chbevd-f(3)

chbevd.f –

Synopsis

Functions/Subroutines

subroutine chbevd (JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Function/Subroutine Documentation

subroutine chbevd (characterJOBZ, characterUPLO, integerN, integerKD, complex, dimension( ldab, * )AB, integerLDAB, real, dimension( * )W, complex, dimension( ldz, * )Z, integerLDZ, complex, dimension( * )WORK, integerLWORK, real, dimension( * )RWORK, integerLRWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)

CHBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

 CHBEVD computes all the eigenvalues and, optionally, eigenvectors of
 a complex Hermitian band matrix A. If eigenvectors are desired, it
 uses a divide and conquer algorithm.
 The divide and conquer algorithm 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.

Parameters:

JOBZ

 JOBZ is CHARACTER*1
 = 'N': Compute eigenvalues only;
 = 'V': Compute eigenvalues and eigenvectors.

UPLO

 UPLO is CHARACTER*1
 = 'U': Upper triangle of A is stored;
 = 'L': Lower triangle of A is stored.

 N is INTEGER
 The order of the matrix A. N >= 0.

 KD is INTEGER
 The number of superdiagonals of the matrix A if UPLO = 'U',
 or the number of subdiagonals if UPLO = 'L'. KD >= 0.

 AB is COMPLEX array, dimension (LDAB, N)
 On entry, the upper or lower triangle of the Hermitian band
 matrix A, stored in the first KD+1 rows of the array. The
 j-th column of A is stored in the j-th column of the array AB
 as follows:
 if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
 if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
 On exit, AB is overwritten by values generated during the
 reduction to tridiagonal form. If UPLO = 'U', the first
 superdiagonal and the diagonal of the tridiagonal matrix T
 are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
 the diagonal and first subdiagonal of T are returned in the
 first two rows of AB.

LDAB

 LDAB is INTEGER
 The leading dimension of the array AB. LDAB >= KD + 1.

 W is REAL array, dimension (N)
 If INFO = 0, the eigenvalues in ascending order.

 Z is COMPLEX array, dimension (LDZ, N)
 If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
 eigenvectors of the matrix A, with the i-th column of Z
 holding the eigenvector associated with W(i).
 If JOBZ = 'N', then Z is not referenced.

LDZ

 LDZ is INTEGER
 The leading dimension of the array Z. LDZ >= 1, and if
 JOBZ = 'V', 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 N <= 1, LWORK must be at least 1.
 If JOBZ = 'N' and N > 1, LWORK must be at least N.
 If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2.
 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 (LRWORK)
 On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

LRWORK

 LRWORK is INTEGER
 The dimension of array RWORK.
 If N <= 1, LRWORK must be at least 1.
 If JOBZ = 'N' and N > 1, LRWORK must be at least N.
 If JOBZ = 'V' and N > 1, LRWORK must be at least
 1 + 5*N + 2*N**2.
 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 array IWORK.
 If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
 If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N .
 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: if INFO = i, the algorithm failed to converge; i
 off-diagonal elements of an intermediate tridiagonal
 form did not converge to zero.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 215 of file chbevd.f.

Author

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