*nix Documentation Project
·  Home
 +   man pages
·  Linux HOWTOs
·  FreeBSD Tips
·  *niX Forums

  man pages->IRIX man pages -> complib/dlaed8 (3)              
Title
Content
Arch
Section
 

Contents


DLAED8(3F)							    DLAED8(3F)


NAME    [Toc]    [Back]

     DLAED8 - merge the	two sets of eigenvalues	together into a	single sorted
     set

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	DLAED8(	ICOMPQ,	K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z,
			DLAMDA,	Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM,
			INDXP, INDX, INFO )

	 INTEGER	CUTPNT,	GIVPTR,	ICOMPQ,	INFO, K, LDQ, LDQ2, N, QSIZ

	 DOUBLE		PRECISION RHO

	 INTEGER	GIVCOL(	2, * ),	INDX( *	), INDXP( * ), INDXQ( *	),
			PERM( *	)

	 DOUBLE		PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), Q( LDQ,
			* ), Q2( LDQ2, * ), W( * ), Z( * )

PURPOSE    [Toc]    [Back]

     DLAED8 merges the two sets	of eigenvalues together	into a single sorted
     set.  Then	it tries to deflate the	size of	the problem.  There are	two
     ways in which deflation can occur:	 when two or more eigenvalues are
     close together or if there	is a tiny element in the Z vector.  For	each
     such occurrence the order of the related secular equation problem is
     reduced by	one.

ARGUMENTS    [Toc]    [Back]

     ICOMPQ  (input) INTEGER
	     = 0:  Compute eigenvalues only.
	     = 1:  Compute eigenvectors	of original dense symmetric matrix
	     also.  On entry, Q	contains the orthogonal	matrix used to reduce
	     the original matrix to tridiagonal	form.

     K	    (output) INTEGER
	    The	number of non-deflated eigenvalues, and	the order of the
	    related secular equation.

     N	    (input) INTEGER
	    The	dimension of the symmetric tridiagonal matrix.	N >= 0.

     QSIZ   (input) INTEGER
	    The	dimension of the orthogonal matrix used	to reduce the full
	    matrix to tridiagonal form.	 QSIZ >= N if ICOMPQ = 1.

     D	    (input/output) DOUBLE PRECISION array, dimension (N)
	    On entry, the eigenvalues of the two submatrices to	be combined.
	    On exit, the trailing (N-K)	updated	eigenvalues (those which were
	    deflated) sorted into increasing order.





									Page 1






DLAED8(3F)							    DLAED8(3F)



     Q	    (input/output) DOUBLE PRECISION array, dimension (LDQ,N)
	    If ICOMPQ =	0, Q is	not referenced.	 Otherwise, on entry, Q
	    contains the eigenvectors of the partially solved system which has
	    been previously updated in matrix multiplies with other partially
	    solved eigensystems.  On exit, Q contains the trailing (N-K)
	    updated eigenvectors (those	which were deflated) in	its last N-K
	    columns.

     LDQ    (input) INTEGER
	    The	leading	dimension of the array Q.  LDQ >= max(1,N).

     INDXQ  (input) INTEGER array, dimension (N)
	    The	permutation which separately sorts the two sub-problems	in D
	    into ascending order.  Note	that elements in the second half of
	    this permutation must first	have CUTPNT added to their values in
	    order to be	accurate.

     RHO    (input/output) DOUBLE PRECISION
	    On entry, the off-diagonal element associated with the rank-1 cut
	    which originally split the two submatrices which are now being
	    recombined.	 On exit, RHO has been modified	to the value required
	    by DLAED3.

	    CUTPNT (input) INTEGER The location	of the last eigenvalue in the
	    leading sub-matrix.	 min(1,N) <= CUTPNT <= N.

     Z	    (input) DOUBLE PRECISION array, dimension (N)
	    On entry, Z	contains the updating vector (the last row of the
	    first sub-eigenvector matrix and the first row of the second subeigenvector
	matrix).  On exit, the contents	of Z are destroyed by
	    the	updating process.

	    DLAMDA (output) DOUBLE PRECISION array, dimension (N) A copy of
	    the	first K	eigenvalues which will be used by DLAED3 to form the
	    secular equation.

     Q2	    (output) DOUBLE PRECISION array, dimension (LDQ2,N)
	    If ICOMPQ =	0, Q2 is not referenced.  Otherwise, a copy of the
	    first K eigenvectors which will be used by DLAED7 in a matrix
	    multiply (DGEMM) to	update the new eigenvectors.

     LDQ2   (input) INTEGER
	    The	leading	dimension of the array Q2.  LDQ2 >= max(1,N).

     W	    (output) DOUBLE PRECISION array, dimension (N)
	    The	first k	values of the final deflation-altered z-vector and
	    will be passed to DLAED3.

     PERM   (output) INTEGER array, dimension (N)
	    The	permutations (from deflation and sorting) to be	applied	to
	    each eigenblock.




									Page 2






DLAED8(3F)							    DLAED8(3F)



	    GIVPTR (output) INTEGER The	number of Givens rotations which took
	    place in this subproblem.

	    GIVCOL (output) INTEGER array, dimension (2, N) Each pair of
	    numbers indicates a	pair of	columns	to take	place in a Givens
	    rotation.

	    GIVNUM (output) DOUBLE PRECISION array, dimension (2, N) Each
	    number indicates the S value to be used in the corresponding
	    Givens rotation.

     INDXP  (workspace)	INTEGER	array, dimension (N)
	    The	permutation used to place deflated values of D at the end of
	    the	array.	INDXP(1:K) points to the nondeflated D-values
	    and	INDXP(K+1:N) points to the deflated eigenvalues.

     INDX   (workspace)	INTEGER	array, dimension (N)
	    The	permutation used to sort the contents of D into	ascending
	    order.

     INFO   (output) INTEGER
	    = 0:  successful exit.
	    < 0:  if INFO = -i,	the i-th argument had an illegal value.
DLAED8(3F)							    DLAED8(3F)


NAME    [Toc]    [Back]

     DLAED8 - merge the	two sets of eigenvalues	together into a	single sorted
     set

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	DLAED8(	ICOMPQ,	K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z,
			DLAMDA,	Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM,
			INDXP, INDX, INFO )

	 INTEGER	CUTPNT,	GIVPTR,	ICOMPQ,	INFO, K, LDQ, LDQ2, N, QSIZ

	 DOUBLE		PRECISION RHO

	 INTEGER	GIVCOL(	2, * ),	INDX( *	), INDXP( * ), INDXQ( *	),
			PERM( *	)

	 DOUBLE		PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), Q( LDQ,
			* ), Q2( LDQ2, * ), W( * ), Z( * )

PURPOSE    [Toc]    [Back]

     DLAED8 merges the two sets	of eigenvalues together	into a single sorted
     set.  Then	it tries to deflate the	size of	the problem.  There are	two
     ways in which deflation can occur:	 when two or more eigenvalues are
     close together or if there	is a tiny element in the Z vector.  For	each
     such occurrence the order of the related secular equation problem is
     reduced by	one.

ARGUMENTS    [Toc]    [Back]

     ICOMPQ  (input) INTEGER
	     = 0:  Compute eigenvalues only.
	     = 1:  Compute eigenvectors	of original dense symmetric matrix
	     also.  On entry, Q	contains the orthogonal	matrix used to reduce
	     the original matrix to tridiagonal	form.

     K	    (output) INTEGER
	    The	number of non-deflated eigenvalues, and	the order of the
	    related secular equation.

     N	    (input) INTEGER
	    The	dimension of the symmetric tridiagonal matrix.	N >= 0.

     QSIZ   (input) INTEGER
	    The	dimension of the orthogonal matrix used	to reduce the full
	    matrix to tridiagonal form.	 QSIZ >= N if ICOMPQ = 1.

     D	    (input/output) DOUBLE PRECISION array, dimension (N)
	    On entry, the eigenvalues of the two submatrices to	be combined.
	    On exit, the trailing (N-K)	updated	eigenvalues (those which were
	    deflated) sorted into increasing order.





									Page 1






DLAED8(3F)							    DLAED8(3F)



     Q	    (input/output) DOUBLE PRECISION array, dimension (LDQ,N)
	    If ICOMPQ =	0, Q is	not referenced.	 Otherwise, on entry, Q
	    contains the eigenvectors of the partially solved system which has
	    been previously updated in matrix multiplies with other partially
	    solved eigensystems.  On exit, Q contains the trailing (N-K)
	    updated eigenvectors (those	which were deflated) in	its last N-K
	    columns.

     LDQ    (input) INTEGER
	    The	leading	dimension of the array Q.  LDQ >= max(1,N).

     INDXQ  (input) INTEGER array, dimension (N)
	    The	permutation which separately sorts the two sub-problems	in D
	    into ascending order.  Note	that elements in the second half of
	    this permutation must first	have CUTPNT added to their values in
	    order to be	accurate.

     RHO    (input/output) DOUBLE PRECISION
	    On entry, the off-diagonal element associated with the rank-1 cut
	    which originally split the two submatrices which are now being
	    recombined.	 On exit, RHO has been modified	to the value required
	    by DLAED3.

	    CUTPNT (input) INTEGER The location	of the last eigenvalue in the
	    leading sub-matrix.	 min(1,N) <= CUTPNT <= N.

     Z	    (input) DOUBLE PRECISION array, dimension (N)
	    On entry, Z	contains the updating vector (the last row of the
	    first sub-eigenvector matrix and the first row of the second subeigenvector
	matrix).  On exit, the contents	of Z are destroyed by
	    the	updating process.

	    DLAMDA (output) DOUBLE PRECISION array, dimension (N) A copy of
	    the	first K	eigenvalues which will be used by DLAED3 to form the
	    secular equation.

     Q2	    (output) DOUBLE PRECISION array, dimension (LDQ2,N)
	    If ICOMPQ =	0, Q2 is not referenced.  Otherwise, a copy of the
	    first K eigenvectors which will be used by DLAED7 in a matrix
	    multiply (DGEMM) to	update the new eigenvectors.

     LDQ2   (input) INTEGER
	    The	leading	dimension of the array Q2.  LDQ2 >= max(1,N).

     W	    (output) DOUBLE PRECISION array, dimension (N)
	    The	first k	values of the final deflation-altered z-vector and
	    will be passed to DLAED3.

     PERM   (output) INTEGER array, dimension (N)
	    The	permutations (from deflation and sorting) to be	applied	to
	    each eigenblock.




									Page 2






DLAED8(3F)							    DLAED8(3F)



	    GIVPTR (output) INTEGER The	number of Givens rotations which took
	    place in this subproblem.

	    GIVCOL (output) INTEGER array, dimension (2, N) Each pair of
	    numbers indicates a	pair of	columns	to take	place in a Givens
	    rotation.

	    GIVNUM (output) DOUBLE PRECISION array, dimension (2, N) Each
	    number indicates the S value to be used in the corresponding
	    Givens rotation.

     INDXP  (workspace)	INTEGER	array, dimension (N)
	    The	permutation used to place deflated values of D at the end of
	    the	array.	INDXP(1:K) points to the nondeflated D-values
	    and	INDXP(K+1:N) points to the deflated eigenvalues.

     INDX   (workspace)	INTEGER	array, dimension (N)
	    The	permutation used to sort the contents of D into	ascending
	    order.

     INFO   (output) INTEGER
	    = 0:  successful exit.
	    < 0:  if INFO = -i,	the i-th argument had an illegal value.


									PPPPaaaaggggeeee 3333
[ Back ]
 Similar pages
Name OS Title
dlaeda IRIX compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS step
slaeda IRIX compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS step
comm Tru64 Compares two sorted files.
bsearch FreeBSD binary search of a sorted table
bsearch NetBSD binary search of a sorted table
bsearch IRIX binary search a sorted table
bsearch OpenBSD binary search of a sorted table
bsearch Linux binary search of a sorted array.
look Tru64 Finds lines in a sorted list
uniq Linux remove duplicate lines from a sorted file
Copyright © 2004-2005 DeniX Solutions SRL
newsletter delivery service