phynexis-deps/lapack
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
Files
e2428ec4cbbbfb86fb48a67a0696347f73aebc21
lapack/SRC/clacon.f
T
Julie e18d437924 Making LAPACK's code eternal... no more version and date in source files. 
GitHub is now enabling us to track accurately version and date.
No need for this anymore.
2021-03-25 10:16:58 -07:00

279 lines
7.1 KiB
FortranFixed
Raw Blame History

*> \brief \b CLACON 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 CLACON + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clacon.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clacon.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clacon.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CLACON( N, V, X, EST, KASE )
*
* .. Scalar Arguments ..
* INTEGER KASE, N
* REAL EST
* ..
* .. Array Arguments ..
* COMPLEX V( N ), X( N )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CLACON 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 CLACON 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 JUMP = 3, EST should be
*> unchanged from the previous call to CLACON.
*> 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 CLACON, 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 CLACON, KASE will again be 0.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complexOTHERauxiliary
*
*> \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 CLACON( N, V, X, EST, KASE )
*
* -- 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 ..
COMPLEX V( N ), X( N )
* ..
*
* =====================================================================
*
* .. 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, ITER, J, JLAST, JUMP
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
* ..
* .. Save statement ..
SAVE
* ..
* .. 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
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 = 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
JUMP = 2
RETURN
*
* ................ ENTRY (JUMP = 2)
* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
*
40 CONTINUE
J = ICMAX1( 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 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
JUMP = 4
RETURN
*
* ................ ENTRY (JUMP = 4)
* X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
*
90 CONTINUE
JLAST = J
J = ICMAX1( 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 ) = CMPLX( ALTSGN*( ONE+REAL( I-1 ) / REAL( 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*( 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 CLACON
*
END
Reference in New Issue View Git Blame Copy Permalink