version 1.3, 2010/08/06 15:28:54
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version 1.8, 2011/07/22 07:38:15
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SUBROUTINE ZHETD2( UPLO, N, A, LDA, D, E, TAU, INFO ) |
SUBROUTINE ZHETD2( 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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* |
* |
* ZHETD2 reduces a complex Hermitian matrix A to real symmetric |
* ZHETD2 reduces a complex Hermitian matrix A to real symmetric |
* tridiagonal form T by a unitary similarity transformation: |
* tridiagonal form T by a unitary similarity transformation: |
* Q' * A * Q = T. |
* Q**H * 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**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+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**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+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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* Test the input parameters |
* Test the input parameters |
* |
* |
INFO = 0 |
INFO = 0 |
UPPER = LSAME( UPLO, 'U' ) |
UPPER = LSAME( UPLO, 'U') |
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN |
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN |
INFO = -1 |
INFO = -1 |
ELSE IF( N.LT.0 ) THEN |
ELSE IF( N.LT.0 ) THEN |
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A( N, N ) = DBLE( A( N, N ) ) |
A( N, N ) = DBLE( A( N, N ) ) |
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**H |
* to annihilate A(1:i-1,i+1) |
* to annihilate A(1:i-1,i+1) |
* |
* |
ALPHA = A( I, I+1 ) |
ALPHA = A( I, I+1 ) |
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CALL ZHEMV( UPLO, I, TAUI, A, LDA, A( 1, I+1 ), 1, ZERO, |
CALL ZHEMV( 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**H * v) * v |
* |
* |
ALPHA = -HALF*TAUI*ZDOTC( I, TAU, 1, A( 1, I+1 ), 1 ) |
ALPHA = -HALF*TAUI*ZDOTC( I, TAU, 1, A( 1, I+1 ), 1 ) |
CALL ZAXPY( I, ALPHA, A( 1, I+1 ), 1, TAU, 1 ) |
CALL ZAXPY( 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**H - w * v**H |
* |
* |
CALL ZHER2( UPLO, I, -ONE, A( 1, I+1 ), 1, TAU, 1, A, |
CALL ZHER2( UPLO, I, -ONE, A( 1, I+1 ), 1, TAU, 1, A, |
$ LDA ) |
$ LDA ) |
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A( 1, 1 ) = DBLE( A( 1, 1 ) ) |
A( 1, 1 ) = DBLE( A( 1, 1 ) ) |
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**H |
* to annihilate A(i+2:n,i) |
* to annihilate A(i+2:n,i) |
* |
* |
ALPHA = A( I+1, I ) |
ALPHA = A( I+1, I ) |
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CALL ZHEMV( UPLO, N-I, TAUI, A( I+1, I+1 ), LDA, |
CALL ZHEMV( 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**H * v) * v |
* |
* |
ALPHA = -HALF*TAUI*ZDOTC( N-I, TAU( I ), 1, A( I+1, I ), |
ALPHA = -HALF*TAUI*ZDOTC( N-I, TAU( I ), 1, A( I+1, I ), |
$ 1 ) |
$ 1 ) |
CALL ZAXPY( N-I, ALPHA, A( I+1, I ), 1, TAU( I ), 1 ) |
CALL ZAXPY( 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**H - w * v**H |
* |
* |
CALL ZHER2( UPLO, N-I, -ONE, A( I+1, I ), 1, TAU( I ), 1, |
CALL ZHER2( UPLO, N-I, -ONE, A( I+1, I ), 1, TAU( I ), 1, |
$ A( I+1, I+1 ), LDA ) |
$ A( I+1, I+1 ), LDA ) |