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dpteqr(3P)		    Sun Performance Library		    dpteqr(3P)

NAME
       dpteqr  -  compute  all	eigenvalues and, optionally, eigenvectors of a
       symmetric positive definite tridiagonal matrix by first	factoring  the
       matrix  using  DPTTRF,  and then calling DBDSQR to compute the singular
       values of the bidiagonal factor

SYNOPSIS
       SUBROUTINE DPTEQR(COMPZ, N, D, E, Z, LDZ, WORK, INFO)

       CHARACTER * 1 COMPZ
       INTEGER N, LDZ, INFO
       DOUBLE PRECISION D(*), E(*), Z(LDZ,*), WORK(*)

       SUBROUTINE DPTEQR_64(COMPZ, N, D, E, Z, LDZ, WORK, INFO)

       CHARACTER * 1 COMPZ
       INTEGER*8 N, LDZ, INFO
       DOUBLE PRECISION D(*), E(*), Z(LDZ,*), WORK(*)

   F95 INTERFACE
       SUBROUTINE PTEQR(COMPZ, [N], D, E, Z, [LDZ], [WORK], [INFO])

       CHARACTER(LEN=1) :: COMPZ
       INTEGER :: N, LDZ, INFO
       REAL(8), DIMENSION(:) :: D, E, WORK
       REAL(8), DIMENSION(:,:) :: Z

       SUBROUTINE PTEQR_64(COMPZ, [N], D, E, Z, [LDZ], [WORK], [INFO])

       CHARACTER(LEN=1) :: COMPZ
       INTEGER(8) :: N, LDZ, INFO
       REAL(8), DIMENSION(:) :: D, E, WORK
       REAL(8), DIMENSION(:,:) :: Z

   C INTERFACE
       #include <sunperf.h>

       void dpteqr(char compz, int n, double *d, double	 *e,  double  *z,  int
		 ldz, int *info);

       void  dpteqr_64(char  compz,  long  n, double *d, double *e, double *z,
		 long ldz, long *info);

PURPOSE
       dpteqr computes all eigenvalues and, optionally, eigenvectors of a sym‐
       metric  positive	 definite  tridiagonal	matrix	by first factoring the
       matrix using DPTTRF, and then calling DBDSQR to	compute	 the  singular
       values of the bidiagonal factor.

       This routine computes the eigenvalues of the positive definite tridiag‐
       onal matrix to high relative accuracy.  This means that if  the	eigen‐
       values  range over many orders of magnitude in size, then the small ei‐
       genvalues and corresponding eigenvectors will be	 computed  more	 accu‐
       rately than, for example, with the standard QR method.

       The  eigenvectors  of a full or band symmetric positive definite matrix
       can also be found if DSYTRD, DSPTRD, or DSBTRD has been used to	reduce
       this  matrix  to	 tridiagonal form. (The reduction to tridiagonal form,
       however, may preclude the possibility of obtaining high relative	 accu‐
       racy  in	 the small eigenvalues of the original matrix, if these eigen‐
       values range over many orders of magnitude.)

ARGUMENTS
       COMPZ (input)
		 = '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.

       N (input) The order of the matrix.  N >= 0.

       D (input/output)
		 On  entry, the n diagonal elements of the tridiagonal matrix.
		 On normal exit, D contains  the  eigenvalues,	in  descending
		 order.

       E (input/output)
		 On  entry,  the (n-1) subdiagonal elements of the tridiagonal
		 matrix.  On exit, E has been destroyed.

       Z (input) 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.

       LDZ (input)
		 The leading dimension of the array Z.	LDZ >= 1, and if COMPZ
		 = 'V' or 'I', LDZ >= max(1,N).

       WORK (workspace)
		 dimension(4*N)

       INFO (output)
		 = 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 i-th princi‐
		 pal minor was not positive definite.  > N   the SVD algorithm
		 failed to converge; if INFO = N+i, i off-diagonal elements of
		 the bidiagonal factor did not converge to zero.

				  6 Mar 2009			    dpteqr(3P)
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