Annotation of rpl/lapack/lapack/dlacon.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DLACON( N, V, X, ISGN, EST, KASE )
! 2: *
! 3: * -- LAPACK auxiliary routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: INTEGER KASE, N
! 10: DOUBLE PRECISION EST
! 11: * ..
! 12: * .. Array Arguments ..
! 13: INTEGER ISGN( * )
! 14: DOUBLE PRECISION V( * ), X( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * DLACON estimates the 1-norm of a square, real matrix A.
! 21: * Reverse communication is used for evaluating matrix-vector products.
! 22: *
! 23: * Arguments
! 24: * =========
! 25: *
! 26: * N (input) INTEGER
! 27: * The order of the matrix. N >= 1.
! 28: *
! 29: * V (workspace) DOUBLE PRECISION array, dimension (N)
! 30: * On the final return, V = A*W, where EST = norm(V)/norm(W)
! 31: * (W is not returned).
! 32: *
! 33: * X (input/output) DOUBLE PRECISION array, dimension (N)
! 34: * On an intermediate return, X should be overwritten by
! 35: * A * X, if KASE=1,
! 36: * A' * X, if KASE=2,
! 37: * and DLACON must be re-called with all the other parameters
! 38: * unchanged.
! 39: *
! 40: * ISGN (workspace) INTEGER array, dimension (N)
! 41: *
! 42: * EST (input/output) DOUBLE PRECISION
! 43: * On entry with KASE = 1 or 2 and JUMP = 3, EST should be
! 44: * unchanged from the previous call to DLACON.
! 45: * On exit, EST is an estimate (a lower bound) for norm(A).
! 46: *
! 47: * KASE (input/output) INTEGER
! 48: * On the initial call to DLACON, KASE should be 0.
! 49: * On an intermediate return, KASE will be 1 or 2, indicating
! 50: * whether X should be overwritten by A * X or A' * X.
! 51: * On the final return from DLACON, KASE will again be 0.
! 52: *
! 53: * Further Details
! 54: * ======= =======
! 55: *
! 56: * Contributed by Nick Higham, University of Manchester.
! 57: * Originally named SONEST, dated March 16, 1988.
! 58: *
! 59: * Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
! 60: * a real or complex matrix, with applications to condition estimation",
! 61: * ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
! 62: *
! 63: * =====================================================================
! 64: *
! 65: * .. Parameters ..
! 66: INTEGER ITMAX
! 67: PARAMETER ( ITMAX = 5 )
! 68: DOUBLE PRECISION ZERO, ONE, TWO
! 69: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
! 70: * ..
! 71: * .. Local Scalars ..
! 72: INTEGER I, ITER, J, JLAST, JUMP
! 73: DOUBLE PRECISION ALTSGN, ESTOLD, TEMP
! 74: * ..
! 75: * .. External Functions ..
! 76: INTEGER IDAMAX
! 77: DOUBLE PRECISION DASUM
! 78: EXTERNAL IDAMAX, DASUM
! 79: * ..
! 80: * .. External Subroutines ..
! 81: EXTERNAL DCOPY
! 82: * ..
! 83: * .. Intrinsic Functions ..
! 84: INTRINSIC ABS, DBLE, NINT, SIGN
! 85: * ..
! 86: * .. Save statement ..
! 87: SAVE
! 88: * ..
! 89: * .. Executable Statements ..
! 90: *
! 91: IF( KASE.EQ.0 ) THEN
! 92: DO 10 I = 1, N
! 93: X( I ) = ONE / DBLE( N )
! 94: 10 CONTINUE
! 95: KASE = 1
! 96: JUMP = 1
! 97: RETURN
! 98: END IF
! 99: *
! 100: GO TO ( 20, 40, 70, 110, 140 )JUMP
! 101: *
! 102: * ................ ENTRY (JUMP = 1)
! 103: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
! 104: *
! 105: 20 CONTINUE
! 106: IF( N.EQ.1 ) THEN
! 107: V( 1 ) = X( 1 )
! 108: EST = ABS( V( 1 ) )
! 109: * ... QUIT
! 110: GO TO 150
! 111: END IF
! 112: EST = DASUM( N, X, 1 )
! 113: *
! 114: DO 30 I = 1, N
! 115: X( I ) = SIGN( ONE, X( I ) )
! 116: ISGN( I ) = NINT( X( I ) )
! 117: 30 CONTINUE
! 118: KASE = 2
! 119: JUMP = 2
! 120: RETURN
! 121: *
! 122: * ................ ENTRY (JUMP = 2)
! 123: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
! 124: *
! 125: 40 CONTINUE
! 126: J = IDAMAX( N, X, 1 )
! 127: ITER = 2
! 128: *
! 129: * MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
! 130: *
! 131: 50 CONTINUE
! 132: DO 60 I = 1, N
! 133: X( I ) = ZERO
! 134: 60 CONTINUE
! 135: X( J ) = ONE
! 136: KASE = 1
! 137: JUMP = 3
! 138: RETURN
! 139: *
! 140: * ................ ENTRY (JUMP = 3)
! 141: * X HAS BEEN OVERWRITTEN BY A*X.
! 142: *
! 143: 70 CONTINUE
! 144: CALL DCOPY( N, X, 1, V, 1 )
! 145: ESTOLD = EST
! 146: EST = DASUM( N, V, 1 )
! 147: DO 80 I = 1, N
! 148: IF( NINT( SIGN( ONE, X( I ) ) ).NE.ISGN( I ) )
! 149: $ GO TO 90
! 150: 80 CONTINUE
! 151: * REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED.
! 152: GO TO 120
! 153: *
! 154: 90 CONTINUE
! 155: * TEST FOR CYCLING.
! 156: IF( EST.LE.ESTOLD )
! 157: $ GO TO 120
! 158: *
! 159: DO 100 I = 1, N
! 160: X( I ) = SIGN( ONE, X( I ) )
! 161: ISGN( I ) = NINT( X( I ) )
! 162: 100 CONTINUE
! 163: KASE = 2
! 164: JUMP = 4
! 165: RETURN
! 166: *
! 167: * ................ ENTRY (JUMP = 4)
! 168: * X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
! 169: *
! 170: 110 CONTINUE
! 171: JLAST = J
! 172: J = IDAMAX( N, X, 1 )
! 173: IF( ( X( JLAST ).NE.ABS( X( J ) ) ) .AND. ( ITER.LT.ITMAX ) ) THEN
! 174: ITER = ITER + 1
! 175: GO TO 50
! 176: END IF
! 177: *
! 178: * ITERATION COMPLETE. FINAL STAGE.
! 179: *
! 180: 120 CONTINUE
! 181: ALTSGN = ONE
! 182: DO 130 I = 1, N
! 183: X( I ) = ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) )
! 184: ALTSGN = -ALTSGN
! 185: 130 CONTINUE
! 186: KASE = 1
! 187: JUMP = 5
! 188: RETURN
! 189: *
! 190: * ................ ENTRY (JUMP = 5)
! 191: * X HAS BEEN OVERWRITTEN BY A*X.
! 192: *
! 193: 140 CONTINUE
! 194: TEMP = TWO*( DASUM( N, X, 1 ) / DBLE( 3*N ) )
! 195: IF( TEMP.GT.EST ) THEN
! 196: CALL DCOPY( N, X, 1, V, 1 )
! 197: EST = TEMP
! 198: END IF
! 199: *
! 200: 150 CONTINUE
! 201: KASE = 0
! 202: RETURN
! 203: *
! 204: * End of DLACON
! 205: *
! 206: END
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