.TH "SRC/dsbgvx.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/dsbgvx.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBdsbgvx\fP (jobz, range, uplo, n, ka, kb, ab, ldab, bb, ldbb, q, ldq, vl, vu, il, iu, abstol, m, w, z, ldz, work, iwork, ifail, info)" .br .RI "\fBDSBGVX\fP " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine dsbgvx (character jobz, character range, character uplo, integer n, integer ka, integer kb, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldbb, * ) bb, integer ldbb, double precision, dimension( ldq, * ) q, integer ldq, double precision vl, double precision vu, integer il, integer iu, double precision abstol, integer m, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)" .PP \fBDSBGVX\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DSBGVX computes selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x\&. Here A and B are assumed to be symmetric 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \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 \fIKA\fP .PP .nf KA is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'\&. KA >= 0\&. .fi .PP .br \fIKB\fP .PP .nf KB is INTEGER The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'\&. KB >= 0\&. .fi .PP .br \fIAB\fP .PP .nf AB is DOUBLE PRECISION array, dimension (LDAB, N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka)\&. On exit, the contents of AB are destroyed\&. .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KA+1\&. .fi .PP .br \fIBB\fP .PP .nf BB is DOUBLE PRECISION array, dimension (LDBB, N) On entry, the upper or lower triangle of the symmetric band matrix B, stored in the first kb+1 rows of the array\&. The j-th column of B is stored in the j-th column of the array BB as follows: if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb)\&. On exit, the factor S from the split Cholesky factorization B = S**T*S, as returned by DPBSTF\&. .fi .PP .br \fILDBB\fP .PP .nf LDBB is INTEGER The leading dimension of the array BB\&. LDBB >= KB+1\&. .fi .PP .br \fIQ\fP .PP .nf Q is DOUBLE PRECISION array, dimension (LDQ, N) If JOBZ = 'V', the n-by-n 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\&. .fi .PP .br \fILDQ\fP .PP .nf LDQ is INTEGER The leading dimension of the array Q\&. If JOBZ = 'N', LDQ >= 1\&. If JOBZ = 'V', LDQ >= max(1,N)\&. .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 A 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) If INFO = 0, the eigenvalues in ascending order\&. .fi .PP .br \fIZ\fP .PP .nf Z is DOUBLE PRECISION array, dimension (LDZ, N) If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of eigenvectors, with the i-th column of Z holding the eigenvector associated with W(i)\&. The eigenvectors are normalized so Z**T*B*Z = I\&. If JOBZ = 'N', then Z is not referenced\&. .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 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 (M) 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 eigenvalues 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 <= N: if INFO = i, then i eigenvectors failed to converge\&. Their indices are stored in IFAIL\&. > N: DPBSTF returned an error code; i\&.e\&., 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 \fB291\fP of file \fBdsbgvx\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.