diff options
Diffstat (limited to 'SRC/slar1v.f')
| -rw-r--r-- | SRC/slar1v.f | 50 |
1 files changed, 25 insertions, 25 deletions
diff --git a/SRC/slar1v.f b/SRC/slar1v.f index 19287c6d..1c059ed0 100644 --- a/SRC/slar1v.f +++ b/SRC/slar1v.f @@ -25,14 +25,14 @@ * * SLAR1V 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 @@ -43,40 +43,40 @@ * ========= * * 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) REAL +* LAMBDA (input) REAL * 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) REAL array, dimension (N-1) +* L (input) REAL array, dimension (N-1) * The (n-1) subdiagonal elements of the unit bidiagonal matrix * L, in elements 1 to N-1. * -* D (input) REAL array, dimension (N) +* D (input) REAL array, dimension (N) * The n diagonal elements of the diagonal matrix D. * -* LD (input) REAL array, dimension (N-1) +* LD (input) REAL array, dimension (N-1) * The n-1 elements L(i)*D(i). * -* LLD (input) REAL array, dimension (N-1) +* LLD (input) REAL array, dimension (N-1) * The n-1 elements L(i)*L(i)*D(i). * -* PIVMIN (input) REAL +* PIVMIN (input) REAL * The minimum pivot in the Sturm sequence. * -* GAPTOL (input) REAL +* GAPTOL (input) REAL * Tolerance that indicates when eigenvector entries are negligible * w.r.t. their contribution to the residual. * -* Z (input/output) REAL array, dimension (N) +* Z (input/output) REAL array, dimension (N) * On input, all entries of Z must be set to 0. * On output, Z contains the (scaled) r-th column of the * inverse. The scaling is such that Z(R) equals 1. @@ -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) REAL +* ZTZ (output) REAL * The square of the 2-norm of Z. * -* MINGMA (output) REAL +* MINGMA (output) REAL * 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 @@ -109,18 +109,18 @@ * The support of the vector in Z, i.e., the vector Z is * nonzero only in elements ISUPPZ(1) through ISUPPZ( 2 ). * -* NRMINV (output) REAL +* NRMINV (output) REAL * NRMINV = 1/SQRT( ZTZ ) * -* RESID (output) REAL +* RESID (output) REAL * The residual of the FP vector. * RESID = ABS( MINGMA )/SQRT( ZTZ ) * -* RQCORR (output) REAL +* RQCORR (output) REAL * The Rayleigh Quotient correction to LAMBDA. * RQCORR = MINGMA*TMP * -* WORK (workspace) REAL array, dimension (4*N) +* WORK (workspace) REAL array, dimension (4*N) * * Further Details * =============== |