CLAR1V man page on IRIX

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CLAR1V(3S)							    CLAR1V(3S)

NAME
     CLAR1V - compute 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

SYNOPSIS
     SUBROUTINE CLAR1V( N, B1, BN, SIGMA, D, L, LD, LLD, GERSCH, Z, ZTZ,
			MINGMA, R, ISUPPZ, WORK )

	 INTEGER	B1, BN, N, R

	 REAL		MINGMA, SIGMA, ZTZ

	 INTEGER	ISUPPZ( * )

	 REAL		D( * ), GERSCH( * ), L( * ), LD( * ), LLD( * ), WORK(
			* )

	 COMPLEX	Z( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     CLAR1V 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. 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, (c) Computation of the
     diagonal elements of the inverse of
	 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
	 twisted factorization obtained by combining the top part of the
	 the stationary and the bottom part of the progressive transform.

ARGUMENTS
     N	      (input) INTEGER
	      The order of the matrix L D L^T.

									Page 1

CLAR1V(3S)							    CLAR1V(3S)

     B1	      (input) INTEGER
	      First index of the submatrix of L D L^T.

     BN	      (input) INTEGER
	      Last index of the submatrix of L D L^T.

     SIGMA    (input) REAL
	      The shift. Initially, when R = 0, SIGMA should be a good
	      approximation to an eigenvalue of L D L^T.

     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)
	      The n diagonal elements of the diagonal matrix D.

     LD	      (input) REAL array, dimension (N-1)
	      The n-1 elements L(i)*D(i).

     LLD      (input) REAL array, dimension (N-1)
	      The n-1 elements L(i)*L(i)*D(i).

     GERSCH   (input) REAL array, dimension (2*N)
	      The n Gerschgorin intervals. These are used to restrict the
	      initial search for R, when R is input as 0.

     Z	      (output) COMPLEX array, dimension (N)
	      The (scaled) r-th column of the inverse. Z(R) is returned to be
	      1.

     ZTZ      (output) REAL
	      The square of the norm of Z.

     MINGMA   (output) REAL
	      The reciprocal of the largest (in magnitude) diagonal element of
	      the inverse of L D L^T - sigma I.

     R	      (input/output) INTEGER
	      Initially, R should be input to be 0 and is then output as the
	      index where the diagonal element of the inverse is largest in
	      magnitude. In later iterations, this same value of R should be
	      input.

     ISUPPZ   (output) INTEGER array, dimension (2)
	      The support of the vector in Z, i.e., the vector Z is nonzero
	      only in elements ISUPPZ(1) through ISUPPZ( 2 ).

     WORK     (workspace) REAL array, dimension (4*N)

									Page 2

CLAR1V(3S)							    CLAR1V(3S)

FURTHER DETAILS
     Based on contributions by
	Inderjit Dhillon, IBM Almaden, USA
	Osni Marques, LBNL/NERSC, USA
	Ken Stanley, Computer Science Division, University of
	  California at Berkeley, USA

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.

									Page 3

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