zhbgvd (l)  Linux Manuals
zhbgvd: computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitiandefinite banded eigenproblem, of the form A*x=(lambda)*B*x
NAME
ZHBGVD  computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitiandefinite banded eigenproblem, of the form A*x=(lambda)*B*xSYNOPSIS
 SUBROUTINE ZHBGVD(
 JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
 CHARACTER JOBZ, UPLO
 INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LRWORK, LWORK, N
 INTEGER IWORK( * )
 DOUBLE PRECISION RWORK( * ), W( * )
 COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ), Z( LDZ, * )
PURPOSE
ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitiandefinite banded eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian and banded, and B is also positive definite. 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 XMP, Cray YMP, Cray C90, or Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
ARGUMENTS
 JOBZ (input) CHARACTER*1

= aqNaq: Compute eigenvalues only;
= aqVaq: Compute eigenvalues and eigenvectors.  UPLO (input) CHARACTER*1

= aqUaq: Upper triangles of A and B are stored;
= aqLaq: Lower triangles of A and B are stored.  N (input) INTEGER
 The order of the matrices A and B. N >= 0.
 KA (input) INTEGER
 The number of superdiagonals of the matrix A if UPLO = aqUaq, or the number of subdiagonals if UPLO = aqLaq. KA >= 0.
 KB (input) INTEGER
 The number of superdiagonals of the matrix B if UPLO = aqUaq, or the number of subdiagonals if UPLO = aqLaq. KB >= 0.
 AB (input/output) COMPLEX*16 array, dimension (LDAB, N)
 On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first ka+1 rows of the array. The jth column of A is stored in the jth column of the array AB as follows: if UPLO = aqUaq, AB(ka+1+ij,j) = A(i,j) for max(1,jka)<=i<=j; if UPLO = aqLaq, AB(1+ij,j) = A(i,j) for j<=i<=min(n,j+ka). On exit, the contents of AB are destroyed.
 LDAB (input) INTEGER
 The leading dimension of the array AB. LDAB >= KA+1.
 BB (input/output) COMPLEX*16 array, dimension (LDBB, N)
 On entry, the upper or lower triangle of the Hermitian band matrix B, stored in the first kb+1 rows of the array. The jth column of B is stored in the jth column of the array BB as follows: if UPLO = aqUaq, BB(kb+1+ij,j) = B(i,j) for max(1,jkb)<=i<=j; if UPLO = aqLaq, BB(1+ij,j) = B(i,j) for j<=i<=min(n,j+kb). On exit, the factor S from the split Cholesky factorization B = S**H*S, as returned by ZPBSTF.
 LDBB (input) INTEGER
 The leading dimension of the array BB. LDBB >= KB+1.
 W (output) DOUBLE PRECISION array, dimension (N)
 If INFO = 0, the eigenvalues in ascending order.
 Z (output) COMPLEX*16 array, dimension (LDZ, N)
 If JOBZ = aqVaq, then if INFO = 0, Z contains the matrix Z of eigenvectors, with the ith column of Z holding the eigenvector associated with W(i). The eigenvectors are normalized so that Z**H*B*Z = I. If JOBZ = aqNaq, then Z is not referenced.
 LDZ (input) INTEGER
 The leading dimension of the array Z. LDZ >= 1, and if JOBZ = aqVaq, LDZ >= N.
 WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
 On exit, if INFO=0, WORK(1) returns the optimal LWORK.
 LWORK (input) INTEGER
 The dimension of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = aqNaq and N > 1, LWORK >= N. If JOBZ = aqVaq and N > 1, LWORK >= 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 (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
 On exit, if INFO=0, RWORK(1) returns the optimal LRWORK.
 LRWORK (input) INTEGER
 The dimension of array RWORK. If N <= 1, LRWORK >= 1. If JOBZ = aqNaq and N > 1, LRWORK >= N. If JOBZ = aqVaq and N > 1, LRWORK >= 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 (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
 On exit, if INFO=0, IWORK(1) returns the optimal LIWORK.
 LIWORK (input) INTEGER
 The dimension of array IWORK. If JOBZ = aqNaq or N <= 1, LIWORK >= 1. If JOBZ = aqVaq and N > 1, LIWORK >= 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 (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: if INFO = i, and i is:
<= N: the algorithm failed to converge: i offdiagonal elements of an intermediate tridiagonal form did not converge to zero; > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
returned INFO = i: B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.
FURTHER DETAILS
Based on contributions byMark Fahey, Department of Mathematics, Univ. of Kentucky, USA