LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  dsbgvd (JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO) 
DSBGST 
subroutine dsbgvd  (  character  JOBZ, 
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( * )  W,  
double precision, dimension( ldz, * )  Z,  
integer  LDZ,  
double precision, dimension( * )  WORK,  
integer  LWORK,  
integer, dimension( * )  IWORK,  
integer  LIWORK,  
integer  INFO  
) 
DSBGST
Download DSBGVD + dependencies [TGZ] [ZIP] [TXT]DSBGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite 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. 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.
[in]  JOBZ  JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. 
[in]  UPLO  UPLO is CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored. 
[in]  N  N is INTEGER The order of the matrices A and B. N >= 0. 
[in]  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. 
[in]  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. 
[in,out]  AB  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 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. 
[in]  LDAB  LDAB is INTEGER The leading dimension of the array AB. LDAB >= KA+1. 
[in,out]  BB  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 jth column of B is stored in the jth column of the array BB as follows: if UPLO = 'U', BB(ka+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**T*S, as returned by DPBSTF. 
[in]  LDBB  LDBB is INTEGER The leading dimension of the array BB. LDBB >= KB+1. 
[out]  W  W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. 
[out]  Z  Z is DOUBLE PRECISION 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 Z**T*B*Z = I. If JOBZ = 'N', then Z is not referenced. 
[in]  LDZ  LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). 
[out]  WORK  WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 
[in]  LWORK  LWORK is INTEGER The dimension of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= 3*N. If JOBZ = 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2. If LWORK = 1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. 
[out]  IWORK  IWORK is INTEGER array, dimension (MAX(1,LIWORK)) On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK. 
[in]  LIWORK  LIWORK is INTEGER The dimension of the array IWORK. If JOBZ = 'N' or N <= 1, LIWORK >= 1. If JOBZ = 'V' 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 and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. 
[out]  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: 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 DPBSTF returned INFO = i: B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. 
Definition at line 227 of file dsbgvd.f.