LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  dspgvx (ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO) 
DSPGST 
subroutine dspgvx  (  integer  ITYPE, 
character  JOBZ,  
character  RANGE,  
character  UPLO,  
integer  N,  
double precision, dimension( * )  AP,  
double precision, dimension( * )  BP,  
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  
) 
DSPGST
Download DSPGVX + dependencies [TGZ] [ZIP] [TXT]DSPGVX computes selected eigenvalues, and optionally, eigenvectors of a real generalized symmetricdefinite 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 symmetric, stored in packed storage, 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.
[in]  ITYPE  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 
[in]  JOBZ  JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. 
[in]  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. 
[in]  UPLO  UPLO is CHARACTER*1 = 'U': Upper triangle of A and B are stored; = 'L': Lower triangle of A and B are stored. 
[in]  N  N is INTEGER The order of the matrix pencil (A,B). N >= 0. 
[in,out]  AP  AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The jth column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j1)*(2*nj)/2) = A(i,j) for j<=i<=n. On exit, the contents of AP are destroyed. 
[in,out]  BP  BP is DOUBLE PRECISION array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix B, packed columnwise in a linear array. The jth column of B is stored in the array BP as follows: if UPLO = 'U', BP(i + (j1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i + (j1)*(2*nj)/2) = B(i,j) for j<=i<=n. On exit, the triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T, in the same storage format as B. 
[in]  VL  VL is DOUBLE PRECISION 
[in]  VU  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'. 
[in]  IL  IL is INTEGER 
[in]  IU  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'. 
[in]  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 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'). 
[out]  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. 
[out]  W  W is DOUBLE PRECISION array, dimension (N) On normal exit, the first M elements contain the selected eigenvalues in ascending order. 
[out]  Z  Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M)) 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 ith column of Z holding the eigenvector associated with W(i). The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3, Z**T*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. 
[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 (8*N) 
[out]  IWORK  IWORK is INTEGER array, dimension (5*N) 
[out]  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. 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value > 0: DPPTRF or DSPEVX returned an error code: <= N: if INFO = i, DSPEVX 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 minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. 
Definition at line 262 of file dspgvx.f.