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author | jason <jason@8a072113-8704-0410-8d35-dd094bca7971> | 2008-10-28 01:38:50 +0000 |
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committer | jason <jason@8a072113-8704-0410-8d35-dd094bca7971> | 2008-10-28 01:38:50 +0000 |
commit | baba851215b44ac3b60b9248eb02bcce7eb76247 (patch) | |
tree | 8c0f5c006875532a30d4409f5e94b0f310ff00a7 /SRC/clacon.f | |
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Move LAPACK trunk into position.
Diffstat (limited to 'SRC/clacon.f')
-rw-r--r-- | SRC/clacon.f | 212 |
1 files changed, 212 insertions, 0 deletions
diff --git a/SRC/clacon.f b/SRC/clacon.f new file mode 100644 index 00000000..2228701d --- /dev/null +++ b/SRC/clacon.f @@ -0,0 +1,212 @@ + SUBROUTINE CLACON( N, V, X, EST, KASE ) +* +* -- 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 .. + COMPLEX V( N ), X( N ) +* .. +* +* Purpose +* ======= +* +* CLACON 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 CLACON must be +* re-called with all the other parameters unchanged. +* +* EST (input/output) REAL +* On entry with KASE = 1 or 2 and JUMP = 3, EST should be +* unchanged from the previous call to CLACON. +* On exit, EST is an estimate (a lower bound) for norm(A). +* +* KASE (input/output) INTEGER +* On the initial call to CLACON, 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 CLACON, KASE will again be 0. +* +* 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 +* +* ===================================================================== +* +* .. 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, ITER, J, JLAST, JUMP + 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 +* .. +* .. Save statement .. + SAVE +* .. +* .. 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 + JUMP = 1 + RETURN + END IF +* + GO TO ( 20, 40, 70, 90, 120 )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 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 + JUMP = 2 + RETURN +* +* ................ ENTRY (JUMP = 2) +* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY CTRANS(A)*X. +* + 40 CONTINUE + J = ICMAX1( N, X, 1 ) + ITER = 2 +* +* MAIN LOOP - ITERATIONS 2,3,...,ITMAX. +* + 50 CONTINUE + DO 60 I = 1, N + X( I ) = CZERO + 60 CONTINUE + X( J ) = CONE + KASE = 1 + JUMP = 3 + RETURN +* +* ................ ENTRY (JUMP = 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 + JUMP = 4 + RETURN +* +* ................ ENTRY (JUMP = 4) +* X HAS BEEN OVERWRITTEN BY CTRANS(A)*X. +* + 90 CONTINUE + JLAST = J + J = ICMAX1( N, X, 1 ) + IF( ( ABS( X( JLAST ) ).NE.ABS( X( J ) ) ) .AND. + $ ( ITER.LT.ITMAX ) ) THEN + ITER = ITER + 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 + JUMP = 5 + RETURN +* +* ................ ENTRY (JUMP = 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 CLACON +* + END |