.TH "SRC/zhpgvx.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/zhpgvx.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBzhpgvx\fP (itype, jobz, range, uplo, n, ap, bp, vl, vu, il, iu, abstol, m, w, z, ldz, work, rwork, iwork, ifail, info)" .br .RI "\fBZHPGVX\fP " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine zhpgvx (integer itype, character jobz, character range, character uplo, integer n, complex*16, dimension( * ) ap, complex*16, dimension( * ) bp, double precision vl, double precision vu, integer il, integer iu, double precision abstol, integer m, double precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)" .PP \fBZHPGVX\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZHPGVX computes selected eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x\&. Here A and B are assumed to be Hermitian, stored in packed format, and B is also positive definite\&. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIITYPE\fP .PP .nf ITYPE is INTEGER Specifies the problem type to be solved: = 1: A*x = (lambda)*B*x = 2: A*B*x = (lambda)*x = 3: B*A*x = (lambda)*x .fi .PP .br \fIJOBZ\fP .PP .nf JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors\&. .fi .PP .br \fIRANGE\fP .PP .nf RANGE is CHARACTER*1 = 'A': all eigenvalues will be found; = 'V': all eigenvalues in the half-open interval (VL,VU] will be found; = 'I': the IL-th through IU-th eigenvalues will be found\&. .fi .PP .br \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrices A and B\&. N >= 0\&. .fi .PP .br \fIAP\fP .PP .nf AP is COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array\&. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n\&. On exit, the contents of AP are destroyed\&. .fi .PP .br \fIBP\fP .PP .nf BP is COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix B, packed columnwise in a linear array\&. The j-th column of B is stored in the array BP as follows: if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n\&. On exit, the triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H, in the same storage format as B\&. .fi .PP .br \fIVL\fP .PP .nf VL is DOUBLE PRECISION If RANGE='V', the lower bound of the interval to be searched for eigenvalues\&. VL < VU\&. Not referenced if RANGE = 'A' or 'I'\&. .fi .PP .br \fIVU\fP .PP .nf VU is DOUBLE PRECISION If RANGE='V', the upper bound of the interval to be searched for eigenvalues\&. VL < VU\&. Not referenced if RANGE = 'A' or 'I'\&. .fi .PP .br \fIIL\fP .PP .nf IL is INTEGER If RANGE='I', the index of the smallest eigenvalue 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'\&. .fi .PP .br \fIIU\fP .PP .nf IU is INTEGER If RANGE='I', the index of the largest eigenvalue 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'\&. .fi .PP .br \fIABSTOL\fP .PP .nf 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 1-norm 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')\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The total number of eigenvalues found\&. 0 <= M <= N\&. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1\&. .fi .PP .br \fIW\fP .PP .nf W is DOUBLE PRECISION array, dimension (N) On normal exit, the first M elements contain the selected eigenvalues in ascending order\&. .fi .PP .br \fIZ\fP .PP .nf Z is COMPLEX*16 array, dimension (LDZ, N) If JOBZ = 'N', then Z is not referenced\&. If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i)\&. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I\&. If an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL\&. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = 'V', the exact value of M is not known in advance and an upper bound must be used\&. .fi .PP .br \fILDZ\fP .PP .nf LDZ is INTEGER The leading dimension of the array Z\&. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (2*N) .fi .PP .br \fIRWORK\fP .PP .nf RWORK is DOUBLE PRECISION array, dimension (7*N) .fi .PP .br \fIIWORK\fP .PP .nf IWORK is INTEGER array, dimension (5*N) .fi .PP .br \fIIFAIL\fP .PP .nf 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\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: ZPPTRF or ZHPEVX returned an error code: <= N: if INFO = i, ZHPEVX failed to converge; i eigenvectors failed to converge\&. Their indices are stored in array IFAIL\&. > N: if INFO = N + i, for 1 <= i <= n, then the leading principal minor of order i of B is not positive\&. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 Mark Fahey, Department of Mathematics, Univ\&. of Kentucky, USA .RE .PP .PP Definition at line \fB274\fP of file \fBzhpgvx\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.