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Diff for /rpl/lapack/lapack/dlatrd.f between versions 1.7 and 1.8

version 1.7, 2010/12/21 13:53:34 version 1.8, 2011/07/22 07:38:08
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       SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW )        SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW )
 *  *
 *  -- LAPACK auxiliary routine (version 3.2) --  *  -- LAPACK auxiliary routine (version 3.3.1) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  *  -- April 2011                                                      --
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          UPLO        CHARACTER          UPLO
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 *  *
 *  DLATRD reduces NB rows and columns of a real symmetric matrix A to  *  DLATRD reduces NB rows and columns of a real symmetric matrix A to
 *  symmetric tridiagonal form by an orthogonal similarity  *  symmetric tridiagonal form by an orthogonal similarity
 *  transformation Q' * A * Q, and returns the matrices V and W which are  *  transformation Q**T * A * Q, and returns the matrices V and W which are
 *  needed to apply the transformation to the unreduced part of A.  *  needed to apply the transformation to the unreduced part of A.
 *  *
 *  If UPLO = 'U', DLATRD reduces the last NB rows and columns of a  *  If UPLO = 'U', DLATRD reduces the last NB rows and columns of a
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 *  *
 *  Each H(i) has the form  *  Each H(i) has the form
 *  *
 *     H(i) = I - tau * v * v'  *     H(i) = I - tau * v * v**T
 *  *
 *  where tau is a real scalar, and v is a real vector with  *  where tau is a real scalar, and v is a real vector with
 *  v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),  *  v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
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 *  *
 *  Each H(i) has the form  *  Each H(i) has the form
 *  *
 *     H(i) = I - tau * v * v'  *     H(i) = I - tau * v * v**T
 *  *
 *  where tau is a real scalar, and v is a real vector with  *  where tau is a real scalar, and v is a real vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),  *  v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
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 *  The elements of the vectors v together form the n-by-nb matrix V  *  The elements of the vectors v together form the n-by-nb matrix V
 *  which is needed, with W, to apply the transformation to the unreduced  *  which is needed, with W, to apply the transformation to the unreduced
 *  part of the matrix, using a symmetric rank-2k update of the form:  *  part of the matrix, using a symmetric rank-2k update of the form:
 *  A := A - V*W' - W*V'.  *  A := A - V*W**T - W*V**T.
 *  *
 *  The contents of A on exit are illustrated by the following examples  *  The contents of A on exit are illustrated by the following examples
 *  with n = 5 and nb = 2:  *  with n = 5 and nb = 2:
Removed from v.1.7  
changed lines
  Added in v.1.8

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