version 1.7, 2010/12/21 13:53:52
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version 1.8, 2011/07/22 07:38:18
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SUBROUTINE ZLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) |
SUBROUTINE ZLATRD( 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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* |
* |
* ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to |
* ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to |
* Hermitian tridiagonal form by a unitary similarity |
* Hermitian tridiagonal form by a unitary similarity |
* transformation Q' * A * Q, and returns the matrices V and W which are |
* transformation Q**H * 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', ZLATRD reduces the last NB rows and columns of a |
* If UPLO = 'U', ZLATRD 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**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(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**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) = 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 Hermitian rank-2k update of the form: |
* part of the matrix, using a Hermitian rank-2k update of the form: |
* A := A - V*W' - W*V'. |
* A := A - V*W**H - W*V**H. |
* |
* |
* 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: |