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Class org.netlib.lapack.DSYTRD

java.lang.Object
   |
   +----org.netlib.lapack.DSYTRD

public class DSYTRD

extends Object

DSYTRD is a simplified interface to the JLAPACK routine dsytrd.
This interface converts Java-style 2D row-major arrays into
the 1D column-major linearized arrays expected by the lower
level JLAPACK routines.  Using this interface also allows you
to omit offset and leading dimension arguments.  However, because
of these conversions, these routines will be slower than the low
level ones.  Following is the description from the original Fortran
source.  Contact seymour@cs.utk.edu with any questions.

 *     ..
 *
 *  Purpose
 *  =======
 *
 *  DSYTRD reduces a real symmetric matrix A to real symmetric
 *  tridiagonal form T by an orthogonal similarity transformation:
 *  Q**T * A * Q = T.
 *
 *  Arguments
 *  =========
 *
 *  UPLO    (input) CHARACTER*1
 *          = 'U':  Upper triangle of A is stored;
 *          = 'L':  Lower triangle of A is stored.
 *
 *  N       (input) INTEGER
 *          The order of the matrix A.  N >= 0.
 *
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
 *          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
 *          N-by-N upper triangular part of A contains the upper
 *          triangular part of the matrix A, and the strictly lower
 *          triangular part of A is not referenced.  If UPLO = 'L', the
 *          leading N-by-N lower triangular part of A contains the lower
 *          triangular part of the matrix A, and the strictly upper
 *          triangular part of A is not referenced.
 *          On exit, if UPLO = 'U', the diagonal and first superdiagonal
 *          of A are overwritten by the corresponding elements of the
 *          tridiagonal matrix T, and the elements above the first
 *          superdiagonal, with the array TAU, represent the orthogonal
 *          matrix Q as a product of elementary reflectors; if UPLO
 *          = 'L', the diagonal and first subdiagonal of A are over-
 *          written by the corresponding elements of the tridiagonal
 *          matrix T, and the elements below the first subdiagonal, with
 *          the array TAU, represent the orthogonal matrix Q as a product
 *          of elementary reflectors. See Further Details.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
 *
 *  D       (output) DOUBLE PRECISION array, dimension (N)
 *          The diagonal elements of the tridiagonal matrix T:
 *          D(i) = A(i,i).
 *
 *  E       (output) DOUBLE PRECISION array, dimension (N-1)
 *          The off-diagonal elements of the tridiagonal matrix T:
 *          E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
 *
 *  TAU     (output) DOUBLE PRECISION array, dimension (N-1)
 *          The scalar factors of the elementary reflectors (see Further
 *          Details).
 *
 *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 *
 *  LWORK   (input) INTEGER
 *          The dimension of the array WORK.  LWORK >= 1.
 *          For optimum performance LWORK >= N*NB, where NB is the
 *          optimal blocksize.
 *
 *  INFO    (output) INTEGER
 *          = 0:  successful exit
 *          < 0:  if INFO = -i, the i-th argument had an illegal value
 *
 *  Further Details
 *  ===============
 *
 *  If UPLO = 'U', the matrix Q is represented as a product of elementary
 *  reflectors
 *
 *     Q = H(n-1) . . . H(2) H(1).
 *
 *  Each H(i) has the form
 *
 *     H(i) = I - tau * v * v'
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
 *  A(1:i-1,i+1), and tau in TAU(i).
 *
 *  If UPLO = 'L', the matrix Q is represented as a product of elementary
 *  reflectors
 *
 *     Q = H(1) H(2) . . . H(n-1).
 *
 *  Each H(i) has the form
 *
 *     H(i) = I - tau * v * v'
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
 *  and tau in TAU(i).
 *
 *  The contents of A on exit are illustrated by the following examples
 *  with n = 5:
 *
 *  if UPLO = 'U':                       if UPLO = 'L':
 *
 *    (  d   e   v2  v3  v4 )              (  d                  )
 *    (      d   e   v3  v4 )              (  e   d              )
 *    (          d   e   v4 )              (  v1  e   d          )
 *    (              d   e  )              (  v1  v2  e   d      )
 *    (                  d  )              (  v1  v2  v3  e   d  )
 *
 *  where d and e denote diagonal and off-diagonal elements of T, and vi
 *  denotes an element of the vector defining H(i).
 *
 *  =====================================================================
 *
 *     .. Parameters ..

DSYTRD()

DSYTRD(String, int, double[][], double[], double[], double[], double[], int, intW)

 public DSYTRD()

 public static void DSYTRD(String uplo,
                           int n,
                           double a[][],
                           double d[],
                           double e[],
                           double tau[],
                           double work[],
                           int lwork,
                           intW info)

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