.TH "SRC/slaed1.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/slaed1.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBslaed1\fP (n, d, q, ldq, indxq, rho, cutpnt, work, iwork, info)"
.br
.RI "\fBSLAED1\fP used by SSTEDC\&. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix\&. Used when the original matrix is tridiagonal\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine slaed1 (integer n, real, dimension( * ) d, real, dimension( ldq, * ) q, integer ldq, integer, dimension( * ) indxq, real rho, integer cutpnt, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)"

.PP
\fBSLAED1\fP used by SSTEDC\&. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix\&. Used when the original matrix is tridiagonal\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SLAED1 computes the updated eigensystem of a diagonal
!> matrix after modification by a rank-one symmetric matrix\&.  This
!> routine is used only for the eigenproblem which requires all
!> eigenvalues and eigenvectors of a tridiagonal matrix\&.  SLAED7 handles
!> the case in which eigenvalues only or eigenvalues and eigenvectors
!> of a full symmetric matrix (which was reduced to tridiagonal form)
!> are desired\&.
!>
!>   T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out)
!>
!>    where Z = Q**T*u, u is a vector of length N with ones in the
!>    CUTPNT and CUTPNT + 1 th elements and zeros elsewhere\&.
!>
!>    The eigenvectors of the original matrix are stored in Q, and the
!>    eigenvalues are in D\&.  The algorithm consists of three stages:
!>
!>       The first stage consists of deflating the size of the problem
!>       when there are multiple eigenvalues or if there is a zero in
!>       the Z vector\&.  For each such occurrence the dimension of the
!>       secular equation problem is reduced by one\&.  This stage is
!>       performed by the routine SLAED2\&.
!>
!>       The second stage consists of calculating the updated
!>       eigenvalues\&. This is done by finding the roots of the secular
!>       equation via the routine SLAED4 (as called by SLAED3)\&.
!>       This routine also calculates the eigenvectors of the current
!>       problem\&.
!>
!>       The final stage consists of computing the updated eigenvectors
!>       directly using the updated eigenvalues\&.  The eigenvectors for
!>       the current problem are multiplied with the eigenvectors from
!>       the overall problem\&.
!> 
.fi
.PP
 
.RE
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\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>         The dimension of the symmetric tridiagonal matrix\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is REAL array, dimension (N)
!>         On entry, the eigenvalues of the rank-1-perturbed matrix\&.
!>         On exit, the eigenvalues of the repaired matrix\&.
!> 
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
!>          Q is REAL array, dimension (LDQ,N)
!>         On entry, the eigenvectors of the rank-1-perturbed matrix\&.
!>         On exit, the eigenvectors of the repaired tridiagonal matrix\&.
!> 
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
!>          LDQ is INTEGER
!>         The leading dimension of the array Q\&.  LDQ >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIINDXQ\fP 
.PP
.nf
!>          INDXQ is INTEGER array, dimension (N)
!>         On entry, the permutation which separately sorts the two
!>         subproblems in D into ascending order\&.
!>         On exit, the permutation which will reintegrate the
!>         subproblems back into sorted order,
!>         i\&.e\&. D( INDXQ( I = 1, N ) ) will be in ascending order\&.
!> 
.fi
.PP
.br
\fIRHO\fP 
.PP
.nf
!>          RHO is REAL
!>         The subdiagonal entry used to create the rank-1 modification\&.
!> 
.fi
.PP
.br
\fICUTPNT\fP 
.PP
.nf
!>          CUTPNT is INTEGER
!>         The location of the last eigenvalue in the leading sub-matrix\&.
!>         min(1,N) <= CUTPNT <= N/2\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (4*N + N**2)
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER 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:  if INFO = 1, an eigenvalue 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
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\fBContributors:\fP
.RS 4
Jeff Rutter, Computer Science Division, University of California at Berkeley, USA 
.br
 Modified by Francoise Tisseur, University of Tennessee 
.RE
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Definition at line \fB161\fP of file \fBslaed1\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.