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authorjofret2009-04-28 07:17:00 +0000
committerjofret2009-04-28 07:17:00 +0000
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Moving lapack to right place
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- SUBROUTINE ZLACON( N, V, X, EST, KASE )
-*
-* -- LAPACK auxiliary routine (version 3.1) --
-* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
-* November 2006
-*
-* .. Scalar Arguments ..
- INTEGER KASE, N
- DOUBLE PRECISION EST
-* ..
-* .. Array Arguments ..
- COMPLEX*16 V( N ), X( N )
-* ..
-*
-* Purpose
-* =======
-*
-* ZLACON estimates the 1-norm of a square, complex matrix A.
-* Reverse communication is used for evaluating matrix-vector products.
-*
-* Arguments
-* =========
-*
-* N (input) INTEGER
-* The order of the matrix. N >= 1.
-*
-* V (workspace) COMPLEX*16 array, dimension (N)
-* On the final return, V = A*W, where EST = norm(V)/norm(W)
-* (W is not returned).
-*
-* X (input/output) COMPLEX*16 array, dimension (N)
-* On an intermediate return, X should be overwritten by
-* A * X, if KASE=1,
-* A' * X, if KASE=2,
-* where A' is the conjugate transpose of A, and ZLACON must be
-* re-called with all the other parameters unchanged.
-*
-* EST (input/output) 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).
-*
-* KASE (input/output) 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' * X.
-* On the final return from ZLACON, KASE will again be 0.
-*
-* Further Details
-* ======= =======
-*
-* Contributed by Nick Higham, University of Manchester.
-* Originally named CONEST, dated March 16, 1988.
-*
-* Reference: 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.
-*
-* Last modified: April, 1999
-*
-* =====================================================================
-*
-* .. 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