dsbtrd.f man page

subroutine dsbtrd (VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
DSBTRD

DSBTRD  

Purpose:

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

Parameters:

VECT

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

UPLO

          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

KD

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

AB

          AB is DOUBLE PRECISION 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

          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.

D

          D is DOUBLE PRECISION array, dimension (N)
          The diagonal elements of the tridiagonal matrix T.

E

          E is DOUBLE PRECISION 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

          Q is DOUBLE PRECISION 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

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

WORK

          WORK is DOUBLE PRECISION array, dimension (N)

INFO

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

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details:

  Modified by Linda Kaufman, Bell Labs.

Definition at line 163 of file dsbtrd.f.