compute singular
                  vectors in compact form;
          = 'I':  Compute singular values and singular vectors\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix B\&.  N >= 0\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is REAL array, dimension (N)
          On entry, the n diagonal elements of the bidiagonal matrix B\&.
          On exit, if INFO=0, the singular values of B\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is REAL array, dimension (N-1)
          On entry, the elements of E contain the offdiagonal
          elements of the bidiagonal matrix whose SVD is desired\&.
          On exit, E has been destroyed\&.
.fi
.PP
.br
\fIU\fP 
.PP
.nf
          U is REAL array, dimension (LDU,N)
          If  COMPQ = 'I', then:
             On exit, if INFO = 0, U contains the left singular vectors
             of the bidiagonal matrix\&.
          For other values of COMPQ, U is not referenced\&.
.fi
.PP
.br
\fILDU\fP 
.PP
.nf
          LDU is INTEGER
          The leading dimension of the array U\&.  LDU >= 1\&.
          If singular vectors are desired, then LDU >= max( 1, N )\&.
.fi
.PP
.br
\fIVT\fP 
.PP
.nf
          VT is REAL array, dimension (LDVT,N)
          If  COMPQ = 'I', then:
             On exit, if INFO = 0, VT**T contains the right singular
             vectors of the bidiagonal matrix\&.
          For other values of COMPQ, VT is not referenced\&.
.fi
.PP
.br
\fILDVT\fP 
.PP
.nf
          LDVT is INTEGER
          The leading dimension of the array VT\&.  LDVT >= 1\&.
          If singular vectors are desired, then LDVT >= max( 1, N )\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          Q is REAL array, dimension (LDQ)
          If  COMPQ = 'P', then:
             On exit, if INFO = 0, Q and IQ contain the left
             and right singular vectors in a compact form,
             requiring O(N log N) space instead of 2*N**2\&.
             In particular, Q contains all the REAL data in
             LDQ >= N*(11 + 2*SMLSIZ + 8*INT(LOG_2(N/(SMLSIZ+1))))
             words of memory, where SMLSIZ is returned by ILAENV and
             is equal to the maximum size of the subproblems at the
             bottom of the computation tree (usually about 25)\&.
          For other values of COMPQ, Q is not referenced\&.
.fi
.PP
.br
\fIIQ\fP 
.PP
.nf
          IQ is INTEGER array, dimension (LDIQ)
          If  COMPQ = 'P', then:
             On exit, if INFO = 0, Q and IQ contain the left
             and right singular vectors in a compact form,
             requiring O(N log N) space instead of 2*N**2\&.
             In particular, IQ contains all INTEGER data in
             LDIQ >= N*(3 + 3*INT(LOG_2(N/(SMLSIZ+1))))
             words of memory, where SMLSIZ is returned by ILAENV and
             is equal to the maximum size of the subproblems at the
             bottom of the computation tree (usually about 25)\&.
          For other values of COMPQ, IQ is not referenced\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (MAX(1,LWORK))
          If COMPQ = 'N' then LWORK >= (4 * N)\&.
          If COMPQ = 'P' then LWORK >= (6 * N)\&.
          If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N)\&.
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (8*N)
.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\&.
          > 0:  The algorithm failed to compute a singular value\&.
                The update process of divide and conquer failed\&.
.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
\fBContributors:\fP
.RS 4
Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA 
.RE
.PP

.PP
Definition at line \fB196\fP of file \fBsbdsdc\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.