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

.in +1c
.ti -1c
.RI "subroutine \fBspteqr\fP (compz, n, d, e, z, ldz, work, info)"
.br
.RI "\fBSPTEQR\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine spteqr (character compz, integer n, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> SPTEQR computes all eigenvalues and, optionally, eigenvectors of a
!> symmetric positive definite tridiagonal matrix by first factoring the
!> matrix using SPTTRF, and then calling SBDSQR to compute the singular
!> values of the bidiagonal factor\&.
!>
!> This routine computes the eigenvalues of the positive definite
!> tridiagonal matrix to high relative accuracy\&.  This means that if the
!> eigenvalues range over many orders of magnitude in size, then the
!> small eigenvalues and corresponding eigenvectors will be computed
!> more accurately than, for example, with the standard QR method\&.
!>
!> The eigenvectors of a full or band symmetric positive definite matrix
!> can also be found if SSYTRD, SSPTRD, or SSBTRD has been used to
!> reduce this matrix to tridiagonal form\&. (The reduction to tridiagonal
!> form, however, may preclude the possibility of obtaining high
!> relative accuracy in the small eigenvalues of the original matrix, if
!> these eigenvalues range over many orders of magnitude\&.)
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fICOMPZ\fP 
.PP
.nf
!>          COMPZ is CHARACTER*1
!>          = 'N':  Compute eigenvalues only\&.
!>          = 'V':  Compute eigenvectors of original symmetric
!>                  matrix also\&.  Array Z contains the orthogonal
!>                  matrix used to reduce the original matrix to
!>                  tridiagonal form\&.
!>          = 'I':  Compute eigenvectors of tridiagonal matrix also\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is REAL array, dimension (N)
!>          On entry, the n diagonal elements of the tridiagonal
!>          matrix\&.
!>          On normal exit, D contains the eigenvalues, in descending
!>          order\&.
!> 
.fi
.PP
.br
\fIE\fP 
.PP
.nf
!>          E is REAL array, dimension (N-1)
!>          On entry, the (n-1) subdiagonal elements of the tridiagonal
!>          matrix\&.
!>          On exit, E has been destroyed\&.
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          Z is REAL array, dimension (LDZ, N)
!>          On entry, if COMPZ = 'V', the orthogonal matrix used in the
!>          reduction to tridiagonal form\&.
!>          On exit, if COMPZ = 'V', the orthonormal eigenvectors of the
!>          original symmetric matrix;
!>          if COMPZ = 'I', the orthonormal eigenvectors of the
!>          tridiagonal matrix\&.
!>          If INFO > 0 on exit, Z contains the eigenvectors associated
!>          with only the stored eigenvalues\&.
!>          If  COMPZ = 'N', then Z is not referenced\&.
!> 
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
!>          LDZ is INTEGER
!>          The leading dimension of the array Z\&.  LDZ >= 1, and if
!>          COMPZ = 'V' or 'I', LDZ >= max(1,N)\&.
!> 
.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:  if INFO = i, and i is:
!>                <= N  the Cholesky factorization of the matrix could
!>                      not be performed because the leading principal
!>                      minor of order i was not positive\&.
!>                > N   the SVD algorithm failed to converge;
!>                      if INFO = N+i, i off-diagonal elements of the
!>                      bidiagonal factor did not converge to zero\&.
!> 
.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 \fB144\fP of file \fBspteqr\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.