.TH "lasd0" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lasd0 \- lasd0: D&C step: top level solver
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBdlasd0\fP (n, sqre, d, e, u, ldu, vt, ldvt, smlsiz, iwork, work, info)"
.br
.RI "\fBDLASD0\fP computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e\&. Used by sbdsdc\&. "
.ti -1c
.RI "subroutine \fBslasd0\fP (n, sqre, d, e, u, ldu, vt, ldvt, smlsiz, iwork, work, info)"
.br
.RI "\fBSLASD0\fP computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e\&. Used by sbdsdc\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine dlasd0 (integer n, integer sqre, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldvt, * ) vt, integer ldvt, integer smlsiz, integer, dimension( * ) iwork, double precision, dimension( * ) work, integer info)"

.PP
\fBDLASD0\fP computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e\&. Used by sbdsdc\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 Using a divide and conquer approach, DLASD0 computes the singular
 value decomposition (SVD) of a real upper bidiagonal N-by-M
 matrix B with diagonal D and offdiagonal E, where M = N + SQRE\&.
 The algorithm computes orthogonal matrices U and VT such that
 B = U * S * VT\&. The singular values S are overwritten on D\&.

 A related subroutine, DLASDA, computes only the singular values,
 and optionally, the singular vectors in compact form\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
         On entry, the row dimension of the upper bidiagonal matrix\&.
         This is also the dimension of the main diagonal array D\&.
.fi
.PP
.br
\fISQRE\fP 
.PP
.nf
          SQRE is INTEGER
         Specifies the column dimension of the bidiagonal matrix\&.
         = 0: The bidiagonal matrix has column dimension M = N;
         = 1: The bidiagonal matrix has column dimension M = N+1;
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
         On entry D contains the main diagonal of the bidiagonal
         matrix\&.
         On exit D, if INFO = 0, contains its singular values\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is DOUBLE PRECISION array, dimension (M-1)
         Contains the subdiagonal entries of the bidiagonal matrix\&.
         On exit, E has been destroyed\&.
.fi
.PP
.br
\fIU\fP 
.PP
.nf
          U is DOUBLE PRECISION array, dimension (LDU, N)
         On exit, U contains the left singular vectors, 
          if U passed in as (N, N) Identity\&.
.fi
.PP
.br
\fILDU\fP 
.PP
.nf
          LDU is INTEGER
         On entry, leading dimension of U\&.
.fi
.PP
.br
\fIVT\fP 
.PP
.nf
          VT is DOUBLE PRECISION array, dimension (LDVT, M)
         On exit, VT**T contains the right singular vectors,
          if VT passed in as (M, M) Identity\&.
.fi
.PP
.br
\fILDVT\fP 
.PP
.nf
          LDVT is INTEGER
         On entry, leading dimension of VT\&.
.fi
.PP
.br
\fISMLSIZ\fP 
.PP
.nf
          SMLSIZ is INTEGER
         On entry, maximum size of the subproblems at the
         bottom of the computation tree\&.
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (8*N)
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (3*M**2+2*M)
.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:  if INFO = 1, a singular value did not converge
.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

.SS "subroutine slasd0 (integer n, integer sqre, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, integer smlsiz, integer, dimension( * ) iwork, real, dimension( * ) work, integer info)"

.PP
\fBSLASD0\fP computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e\&. Used by sbdsdc\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 Using a divide and conquer approach, SLASD0 computes the singular
 value decomposition (SVD) of a real upper bidiagonal N-by-M
 matrix B with diagonal D and offdiagonal E, where M = N + SQRE\&.
 The algorithm computes orthogonal matrices U and VT such that
 B = U * S * VT\&. The singular values S are overwritten on D\&.

 A related subroutine, SLASDA, computes only the singular values,
 and optionally, the singular vectors in compact form\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
         On entry, the row dimension of the upper bidiagonal matrix\&.
         This is also the dimension of the main diagonal array D\&.
.fi
.PP
.br
\fISQRE\fP 
.PP
.nf
          SQRE is INTEGER
         Specifies the column dimension of the bidiagonal matrix\&.
         = 0: The bidiagonal matrix has column dimension M = N;
         = 1: The bidiagonal matrix has column dimension M = N+1;
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is REAL array, dimension (N)
         On entry D contains the main diagonal of the bidiagonal
         matrix\&.
         On exit D, if INFO = 0, contains its singular values\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is REAL array, dimension (M-1)
         Contains the subdiagonal entries of the bidiagonal matrix\&.
         On exit, E has been destroyed\&.
.fi
.PP
.br
\fIU\fP 
.PP
.nf
          U is REAL array, dimension (LDU, N)
         On exit, U contains the left singular vectors,
          if U passed in as (N, N) Identity\&.
.fi
.PP
.br
\fILDU\fP 
.PP
.nf
          LDU is INTEGER
         On entry, leading dimension of U\&.
.fi
.PP
.br
\fIVT\fP 
.PP
.nf
          VT is REAL array, dimension (LDVT, M)
         On exit, VT**T contains the right singular vectors,
          if VT passed in as (M, M) Identity\&.
.fi
.PP
.br
\fILDVT\fP 
.PP
.nf
          LDVT is INTEGER
         On entry, leading dimension of VT\&.
.fi
.PP
.br
\fISMLSIZ\fP 
.PP
.nf
          SMLSIZ is INTEGER
         On entry, maximum size of the subproblems at the
         bottom of the computation tree\&.
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (8*N)
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (3*M**2+2*M)
.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:  if INFO = 1, a singular value did not converge
.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

.SH "Author"
.PP 
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