--- rpl/lapack/lapack/dptcon.f 2010/08/07 13:22:24 1.5 +++ rpl/lapack/lapack/dptcon.f 2011/11/21 22:19:38 1.10 @@ -1,9 +1,127 @@ +*> \brief \b DPTCON +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DPTCON + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DPTCON( N, D, E, ANORM, RCOND, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, N +* DOUBLE PRECISION ANORM, RCOND +* .. +* .. Array Arguments .. +* DOUBLE PRECISION D( * ), E( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DPTCON computes the reciprocal of the condition number (in the +*> 1-norm) of a real symmetric positive definite tridiagonal matrix +*> using the factorization A = L*D*L**T or A = U**T*D*U computed by +*> DPTTRF. +*> +*> 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))). +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> The n diagonal elements of the diagonal matrix D from the +*> factorization of A, as computed by DPTTRF. +*> \endverbatim +*> +*> \param[in] E +*> \verbatim +*> E is DOUBLE PRECISION 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 DPTTRF. +*> \endverbatim +*> +*> \param[in] ANORM +*> \verbatim +*> ANORM is DOUBLE PRECISION +*> The 1-norm of the original matrix A. +*> \endverbatim +*> +*> \param[out] RCOND +*> \verbatim +*> RCOND is DOUBLE PRECISION +*> The reciprocal of the condition number of the matrix A, +*> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the +*> 1-norm of inv(A) computed in this routine. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleOTHERcomputational +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The method used is described in Nicholas J. Higham, "Efficient +*> Algorithms for Computing the Condition Number of a Tridiagonal +*> Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986. +*> \endverbatim +*> +* ===================================================================== SUBROUTINE DPTCON( N, D, E, ANORM, RCOND, WORK, INFO ) * -* -- LAPACK routine (version 3.2) -- +* -- LAPACK computational routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* November 2011 * * .. Scalar Arguments .. INTEGER INFO, N @@ -13,53 +131,6 @@ DOUBLE PRECISION D( * ), E( * ), WORK( * ) * .. * -* Purpose -* ======= -* -* DPTCON computes the reciprocal of the condition number (in the -* 1-norm) of a real symmetric positive definite tridiagonal matrix -* using the factorization A = L*D*L**T or A = U**T*D*U computed by -* DPTTRF. -* -* 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))). -* -* Arguments -* ========= -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* D (input) DOUBLE PRECISION array, dimension (N) -* The n diagonal elements of the diagonal matrix D from the -* factorization of A, as computed by DPTTRF. -* -* E (input) DOUBLE PRECISION 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 DPTTRF. -* -* ANORM (input) DOUBLE PRECISION -* The 1-norm of the original matrix A. -* -* RCOND (output) DOUBLE PRECISION -* The reciprocal of the condition number of the matrix A, -* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the -* 1-norm of inv(A) computed in this routine. -* -* WORK (workspace) DOUBLE PRECISION array, dimension (N) -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* -* Further Details -* =============== -* -* The method used is described in Nicholas J. Higham, "Efficient -* Algorithms for Computing the Condition Number of a Tridiagonal -* Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986. -* * ===================================================================== * * .. Parameters .. @@ -117,7 +188,7 @@ * m(i,j) = abs(A(i,j)), i = j, * m(i,j) = -abs(A(i,j)), i .ne. j, * -* and e = [ 1, 1, ..., 1 ]'. Note M(A) = M(L)*D*M(L)'. +* and e = [ 1, 1, ..., 1 ]**T. Note M(A) = M(L)*D*M(L)**T. * * Solve M(L) * x = e. * @@ -126,7 +197,7 @@ WORK( I ) = ONE + WORK( I-1 )*ABS( E( I-1 ) ) 20 CONTINUE * -* Solve D * M(L)' * x = b. +* Solve D * M(L)**T * x = b. * WORK( N ) = WORK( N ) / D( N ) DO 30 I = N - 1, 1, -1