dsbgv dsbgvd dsbgvx dspgv dspgvd dspgvx dsygv dsygvd dsygvx

dspgvd() void dspgvd ( int  itype, char  jobz, char  uplo, int  n, double  ap[], double  bp[], double  w[], int  ldz, double  z[], double  work[], int  lwork, int  iwork[], int  liwork, int *  info  ) (Divide and conquer driver) Generalized eigenvalue problem of symmetric matrices in packed form Purpose This routine computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-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 symmetric, stored in packed form, and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm. Parameters [in] itype 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 = 'N': Compute eigenvalues only. = 'V': Compute eigenvalues and eigenvectors. [in] uplo = 'U': Upper triangles of A and B are stored. = 'L': Lower triangles of A and B are stored. [in] n Order of the matrices A and B. (n >= 0) (If n = 0, returns without computation) [in,out] ap[] Array ap[lap] (lap >= n(n + 1)/2) [in] The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array ap[] as follows. uplo = 'U': ap[i + j*(j + 1)/2] = Aij for 0 <= i <= j <= n - 1. uplo = 'L': ap[(i + j*(2*n - j - 1)/2] = Aij for 0 <= j < = i <= n - 1. [out] The contents of ap[] are destroyed. [in,out] bp[] Array bp[lbp] (lbp >= n(n + 1)/2) [in] The upper or lower triangle of the symmetric positive definite matrix B, packed columnwise in a linear array. The j-th column of B is stored in the array bp[] as follows. uplo = 'U': bp[i + j*(j + 1)/2] = Bij for 0 <= i <= j <= n - 1. uplo = 'L': bp[(i + j*(2*n - j - 1)/2] = Bij for 0 <= j < = i <= n - 1. [out] 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. [out] w[] Array w[lw] (lw >= n) If info = 0, the eigenvalues in ascending order. [in] ldz Leading dimension of the two dimensional array z[][]. (ldz >= 1 if jobz = 'N', ldz >= max(1, n) if jobz = 'V') [out] z[][] Array z[lz][ldz] (lz >= n) jobz = 'V': If info = 0, z[][] contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows:   itype = 1 or 2: Z^T*B*Z = I   itype = 3: Z^T*inv(B)*Z = I jobz = 'N': z[][] is not referenced. [out] work[] Array work[lwork] Work array. On exit, if info = 0, work[0] returns the optimal lwork. [in] lwork The size of work[]. (lwork >= 1 (if n <= 1), 2*n (if jobz = 'N'), 2*n^2 + 6*n + 1 (if jobz = 'V')) If lwork = -1, then a workspace query is assumed. The routine only calculates the optimal size of the work[] and iwork[] arrays, and returns these values in work[0] and iwork[0]. [out] iwork[] Array iwork[liwork] Integer work array. On exit, if info = 0, iwork[0] returns the optimal liwork. [in] liwork The size of iwork[]. (liwork >= 1 (if n <= 1), 1 (if jobz = 'N'), 5*n + 3 (if jobz = 'V')) If liwork = -1, then a workspace query is assumed. The routine only calculates the optimal size of the work[] and iwork[] arrays, and returns these values in work[0] and iwork[0]. [out] info = 0: Successful exit = -1: The argument itype had an illegal value (itype < 1 or itype > 3) = -2: The argument jobz had an illegal value (jobz != 'V' nor 'N') = -3: The argument uplo had an illegal value (uplo != 'U' nor 'L') = -4: The argument n had an illegal value (n < 0) = -8: The argument ldz had an illegal value (ldz too small) = -11: The argument lwork had an illegal value (lwork too small) = -13: The argument liwork had an illegal value (liwork too small) = i (0 < i <= n): dspevd failed to converge. i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. = i (n < i <= 2n): The leading minor of order i-n of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. Reference LAPACK