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Diff for /rpl/lapack/lapack/zlahr2.f between versions 1.7 and 1.8

version 1.7, 2010/12/21 13:53:49 version 1.8, 2011/07/22 07:38:17
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       SUBROUTINE ZLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )        SUBROUTINE ZLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
 *  *
 *  -- LAPACK auxiliary routine (version 3.2.1)                        --  *  -- 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..--
 *  -- April 2009                                                      --  *  -- April 2009                                                      --
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 *  ZLAHR2 reduces the first NB columns of A complex general n-BY-(n-k+1)  *  ZLAHR2 reduces the first NB columns of A complex general n-BY-(n-k+1)
 *  matrix A so that elements below the k-th subdiagonal are zero. The  *  matrix A so that elements below the k-th subdiagonal are zero. The
 *  reduction is performed by an unitary similarity transformation  *  reduction is performed by an unitary similarity transformation
 *  Q' * A * Q. The routine returns the matrices V and T which determine  *  Q**H * A * Q. The routine returns the matrices V and T which determine
 *  Q as a block reflector I - V*T*V', and also the matrix Y = A * V * T.  *  Q as a block reflector I - V*T*V**H, and also the matrix Y = A * V * T.
 *  *
 *  This is an auxiliary routine called by ZGEHRD.  *  This is an auxiliary routine called by ZGEHRD.
 *  *
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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**H
 *  *
 *  where tau is a complex scalar, and v is a complex vector with  *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in  *  v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
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 *  The elements of the vectors v together form the (n-k+1)-by-nb matrix  *  The elements of the vectors v together form the (n-k+1)-by-nb matrix
 *  V which is needed, with T and Y, to apply the transformation to the  *  V which is needed, with T and Y, to apply the transformation to the
 *  unreduced part of the matrix, using an update of the form:  *  unreduced part of the matrix, using an update of the form:
 *  A := (I - V*T*V') * (A - Y*V').  *  A := (I - V*T*V**H) * (A - Y*V**H).
 *  *
 *  The contents of A on exit are illustrated by the following example  *  The contents of A on exit are illustrated by the following example
 *  with n = 7, k = 3 and nb = 2:  *  with n = 7, k = 3 and nb = 2:
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 *  *
 *           Update A(K+1:N,I)  *           Update A(K+1:N,I)
 *  *
 *           Update I-th column of A - Y * V'  *           Update I-th column of A - Y * V**H
 *  *
             CALL ZLACGV( I-1, A( K+I-1, 1 ), LDA )               CALL ZLACGV( I-1, A( K+I-1, 1 ), LDA ) 
             CALL ZGEMV( 'NO TRANSPOSE', N-K, I-1, -ONE, Y(K+1,1), LDY,              CALL ZGEMV( 'NO TRANSPOSE', N-K, I-1, -ONE, Y(K+1,1), LDY,
      $                  A( K+I-1, 1 ), LDA, ONE, A( K+1, I ), 1 )       $                  A( K+I-1, 1 ), LDA, ONE, A( K+1, I ), 1 )
             CALL ZLACGV( I-1, A( K+I-1, 1 ), LDA )               CALL ZLACGV( I-1, A( K+I-1, 1 ), LDA ) 
 *  *
 *           Apply I - V * T' * V' to this column (call it b) from the  *           Apply I - V * T**H * V**H to this column (call it b) from the
 *           left, using the last column of T as workspace  *           left, using the last column of T as workspace
 *  *
 *           Let  V = ( V1 )   and   b = ( b1 )   (first I-1 rows)  *           Let  V = ( V1 )   and   b = ( b1 )   (first I-1 rows)
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 *  *
 *           where V1 is unit lower triangular  *           where V1 is unit lower triangular
 *  *
 *           w := V1' * b1  *           w := V1**H * b1
 *  *
             CALL ZCOPY( I-1, A( K+1, I ), 1, T( 1, NB ), 1 )              CALL ZCOPY( I-1, A( K+1, I ), 1, T( 1, NB ), 1 )
             CALL ZTRMV( 'Lower', 'Conjugate transpose', 'UNIT',               CALL ZTRMV( 'Lower', 'Conjugate transpose', 'UNIT', 
      $                  I-1, A( K+1, 1 ),       $                  I-1, A( K+1, 1 ),
      $                  LDA, T( 1, NB ), 1 )       $                  LDA, T( 1, NB ), 1 )
 *  *
 *           w := w + V2'*b2  *           w := w + V2**H * b2
 *  *
             CALL ZGEMV( 'Conjugate transpose', N-K-I+1, I-1,               CALL ZGEMV( 'Conjugate transpose', N-K-I+1, I-1, 
      $                  ONE, A( K+I, 1 ),       $                  ONE, A( K+I, 1 ),
      $                  LDA, A( K+I, I ), 1, ONE, T( 1, NB ), 1 )       $                  LDA, A( K+I, I ), 1, ONE, T( 1, NB ), 1 )
 *  *
 *           w := T'*w  *           w := T**H * w
 *  *
             CALL ZTRMV( 'Upper', 'Conjugate transpose', 'NON-UNIT',               CALL ZTRMV( 'Upper', 'Conjugate transpose', 'NON-UNIT', 
      $                  I-1, T, LDT,       $                  I-1, T, LDT,
Removed from v.1.7  
changed lines
  Added in v.1.8

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