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296 lines
7.7 KiB
296 lines
7.7 KiB
2 years ago
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*> \brief \b ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
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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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*> \htmlonly
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*> Download ZLACN2 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlacn2.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlacn2.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlacn2.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZLACN2( N, V, X, EST, KASE, ISAVE )
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*
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* .. Scalar Arguments ..
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* INTEGER KASE, N
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* DOUBLE PRECISION EST
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* ..
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* .. Array Arguments ..
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* INTEGER ISAVE( 3 )
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* COMPLEX*16 V( * ), X( * )
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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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*> ZLACN2 estimates the 1-norm of a square, complex matrix A.
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*> Reverse communication is used for evaluating matrix-vector products.
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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. N >= 1.
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*> \endverbatim
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*>
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*> \param[out] V
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*> \verbatim
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*> V is COMPLEX*16 array, dimension (N)
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*> On the final return, V = A*W, where EST = norm(V)/norm(W)
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*> (W is not returned).
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*> \endverbatim
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*>
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*> \param[in,out] X
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*> \verbatim
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*> X is COMPLEX*16 array, dimension (N)
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*> On an intermediate return, X should be overwritten by
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*> A * X, if KASE=1,
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*> A**H * X, if KASE=2,
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*> where A**H is the conjugate transpose of A, and ZLACN2 must be
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*> re-called with all the other parameters unchanged.
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*> \endverbatim
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*>
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*> \param[in,out] EST
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*> \verbatim
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*> EST is DOUBLE PRECISION
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*> On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be
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*> unchanged from the previous call to ZLACN2.
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*> On exit, EST is an estimate (a lower bound) for norm(A).
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*> \endverbatim
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*>
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*> \param[in,out] KASE
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*> \verbatim
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*> KASE is INTEGER
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*> On the initial call to ZLACN2, KASE should be 0.
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*> On an intermediate return, KASE will be 1 or 2, indicating
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*> whether X should be overwritten by A * X or A**H * X.
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*> On the final return from ZLACN2, KASE will again be 0.
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*> \endverbatim
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*>
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*> \param[in,out] ISAVE
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*> \verbatim
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*> ISAVE is INTEGER array, dimension (3)
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*> ISAVE is used to save variables between calls to ZLACN2
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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 complex16OTHERauxiliary
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> Originally named CONEST, dated March 16, 1988.
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*>
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*> Last modified: April, 1999
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*>
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*> This is a thread safe version of ZLACON, which uses the array ISAVE
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*> in place of a SAVE statement, as follows:
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*>
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*> ZLACON ZLACN2
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*> JUMP ISAVE(1)
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*> J ISAVE(2)
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*> ITER ISAVE(3)
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*> \endverbatim
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*
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*> \par Contributors:
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* ==================
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*>
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*> Nick Higham, University of Manchester
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*
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*> \par References:
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* ================
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*>
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*> N.J. Higham, "FORTRAN codes for estimating the one-norm of
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*> a real or complex matrix, with applications to condition estimation",
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*> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
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*>
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* =====================================================================
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SUBROUTINE ZLACN2( N, V, X, EST, KASE, ISAVE )
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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 KASE, N
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DOUBLE PRECISION EST
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* ..
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* .. Array Arguments ..
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INTEGER ISAVE( 3 )
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COMPLEX*16 V( * ), X( * )
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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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INTEGER ITMAX
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PARAMETER ( ITMAX = 5 )
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DOUBLE PRECISION ONE, TWO
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PARAMETER ( ONE = 1.0D0, TWO = 2.0D0 )
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COMPLEX*16 CZERO, CONE
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PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ),
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$ CONE = ( 1.0D0, 0.0D0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER I, JLAST
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DOUBLE PRECISION ABSXI, ALTSGN, ESTOLD, SAFMIN, TEMP
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* ..
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* .. External Functions ..
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INTEGER IZMAX1
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DOUBLE PRECISION DLAMCH, DZSUM1
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EXTERNAL IZMAX1, DLAMCH, DZSUM1
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* ..
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* .. External Subroutines ..
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EXTERNAL ZCOPY
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, DCMPLX, DIMAG
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* ..
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* .. Executable Statements ..
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*
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SAFMIN = DLAMCH( 'Safe minimum' )
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IF( KASE.EQ.0 ) THEN
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DO 10 I = 1, N
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X( I ) = DCMPLX( ONE / DBLE( N ) )
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10 CONTINUE
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KASE = 1
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ISAVE( 1 ) = 1
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RETURN
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END IF
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*
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GO TO ( 20, 40, 70, 90, 120 )ISAVE( 1 )
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*
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* ................ ENTRY (ISAVE( 1 ) = 1)
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* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
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*
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20 CONTINUE
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IF( N.EQ.1 ) THEN
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V( 1 ) = X( 1 )
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EST = ABS( V( 1 ) )
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* ... QUIT
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GO TO 130
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END IF
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EST = DZSUM1( N, X, 1 )
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*
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DO 30 I = 1, N
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ABSXI = ABS( X( I ) )
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IF( ABSXI.GT.SAFMIN ) THEN
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X( I ) = DCMPLX( DBLE( X( I ) ) / ABSXI,
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$ DIMAG( X( I ) ) / ABSXI )
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ELSE
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X( I ) = CONE
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END IF
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30 CONTINUE
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KASE = 2
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ISAVE( 1 ) = 2
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RETURN
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*
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* ................ ENTRY (ISAVE( 1 ) = 2)
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* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
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*
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40 CONTINUE
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ISAVE( 2 ) = IZMAX1( N, X, 1 )
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ISAVE( 3 ) = 2
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*
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* MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
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*
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50 CONTINUE
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DO 60 I = 1, N
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X( I ) = CZERO
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60 CONTINUE
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X( ISAVE( 2 ) ) = CONE
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KASE = 1
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ISAVE( 1 ) = 3
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RETURN
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*
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* ................ ENTRY (ISAVE( 1 ) = 3)
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* X HAS BEEN OVERWRITTEN BY A*X.
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*
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70 CONTINUE
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CALL ZCOPY( N, X, 1, V, 1 )
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ESTOLD = EST
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EST = DZSUM1( N, V, 1 )
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*
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* TEST FOR CYCLING.
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IF( EST.LE.ESTOLD )
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$ GO TO 100
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*
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DO 80 I = 1, N
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ABSXI = ABS( X( I ) )
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IF( ABSXI.GT.SAFMIN ) THEN
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X( I ) = DCMPLX( DBLE( X( I ) ) / ABSXI,
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$ DIMAG( X( I ) ) / ABSXI )
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ELSE
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X( I ) = CONE
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END IF
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80 CONTINUE
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KASE = 2
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ISAVE( 1 ) = 4
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RETURN
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*
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* ................ ENTRY (ISAVE( 1 ) = 4)
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* X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
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*
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90 CONTINUE
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JLAST = ISAVE( 2 )
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ISAVE( 2 ) = IZMAX1( N, X, 1 )
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IF( ( ABS( X( JLAST ) ).NE.ABS( X( ISAVE( 2 ) ) ) ) .AND.
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$ ( ISAVE( 3 ).LT.ITMAX ) ) THEN
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ISAVE( 3 ) = ISAVE( 3 ) + 1
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GO TO 50
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END IF
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*
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* ITERATION COMPLETE. FINAL STAGE.
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*
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100 CONTINUE
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ALTSGN = ONE
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DO 110 I = 1, N
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X( I ) = DCMPLX( ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) ) )
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ALTSGN = -ALTSGN
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110 CONTINUE
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KASE = 1
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ISAVE( 1 ) = 5
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RETURN
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*
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* ................ ENTRY (ISAVE( 1 ) = 5)
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* X HAS BEEN OVERWRITTEN BY A*X.
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*
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120 CONTINUE
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TEMP = TWO*( DZSUM1( N, X, 1 ) / DBLE( 3*N ) )
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IF( TEMP.GT.EST ) THEN
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CALL ZCOPY( N, X, 1, V, 1 )
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EST = TEMP
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END IF
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*
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130 CONTINUE
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KASE = 0
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RETURN
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*
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* End of ZLACN2
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*
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END
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