CPTCON(1) LAPACK routine (version 3.2) CPTCON(1)[top]NAMECPTCON - computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRFSYNOPSISSUBROUTINE CPTCON( N, D, E, ANORM, RCOND, RWORK, INFO ) INTEGER INFO, N REAL ANORM, RCOND REAL D( * ), RWORK( * ) COMPLEX E( * )PURPOSECPTCON computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF. Norm(inv(A)) is computed by a direct method, and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).ARGUMENTSN (input) INTEGER The order of the matrix A. N >= 0. D (input) REAL array, dimension (N) The n diagonal elements of the diagonal matrix D from the fac‐ torization of A, as computed by CPTTRF. E (input) COMPLEX array, dimension (N-1) The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization of A, as computed by CPTTRF. ANORM (input) REAL The 1-norm of the original matrix A. RCOND (output) REAL The reciprocal of the condition number of the matrix A, com‐ puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is the 1-norm of inv(A) computed in this routine. RWORK (workspace) REAL array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value-iFURTHER DETAILSThe method used is described in Nicholas J. Higham, "Efficient Algo‐ rithms for Computing the Condition Number of a Tridiagonal Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986. LAPACK routine (version 3.2) November 2008 CPTCON(1)

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