Annotation of rpl/lapack/lapack/zlaein.f, revision 1.1
1.1 ! bertrand 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
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