222 lines
5.9 KiB
FortranFixed
Executable File
222 lines
5.9 KiB
FortranFixed
Executable File
SUBROUTINE CLACN2( N, V, X, EST, KASE, ISAVE )
|
|
*
|
|
* -- LAPACK auxiliary routine (version 3.1) --
|
|
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
|
|
* November 2006
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER KASE, N
|
|
REAL EST
|
|
* ..
|
|
* .. Array Arguments ..
|
|
INTEGER ISAVE( 3 )
|
|
COMPLEX V( * ), X( * )
|
|
* ..
|
|
*
|
|
* Purpose
|
|
* =======
|
|
*
|
|
* CLACN2 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 array, dimension (N)
|
|
* On the final return, V = A*W, where EST = norm(V)/norm(W)
|
|
* (W is not returned).
|
|
*
|
|
* X (input/output) COMPLEX 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 CLACN2 must be
|
|
* re-called with all the other parameters unchanged.
|
|
*
|
|
* EST (input/output) 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).
|
|
*
|
|
* KASE (input/output) 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' * X.
|
|
* On the final return from CLACN2, KASE will again be 0.
|
|
*
|
|
* ISAVE (input/output) INTEGER array, dimension (3)
|
|
* ISAVE is used to save variables between calls to SLACN2
|
|
*
|
|
* 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
|
|
*
|
|
* 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)
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. 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
|