version 1.2, 2010/04/21 13:45:35
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version 1.8, 2011/07/22 07:38:17
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$ PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA, |
$ PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA, |
$ R, ISUPPZ, NRMINV, RESID, RQCORR, WORK ) |
$ 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, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* -- April 2011 -- |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
LOGICAL WANTNC |
LOGICAL WANTNC |
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* |
* |
* ZLAR1V computes the (scaled) r-th column of the inverse of |
* ZLAR1V computes the (scaled) r-th column of the inverse of |
* the sumbmatrix in rows B1 through BN of the tridiagonal matrix |
* 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 |
* computed vector is an accurate eigenvector. Usually, r corresponds |
* to the index where the eigenvector is largest in magnitude. |
* to the index where the eigenvector is largest in magnitude. |
* The following steps accomplish this computation : |
* The following steps accomplish this computation : |
* (a) Stationary qd transform, L D L^T - sigma I = L(+) D(+) L(+)^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, |
* (b) Progressive qd transform, L D L**T - sigma I = U(-) D(-) U(-)**T, |
* (c) Computation of the diagonal elements of the inverse of |
* (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) |
* r as the index where the diagonal of the inverse is (one of the) |
* largest in magnitude. |
* largest in magnitude. |
* (d) Computation of the (scaled) r-th column of the inverse using the |
* (d) Computation of the (scaled) r-th column of the inverse using the |
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* ========= |
* ========= |
* |
* |
* N (input) INTEGER |
* N (input) INTEGER |
* The order of the matrix L D L^T. |
* The order of the matrix L D L**T. |
* |
* |
* B1 (input) INTEGER |
* 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 |
* 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 |
* LAMBDA (input) DOUBLE PRECISION |
* The shift. In order to compute an accurate eigenvector, |
* The shift. In order to compute an accurate eigenvector, |
* LAMBDA should be a good approximation to an eigenvalue |
* 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) |
* L (input) DOUBLE PRECISION array, dimension (N-1) |
* The (n-1) subdiagonal elements of the unit bidiagonal matrix |
* The (n-1) subdiagonal elements of the unit bidiagonal matrix |
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* |
* |
* NEGCNT (output) INTEGER |
* NEGCNT (output) INTEGER |
* If WANTNC is .TRUE. then NEGCNT = the number of pivots < pivmin |
* 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 |
* ZTZ (output) DOUBLE PRECISION |
* The square of the 2-norm of Z. |
* The square of the 2-norm of Z. |
* |
* |
* MINGMA (output) DOUBLE PRECISION |
* MINGMA (output) DOUBLE PRECISION |
* The reciprocal of the largest (in magnitude) diagonal |
* 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 |
* R (input/output) INTEGER |
* The twist index for the twisted factorization used to |
* The twist index for the twisted factorization used to |
* compute Z. |
* compute Z. |
* On input, 0 <= R <= N. If R is input as 0, R is set to |
* 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. |
* in magnitude. If 1 <= R <= N, R is unchanged. |
* On output, R contains the twist index used to compute Z. |
* On output, R contains the twist index used to compute Z. |
* Ideally, R designates the position of the maximum entry in the |
* Ideally, R designates the position of the maximum entry in the |