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446 lines
13 KiB
446 lines
13 KiB
*> \brief \b DLATM4
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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 DLATM4( ITYPE, N, NZ1, NZ2, ISIGN, AMAGN, RCOND,
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* TRIANG, IDIST, ISEED, A, LDA )
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*
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* .. Scalar Arguments ..
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* INTEGER IDIST, ISIGN, ITYPE, LDA, N, NZ1, NZ2
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* DOUBLE PRECISION AMAGN, RCOND, TRIANG
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* ..
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* .. Array Arguments ..
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* INTEGER ISEED( 4 )
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* DOUBLE PRECISION A( LDA, * )
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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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*> DLATM4 generates basic square matrices, which may later be
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*> multiplied by others in order to produce test matrices. It is
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*> intended mainly to be used to test the generalized eigenvalue
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*> routines.
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*>
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*> It first generates the diagonal and (possibly) subdiagonal,
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*> according to the value of ITYPE, NZ1, NZ2, ISIGN, AMAGN, and RCOND.
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*> It then fills in the upper triangle with random numbers, if TRIANG is
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*> non-zero.
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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] ITYPE
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*> \verbatim
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*> ITYPE is INTEGER
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*> The "type" of matrix on the diagonal and sub-diagonal.
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*> If ITYPE < 0, then type abs(ITYPE) is generated and then
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*> swapped end for end (A(I,J) := A'(N-J,N-I).) See also
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*> the description of AMAGN and ISIGN.
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*>
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*> Special types:
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*> = 0: the zero matrix.
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*> = 1: the identity.
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*> = 2: a transposed Jordan block.
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*> = 3: If N is odd, then a k+1 x k+1 transposed Jordan block
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*> followed by a k x k identity block, where k=(N-1)/2.
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*> If N is even, then k=(N-2)/2, and a zero diagonal entry
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*> is tacked onto the end.
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*>
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*> Diagonal types. The diagonal consists of NZ1 zeros, then
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*> k=N-NZ1-NZ2 nonzeros. The subdiagonal is zero. ITYPE
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*> specifies the nonzero diagonal entries as follows:
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*> = 4: 1, ..., k
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*> = 5: 1, RCOND, ..., RCOND
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*> = 6: 1, ..., 1, RCOND
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*> = 7: 1, a, a^2, ..., a^(k-1)=RCOND
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*> = 8: 1, 1-d, 1-2*d, ..., 1-(k-1)*d=RCOND
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*> = 9: random numbers chosen from (RCOND,1)
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*> = 10: random numbers with distribution IDIST (see DLARND.)
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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 order of the matrix.
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*> \endverbatim
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*>
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*> \param[in] NZ1
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*> \verbatim
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*> NZ1 is INTEGER
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*> If abs(ITYPE) > 3, then the first NZ1 diagonal entries will
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*> be zero.
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*> \endverbatim
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*>
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*> \param[in] NZ2
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*> \verbatim
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*> NZ2 is INTEGER
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*> If abs(ITYPE) > 3, then the last NZ2 diagonal entries will
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*> be zero.
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*> \endverbatim
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*>
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*> \param[in] ISIGN
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*> \verbatim
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*> ISIGN is INTEGER
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*> = 0: The sign of the diagonal and subdiagonal entries will
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*> be left unchanged.
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*> = 1: The diagonal and subdiagonal entries will have their
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*> sign changed at random.
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*> = 2: If ITYPE is 2 or 3, then the same as ISIGN=1.
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*> Otherwise, with probability 0.5, odd-even pairs of
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*> diagonal entries A(2*j-1,2*j-1), A(2*j,2*j) will be
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*> converted to a 2x2 block by pre- and post-multiplying
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*> by distinct random orthogonal rotations. The remaining
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*> diagonal entries will have their sign changed at random.
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*> \endverbatim
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*>
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*> \param[in] AMAGN
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*> \verbatim
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*> AMAGN is DOUBLE PRECISION
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*> The diagonal and subdiagonal entries will be multiplied by
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*> AMAGN.
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*> \endverbatim
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*>
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*> \param[in] RCOND
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*> \verbatim
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*> RCOND is DOUBLE PRECISION
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*> If abs(ITYPE) > 4, then the smallest diagonal entry will be
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*> entry will be RCOND. RCOND must be between 0 and 1.
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*> \endverbatim
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*>
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*> \param[in] TRIANG
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*> \verbatim
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*> TRIANG is DOUBLE PRECISION
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*> The entries above the diagonal will be random numbers with
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*> magnitude bounded by TRIANG (i.e., random numbers multiplied
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*> by TRIANG.)
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*> \endverbatim
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*>
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*> \param[in] IDIST
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*> \verbatim
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*> IDIST is INTEGER
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*> Specifies the type of distribution to be used to generate a
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*> random matrix.
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*> = 1: UNIFORM( 0, 1 )
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*> = 2: UNIFORM( -1, 1 )
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*> = 3: NORMAL ( 0, 1 )
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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 ISEED specifies the seed of the random number
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*> generator. The values of ISEED are changed on exit, and can
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*> be used in the next call to DLATM4 to continue the same
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*> random number sequence.
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*> Note: ISEED(4) should be odd, for the random number generator
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*> used at present.
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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 DOUBLE PRECISION array, dimension (LDA, N)
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*> Array to be computed.
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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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*> Leading dimension of A. Must be at least 1 and at least N.
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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 double_eig
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*
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* =====================================================================
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SUBROUTINE DLATM4( ITYPE, N, NZ1, NZ2, ISIGN, AMAGN, RCOND,
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$ TRIANG, IDIST, ISEED, A, LDA )
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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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INTEGER IDIST, ISIGN, ITYPE, LDA, N, NZ1, NZ2
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DOUBLE PRECISION AMAGN, RCOND, TRIANG
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* ..
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* .. Array Arguments ..
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INTEGER ISEED( 4 )
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DOUBLE PRECISION A( LDA, * )
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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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DOUBLE PRECISION ZERO, ONE, TWO
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PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0 )
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DOUBLE PRECISION HALF
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PARAMETER ( HALF = ONE / TWO )
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* ..
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* .. Local Scalars ..
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INTEGER I, IOFF, ISDB, ISDE, JC, JD, JR, K, KBEG, KEND,
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$ KLEN
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DOUBLE PRECISION ALPHA, CL, CR, SAFMIN, SL, SR, SV1, SV2, TEMP
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH, DLARAN, DLARND
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EXTERNAL DLAMCH, DLARAN, DLARND
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* ..
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* .. External Subroutines ..
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EXTERNAL DLASET
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, EXP, LOG, MAX, MIN, MOD, SQRT
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* ..
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* .. Executable Statements ..
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*
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IF( N.LE.0 )
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$ RETURN
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CALL DLASET( 'Full', N, N, ZERO, ZERO, A, LDA )
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*
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* Insure a correct ISEED
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*
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IF( MOD( ISEED( 4 ), 2 ).NE.1 )
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$ ISEED( 4 ) = ISEED( 4 ) + 1
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*
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* Compute diagonal and subdiagonal according to ITYPE, NZ1, NZ2,
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* and RCOND
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*
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IF( ITYPE.NE.0 ) THEN
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IF( ABS( ITYPE ).GE.4 ) THEN
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KBEG = MAX( 1, MIN( N, NZ1+1 ) )
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KEND = MAX( KBEG, MIN( N, N-NZ2 ) )
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KLEN = KEND + 1 - KBEG
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ELSE
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KBEG = 1
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KEND = N
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KLEN = N
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END IF
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ISDB = 1
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ISDE = 0
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GO TO ( 10, 30, 50, 80, 100, 120, 140, 160,
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$ 180, 200 )ABS( ITYPE )
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*
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* abs(ITYPE) = 1: Identity
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*
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10 CONTINUE
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DO 20 JD = 1, N
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A( JD, JD ) = ONE
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20 CONTINUE
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GO TO 220
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*
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* abs(ITYPE) = 2: Transposed Jordan block
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*
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30 CONTINUE
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DO 40 JD = 1, N - 1
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A( JD+1, JD ) = ONE
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40 CONTINUE
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ISDB = 1
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ISDE = N - 1
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GO TO 220
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*
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* abs(ITYPE) = 3: Transposed Jordan block, followed by the
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* identity.
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*
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50 CONTINUE
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K = ( N-1 ) / 2
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DO 60 JD = 1, K
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A( JD+1, JD ) = ONE
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60 CONTINUE
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ISDB = 1
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ISDE = K
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DO 70 JD = K + 2, 2*K + 1
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A( JD, JD ) = ONE
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70 CONTINUE
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GO TO 220
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*
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* abs(ITYPE) = 4: 1,...,k
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*
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80 CONTINUE
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DO 90 JD = KBEG, KEND
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A( JD, JD ) = DBLE( JD-NZ1 )
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90 CONTINUE
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GO TO 220
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*
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* abs(ITYPE) = 5: One large D value:
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*
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100 CONTINUE
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DO 110 JD = KBEG + 1, KEND
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A( JD, JD ) = RCOND
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110 CONTINUE
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A( KBEG, KBEG ) = ONE
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GO TO 220
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*
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* abs(ITYPE) = 6: One small D value:
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*
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120 CONTINUE
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DO 130 JD = KBEG, KEND - 1
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A( JD, JD ) = ONE
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130 CONTINUE
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A( KEND, KEND ) = RCOND
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GO TO 220
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*
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* abs(ITYPE) = 7: Exponentially distributed D values:
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*
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140 CONTINUE
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A( KBEG, KBEG ) = ONE
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IF( KLEN.GT.1 ) THEN
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ALPHA = RCOND**( ONE / DBLE( KLEN-1 ) )
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DO 150 I = 2, KLEN
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A( NZ1+I, NZ1+I ) = ALPHA**DBLE( I-1 )
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150 CONTINUE
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END IF
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GO TO 220
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*
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* abs(ITYPE) = 8: Arithmetically distributed D values:
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*
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160 CONTINUE
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A( KBEG, KBEG ) = ONE
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IF( KLEN.GT.1 ) THEN
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ALPHA = ( ONE-RCOND ) / DBLE( KLEN-1 )
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DO 170 I = 2, KLEN
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A( NZ1+I, NZ1+I ) = DBLE( KLEN-I )*ALPHA + RCOND
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170 CONTINUE
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END IF
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GO TO 220
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*
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* abs(ITYPE) = 9: Randomly distributed D values on ( RCOND, 1):
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*
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180 CONTINUE
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ALPHA = LOG( RCOND )
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DO 190 JD = KBEG, KEND
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A( JD, JD ) = EXP( ALPHA*DLARAN( ISEED ) )
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190 CONTINUE
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GO TO 220
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*
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* abs(ITYPE) = 10: Randomly distributed D values from DIST
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*
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200 CONTINUE
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DO 210 JD = KBEG, KEND
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A( JD, JD ) = DLARND( IDIST, ISEED )
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210 CONTINUE
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*
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220 CONTINUE
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*
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* Scale by AMAGN
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*
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DO 230 JD = KBEG, KEND
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A( JD, JD ) = AMAGN*DBLE( A( JD, JD ) )
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230 CONTINUE
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DO 240 JD = ISDB, ISDE
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A( JD+1, JD ) = AMAGN*DBLE( A( JD+1, JD ) )
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240 CONTINUE
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*
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* If ISIGN = 1 or 2, assign random signs to diagonal and
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* subdiagonal
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*
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IF( ISIGN.GT.0 ) THEN
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DO 250 JD = KBEG, KEND
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IF( DBLE( A( JD, JD ) ).NE.ZERO ) THEN
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IF( DLARAN( ISEED ).GT.HALF )
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$ A( JD, JD ) = -A( JD, JD )
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END IF
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250 CONTINUE
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DO 260 JD = ISDB, ISDE
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IF( DBLE( A( JD+1, JD ) ).NE.ZERO ) THEN
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IF( DLARAN( ISEED ).GT.HALF )
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$ A( JD+1, JD ) = -A( JD+1, JD )
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END IF
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260 CONTINUE
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END IF
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*
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* Reverse if ITYPE < 0
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*
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IF( ITYPE.LT.0 ) THEN
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DO 270 JD = KBEG, ( KBEG+KEND-1 ) / 2
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TEMP = A( JD, JD )
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A( JD, JD ) = A( KBEG+KEND-JD, KBEG+KEND-JD )
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A( KBEG+KEND-JD, KBEG+KEND-JD ) = TEMP
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270 CONTINUE
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DO 280 JD = 1, ( N-1 ) / 2
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TEMP = A( JD+1, JD )
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A( JD+1, JD ) = A( N+1-JD, N-JD )
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A( N+1-JD, N-JD ) = TEMP
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280 CONTINUE
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END IF
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*
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* If ISIGN = 2, and no subdiagonals already, then apply
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* random rotations to make 2x2 blocks.
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*
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IF( ISIGN.EQ.2 .AND. ITYPE.NE.2 .AND. ITYPE.NE.3 ) THEN
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SAFMIN = DLAMCH( 'S' )
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DO 290 JD = KBEG, KEND - 1, 2
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IF( DLARAN( ISEED ).GT.HALF ) THEN
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*
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* Rotation on left.
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*
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CL = TWO*DLARAN( ISEED ) - ONE
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SL = TWO*DLARAN( ISEED ) - ONE
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TEMP = ONE / MAX( SAFMIN, SQRT( CL**2+SL**2 ) )
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CL = CL*TEMP
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SL = SL*TEMP
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*
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* Rotation on right.
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*
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CR = TWO*DLARAN( ISEED ) - ONE
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SR = TWO*DLARAN( ISEED ) - ONE
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TEMP = ONE / MAX( SAFMIN, SQRT( CR**2+SR**2 ) )
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CR = CR*TEMP
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SR = SR*TEMP
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*
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* Apply
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*
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SV1 = A( JD, JD )
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SV2 = A( JD+1, JD+1 )
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A( JD, JD ) = CL*CR*SV1 + SL*SR*SV2
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A( JD+1, JD ) = -SL*CR*SV1 + CL*SR*SV2
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A( JD, JD+1 ) = -CL*SR*SV1 + SL*CR*SV2
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A( JD+1, JD+1 ) = SL*SR*SV1 + CL*CR*SV2
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END IF
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290 CONTINUE
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END IF
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*
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END IF
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*
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* Fill in upper triangle (except for 2x2 blocks)
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*
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IF( TRIANG.NE.ZERO ) THEN
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IF( ISIGN.NE.2 .OR. ITYPE.EQ.2 .OR. ITYPE.EQ.3 ) THEN
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IOFF = 1
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ELSE
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IOFF = 2
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DO 300 JR = 1, N - 1
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IF( A( JR+1, JR ).EQ.ZERO )
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$ A( JR, JR+1 ) = TRIANG*DLARND( IDIST, ISEED )
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300 CONTINUE
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END IF
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*
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DO 320 JC = 2, N
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DO 310 JR = 1, JC - IOFF
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A( JR, JC ) = TRIANG*DLARND( IDIST, ISEED )
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310 CONTINUE
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320 CONTINUE
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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 DLATM4
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*
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END
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