version 1.1.1.1, 2010/01/26 15:22:45
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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 ) |