Annotation of rpl/lapack/lapack/zlacn2.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZLACN2( N, V, X, 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 ISAVE( 3 )
! 14: COMPLEX*16 V( * ), X( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZLACN2 estimates the 1-norm of a square, complex 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) COMPLEX*16 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) COMPLEX*16 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: * where A' is the conjugate transpose of A, and ZLACN2 must be
! 38: * re-called with all the other parameters unchanged.
! 39: *
! 40: * EST (input/output) DOUBLE PRECISION
! 41: * On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be
! 42: * unchanged from the previous call to ZLACN2.
! 43: * On exit, EST is an estimate (a lower bound) for norm(A).
! 44: *
! 45: * KASE (input/output) INTEGER
! 46: * On the initial call to ZLACN2, KASE should be 0.
! 47: * On an intermediate return, KASE will be 1 or 2, indicating
! 48: * whether X should be overwritten by A * X or A' * X.
! 49: * On the final return from ZLACN2, KASE will again be 0.
! 50: *
! 51: * ISAVE (input/output) INTEGER array, dimension (3)
! 52: * ISAVE is used to save variables between calls to ZLACN2
! 53: *
! 54: * Further Details
! 55: * ======= =======
! 56: *
! 57: * Contributed by Nick Higham, University of Manchester.
! 58: * Originally named CONEST, dated March 16, 1988.
! 59: *
! 60: * Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
! 61: * a real or complex matrix, with applications to condition estimation",
! 62: * ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
! 63: *
! 64: * Last modified: April, 1999
! 65: *
! 66: * This is a thread safe version of ZLACON, which uses the array ISAVE
! 67: * in place of a SAVE statement, as follows:
! 68: *
! 69: * ZLACON ZLACN2
! 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 ONE, TWO
! 80: PARAMETER ( ONE = 1.0D0, TWO = 2.0D0 )
! 81: COMPLEX*16 CZERO, CONE
! 82: PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ),
! 83: $ CONE = ( 1.0D0, 0.0D0 ) )
! 84: * ..
! 85: * .. Local Scalars ..
! 86: INTEGER I, JLAST
! 87: DOUBLE PRECISION ABSXI, ALTSGN, ESTOLD, SAFMIN, TEMP
! 88: * ..
! 89: * .. External Functions ..
! 90: INTEGER IZMAX1
! 91: DOUBLE PRECISION DLAMCH, DZSUM1
! 92: EXTERNAL IZMAX1, DLAMCH, DZSUM1
! 93: * ..
! 94: * .. External Subroutines ..
! 95: EXTERNAL ZCOPY
! 96: * ..
! 97: * .. Intrinsic Functions ..
! 98: INTRINSIC ABS, DBLE, DCMPLX, DIMAG
! 99: * ..
! 100: * .. Executable Statements ..
! 101: *
! 102: SAFMIN = DLAMCH( 'Safe minimum' )
! 103: IF( KASE.EQ.0 ) THEN
! 104: DO 10 I = 1, N
! 105: X( I ) = DCMPLX( ONE / DBLE( N ) )
! 106: 10 CONTINUE
! 107: KASE = 1
! 108: ISAVE( 1 ) = 1
! 109: RETURN
! 110: END IF
! 111: *
! 112: GO TO ( 20, 40, 70, 90, 120 )ISAVE( 1 )
! 113: *
! 114: * ................ ENTRY (ISAVE( 1 ) = 1)
! 115: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
! 116: *
! 117: 20 CONTINUE
! 118: IF( N.EQ.1 ) THEN
! 119: V( 1 ) = X( 1 )
! 120: EST = ABS( V( 1 ) )
! 121: * ... QUIT
! 122: GO TO 130
! 123: END IF
! 124: EST = DZSUM1( N, X, 1 )
! 125: *
! 126: DO 30 I = 1, N
! 127: ABSXI = ABS( X( I ) )
! 128: IF( ABSXI.GT.SAFMIN ) THEN
! 129: X( I ) = DCMPLX( DBLE( X( I ) ) / ABSXI,
! 130: $ DIMAG( X( I ) ) / ABSXI )
! 131: ELSE
! 132: X( I ) = CONE
! 133: END IF
! 134: 30 CONTINUE
! 135: KASE = 2
! 136: ISAVE( 1 ) = 2
! 137: RETURN
! 138: *
! 139: * ................ ENTRY (ISAVE( 1 ) = 2)
! 140: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
! 141: *
! 142: 40 CONTINUE
! 143: ISAVE( 2 ) = IZMAX1( N, X, 1 )
! 144: ISAVE( 3 ) = 2
! 145: *
! 146: * MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
! 147: *
! 148: 50 CONTINUE
! 149: DO 60 I = 1, N
! 150: X( I ) = CZERO
! 151: 60 CONTINUE
! 152: X( ISAVE( 2 ) ) = CONE
! 153: KASE = 1
! 154: ISAVE( 1 ) = 3
! 155: RETURN
! 156: *
! 157: * ................ ENTRY (ISAVE( 1 ) = 3)
! 158: * X HAS BEEN OVERWRITTEN BY A*X.
! 159: *
! 160: 70 CONTINUE
! 161: CALL ZCOPY( N, X, 1, V, 1 )
! 162: ESTOLD = EST
! 163: EST = DZSUM1( N, V, 1 )
! 164: *
! 165: * TEST FOR CYCLING.
! 166: IF( EST.LE.ESTOLD )
! 167: $ GO TO 100
! 168: *
! 169: DO 80 I = 1, N
! 170: ABSXI = ABS( X( I ) )
! 171: IF( ABSXI.GT.SAFMIN ) THEN
! 172: X( I ) = DCMPLX( DBLE( X( I ) ) / ABSXI,
! 173: $ DIMAG( X( I ) ) / ABSXI )
! 174: ELSE
! 175: X( I ) = CONE
! 176: END IF
! 177: 80 CONTINUE
! 178: KASE = 2
! 179: ISAVE( 1 ) = 4
! 180: RETURN
! 181: *
! 182: * ................ ENTRY (ISAVE( 1 ) = 4)
! 183: * X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
! 184: *
! 185: 90 CONTINUE
! 186: JLAST = ISAVE( 2 )
! 187: ISAVE( 2 ) = IZMAX1( N, X, 1 )
! 188: IF( ( ABS( X( JLAST ) ).NE.ABS( X( ISAVE( 2 ) ) ) ) .AND.
! 189: $ ( ISAVE( 3 ).LT.ITMAX ) ) THEN
! 190: ISAVE( 3 ) = ISAVE( 3 ) + 1
! 191: GO TO 50
! 192: END IF
! 193: *
! 194: * ITERATION COMPLETE. FINAL STAGE.
! 195: *
! 196: 100 CONTINUE
! 197: ALTSGN = ONE
! 198: DO 110 I = 1, N
! 199: X( I ) = DCMPLX( ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) ) )
! 200: ALTSGN = -ALTSGN
! 201: 110 CONTINUE
! 202: KASE = 1
! 203: ISAVE( 1 ) = 5
! 204: RETURN
! 205: *
! 206: * ................ ENTRY (ISAVE( 1 ) = 5)
! 207: * X HAS BEEN OVERWRITTEN BY A*X.
! 208: *
! 209: 120 CONTINUE
! 210: TEMP = TWO*( DZSUM1( N, X, 1 ) / DBLE( 3*N ) )
! 211: IF( TEMP.GT.EST ) THEN
! 212: CALL ZCOPY( N, X, 1, V, 1 )
! 213: EST = TEMP
! 214: END IF
! 215: *
! 216: 130 CONTINUE
! 217: KASE = 0
! 218: RETURN
! 219: *
! 220: * End of ZLACN2
! 221: *
! 222: END
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