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259 lines
6.7 KiB
259 lines
6.7 KiB
2 years ago
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*> \brief \b SLAGSY
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, K, LDA, N
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* ..
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* .. Array Arguments ..
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* INTEGER ISEED( 4 )
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* REAL A( LDA, * ), D( * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SLAGSY generates a real symmetric matrix A, by pre- and post-
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*> multiplying a real diagonal matrix D with a random orthogonal matrix:
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*> A = U*D*U'. The semi-bandwidth may then be reduced to k by additional
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*> orthogonal transformations.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] K
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*> \verbatim
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*> K is INTEGER
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*> The number of nonzero subdiagonals within the band of A.
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*> 0 <= K <= N-1.
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*> \endverbatim
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*>
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*> \param[in] D
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*> \verbatim
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*> D is REAL array, dimension (N)
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*> The diagonal elements of the diagonal matrix D.
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*> \endverbatim
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*>
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*> \param[out] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,N)
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*> The generated n by n symmetric matrix A (the full matrix is
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*> stored).
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= N.
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*> \endverbatim
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*>
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*> \param[in,out] ISEED
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*> \verbatim
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*> ISEED is INTEGER array, dimension (4)
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*> On entry, the seed of the random number generator; the array
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*> elements must be between 0 and 4095, and ISEED(4) must be
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*> odd.
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*> On exit, the seed is updated.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (2*N)
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup real_matgen
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*
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* =====================================================================
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SUBROUTINE SLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO )
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*
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* -- LAPACK auxiliary routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER INFO, K, LDA, N
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* ..
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* .. Array Arguments ..
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INTEGER ISEED( 4 )
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REAL A( LDA, * ), D( * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE, HALF
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, HALF = 0.5E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J
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REAL ALPHA, TAU, WA, WB, WN
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* ..
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* .. External Subroutines ..
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EXTERNAL SAXPY, SGEMV, SGER, SLARNV, SSCAL, SSYMV,
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$ SSYR2, XERBLA
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* ..
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* .. External Functions ..
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REAL SDOT, SNRM2
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EXTERNAL SDOT, SNRM2
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, SIGN
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments
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*
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INFO = 0
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IF( N.LT.0 ) THEN
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INFO = -1
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ELSE IF( K.LT.0 .OR. K.GT.N-1 ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -5
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END IF
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IF( INFO.LT.0 ) THEN
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CALL XERBLA( 'SLAGSY', -INFO )
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RETURN
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END IF
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*
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* initialize lower triangle of A to diagonal matrix
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*
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DO 20 J = 1, N
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DO 10 I = J + 1, N
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A( I, J ) = ZERO
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10 CONTINUE
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20 CONTINUE
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DO 30 I = 1, N
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A( I, I ) = D( I )
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30 CONTINUE
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*
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* Generate lower triangle of symmetric matrix
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*
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DO 40 I = N - 1, 1, -1
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*
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* generate random reflection
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*
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CALL SLARNV( 3, ISEED, N-I+1, WORK )
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WN = SNRM2( N-I+1, WORK, 1 )
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WA = SIGN( WN, WORK( 1 ) )
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IF( WN.EQ.ZERO ) THEN
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TAU = ZERO
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ELSE
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WB = WORK( 1 ) + WA
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CALL SSCAL( N-I, ONE / WB, WORK( 2 ), 1 )
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WORK( 1 ) = ONE
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TAU = WB / WA
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END IF
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*
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* apply random reflection to A(i:n,i:n) from the left
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* and the right
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*
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* compute y := tau * A * u
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*
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CALL SSYMV( 'Lower', N-I+1, TAU, A( I, I ), LDA, WORK, 1, ZERO,
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$ WORK( N+1 ), 1 )
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*
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* compute v := y - 1/2 * tau * ( y, u ) * u
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*
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ALPHA = -HALF*TAU*SDOT( N-I+1, WORK( N+1 ), 1, WORK, 1 )
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CALL SAXPY( N-I+1, ALPHA, WORK, 1, WORK( N+1 ), 1 )
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*
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* apply the transformation as a rank-2 update to A(i:n,i:n)
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*
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CALL SSYR2( 'Lower', N-I+1, -ONE, WORK, 1, WORK( N+1 ), 1,
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$ A( I, I ), LDA )
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40 CONTINUE
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*
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* Reduce number of subdiagonals to K
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*
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DO 60 I = 1, N - 1 - K
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*
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* generate reflection to annihilate A(k+i+1:n,i)
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*
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WN = SNRM2( N-K-I+1, A( K+I, I ), 1 )
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WA = SIGN( WN, A( K+I, I ) )
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IF( WN.EQ.ZERO ) THEN
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TAU = ZERO
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ELSE
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WB = A( K+I, I ) + WA
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CALL SSCAL( N-K-I, ONE / WB, A( K+I+1, I ), 1 )
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A( K+I, I ) = ONE
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TAU = WB / WA
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END IF
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*
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* apply reflection to A(k+i:n,i+1:k+i-1) from the left
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*
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CALL SGEMV( 'Transpose', N-K-I+1, K-1, ONE, A( K+I, I+1 ), LDA,
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$ A( K+I, I ), 1, ZERO, WORK, 1 )
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CALL SGER( N-K-I+1, K-1, -TAU, A( K+I, I ), 1, WORK, 1,
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$ A( K+I, I+1 ), LDA )
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*
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* apply reflection to A(k+i:n,k+i:n) from the left and the right
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*
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* compute y := tau * A * u
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*
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CALL SSYMV( 'Lower', N-K-I+1, TAU, A( K+I, K+I ), LDA,
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$ A( K+I, I ), 1, ZERO, WORK, 1 )
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*
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* compute v := y - 1/2 * tau * ( y, u ) * u
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*
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ALPHA = -HALF*TAU*SDOT( N-K-I+1, WORK, 1, A( K+I, I ), 1 )
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CALL SAXPY( N-K-I+1, ALPHA, A( K+I, I ), 1, WORK, 1 )
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*
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* apply symmetric rank-2 update to A(k+i:n,k+i:n)
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*
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CALL SSYR2( 'Lower', N-K-I+1, -ONE, A( K+I, I ), 1, WORK, 1,
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$ A( K+I, K+I ), LDA )
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*
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A( K+I, I ) = -WA
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DO 50 J = K + I + 1, N
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A( J, I ) = ZERO
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50 CONTINUE
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60 CONTINUE
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*
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* Store full symmetric matrix
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*
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DO 80 J = 1, N
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DO 70 I = J + 1, N
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A( J, I ) = A( I, J )
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70 CONTINUE
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80 CONTINUE
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RETURN
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*
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* End of SLAGSY
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*
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END
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