.TH "lasq1" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lasq1 \- lasq1: dqds step
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBdlasq1\fP (n, d, e, work, info)"
.br
.RI "\fBDLASQ1\fP computes the singular values of a real square bidiagonal matrix\&. Used by sbdsqr\&. "
.ti -1c
.RI "subroutine \fBslasq1\fP (n, d, e, work, info)"
.br
.RI "\fBSLASQ1\fP computes the singular values of a real square bidiagonal matrix\&. Used by sbdsqr\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine dlasq1 (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( * ) work, integer info)"

.PP
\fBDLASQ1\fP computes the singular values of a real square bidiagonal matrix\&. Used by sbdsqr\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> DLASQ1 computes the singular values of a real N-by-N bidiagonal
!> matrix with diagonal D and off-diagonal E\&. The singular values
!> are computed to high relative accuracy, in the absence of
!> denormalization, underflow and overflow\&. The algorithm was first
!> presented in
!>
!>  by K\&. V\&.
!> Fernando and B\&. N\&. Parlett, Numer\&. Math\&., Vol-67, No\&. 2, pp\&. 191-230,
!> 1994,
!>
!> and the present implementation is described in , LAPACK Working Note\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>        The number of rows and columns in the matrix\&. N >= 0\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is DOUBLE PRECISION array, dimension (N)
!>        On entry, D contains the diagonal elements of the
!>        bidiagonal matrix whose SVD is desired\&. On normal exit,
!>        D contains the singular values in decreasing order\&.
!> 
.fi
.PP
.br
\fIE\fP 
.PP
.nf
!>          E is DOUBLE PRECISION array, dimension (N)
!>        On entry, elements E(1:N-1) contain the off-diagonal elements
!>        of the bidiagonal matrix whose SVD is desired\&.
!>        On exit, E is overwritten\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is DOUBLE PRECISION array, dimension (4*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
!>             = 1, a split was marked by a positive value in E
!>             = 2, current block of Z not diagonalized after 100*N
!>                  iterations (in inner while loop)  On exit D and E
!>                  represent a matrix with the same singular values
!>                  which the calling subroutine could use to finish the
!>                  computation, or even feed back into DLASQ1
!>             = 3, termination criterion of outer while loop not met
!>                  (program created more than N unreduced blocks)
!> 
.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

.PP
Definition at line \fB107\fP of file \fBdlasq1\&.f\fP\&.
.SS "subroutine slasq1 (integer n, real, dimension( * ) d, real, dimension( * ) e, real, dimension( * ) work, integer info)"

.PP
\fBSLASQ1\fP computes the singular values of a real square bidiagonal matrix\&. Used by sbdsqr\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SLASQ1 computes the singular values of a real N-by-N bidiagonal
!> matrix with diagonal D and off-diagonal E\&. The singular values
!> are computed to high relative accuracy, in the absence of
!> denormalization, underflow and overflow\&. The algorithm was first
!> presented in
!>
!>  by K\&. V\&.
!> Fernando and B\&. N\&. Parlett, Numer\&. Math\&., Vol-67, No\&. 2, pp\&. 191-230,
!> 1994,
!>
!> and the present implementation is described in , LAPACK Working Note\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>        The number of rows and columns in the matrix\&. N >= 0\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is REAL array, dimension (N)
!>        On entry, D contains the diagonal elements of the
!>        bidiagonal matrix whose SVD is desired\&. On normal exit,
!>        D contains the singular values in decreasing order\&.
!> 
.fi
.PP
.br
\fIE\fP 
.PP
.nf
!>          E is REAL array, dimension (N)
!>        On entry, elements E(1:N-1) contain the off-diagonal elements
!>        of the bidiagonal matrix whose SVD is desired\&.
!>        On exit, E is overwritten\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (4*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
!>             = 1, a split was marked by a positive value in E
!>             = 2, current block of Z not diagonalized after 100*N
!>                  iterations (in inner while loop)  On exit D and E
!>                  represent a matrix with the same singular values
!>                  which the calling subroutine could use to finish the
!>                  computation, or even feed back into SLASQ1
!>             = 3, termination criterion of outer while loop not met
!>                  (program created more than N unreduced blocks)
!> 
.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

.PP
Definition at line \fB107\fP of file \fBslasq1\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.