forked from lijiext/lammps
216 lines
5.7 KiB
Fortran
216 lines
5.7 KiB
Fortran
SUBROUTINE DLACN2( N, V, X, ISGN, EST, KASE, ISAVE )
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*
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* -- LAPACK auxiliary routine (version 3.2) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2006
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*
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* .. Scalar Arguments ..
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INTEGER KASE, N
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DOUBLE PRECISION EST
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* ..
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* .. Array Arguments ..
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INTEGER ISGN( * ), ISAVE( 3 )
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DOUBLE PRECISION V( * ), X( * )
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* ..
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*
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* Purpose
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* =======
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*
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* DLACN2 estimates the 1-norm of a square, real matrix A.
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* Reverse communication is used for evaluating matrix-vector products.
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*
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* Arguments
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* =========
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*
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* N (input) INTEGER
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* The order of the matrix. N >= 1.
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*
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* V (workspace) DOUBLE PRECISION array, dimension (N)
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* On the final return, V = A*W, where EST = norm(V)/norm(W)
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* (W is not returned).
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*
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* X (input/output) DOUBLE PRECISION array, dimension (N)
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* On an intermediate return, X should be overwritten by
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* A * X, if KASE=1,
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* A' * X, if KASE=2,
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* and DLACN2 must be re-called with all the other parameters
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* unchanged.
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*
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* ISGN (workspace) INTEGER array, dimension (N)
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*
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* EST (input/output) DOUBLE PRECISION
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* On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be
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* unchanged from the previous call to DLACN2.
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* On exit, EST is an estimate (a lower bound) for norm(A).
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*
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* KASE (input/output) INTEGER
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* On the initial call to DLACN2, KASE should be 0.
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* On an intermediate return, KASE will be 1 or 2, indicating
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* whether X should be overwritten by A * X or A' * X.
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* On the final return from DLACN2, KASE will again be 0.
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*
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* ISAVE (input/output) INTEGER array, dimension (3)
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* ISAVE is used to save variables between calls to DLACN2
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*
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* Further Details
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* ======= =======
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*
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* Contributed by Nick Higham, University of Manchester.
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* Originally named SONEST, dated March 16, 1988.
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*
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* Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
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* a real or complex matrix, with applications to condition estimation",
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* ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
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*
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* This is a thread safe version of DLACON, which uses the array ISAVE
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* in place of a SAVE statement, as follows:
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*
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* DLACON DLACN2
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* JUMP ISAVE(1)
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* J ISAVE(2)
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* ITER ISAVE(3)
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*
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* =====================================================================
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*
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* .. Parameters ..
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INTEGER ITMAX
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PARAMETER ( ITMAX = 5 )
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DOUBLE PRECISION ZERO, ONE, TWO
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, JLAST
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DOUBLE PRECISION ALTSGN, ESTOLD, TEMP
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* ..
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* .. External Functions ..
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INTEGER IDAMAX
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DOUBLE PRECISION DASUM
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EXTERNAL IDAMAX, DASUM
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* ..
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* .. External Subroutines ..
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EXTERNAL DCOPY
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, NINT, SIGN
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* ..
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* .. Executable Statements ..
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*
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IF( KASE.EQ.0 ) THEN
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DO 10 I = 1, N
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X( I ) = ONE / DBLE( N )
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10 CONTINUE
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KASE = 1
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ISAVE( 1 ) = 1
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RETURN
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END IF
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*
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GO TO ( 20, 40, 70, 110, 140 )ISAVE( 1 )
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*
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* ................ ENTRY (ISAVE( 1 ) = 1)
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* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
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*
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20 CONTINUE
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IF( N.EQ.1 ) THEN
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V( 1 ) = X( 1 )
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EST = ABS( V( 1 ) )
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* ... QUIT
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GO TO 150
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END IF
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EST = DASUM( N, X, 1 )
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*
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DO 30 I = 1, N
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X( I ) = SIGN( ONE, X( I ) )
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ISGN( I ) = NINT( X( I ) )
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30 CONTINUE
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KASE = 2
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ISAVE( 1 ) = 2
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RETURN
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*
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* ................ ENTRY (ISAVE( 1 ) = 2)
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* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
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*
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40 CONTINUE
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ISAVE( 2 ) = IDAMAX( N, X, 1 )
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ISAVE( 3 ) = 2
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*
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* MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
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*
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50 CONTINUE
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DO 60 I = 1, N
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X( I ) = ZERO
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60 CONTINUE
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X( ISAVE( 2 ) ) = ONE
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KASE = 1
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ISAVE( 1 ) = 3
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RETURN
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*
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* ................ ENTRY (ISAVE( 1 ) = 3)
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* X HAS BEEN OVERWRITTEN BY A*X.
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*
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70 CONTINUE
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CALL DCOPY( N, X, 1, V, 1 )
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ESTOLD = EST
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EST = DASUM( N, V, 1 )
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DO 80 I = 1, N
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IF( NINT( SIGN( ONE, X( I ) ) ).NE.ISGN( I ) )
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$ GO TO 90
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80 CONTINUE
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* REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED.
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GO TO 120
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*
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90 CONTINUE
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* TEST FOR CYCLING.
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IF( EST.LE.ESTOLD )
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$ GO TO 120
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*
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DO 100 I = 1, N
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X( I ) = SIGN( ONE, X( I ) )
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ISGN( I ) = NINT( X( I ) )
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100 CONTINUE
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KASE = 2
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ISAVE( 1 ) = 4
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RETURN
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*
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* ................ ENTRY (ISAVE( 1 ) = 4)
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* X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
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*
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110 CONTINUE
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JLAST = ISAVE( 2 )
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ISAVE( 2 ) = IDAMAX( N, X, 1 )
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IF( ( X( JLAST ).NE.ABS( X( ISAVE( 2 ) ) ) ) .AND.
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$ ( ISAVE( 3 ).LT.ITMAX ) ) THEN
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ISAVE( 3 ) = ISAVE( 3 ) + 1
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GO TO 50
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END IF
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*
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* ITERATION COMPLETE. FINAL STAGE.
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*
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120 CONTINUE
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ALTSGN = ONE
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DO 130 I = 1, N
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X( I ) = ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) )
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ALTSGN = -ALTSGN
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130 CONTINUE
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KASE = 1
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ISAVE( 1 ) = 5
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RETURN
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*
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* ................ ENTRY (ISAVE( 1 ) = 5)
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* X HAS BEEN OVERWRITTEN BY A*X.
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*
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140 CONTINUE
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TEMP = TWO*( DASUM( N, X, 1 ) / DBLE( 3*N ) )
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IF( TEMP.GT.EST ) THEN
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CALL DCOPY( N, X, 1, V, 1 )
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EST = TEMP
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END IF
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*
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150 CONTINUE
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KASE = 0
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RETURN
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*
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* End of DLACN2
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*
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END
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