version 1.5, 2010/08/07 13:22:21
|
version 1.8, 2011/07/22 07:38:08
|
Line 1
|
Line 1
|
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 |
Line 18
|
Line 18
|
* |
* |
* 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 |
Line 95
|
Line 95
|
* |
* |
* 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), |
Line 108
|
Line 108
|
* |
* |
* 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), |
Line 117
|
Line 117
|
* 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: |