*> \brief \b DLACN2 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 DLACN2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLACN2( N, V, X, ISGN, EST, KASE, ISAVE ) * * .. Scalar Arguments .. * INTEGER KASE, N * DOUBLE PRECISION EST * .. * .. Array Arguments .. * INTEGER ISGN( * ), ISAVE( 3 ) * DOUBLE PRECISION V( * ), X( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLACN2 estimates the 1-norm of a square, real 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N) *> On an intermediate return, X should be overwritten by *> A * X, if KASE=1, *> A**T * X, if KASE=2, *> and DLACN2 must be re-called with all the other parameters *> unchanged. *> \endverbatim *> *> \param[out] ISGN *> \verbatim *> ISGN is INTEGER array, dimension (N) *> \endverbatim *> *> \param[in,out] EST *> \verbatim *> EST is DOUBLE PRECISION *> On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be *> unchanged from the previous call to DLACN2. *> 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 DLACN2, 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**T * X. *> On the final return from DLACN2, 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 DLACN2 *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date September 2012 * *> \ingroup doubleOTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> Originally named SONEST, dated March 16, 1988. *> *> This is a thread safe version of DLACON, which uses the array ISAVE *> in place of a SAVE statement, as follows: *> *> DLACON DLACN2 *> 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 DLACN2( N, V, X, ISGN, EST, KASE, ISAVE ) * * -- LAPACK auxiliary routine (version 3.4.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * September 2012 * * .. Scalar Arguments .. INTEGER KASE, N DOUBLE PRECISION EST * .. * .. Array Arguments .. INTEGER ISGN( * ), ISAVE( 3 ) DOUBLE PRECISION V( * ), X( * ) * .. * * ===================================================================== * * .. Parameters .. INTEGER ITMAX PARAMETER ( ITMAX = 5 ) DOUBLE PRECISION ZERO, ONE, TWO PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 ) * .. * .. Local Scalars .. INTEGER I, JLAST DOUBLE PRECISION ALTSGN, ESTOLD, TEMP * .. * .. External Functions .. INTEGER IDAMAX DOUBLE PRECISION DASUM EXTERNAL IDAMAX, DASUM * .. * .. External Subroutines .. EXTERNAL DCOPY * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, NINT, SIGN * .. * .. Executable Statements .. * IF( KASE.EQ.0 ) THEN DO 10 I = 1, N X( I ) = ONE / DBLE( N ) 10 CONTINUE KASE = 1 ISAVE( 1 ) = 1 RETURN END IF * GO TO ( 20, 40, 70, 110, 140 )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 150 END IF EST = DASUM( N, X, 1 ) * DO 30 I = 1, N X( I ) = SIGN( ONE, X( I ) ) ISGN( I ) = NINT( X( I ) ) 30 CONTINUE KASE = 2 ISAVE( 1 ) = 2 RETURN * * ................ ENTRY (ISAVE( 1 ) = 2) * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. * 40 CONTINUE ISAVE( 2 ) = IDAMAX( N, X, 1 ) ISAVE( 3 ) = 2 * * MAIN LOOP - ITERATIONS 2,3,...,ITMAX. * 50 CONTINUE DO 60 I = 1, N X( I ) = ZERO 60 CONTINUE X( ISAVE( 2 ) ) = ONE KASE = 1 ISAVE( 1 ) = 3 RETURN * * ................ ENTRY (ISAVE( 1 ) = 3) * X HAS BEEN OVERWRITTEN BY A*X. * 70 CONTINUE CALL DCOPY( N, X, 1, V, 1 ) ESTOLD = EST EST = DASUM( N, V, 1 ) DO 80 I = 1, N IF( NINT( SIGN( ONE, X( I ) ) ).NE.ISGN( I ) ) $ GO TO 90 80 CONTINUE * REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED. GO TO 120 * 90 CONTINUE * TEST FOR CYCLING. IF( EST.LE.ESTOLD ) $ GO TO 120 * DO 100 I = 1, N X( I ) = SIGN( ONE, X( I ) ) ISGN( I ) = NINT( X( I ) ) 100 CONTINUE KASE = 2 ISAVE( 1 ) = 4 RETURN * * ................ ENTRY (ISAVE( 1 ) = 4) * X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. * 110 CONTINUE JLAST = ISAVE( 2 ) ISAVE( 2 ) = IDAMAX( N, X, 1 ) IF( ( 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. * 120 CONTINUE ALTSGN = ONE DO 130 I = 1, N X( I ) = ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) ) ALTSGN = -ALTSGN 130 CONTINUE KASE = 1 ISAVE( 1 ) = 5 RETURN * * ................ ENTRY (ISAVE( 1 ) = 5) * X HAS BEEN OVERWRITTEN BY A*X. * 140 CONTINUE TEMP = TWO*( DASUM( N, X, 1 ) / DBLE( 3*N ) ) IF( TEMP.GT.EST ) THEN CALL DCOPY( N, X, 1, V, 1 ) EST = TEMP END IF * 150 CONTINUE KASE = 0 RETURN * * End of DLACN2 * END