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Diffstat (limited to '2.3-1/src/fortran/lapack/dlacn2.f')
| -rw-r--r-- | 2.3-1/src/fortran/lapack/dlacn2.f | 214 |
1 files changed, 214 insertions, 0 deletions
diff --git a/2.3-1/src/fortran/lapack/dlacn2.f b/2.3-1/src/fortran/lapack/dlacn2.f new file mode 100644 index 00000000..6705d256 --- /dev/null +++ b/2.3-1/src/fortran/lapack/dlacn2.f @@ -0,0 +1,214 @@ + SUBROUTINE DLACN2( N, V, X, ISGN, 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 + DOUBLE PRECISION EST +* .. +* .. Array Arguments .. + INTEGER ISGN( * ), ISAVE( 3 ) + DOUBLE PRECISION V( * ), X( * ) +* .. +* +* Purpose +* ======= +* +* DLACN2 estimates the 1-norm of a square, real matrix A. +* Reverse communication is used for evaluating matrix-vector products. +* +* Arguments +* ========= +* +* N (input) INTEGER +* The order of the matrix. N >= 1. +* +* V (workspace) DOUBLE PRECISION array, dimension (N) +* On the final return, V = A*W, where EST = norm(V)/norm(W) +* (W is not returned). +* +* X (input/output) DOUBLE PRECISION array, dimension (N) +* On an intermediate return, X should be overwritten by +* A * X, if KASE=1, +* A' * X, if KASE=2, +* and DLACN2 must be re-called with all the other parameters +* unchanged. +* +* ISGN (workspace) INTEGER array, dimension (N) +* +* EST (input/output) 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). +* +* KASE (input/output) 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' * X. +* On the final return from DLACN2, KASE will again be 0. +* +* ISAVE (input/output) INTEGER array, dimension (3) +* ISAVE is used to save variables between calls to DLACN2 +* +* Further Details +* ======= ======= +* +* Contributed by Nick Higham, University of Manchester. +* Originally named SONEST, 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. +* +* 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) +* +* ===================================================================== +* +* .. 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 |