Annotation of rpl/lapack/lapack/dlacn2.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DLACN2( N, V, X, ISGN, EST, KASE, ISAVE )
! 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( * ), ISAVE( 3 )
! 14: DOUBLE PRECISION V( * ), X( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * DLACN2 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 DLACN2 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 ISAVE(1) = 3, EST should be
! 44: * unchanged from the previous call to DLACN2.
! 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 DLACN2, 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 DLACN2, KASE will again be 0.
! 52: *
! 53: * ISAVE (input/output) INTEGER array, dimension (3)
! 54: * ISAVE is used to save variables between calls to DLACN2
! 55: *
! 56: * Further Details
! 57: * ======= =======
! 58: *
! 59: * Contributed by Nick Higham, University of Manchester.
! 60: * Originally named SONEST, dated March 16, 1988.
! 61: *
! 62: * Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
! 63: * a real or complex matrix, with applications to condition estimation",
! 64: * ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
! 65: *
! 66: * This is a thread safe version of DLACON, which uses the array ISAVE
! 67: * in place of a SAVE statement, as follows:
! 68: *
! 69: * DLACON DLACN2
! 70: * JUMP ISAVE(1)
! 71: * J ISAVE(2)
! 72: * ITER ISAVE(3)
! 73: *
! 74: * =====================================================================
! 75: *
! 76: * .. Parameters ..
! 77: INTEGER ITMAX
! 78: PARAMETER ( ITMAX = 5 )
! 79: DOUBLE PRECISION ZERO, ONE, TWO
! 80: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
! 81: * ..
! 82: * .. Local Scalars ..
! 83: INTEGER I, JLAST
! 84: DOUBLE PRECISION ALTSGN, ESTOLD, TEMP
! 85: * ..
! 86: * .. External Functions ..
! 87: INTEGER IDAMAX
! 88: DOUBLE PRECISION DASUM
! 89: EXTERNAL IDAMAX, DASUM
! 90: * ..
! 91: * .. External Subroutines ..
! 92: EXTERNAL DCOPY
! 93: * ..
! 94: * .. Intrinsic Functions ..
! 95: INTRINSIC ABS, DBLE, NINT, SIGN
! 96: * ..
! 97: * .. Executable Statements ..
! 98: *
! 99: IF( KASE.EQ.0 ) THEN
! 100: DO 10 I = 1, N
! 101: X( I ) = ONE / DBLE( N )
! 102: 10 CONTINUE
! 103: KASE = 1
! 104: ISAVE( 1 ) = 1
! 105: RETURN
! 106: END IF
! 107: *
! 108: GO TO ( 20, 40, 70, 110, 140 )ISAVE( 1 )
! 109: *
! 110: * ................ ENTRY (ISAVE( 1 ) = 1)
! 111: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
! 112: *
! 113: 20 CONTINUE
! 114: IF( N.EQ.1 ) THEN
! 115: V( 1 ) = X( 1 )
! 116: EST = ABS( V( 1 ) )
! 117: * ... QUIT
! 118: GO TO 150
! 119: END IF
! 120: EST = DASUM( N, X, 1 )
! 121: *
! 122: DO 30 I = 1, N
! 123: X( I ) = SIGN( ONE, X( I ) )
! 124: ISGN( I ) = NINT( X( I ) )
! 125: 30 CONTINUE
! 126: KASE = 2
! 127: ISAVE( 1 ) = 2
! 128: RETURN
! 129: *
! 130: * ................ ENTRY (ISAVE( 1 ) = 2)
! 131: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
! 132: *
! 133: 40 CONTINUE
! 134: ISAVE( 2 ) = IDAMAX( N, X, 1 )
! 135: ISAVE( 3 ) = 2
! 136: *
! 137: * MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
! 138: *
! 139: 50 CONTINUE
! 140: DO 60 I = 1, N
! 141: X( I ) = ZERO
! 142: 60 CONTINUE
! 143: X( ISAVE( 2 ) ) = ONE
! 144: KASE = 1
! 145: ISAVE( 1 ) = 3
! 146: RETURN
! 147: *
! 148: * ................ ENTRY (ISAVE( 1 ) = 3)
! 149: * X HAS BEEN OVERWRITTEN BY A*X.
! 150: *
! 151: 70 CONTINUE
! 152: CALL DCOPY( N, X, 1, V, 1 )
! 153: ESTOLD = EST
! 154: EST = DASUM( N, V, 1 )
! 155: DO 80 I = 1, N
! 156: IF( NINT( SIGN( ONE, X( I ) ) ).NE.ISGN( I ) )
! 157: $ GO TO 90
! 158: 80 CONTINUE
! 159: * REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED.
! 160: GO TO 120
! 161: *
! 162: 90 CONTINUE
! 163: * TEST FOR CYCLING.
! 164: IF( EST.LE.ESTOLD )
! 165: $ GO TO 120
! 166: *
! 167: DO 100 I = 1, N
! 168: X( I ) = SIGN( ONE, X( I ) )
! 169: ISGN( I ) = NINT( X( I ) )
! 170: 100 CONTINUE
! 171: KASE = 2
! 172: ISAVE( 1 ) = 4
! 173: RETURN
! 174: *
! 175: * ................ ENTRY (ISAVE( 1 ) = 4)
! 176: * X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
! 177: *
! 178: 110 CONTINUE
! 179: JLAST = ISAVE( 2 )
! 180: ISAVE( 2 ) = IDAMAX( N, X, 1 )
! 181: IF( ( X( JLAST ).NE.ABS( X( ISAVE( 2 ) ) ) ) .AND.
! 182: $ ( ISAVE( 3 ).LT.ITMAX ) ) THEN
! 183: ISAVE( 3 ) = ISAVE( 3 ) + 1
! 184: GO TO 50
! 185: END IF
! 186: *
! 187: * ITERATION COMPLETE. FINAL STAGE.
! 188: *
! 189: 120 CONTINUE
! 190: ALTSGN = ONE
! 191: DO 130 I = 1, N
! 192: X( I ) = ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) )
! 193: ALTSGN = -ALTSGN
! 194: 130 CONTINUE
! 195: KASE = 1
! 196: ISAVE( 1 ) = 5
! 197: RETURN
! 198: *
! 199: * ................ ENTRY (ISAVE( 1 ) = 5)
! 200: * X HAS BEEN OVERWRITTEN BY A*X.
! 201: *
! 202: 140 CONTINUE
! 203: TEMP = TWO*( DASUM( N, X, 1 ) / DBLE( 3*N ) )
! 204: IF( TEMP.GT.EST ) THEN
! 205: CALL DCOPY( N, X, 1, V, 1 )
! 206: EST = TEMP
! 207: END IF
! 208: *
! 209: 150 CONTINUE
! 210: KASE = 0
! 211: RETURN
! 212: *
! 213: * End of DLACN2
! 214: *
! 215: END
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