*> \brief \b SLACON 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 SLACON + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SLACON( N, V, X, ISGN, EST, KASE ) * * .. Scalar Arguments .. * INTEGER KASE, N * REAL EST * .. * .. Array Arguments .. * INTEGER ISGN( * ) * REAL V( * ), X( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SLACON 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 REAL 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 REAL array, dimension (N) *> On an intermediate return, X should be overwritten by *> A * X, if KASE=1, *> A**T * X, if KASE=2, *> and SLACON 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 REAL *> On entry with KASE = 1 or 2 and JUMP = 3, EST should be *> unchanged from the previous call to SLACON. *> 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 SLACON, 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 SLACON, KASE will again be 0. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup realOTHERauxiliary * *> \par Contributors: * ================== *> *> Nick Higham, University of Manchester. \n *> Originally named SONEST, dated March 16, 1988. * *> \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 SLACON( N, V, X, ISGN, EST, KASE ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER KASE, N REAL EST * .. * .. Array Arguments .. INTEGER ISGN( * ) REAL V( * ), X( * ) * .. * * ===================================================================== * * .. Parameters .. INTEGER ITMAX PARAMETER ( ITMAX = 5 ) REAL ZERO, ONE, TWO PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TWO = 2.0E+0 ) * .. * .. Local Scalars .. INTEGER I, ITER, J, JLAST, JUMP REAL ALTSGN, ESTOLD, TEMP * .. * .. External Functions .. INTEGER ISAMAX REAL SASUM EXTERNAL ISAMAX, SASUM * .. * .. External Subroutines .. EXTERNAL SCOPY * .. * .. Intrinsic Functions .. INTRINSIC ABS, NINT, REAL, SIGN * .. * .. Save statement .. SAVE * .. * .. Executable Statements .. * IF( KASE.EQ.0 ) THEN DO 10 I = 1, N X( I ) = ONE / REAL( N ) 10 CONTINUE KASE = 1 JUMP = 1 RETURN END IF * GO TO ( 20, 40, 70, 110, 140 )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 150 END IF EST = SASUM( N, X, 1 ) * DO 30 I = 1, N X( I ) = SIGN( ONE, X( I ) ) ISGN( I ) = NINT( X( I ) ) 30 CONTINUE KASE = 2 JUMP = 2 RETURN * * ................ ENTRY (JUMP = 2) * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. * 40 CONTINUE J = ISAMAX( N, X, 1 ) ITER = 2 * * MAIN LOOP - ITERATIONS 2,3,...,ITMAX. * 50 CONTINUE DO 60 I = 1, N X( I ) = ZERO 60 CONTINUE X( J ) = ONE KASE = 1 JUMP = 3 RETURN * * ................ ENTRY (JUMP = 3) * X HAS BEEN OVERWRITTEN BY A*X. * 70 CONTINUE CALL SCOPY( N, X, 1, V, 1 ) ESTOLD = EST EST = SASUM( 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 JUMP = 4 RETURN * * ................ ENTRY (JUMP = 4) * X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. * 110 CONTINUE JLAST = J J = ISAMAX( N, X, 1 ) IF( ( X( JLAST ).NE.ABS( X( J ) ) ) .AND. ( ITER.LT.ITMAX ) ) THEN ITER = ITER + 1 GO TO 50 END IF * * ITERATION COMPLETE. FINAL STAGE. * 120 CONTINUE ALTSGN = ONE DO 130 I = 1, N X( I ) = ALTSGN*( ONE+REAL( I-1 ) / REAL( N-1 ) ) ALTSGN = -ALTSGN 130 CONTINUE KASE = 1 JUMP = 5 RETURN * * ................ ENTRY (JUMP = 5) * X HAS BEEN OVERWRITTEN BY A*X. * 140 CONTINUE TEMP = TWO*( SASUM( N, X, 1 ) / REAL( 3*N ) ) IF( TEMP.GT.EST ) THEN CALL SCOPY( N, X, 1, V, 1 ) EST = TEMP END IF * 150 CONTINUE KASE = 0 RETURN * * End of SLACON * END