Ddisna Dopgtr Dopmtr Dorgtr Dormtr Dpteqr Dsbtrd Dsptrd Dstebz Dstedc Dstein Dstemr Dsteqr Dsterf Dsytrd

Ddisna() Sub Ddisna ( Job As  String, M As  Long, N As  Long, D() As  Double, Sep() As  Double, Info As  Long  ) Condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix, or for the singular vectors of a general matrix Purpose This routine computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m x n matrix. The reciprocal condition number is the 'gap' between the corresponding eigenvalue or singular value and the nearest other one. The bound on the error, measured by angle in radians, in the I-th computed vector is given by Dlamch("E") * (anorm/sep(i)) where anorm = 2-norm(A) = max(abs(D(j))). sep(i) is not allowed to be smaller than Dlamch("E")*anorm in order to limit the size of the error bound. Ddisna may also be used to compute error bounds for eigenvectors of the generalized symmetric definite eigenproblem. Parameters [in] Job Specifies for which problem the reciprocal condition numbers should be computed. = "E": The eigenvectors of a symmetric/Hermitian matrix. = "L": The left singular vectors of a general matrix. = "R": The right singular vectors of a general matrix. [in] M Number of rows of the matrix. (M >= 0) (If M = 0, returns without computation) [in] N job = "L" or "R": Number of columns of the matrix. (N >= 0) (If N = 0, returns without computation) job = "E": To be ignored. [in] D() Array D(LD - 1) (LD >= M if Job = "E", LD >= min(M, N) if Job = "L" or "R") Job = "E": The eigenvalues of the matrix in either increasing or decreasing order. Job = "L" or "R": The singular values of the matrix in either increasing or decreasing order. (Singular values >= 0) [out] Sep() Array Spe(LSep - 1) (LSep >= M if Job = "E", LSep >= min(M, N) if Job = "L" or "R") Job = "E": The reciprocal condition numbers of the eigenvectors. Job = "L" or "R": The reciprocal condition numbers of the singular vectors. [out] Info = 0: Successful exit. = -1: The argument Job had an illegal value. (Job <> "E", "L" nor "R") = -2: The argument M had an illegal value. (M < 0) = -3: The argument N had an illegal value. (N < 0) = -4: The argument D() is invalid. = -5: The argument Sep() is invalid. Reference LAPACK