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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK, 2: $ EPS3, SMLNUM, INFO ) 3: * 4: * -- LAPACK auxiliary routine (version 3.2) -- 5: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 7: * November 2006 8: * 9: * .. Scalar Arguments .. 10: LOGICAL NOINIT, RIGHTV 11: INTEGER INFO, LDB, LDH, N 12: DOUBLE PRECISION EPS3, SMLNUM 13: COMPLEX*16 W 14: * .. 15: * .. Array Arguments .. 16: DOUBLE PRECISION RWORK( * ) 17: COMPLEX*16 B( LDB, * ), H( LDH, * ), V( * ) 18: * .. 19: * 20: * Purpose 21: * ======= 22: * 23: * ZLAEIN uses inverse iteration to find a right or left eigenvector 24: * corresponding to the eigenvalue W of a complex upper Hessenberg 25: * matrix H. 26: * 27: * Arguments 28: * ========= 29: * 30: * RIGHTV (input) LOGICAL 31: * = .TRUE. : compute right eigenvector; 32: * = .FALSE.: compute left eigenvector. 33: * 34: * NOINIT (input) LOGICAL 35: * = .TRUE. : no initial vector supplied in V 36: * = .FALSE.: initial vector supplied in V. 37: * 38: * N (input) INTEGER 39: * The order of the matrix H. N >= 0. 40: * 41: * H (input) COMPLEX*16 array, dimension (LDH,N) 42: * The upper Hessenberg matrix H. 43: * 44: * LDH (input) INTEGER 45: * The leading dimension of the array H. LDH >= max(1,N). 46: * 47: * W (input) COMPLEX*16 48: * The eigenvalue of H whose corresponding right or left 49: * eigenvector is to be computed. 50: * 51: * V (input/output) COMPLEX*16 array, dimension (N) 52: * On entry, if NOINIT = .FALSE., V must contain a starting 53: * vector for inverse iteration; otherwise V need not be set. 54: * On exit, V contains the computed eigenvector, normalized so 55: * that the component of largest magnitude has magnitude 1; here 56: * the magnitude of a complex number (x,y) is taken to be 57: * |x| + |y|. 58: * 59: * B (workspace) COMPLEX*16 array, dimension (LDB,N) 60: * 61: * LDB (input) INTEGER 62: * The leading dimension of the array B. LDB >= max(1,N). 63: * 64: * RWORK (workspace) DOUBLE PRECISION array, dimension (N) 65: * 66: * EPS3 (input) DOUBLE PRECISION 67: * A small machine-dependent value which is used to perturb 68: * close eigenvalues, and to replace zero pivots. 69: * 70: * SMLNUM (input) DOUBLE PRECISION 71: * A machine-dependent value close to the underflow threshold. 72: * 73: * INFO (output) INTEGER 74: * = 0: successful exit 75: * = 1: inverse iteration did not converge; V is set to the 76: * last iterate. 77: * 78: * ===================================================================== 79: * 80: * .. Parameters .. 81: DOUBLE PRECISION ONE, TENTH 82: PARAMETER ( ONE = 1.0D+0, TENTH = 1.0D-1 ) 83: COMPLEX*16 ZERO 84: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) 85: * .. 86: * .. Local Scalars .. 87: CHARACTER NORMIN, TRANS 88: INTEGER I, IERR, ITS, J 89: DOUBLE PRECISION GROWTO, NRMSML, ROOTN, RTEMP, SCALE, VNORM 90: COMPLEX*16 CDUM, EI, EJ, TEMP, X 91: * .. 92: * .. External Functions .. 93: INTEGER IZAMAX 94: DOUBLE PRECISION DZASUM, DZNRM2 95: COMPLEX*16 ZLADIV 96: EXTERNAL IZAMAX, DZASUM, DZNRM2, ZLADIV 97: * .. 98: * .. External Subroutines .. 99: EXTERNAL ZDSCAL, ZLATRS 100: * .. 101: * .. Intrinsic Functions .. 102: INTRINSIC ABS, DBLE, DIMAG, MAX, SQRT 103: * .. 104: * .. Statement Functions .. 105: DOUBLE PRECISION CABS1 106: * .. 107: * .. Statement Function definitions .. 108: CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) ) 109: * .. 110: * .. Executable Statements .. 111: * 112: INFO = 0 113: * 114: * GROWTO is the threshold used in the acceptance test for an 115: * eigenvector. 116: * 117: ROOTN = SQRT( DBLE( N ) ) 118: GROWTO = TENTH / ROOTN 119: NRMSML = MAX( ONE, EPS3*ROOTN )*SMLNUM 120: * 121: * Form B = H - W*I (except that the subdiagonal elements are not 122: * stored). 123: * 124: DO 20 J = 1, N 125: DO 10 I = 1, J - 1 126: B( I, J ) = H( I, J ) 127: 10 CONTINUE 128: B( J, J ) = H( J, J ) - W 129: 20 CONTINUE 130: * 131: IF( NOINIT ) THEN 132: * 133: * Initialize V. 134: * 135: DO 30 I = 1, N 136: V( I ) = EPS3 137: 30 CONTINUE 138: ELSE 139: * 140: * Scale supplied initial vector. 141: * 142: VNORM = DZNRM2( N, V, 1 ) 143: CALL ZDSCAL( N, ( EPS3*ROOTN ) / MAX( VNORM, NRMSML ), V, 1 ) 144: END IF 145: * 146: IF( RIGHTV ) THEN 147: * 148: * LU decomposition with partial pivoting of B, replacing zero 149: * pivots by EPS3. 150: * 151: DO 60 I = 1, N - 1 152: EI = H( I+1, I ) 153: IF( CABS1( B( I, I ) ).LT.CABS1( EI ) ) THEN 154: * 155: * Interchange rows and eliminate. 156: * 157: X = ZLADIV( B( I, I ), EI ) 158: B( I, I ) = EI 159: DO 40 J = I + 1, N 160: TEMP = B( I+1, J ) 161: B( I+1, J ) = B( I, J ) - X*TEMP 162: B( I, J ) = TEMP 163: 40 CONTINUE 164: ELSE 165: * 166: * Eliminate without interchange. 167: * 168: IF( B( I, I ).EQ.ZERO ) 169: $ B( I, I ) = EPS3 170: X = ZLADIV( EI, B( I, I ) ) 171: IF( X.NE.ZERO ) THEN 172: DO 50 J = I + 1, N 173: B( I+1, J ) = B( I+1, J ) - X*B( I, J ) 174: 50 CONTINUE 175: END IF 176: END IF 177: 60 CONTINUE 178: IF( B( N, N ).EQ.ZERO ) 179: $ B( N, N ) = EPS3 180: * 181: TRANS = 'N' 182: * 183: ELSE 184: * 185: * UL decomposition with partial pivoting of B, replacing zero 186: * pivots by EPS3. 187: * 188: DO 90 J = N, 2, -1 189: EJ = H( J, J-1 ) 190: IF( CABS1( B( J, J ) ).LT.CABS1( EJ ) ) THEN 191: * 192: * Interchange columns and eliminate. 193: * 194: X = ZLADIV( B( J, J ), EJ ) 195: B( J, J ) = EJ 196: DO 70 I = 1, J - 1 197: TEMP = B( I, J-1 ) 198: B( I, J-1 ) = B( I, J ) - X*TEMP 199: B( I, J ) = TEMP 200: 70 CONTINUE 201: ELSE 202: * 203: * Eliminate without interchange. 204: * 205: IF( B( J, J ).EQ.ZERO ) 206: $ B( J, J ) = EPS3 207: X = ZLADIV( EJ, B( J, J ) ) 208: IF( X.NE.ZERO ) THEN 209: DO 80 I = 1, J - 1 210: B( I, J-1 ) = B( I, J-1 ) - X*B( I, J ) 211: 80 CONTINUE 212: END IF 213: END IF 214: 90 CONTINUE 215: IF( B( 1, 1 ).EQ.ZERO ) 216: $ B( 1, 1 ) = EPS3 217: * 218: TRANS = 'C' 219: * 220: END IF 221: * 222: NORMIN = 'N' 223: DO 110 ITS = 1, N 224: * 225: * Solve U*x = scale*v for a right eigenvector 226: * or U'*x = scale*v for a left eigenvector, 227: * overwriting x on v. 228: * 229: CALL ZLATRS( 'Upper', TRANS, 'Nonunit', NORMIN, N, B, LDB, V, 230: $ SCALE, RWORK, IERR ) 231: NORMIN = 'Y' 232: * 233: * Test for sufficient growth in the norm of v. 234: * 235: VNORM = DZASUM( N, V, 1 ) 236: IF( VNORM.GE.GROWTO*SCALE ) 237: $ GO TO 120 238: * 239: * Choose new orthogonal starting vector and try again. 240: * 241: RTEMP = EPS3 / ( ROOTN+ONE ) 242: V( 1 ) = EPS3 243: DO 100 I = 2, N 244: V( I ) = RTEMP 245: 100 CONTINUE 246: V( N-ITS+1 ) = V( N-ITS+1 ) - EPS3*ROOTN 247: 110 CONTINUE 248: * 249: * Failure to find eigenvector in N iterations. 250: * 251: INFO = 1 252: * 253: 120 CONTINUE 254: * 255: * Normalize eigenvector. 256: * 257: I = IZAMAX( N, V, 1 ) 258: CALL ZDSCAL( N, ONE / CABS1( V( I ) ), V, 1 ) 259: * 260: RETURN 261: * 262: * End of ZLAEIN 263: * 264: END