ssbtrd(3S)

NAME
     SSBTRD - reduce a real symmetric band matrix A to symmetric tridiagonal
     form T by an orthogonal similarity transformation

SYNOPSIS
     SUBROUTINE SSBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO
                        )

         CHARACTER      UPLO, VECT

         INTEGER        INFO, KD, LDAB, LDQ, N

         REAL           AB( LDAB, * ), D( * ), E( * ), Q( LDQ, * ), WORK( * )

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
     SSBTRD reduces a real symmetric band matrix A to symmetric tridiagonal
     form T by an orthogonal similarity transformation: Q**T * A * Q = T.


ARGUMENTS
     VECT    (input) CHARACTER*1
             = 'N':  do not form Q;
             = 'V':  form Q;
             = 'U':  update a matrix X, by forming X*Q.

     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.

     KD      (input) INTEGER
             The number of superdiagonals of the matrix A if UPLO = 'U', or
             the number of subdiagonals if UPLO = 'L'.  KD >= 0.

     AB      (input/output) REAL array, dimension (LDAB,N)
             On entry, the upper or lower triangle of the symmetric band
             matrix A, stored in the first KD+1 rows of the array.  The j-th
             column of A is stored in the j-th column of the array AB as
             follows:  if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-
             kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for
             j<=i<=min(n,j+kd).  On exit, the diagonal elements of AB are
             overwritten by the diagonal elements of the tridiagonal matrix T;
             if KD > 0, the elements on the first superdiagonal (if UPLO =
             'U') or the first subdiagonal (if UPLO = 'L') are overwritten by
             the off-diagonal elements of T; the rest of AB is overwritten by
             values generated during the reduction.

     LDAB    (input) INTEGER
             The leading dimension of the array AB.  LDAB >= KD+1.

     D       (output) REAL array, dimension (N)
             The diagonal elements of the tridiagonal matrix T.

     E       (output) REAL array, dimension (N-1)
             The off-diagonal elements of the tridiagonal matrix T:  E(i) =
             T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.

     Q       (input/output) REAL array, dimension (LDQ,N)
             On entry, if VECT = 'U', then Q must contain an N-by-N matrix X;
             if VECT = 'N' or 'V', then Q need not be set.

             On exit:  if VECT = 'V', Q contains the N-by-N orthogonal matrix
             Q; if VECT = 'U', Q contains the product X*Q; if VECT = 'N', the
             array Q is not referenced.

     LDQ     (input) INTEGER
             The leading dimension of the array Q.  LDQ >= 1, and LDQ >= N if
             VECT = 'V' or 'U'.

     WORK    (workspace) REAL array, dimension (N)

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value

FURTHER DETAILS
     Modified by Linda Kaufman, Bell Labs.


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

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