dsbgv dsbgvd dsbgvx dspgv dspgvd dspgvx dsygv dsygvd dsygvx

dsbgvx() void dsbgvx ( char  jobz, char  range, char  uplo, int  n, int  ka, int  kb, int  ldab, double  ab[], int  ldbb, double  bb[], int  ldq, double  q[], double  vl, double  vu, int  il, int  iu, double  abstol, int *  m, double  w[], int  ldz, double  z[], double  work[], int  iwork[], int  ifail[], int *  info  ) (Expert driver) Generalized eigenvalue problem of symmetric band matrices Purpose This routine 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. Parameters [in] jobz = 'N': Compute eigenvalues only. = 'V': Compute eigenvalues and eigenvectors. [in] range = '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. [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] ka Number of super-diagonals of the matrix A if uplo='U' or the number of sub-diagonals if uplo = 'L'. (ka >= 0) [in] kb Number of super-diagonals of the matrix B if uplo='U' or the number of sub-diagonals if uplo = 'L'. (kb >= 0) [in] ldab Leading dimension of the two dimensional array ab[][]. (ldab >= ka + 1) [in,out] ab[][] Array ab[lab][ldab] (lab >= n) [in] The upper or lower triangle of the symmetric band matrix A, stored in the first ka+1 columns of the array. The j-th column of A is stored in the j-th row of the array ab as follows. uplo = 'U': ab[j][ka + i - j] = Aij for max(0, j - ka - 1) <= i <= j <= n - 1. uplo = 'L': ab[j][i - j] = Aij for 0 <= j <= i <= min(n - 1, j + ka - 1). [out] The contents of ab[][] are destroyed. [in] ldbb Leading dimension of the two dimensional array bb[][]. (ldbb >= kb + 1) [in,out] bb[][] Array bb[lbb][ldbb] (lbb >= n) [in] The upper or lower triangle of the symmetric positive definite band matrix B, stored in the first kb+1 columns of the array. The j-th column of B is stored in the j-th row of the array bb as follows. uplo = 'U': bb[j][kb + i - j] = Bij for max(0, j - kb - 1) <= i <= j <= n - 1. uplo = 'L': bb[j][i - j] = Bij for 0 <= j <= i <= min(n - 1, j + kb - 1). [out] The factor S from the split Cholesky factorization B = S^T*S, as returned by dpbstf. [in] ldq Leading dimension of the two dimensional array q[][]. (ldq >= 1 if jobz = 'N', ldq >= max(1, n) if jobz = 'V') [out] q[][] Array q[lq][ldq] (lq >= n) jobz = 'V': The n x 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. jobz = 'N': The array q[][] is not referenced. [in] vl range = 'V': The lower bound of the interval to be searched for eigenvalues. (vl < vu) range = 'A' or 'I': Not referenced. [in] vu range = 'V': The upper bound of the interval to be searched for eigenvalues. (vl < vu) range = 'A' or 'I': Not referenced. [in] il 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) range = 'A' or 'V': Not referenced. [in] iu range = 'I': The index of the largest eigenvalues to be returned. (1 <= il <= iu <= n, if n > 0; il = 1 and iu = 0 if n = 0) range = 'A' or 'V': Not referenced. [in] abstol 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'). [out] m The total number of eigenvalues found. (0 <= m <= n) If range = 'A', m = n, and if range = 'I', m = iu - il + 1. [out] w[] Array w[lw] (lw >= n) On normal exit, the first m elements contain the selected 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 >= max(1, m)) jobz = 'V': 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 so that Z^T*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[]. jobz = 'N': z[][] is not referenced. 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. [out] work[] Array work[lwork] (lwork >= 7*n) Work array. [out] iwork[] Array iwork[liwork] (liwork >= 5*n) Integer work array. [out] ifail[] Array ifail[lifail] (lifail >= n) jobz = 'V': 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. jobz = 'N': ifail[] is not referenced. [out] info = 0: Successful exit = -1: The argument jobz had an illegal value (jobz != 'V' nor 'N') = -2: The argument range had an illegal value (range != 'A', 'V' nor 'I') = -3: The argument uplo had an illegal value (uplo != 'U' nor 'L') = -4: The argument n had an illegal value (n < 0) = -5: The argument ka had an illegal value (ka < 0) = -6: The argument kb had an illegal value (kb < 0 or kb > ka) = -7: The argument ldab had an illegal value (ldab < ka + 1) = -9: The argument ldbb had an illegal value (ldbb < kb + 1) = -11: The argument ldq had an illegal value (ldq too small) = -14: The argument vu had an illegal value (vu <= vl) = -15: The argument il had an illegal value (il < 1 or il > n) = -16: The argument iu had an illegal value (iu < min(n, il) or iu > n) = -20: The argument ldz had an illegal value (ldz too small) = i (0 < i <= n): i eigenvectors failed to converge. Their indices are stored in ifail[]. = i (i > n): dpbstf returned info = i-n; 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