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*> \brief \b CLACN2 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 CLACN2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clacn2.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clacn2.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clacn2.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CLACN2( N, V, X, EST, KASE, ISAVE )
*
* .. Scalar Arguments ..
* INTEGER KASE, N
* REAL EST
* ..
* .. Array Arguments ..
* INTEGER ISAVE( 3 )
* COMPLEX V( * ), X( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CLACN2 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 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 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 CLACN2 must be
*> re-called with all the other parameters unchanged.
*> \endverbatim
*>
*> \param[in,out] EST
*> \verbatim
*> EST is REAL
*> On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be
*> unchanged from the previous call to CLACN2.
*> 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 CLACN2, 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 CLACN2, KASE will again be 0.
*> \endverbatim
*>
*> \param[in,out] ISAVE
*> \verbatim
*> ISAVE is INTEGER array, dimension (3)
*> ISAVE is used to save variables between calls to SLACN2
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup complexOTHERauxiliary
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Originally named CONEST, dated March 16, 1988.
*>
*> Last modified: April, 1999
*>
*> This is a thread safe version of CLACON, which uses the array ISAVE
*> in place of a SAVE statement, as follows:
*>
*> CLACON CLACN2
*> JUMP ISAVE(1)
*> J ISAVE(2)
*> ITER ISAVE(3)
*> \endverbatim
*
*> \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 CLACN2( N, V, X, EST, KASE, ISAVE )
*
* -- LAPACK auxiliary routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
INTEGER KASE, N
REAL EST
* ..
* .. Array Arguments ..
INTEGER ISAVE( 3 )
COMPLEX V( * ), X( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
INTEGER ITMAX
PARAMETER ( ITMAX = 5 )
REAL ONE, TWO
PARAMETER ( ONE = 1.0E0, TWO = 2.0E0 )
COMPLEX CZERO, CONE
PARAMETER ( CZERO = ( 0.0E0, 0.0E0 ),
$ CONE = ( 1.0E0, 0.0E0 ) )
* ..
* .. Local Scalars ..
INTEGER I, JLAST
REAL ABSXI, ALTSGN, ESTOLD, SAFMIN, TEMP
* ..
* .. External Functions ..
INTEGER ICMAX1
REAL SCSUM1, SLAMCH
EXTERNAL ICMAX1, SCSUM1, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL CCOPY
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, AIMAG, CMPLX, REAL
* ..
* .. Executable Statements ..
*
SAFMIN = SLAMCH( 'Safe minimum' )
IF( KASE.EQ.0 ) THEN
DO 10 I = 1, N
X( I ) = CMPLX( ONE / REAL( N ) )
10 CONTINUE
KASE = 1
ISAVE( 1 ) = 1
RETURN
END IF
*
GO TO ( 20, 40, 70, 90, 120 )ISAVE( 1 )
*
* ................ ENTRY (ISAVE( 1 ) = 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 = SCSUM1( N, X, 1 )
*
DO 30 I = 1, N
ABSXI = ABS( X( I ) )
IF( ABSXI.GT.SAFMIN ) THEN
X( I ) = CMPLX( REAL( X( I ) ) / ABSXI,
$ AIMAG( X( I ) ) / ABSXI )
ELSE
X( I ) = CONE
END IF
30 CONTINUE
KASE = 2
ISAVE( 1 ) = 2
RETURN
*
* ................ ENTRY (ISAVE( 1 ) = 2)
* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
*
40 CONTINUE
ISAVE( 2 ) = ICMAX1( N, X, 1 )
ISAVE( 3 ) = 2
*
* MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
*
50 CONTINUE
DO 60 I = 1, N
X( I ) = CZERO
60 CONTINUE
X( ISAVE( 2 ) ) = CONE
KASE = 1
ISAVE( 1 ) = 3
RETURN
*
* ................ ENTRY (ISAVE( 1 ) = 3)
* X HAS BEEN OVERWRITTEN BY A*X.
*
70 CONTINUE
CALL CCOPY( N, X, 1, V, 1 )
ESTOLD = EST
EST = SCSUM1( 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 ) = CMPLX( REAL( X( I ) ) / ABSXI,
$ AIMAG( X( I ) ) / ABSXI )
ELSE
X( I ) = CONE
END IF
80 CONTINUE
KASE = 2
ISAVE( 1 ) = 4
RETURN
*
* ................ ENTRY (ISAVE( 1 ) = 4)
* X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
*
90 CONTINUE
JLAST = ISAVE( 2 )
ISAVE( 2 ) = ICMAX1( N, X, 1 )
IF( ( ABS( X( JLAST ) ).NE.ABS( X( ISAVE( 2 ) ) ) ) .AND.
$ ( ISAVE( 3 ).LT.ITMAX ) ) THEN
ISAVE( 3 ) = ISAVE( 3 ) + 1
GO TO 50
END IF
*
* ITERATION COMPLETE. FINAL STAGE.
*
100 CONTINUE
ALTSGN = ONE
DO 110 I = 1, N
X( I ) = CMPLX( ALTSGN*( ONE + REAL( I-1 ) / REAL( N-1 ) ) )
ALTSGN = -ALTSGN
110 CONTINUE
KASE = 1
ISAVE( 1 ) = 5
RETURN
*
* ................ ENTRY (ISAVE( 1 ) = 5)
* X HAS BEEN OVERWRITTEN BY A*X.
*
120 CONTINUE
TEMP = TWO*( SCSUM1( N, X, 1 ) / REAL( 3*N ) )
IF( TEMP.GT.EST ) THEN
CALL CCOPY( N, X, 1, V, 1 )
EST = TEMP
END IF
*
130 CONTINUE
KASE = 0
RETURN
*
* End of CLACN2
*
END
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