You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
295 lines
7.7 KiB
295 lines
7.7 KiB
*> \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.
|
|
*
|
|
*> \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 --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
*
|
|
* .. 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
|
|
|