version 1.5, 2010/08/07 13:22:13
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version 1.8, 2011/07/22 07:38:04
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SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) |
SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2.1) -- |
* -- 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..-- |
* -- April 2009 -- |
* -- April 2009 -- |
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* ======= |
* ======= |
* |
* |
* DGEHRD reduces a real general matrix A to upper Hessenberg form H by |
* DGEHRD reduces a real general matrix A to upper Hessenberg form H by |
* an orthogonal similarity transformation: Q' * A * Q = H . |
* an orthogonal similarity transformation: Q**T * A * Q = H . |
* |
* |
* 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(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on |
* v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on |
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IB = MIN( NB, IHI-I ) |
IB = MIN( NB, IHI-I ) |
* |
* |
* Reduce columns i:i+ib-1 to Hessenberg form, returning the |
* Reduce columns i:i+ib-1 to Hessenberg form, returning the |
* matrices V and T of the block reflector H = I - V*T*V' |
* matrices V and T of the block reflector H = I - V*T*V**T |
* which performs the reduction, and also the matrix Y = A*V*T |
* which performs the reduction, and also the matrix Y = A*V*T |
* |
* |
CALL DLAHR2( IHI, I, IB, A( 1, I ), LDA, TAU( I ), T, LDT, |
CALL DLAHR2( IHI, I, IB, A( 1, I ), LDA, TAU( I ), T, LDT, |
$ WORK, LDWORK ) |
$ WORK, LDWORK ) |
* |
* |
* Apply the block reflector H to A(1:ihi,i+ib:ihi) from the |
* Apply the block reflector H to A(1:ihi,i+ib:ihi) from the |
* right, computing A := A - Y * V'. V(i+ib,ib-1) must be set |
* right, computing A := A - Y * V**T. V(i+ib,ib-1) must be set |
* to 1 |
* to 1 |
* |
* |
EI = A( I+IB, I+IB-1 ) |
EI = A( I+IB, I+IB-1 ) |