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Diff for /rpl/lapack/lapack/dsytd2.f between versions 1.7 and 1.8

version 1.7, 2010/12/21 13:53:39 version 1.8, 2011/07/22 07:38:11
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       SUBROUTINE DSYTD2( UPLO, N, A, LDA, D, E, TAU, INFO )        SUBROUTINE DSYTD2( UPLO, N, A, LDA, D, E, TAU, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- LAPACK 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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 *  =======  *  =======
 *  *
 *  DSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal  *  DSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal
 *  form T by an orthogonal similarity transformation: Q' * A * Q = T.  *  form T by an orthogonal similarity transformation: Q**T * A * Q = T.
 *  *
 *  Arguments  *  Arguments
 *  =========  *  =========
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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+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in  *  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
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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+2:n) is stored on exit in A(i+2:n,i),  *  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
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 *  *
          DO 10 I = N - 1, 1, -1           DO 10 I = N - 1, 1, -1
 *  *
 *           Generate elementary reflector H(i) = I - tau * v * v'  *           Generate elementary reflector H(i) = I - tau * v * v**T
 *           to annihilate A(1:i-1,i+1)  *           to annihilate A(1:i-1,i+1)
 *  *
             CALL DLARFG( I, A( I, I+1 ), A( 1, I+1 ), 1, TAUI )              CALL DLARFG( I, A( I, I+1 ), A( 1, I+1 ), 1, TAUI )
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                CALL DSYMV( UPLO, I, TAUI, A, LDA, A( 1, I+1 ), 1, ZERO,                 CALL DSYMV( UPLO, I, TAUI, A, LDA, A( 1, I+1 ), 1, ZERO,
      $                     TAU, 1 )       $                     TAU, 1 )
 *  *
 *              Compute  w := x - 1/2 * tau * (x'*v) * v  *              Compute  w := x - 1/2 * tau * (x**T * v) * v
 *  *
                ALPHA = -HALF*TAUI*DDOT( I, TAU, 1, A( 1, I+1 ), 1 )                 ALPHA = -HALF*TAUI*DDOT( I, TAU, 1, A( 1, I+1 ), 1 )
                CALL DAXPY( I, ALPHA, A( 1, I+1 ), 1, TAU, 1 )                 CALL DAXPY( I, ALPHA, A( 1, I+1 ), 1, TAU, 1 )
 *  *
 *              Apply the transformation as a rank-2 update:  *              Apply the transformation as a rank-2 update:
 *                 A := A - v * w' - w * v'  *                 A := A - v * w**T - w * v**T
 *  *
                CALL DSYR2( UPLO, I, -ONE, A( 1, I+1 ), 1, TAU, 1, A,                 CALL DSYR2( UPLO, I, -ONE, A( 1, I+1 ), 1, TAU, 1, A,
      $                     LDA )       $                     LDA )
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 *  *
          DO 20 I = 1, N - 1           DO 20 I = 1, N - 1
 *  *
 *           Generate elementary reflector H(i) = I - tau * v * v'  *           Generate elementary reflector H(i) = I - tau * v * v**T
 *           to annihilate A(i+2:n,i)  *           to annihilate A(i+2:n,i)
 *  *
             CALL DLARFG( N-I, A( I+1, I ), A( MIN( I+2, N ), I ), 1,              CALL DLARFG( N-I, A( I+1, I ), A( MIN( I+2, N ), I ), 1,
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                CALL DSYMV( UPLO, N-I, TAUI, A( I+1, I+1 ), LDA,                 CALL DSYMV( UPLO, N-I, TAUI, A( I+1, I+1 ), LDA,
      $                     A( I+1, I ), 1, ZERO, TAU( I ), 1 )       $                     A( I+1, I ), 1, ZERO, TAU( I ), 1 )
 *  *
 *              Compute  w := x - 1/2 * tau * (x'*v) * v  *              Compute  w := x - 1/2 * tau * (x**T * v) * v
 *  *
                ALPHA = -HALF*TAUI*DDOT( N-I, TAU( I ), 1, A( I+1, I ),                 ALPHA = -HALF*TAUI*DDOT( N-I, TAU( I ), 1, A( I+1, I ),
      $                 1 )       $                 1 )
                CALL DAXPY( N-I, ALPHA, A( I+1, I ), 1, TAU( I ), 1 )                 CALL DAXPY( N-I, ALPHA, A( I+1, I ), 1, TAU( I ), 1 )
 *  *
 *              Apply the transformation as a rank-2 update:  *              Apply the transformation as a rank-2 update:
 *                 A := A - v * w' - w * v'  *                 A := A - v * w**T - w * v**T
 *  *
                CALL DSYR2( UPLO, N-I, -ONE, A( I+1, I ), 1, TAU( I ), 1,                 CALL DSYR2( UPLO, N-I, -ONE, A( I+1, I ), 1, TAU( I ), 1,
      $                     A( I+1, I+1 ), LDA )       $                     A( I+1, I+1 ), LDA )
Removed from v.1.7  
changed lines
  Added in v.1.8

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