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*> \brief \b ZLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZLACON + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlacon.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlacon.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlacon.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZLACON( N, V, X, EST, KASE )
*
* .. Scalar Arguments ..
* INTEGER KASE, N
* DOUBLE PRECISION EST
* ..
* .. Array Arguments ..
* COMPLEX*16 V( N ), X( N )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZLACON estimates the 1-norm of a square, complex matrix A.
*> Reverse communication is used for evaluating matrix-vector products.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix. N >= 1.
*> \endverbatim
*>
*> \param[out] V
*> \verbatim
*> V is COMPLEX*16 array, dimension (N)
*> On the final return, V = A*W, where EST = norm(V)/norm(W)
*> (W is not returned).
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*> X is COMPLEX*16 array, dimension (N)
*> On an intermediate return, X should be overwritten by
*> A * X, if KASE=1,
*> A**H * X, if KASE=2,
*> where A**H is the conjugate transpose of A, and ZLACON must be
*> re-called with all the other parameters unchanged.
*> \endverbatim
*>
*> \param[in,out] EST
*> \verbatim
*> EST is DOUBLE PRECISION
*> On entry with KASE = 1 or 2 and JUMP = 3, EST should be
*> unchanged from the previous call to ZLACON.
*> On exit, EST is an estimate (a lower bound) for norm(A).
*> \endverbatim
*>
*> \param[in,out] KASE
*> \verbatim
*> KASE is INTEGER
*> On the initial call to ZLACON, KASE should be 0.
*> On an intermediate return, KASE will be 1 or 2, indicating
*> whether X should be overwritten by A * X or A**H * X.
*> On the final return from ZLACON, KASE will again be 0.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex16OTHERauxiliary
*
*> \par Further Details:
* =====================
*>
*> Originally named CONEST, dated March 16, 1988. \n
*> Last modified: April, 1999
*
*> \par Contributors:
* ==================
*>
*> Nick Higham, University of Manchester
*
*> \par References:
* ================
*>
*> N.J. Higham, "FORTRAN codes for estimating the one-norm of
*> a real or complex matrix, with applications to condition estimation",
*> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
*>
* =====================================================================
SUBROUTINE ZLACON( N, V, X, EST, KASE )
*
* -- LAPACK auxiliary routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER KASE, N
DOUBLE PRECISION EST
* ..
* .. Array Arguments ..
COMPLEX*16 V( N ), X( N )
* ..
*
* =====================================================================
*
* .. Parameters ..
INTEGER ITMAX
PARAMETER ( ITMAX = 5 )
DOUBLE PRECISION ONE, TWO
PARAMETER ( ONE = 1.0D0, TWO = 2.0D0 )
COMPLEX*16 CZERO, CONE
PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ),
$ CONE = ( 1.0D0, 0.0D0 ) )
* ..
* .. Local Scalars ..
INTEGER I, ITER, J, JLAST, JUMP
DOUBLE PRECISION ABSXI, ALTSGN, ESTOLD, SAFMIN, TEMP
* ..
* .. External Functions ..
INTEGER IZMAX1
DOUBLE PRECISION DLAMCH, DZSUM1
EXTERNAL IZMAX1, DLAMCH, DZSUM1
* ..
* .. External Subroutines ..
EXTERNAL ZCOPY
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DCMPLX, DIMAG
* ..
* .. Save statement ..
SAVE
* ..
* .. Executable Statements ..
*
SAFMIN = DLAMCH( 'Safe minimum' )
IF( KASE.EQ.0 ) THEN
DO 10 I = 1, N
X( I ) = DCMPLX( ONE / DBLE( N ) )
10 CONTINUE
KASE = 1
JUMP = 1
RETURN
END IF
*
GO TO ( 20, 40, 70, 90, 120 )JUMP
*
* ................ ENTRY (JUMP = 1)
* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
*
20 CONTINUE
IF( N.EQ.1 ) THEN
V( 1 ) = X( 1 )
EST = ABS( V( 1 ) )
* ... QUIT
GO TO 130
END IF
EST = DZSUM1( N, X, 1 )
*
DO 30 I = 1, N
ABSXI = ABS( X( I ) )
IF( ABSXI.GT.SAFMIN ) THEN
X( I ) = DCMPLX( DBLE( X( I ) ) / ABSXI,
$ DIMAG( X( I ) ) / ABSXI )
ELSE
X( I ) = CONE
END IF
30 CONTINUE
KASE = 2
JUMP = 2
RETURN
*
* ................ ENTRY (JUMP = 2)
* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
*
40 CONTINUE
J = IZMAX1( N, X, 1 )
ITER = 2
*
* MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
*
50 CONTINUE
DO 60 I = 1, N
X( I ) = CZERO
60 CONTINUE
X( J ) = CONE
KASE = 1
JUMP = 3
RETURN
*
* ................ ENTRY (JUMP = 3)
* X HAS BEEN OVERWRITTEN BY A*X.
*
70 CONTINUE
CALL ZCOPY( N, X, 1, V, 1 )
ESTOLD = EST
EST = DZSUM1( N, V, 1 )
*
* TEST FOR CYCLING.
IF( EST.LE.ESTOLD )
$ GO TO 100
*
DO 80 I = 1, N
ABSXI = ABS( X( I ) )
IF( ABSXI.GT.SAFMIN ) THEN
X( I ) = DCMPLX( DBLE( X( I ) ) / ABSXI,
$ DIMAG( X( I ) ) / ABSXI )
ELSE
X( I ) = CONE
END IF
80 CONTINUE
KASE = 2
JUMP = 4
RETURN
*
* ................ ENTRY (JUMP = 4)
* X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
*
90 CONTINUE
JLAST = J
J = IZMAX1( N, X, 1 )
IF( ( ABS( X( JLAST ) ).NE.ABS( X( J ) ) ) .AND.
$ ( ITER.LT.ITMAX ) ) THEN
ITER = ITER + 1
GO TO 50
END IF
*
* ITERATION COMPLETE. FINAL STAGE.
*
100 CONTINUE
ALTSGN = ONE
DO 110 I = 1, N
X( I ) = DCMPLX( ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) ) )
ALTSGN = -ALTSGN
110 CONTINUE
KASE = 1
JUMP = 5
RETURN
*
* ................ ENTRY (JUMP = 5)
* X HAS BEEN OVERWRITTEN BY A*X.
*
120 CONTINUE
TEMP = TWO*( DZSUM1( N, X, 1 ) / DBLE( 3*N ) )
IF( TEMP.GT.EST ) THEN
CALL ZCOPY( N, X, 1, V, 1 )
EST = TEMP
END IF
*
130 CONTINUE
KASE = 0
RETURN
*
* End of ZLACON
*
END
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