--- rpl/lapack/lapack/zlar1v.f 2010/12/21 13:53:51 1.7 +++ rpl/lapack/lapack/zlar1v.f 2011/07/22 07:38:17 1.8 @@ -2,10 +2,10 @@ $ PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA, $ R, ISUPPZ, NRMINV, RESID, RQCORR, WORK ) * -* -- LAPACK auxiliary routine (version 3.2) -- +* -- LAPACK auxiliary routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* -- April 2011 -- * * .. Scalar Arguments .. LOGICAL WANTNC @@ -25,14 +25,14 @@ * * ZLAR1V computes the (scaled) r-th column of the inverse of * the sumbmatrix in rows B1 through BN of the tridiagonal matrix -* L D L^T - sigma I. When sigma is close to an eigenvalue, the +* L D L**T - sigma I. When sigma is close to an eigenvalue, the * computed vector is an accurate eigenvector. Usually, r corresponds * to the index where the eigenvector is largest in magnitude. * The following steps accomplish this computation : -* (a) Stationary qd transform, L D L^T - sigma I = L(+) D(+) L(+)^T, -* (b) Progressive qd transform, L D L^T - sigma I = U(-) D(-) U(-)^T, +* (a) Stationary qd transform, L D L**T - sigma I = L(+) D(+) L(+)**T, +* (b) Progressive qd transform, L D L**T - sigma I = U(-) D(-) U(-)**T, * (c) Computation of the diagonal elements of the inverse of -* L D L^T - sigma I by combining the above transforms, and choosing +* L D L**T - sigma I by combining the above transforms, and choosing * r as the index where the diagonal of the inverse is (one of the) * largest in magnitude. * (d) Computation of the (scaled) r-th column of the inverse using the @@ -43,18 +43,18 @@ * ========= * * N (input) INTEGER -* The order of the matrix L D L^T. +* The order of the matrix L D L**T. * * B1 (input) INTEGER -* First index of the submatrix of L D L^T. +* First index of the submatrix of L D L**T. * * BN (input) INTEGER -* Last index of the submatrix of L D L^T. +* Last index of the submatrix of L D L**T. * * LAMBDA (input) DOUBLE PRECISION * The shift. In order to compute an accurate eigenvector, * LAMBDA should be a good approximation to an eigenvalue -* of L D L^T. +* of L D L**T. * * L (input) DOUBLE PRECISION array, dimension (N-1) * The (n-1) subdiagonal elements of the unit bidiagonal matrix @@ -86,20 +86,20 @@ * * NEGCNT (output) INTEGER * If WANTNC is .TRUE. then NEGCNT = the number of pivots < pivmin -* in the matrix factorization L D L^T, and NEGCNT = -1 otherwise. +* in the matrix factorization L D L**T, and NEGCNT = -1 otherwise. * * ZTZ (output) DOUBLE PRECISION * The square of the 2-norm of Z. * * MINGMA (output) DOUBLE PRECISION * The reciprocal of the largest (in magnitude) diagonal -* element of the inverse of L D L^T - sigma I. +* element of the inverse of L D L**T - sigma I. * * R (input/output) INTEGER * The twist index for the twisted factorization used to * compute Z. * On input, 0 <= R <= N. If R is input as 0, R is set to -* the index where (L D L^T - sigma I)^{-1} is largest +* the index where (L D L**T - sigma I)^{-1} is largest * in magnitude. If 1 <= R <= N, R is unchanged. * On output, R contains the twist index used to compute Z. * Ideally, R designates the position of the maximum entry in the