259 lines
7.0 KiB
Fortran
259 lines
7.0 KiB
Fortran
*> \brief \b ZLATSY
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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 ZLATSY( UPLO, N, X, LDX, ISEED )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER LDX, N
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* ..
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* .. Array Arguments ..
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* INTEGER ISEED( * )
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* COMPLEX*16 X( LDX, * )
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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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*> ZLATSY generates a special test matrix for the complex symmetric
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*> (indefinite) factorization. The pivot blocks of the generated matrix
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*> will be in the following order:
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*> 2x2 pivot block, non diagonalizable
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*> 1x1 pivot block
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*> 2x2 pivot block, diagonalizable
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*> (cycle repeats)
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*> A row interchange is required for each non-diagonalizable 2x2 block.
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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] UPLO
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*> \verbatim
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*> UPLO is CHARACTER
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*> Specifies whether the generated matrix is to be upper or
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*> lower triangular.
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*> = 'U': Upper triangular
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*> = 'L': Lower triangular
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*> \endverbatim
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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 dimension of the matrix to be generated.
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*> \endverbatim
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*>
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*> \param[out] X
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*> \verbatim
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*> X is COMPLEX*16 array, dimension (LDX,N)
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*> The generated matrix, consisting of 3x3 and 2x2 diagonal
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*> blocks which result in the pivot sequence given above.
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*> The matrix outside of these diagonal blocks is zero.
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*> \endverbatim
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*>
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*> \param[in] LDX
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*> \verbatim
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*> LDX is INTEGER
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*> The leading dimension of the array X.
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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 for the random number generator. The last
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*> of the four integers must be odd. (modified on exit)
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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 complex16_lin
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*
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* =====================================================================
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SUBROUTINE ZLATSY( UPLO, N, X, LDX, ISEED )
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*
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* -- LAPACK test 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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CHARACTER UPLO
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INTEGER LDX, N
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* ..
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* .. Array Arguments ..
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INTEGER ISEED( * )
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COMPLEX*16 X( LDX, * )
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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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COMPLEX*16 EYE
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PARAMETER ( EYE = ( 0.0D0, 1.0D0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER I, J, N5
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DOUBLE PRECISION ALPHA, ALPHA3, BETA
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COMPLEX*16 A, B, C, R
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* ..
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* .. External Functions ..
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COMPLEX*16 ZLARND
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EXTERNAL ZLARND
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, SQRT
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* ..
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* .. Executable Statements ..
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*
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* Initialize constants
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*
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ALPHA = ( 1.D0+SQRT( 17.D0 ) ) / 8.D0
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BETA = ALPHA - 1.D0 / 1000.D0
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ALPHA3 = ALPHA*ALPHA*ALPHA
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*
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* UPLO = 'U': Upper triangular storage
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*
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IF( UPLO.EQ.'U' ) THEN
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*
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* Fill the upper triangle of the matrix with zeros.
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*
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DO 20 J = 1, N
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DO 10 I = 1, J
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X( I, J ) = 0.0D0
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10 CONTINUE
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20 CONTINUE
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N5 = N / 5
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N5 = N - 5*N5 + 1
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*
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DO 30 I = N, N5, -5
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A = ALPHA3*ZLARND( 5, ISEED )
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B = ZLARND( 5, ISEED ) / ALPHA
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C = A - 2.D0*B*EYE
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R = C / BETA
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X( I, I ) = A
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X( I-2, I ) = B
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X( I-2, I-1 ) = R
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X( I-2, I-2 ) = C
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X( I-1, I-1 ) = ZLARND( 2, ISEED )
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X( I-3, I-3 ) = ZLARND( 2, ISEED )
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X( I-4, I-4 ) = ZLARND( 2, ISEED )
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IF( ABS( X( I-3, I-3 ) ).GT.ABS( X( I-4, I-4 ) ) ) THEN
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X( I-4, I-3 ) = 2.0D0*X( I-3, I-3 )
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ELSE
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X( I-4, I-3 ) = 2.0D0*X( I-4, I-4 )
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END IF
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30 CONTINUE
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*
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* Clean-up for N not a multiple of 5.
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*
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I = N5 - 1
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IF( I.GT.2 ) THEN
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A = ALPHA3*ZLARND( 5, ISEED )
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B = ZLARND( 5, ISEED ) / ALPHA
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C = A - 2.D0*B*EYE
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R = C / BETA
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X( I, I ) = A
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X( I-2, I ) = B
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X( I-2, I-1 ) = R
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X( I-2, I-2 ) = C
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X( I-1, I-1 ) = ZLARND( 2, ISEED )
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I = I - 3
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END IF
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IF( I.GT.1 ) THEN
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X( I, I ) = ZLARND( 2, ISEED )
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X( I-1, I-1 ) = ZLARND( 2, ISEED )
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IF( ABS( X( I, I ) ).GT.ABS( X( I-1, I-1 ) ) ) THEN
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X( I-1, I ) = 2.0D0*X( I, I )
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ELSE
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X( I-1, I ) = 2.0D0*X( I-1, I-1 )
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END IF
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I = I - 2
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ELSE IF( I.EQ.1 ) THEN
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X( I, I ) = ZLARND( 2, ISEED )
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I = I - 1
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END IF
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*
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* UPLO = 'L': Lower triangular storage
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*
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ELSE
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*
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* Fill the lower triangle of the matrix with zeros.
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*
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DO 50 J = 1, N
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DO 40 I = J, N
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X( I, J ) = 0.0D0
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40 CONTINUE
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50 CONTINUE
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N5 = N / 5
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N5 = N5*5
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*
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DO 60 I = 1, N5, 5
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A = ALPHA3*ZLARND( 5, ISEED )
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B = ZLARND( 5, ISEED ) / ALPHA
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C = A - 2.D0*B*EYE
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R = C / BETA
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X( I, I ) = A
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X( I+2, I ) = B
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X( I+2, I+1 ) = R
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X( I+2, I+2 ) = C
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X( I+1, I+1 ) = ZLARND( 2, ISEED )
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X( I+3, I+3 ) = ZLARND( 2, ISEED )
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X( I+4, I+4 ) = ZLARND( 2, ISEED )
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IF( ABS( X( I+3, I+3 ) ).GT.ABS( X( I+4, I+4 ) ) ) THEN
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X( I+4, I+3 ) = 2.0D0*X( I+3, I+3 )
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ELSE
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X( I+4, I+3 ) = 2.0D0*X( I+4, I+4 )
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END IF
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60 CONTINUE
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*
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* Clean-up for N not a multiple of 5.
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*
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I = N5 + 1
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IF( I.LT.N-1 ) THEN
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A = ALPHA3*ZLARND( 5, ISEED )
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B = ZLARND( 5, ISEED ) / ALPHA
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C = A - 2.D0*B*EYE
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R = C / BETA
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X( I, I ) = A
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X( I+2, I ) = B
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X( I+2, I+1 ) = R
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X( I+2, I+2 ) = C
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X( I+1, I+1 ) = ZLARND( 2, ISEED )
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I = I + 3
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END IF
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IF( I.LT.N ) THEN
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X( I, I ) = ZLARND( 2, ISEED )
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X( I+1, I+1 ) = ZLARND( 2, ISEED )
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IF( ABS( X( I, I ) ).GT.ABS( X( I+1, I+1 ) ) ) THEN
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X( I+1, I ) = 2.0D0*X( I, I )
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ELSE
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X( I+1, I ) = 2.0D0*X( I+1, I+1 )
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END IF
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I = I + 2
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ELSE IF( I.EQ.N ) THEN
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X( I, I ) = ZLARND( 2, ISEED )
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I = I + 1
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END IF
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END IF
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*
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RETURN
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*
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* End of ZLATSY
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*
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END
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