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cstedc-f(3)

cstedc.f –

Synopsis

Functions/Subroutines

subroutine cstedc (COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CSTEDC

Function/Subroutine Documentation

subroutine cstedc (characterCOMPZ, integerN, real, dimension( * )D, real, dimension( * )E, complex, dimension( ldz, * )Z, integerLDZ, complex, dimension( * )WORK, integerLWORK, real, dimension( * )RWORK, integerLRWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)

CSTEDC

Purpose:

 CSTEDC computes all eigenvalues and, optionally, eigenvectors of a
 symmetric tridiagonal matrix using the divide and conquer method.
 The eigenvectors of a full or band complex Hermitian matrix can also
 be found if CHETRD or CHPTRD or CHBTRD has been used to reduce this
 matrix to tridiagonal form.
 This code makes very mild assumptions about floating point
 arithmetic. It will work on machines with a guard digit in
 add/subtract, or on those binary machines without guard digits
 which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
 It could conceivably fail on hexadecimal or decimal machines
 without guard digits, but we know of none. See SLAED3 for details.

 

Parameters:

COMPZ

 COMPZ is CHARACTER*1
 = 'N': Compute eigenvalues only.
 = 'I': Compute eigenvectors of tridiagonal matrix also.
 = 'V': Compute eigenvectors of original Hermitian matrix
 also. On entry, Z contains the unitary matrix used
 to reduce the original matrix to tridiagonal form.

N

 N is INTEGER
 The dimension of the symmetric tridiagonal matrix. N >= 0.

D

 D is REAL array, dimension (N)
 On entry, the diagonal elements of the tridiagonal matrix.
 On exit, if INFO = 0, the eigenvalues in ascending order.

E

 E is REAL array, dimension (N-1)
 On entry, the subdiagonal elements of the tridiagonal matrix.
 On exit, E has been destroyed.

Z

 Z is COMPLEX array, dimension (LDZ,N)
 On entry, if COMPZ = 'V', then Z contains the unitary
 matrix used in the reduction to tridiagonal form.
 On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
 orthonormal eigenvectors of the original Hermitian matrix,
 and if COMPZ = 'I', Z contains the orthonormal eigenvectors
 of the symmetric tridiagonal matrix.
 If COMPZ = 'N', then Z is not referenced.

LDZ

 LDZ is INTEGER
 The leading dimension of the array Z. LDZ >= 1.
 If eigenvectors are desired, then LDZ >= max(1,N).

WORK

 WORK is COMPLEX array, dimension (MAX(1,LWORK))
 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

 LWORK is INTEGER
 The dimension of the array WORK.
 If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1.
 If COMPZ = 'V' and N > 1, LWORK must be at least N*N.
 Note that for COMPZ = 'V', then if N is less than or
 equal to the minimum divide size, usually 25, then LWORK need
 only be 1.
 If LWORK = -1, then a workspace query is assumed; the routine
 only calculates the optimal sizes of the WORK, RWORK and
 IWORK arrays, returns these values as the first entries of
 the WORK, RWORK and IWORK arrays, and no error message
 related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK

 RWORK is REAL array, dimension (MAX(1,LRWORK))
 On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

LRWORK

 LRWORK is INTEGER
 The dimension of the array RWORK.
 If COMPZ = 'N' or N <= 1, LRWORK must be at least 1.
 If COMPZ = 'V' and N > 1, LRWORK must be at least
 1 + 3*N + 2*N*lg N + 4*N**2 ,
 where lg( N ) = smallest integer k such
 that 2**k >= N.
 If COMPZ = 'I' and N > 1, LRWORK must be at least
 1 + 4*N + 2*N**2 .
 Note that for COMPZ = 'I' or 'V', then if N is less than or
 equal to the minimum divide size, usually 25, then LRWORK
 need only be max(1,2*(N-1)).
 If LRWORK = -1, then a workspace query is assumed; the
 routine only calculates the optimal sizes of the WORK, RWORK
 and IWORK arrays, returns these values as the first entries
 of the WORK, RWORK and IWORK arrays, and no error message
 related to LWORK or LRWORK or LIWORK is issued by XERBLA.

IWORK

 IWORK is INTEGER array, dimension (MAX(1,LIWORK))
 On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

 LIWORK is INTEGER
 The dimension of the array IWORK.
 If COMPZ = 'N' or N <= 1, LIWORK must be at least 1.
 If COMPZ = 'V' or N > 1, LIWORK must be at least
 6 + 6*N + 5*N*lg N.
 If COMPZ = 'I' or N > 1, LIWORK must be at least
 3 + 5*N .
 Note that for COMPZ = 'I' or 'V', then if N is less than or
 equal to the minimum divide size, usually 25, then LIWORK
 need only be 1.
 If LIWORK = -1, then a workspace query is assumed; the
 routine only calculates the optimal sizes of the WORK, RWORK
 and IWORK arrays, returns these values as the first entries
 of the WORK, RWORK and IWORK arrays, and no error message
 related to LWORK or LRWORK or LIWORK is issued by XERBLA.

INFO

 INFO is INTEGER
 = 0: successful exit.
 < 0: if INFO = -i, the i-th argument had an illegal value.
 > 0: The algorithm failed to compute an eigenvalue while
 working on the submatrix lying in rows and columns
 INFO/(N+1) through mod(INFO,N+1).

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 212 of file cstedc.f.

Author

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