
NAMEzhbgvx.f SYNOPSISFunctions/Subroutinessubroutine zhbgvx (JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO) Function/Subroutine Documentationsubroutine zhbgvx (characterJOBZ, characterRANGE, characterUPLO, integerN, integerKA, integerKB, complex*16, dimension( ldab, * )AB, integerLDAB, complex*16, dimension( ldbb, * )BB, integerLDBB, complex*16, dimension( ldq, * )Q, integerLDQ, double precisionVL, double precisionVU, integerIL, integerIU, double precisionABSTOL, integerM, double precision, dimension( * )W, complex*16, dimension( ldz, * )Z, integerLDZ, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integer, dimension( * )IWORK, integer, dimension( * )IFAIL, integerINFO)ZHBGST Purpose:ZHBGVX 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. Eigenvalues and eigenvectors can be selected by specifying either all eigenvalues, a range of values or a range of indices for the desired eigenvalues. JOBZ
Author:
JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors.RANGE RANGE is CHARACTER*1 = 'A': all eigenvalues will be found; = 'V': all eigenvalues in the halfopen interval (VL,VU] will be found; = 'I': the ILth through IUth eigenvalues will be found.UPLO UPLO is CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored.N N is INTEGER The order of the matrices A and B. N >= 0.KA KA is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0.KB KB is INTEGER The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KB >= 0.AB AB is 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 = 'U', AB(ka+1+ij,j) = A(i,j) for max(1,jka)<=i<=j; if UPLO = 'L', AB(1+ij,j) = A(i,j) for j<=i<=min(n,j+ka). On exit, the contents of AB are destroyed.LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KA+1.BB BB is 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 = 'U', BB(kb+1+ij,j) = B(i,j) for max(1,jkb)<=i<=j; if UPLO = 'L', 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 LDBB is INTEGER The leading dimension of the array BB. LDBB >= KB+1.Q Q is COMPLEX*16 array, dimension (LDQ, N) If JOBZ = 'V', the nbyn matrix used in the reduction of A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x, and consequently C to tridiagonal form. If JOBZ = 'N', the array Q is not referenced.LDQ LDQ is INTEGER The leading dimension of the array Q. If JOBZ = 'N', LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N).VL VL is DOUBLE PRECISIONVU VU is DOUBLE PRECISION If RANGE='V', the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'.IL IL is INTEGERIU IU is INTEGER If RANGE='I', the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'.ABSTOL ABSTOL is DOUBLE PRECISION The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( a,b ) , where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*T will be used in its place, where T is the 1norm of the tridiagonal matrix obtained by reducing AP to tridiagonal form. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*DLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*DLAMCH('S').M M is INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IUIL+1.W W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order.Z Z is COMPLEX*16 array, dimension (LDZ, N) If JOBZ = 'V', 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 = 'N', then Z is not referenced.LDZ LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= N.WORK WORK is COMPLEX*16 array, dimension (N)RWORK RWORK is DOUBLE PRECISION array, dimension (7*N)IWORK IWORK is INTEGER array, dimension (5*N)IFAIL IFAIL is INTEGER array, dimension (N) If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = 'N', then IFAIL is not referenced.INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value > 0: if INFO = i, and i is: <= N: then i eigenvectors failed to converge. Their indices are stored in array IFAIL. > 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. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Contributors:
Mark Fahey, Department of Mathematics, Univ. of Kentucky,
USA
Definition at line 290 of file zhbgvx.f.
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