Annotation of rpl/lapack/lapack/dlatdf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV,
! 2: $ JPIV )
! 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: INTEGER IJOB, LDZ, N
! 11: DOUBLE PRECISION RDSCAL, RDSUM
! 12: * ..
! 13: * .. Array Arguments ..
! 14: INTEGER IPIV( * ), JPIV( * )
! 15: DOUBLE PRECISION RHS( * ), Z( LDZ, * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * DLATDF uses the LU factorization of the n-by-n matrix Z computed by
! 22: * DGETC2 and computes a contribution to the reciprocal Dif-estimate
! 23: * by solving Z * x = b for x, and choosing the r.h.s. b such that
! 24: * the norm of x is as large as possible. On entry RHS = b holds the
! 25: * contribution from earlier solved sub-systems, and on return RHS = x.
! 26: *
! 27: * The factorization of Z returned by DGETC2 has the form Z = P*L*U*Q,
! 28: * where P and Q are permutation matrices. L is lower triangular with
! 29: * unit diagonal elements and U is upper triangular.
! 30: *
! 31: * Arguments
! 32: * =========
! 33: *
! 34: * IJOB (input) INTEGER
! 35: * IJOB = 2: First compute an approximative null-vector e
! 36: * of Z using DGECON, e is normalized and solve for
! 37: * Zx = +-e - f with the sign giving the greater value
! 38: * of 2-norm(x). About 5 times as expensive as Default.
! 39: * IJOB .ne. 2: Local look ahead strategy where all entries of
! 40: * the r.h.s. b is choosen as either +1 or -1 (Default).
! 41: *
! 42: * N (input) INTEGER
! 43: * The number of columns of the matrix Z.
! 44: *
! 45: * Z (input) DOUBLE PRECISION array, dimension (LDZ, N)
! 46: * On entry, the LU part of the factorization of the n-by-n
! 47: * matrix Z computed by DGETC2: Z = P * L * U * Q
! 48: *
! 49: * LDZ (input) INTEGER
! 50: * The leading dimension of the array Z. LDA >= max(1, N).
! 51: *
! 52: * RHS (input/output) DOUBLE PRECISION array, dimension N.
! 53: * On entry, RHS contains contributions from other subsystems.
! 54: * On exit, RHS contains the solution of the subsystem with
! 55: * entries acoording to the value of IJOB (see above).
! 56: *
! 57: * RDSUM (input/output) DOUBLE PRECISION
! 58: * On entry, the sum of squares of computed contributions to
! 59: * the Dif-estimate under computation by DTGSYL, where the
! 60: * scaling factor RDSCAL (see below) has been factored out.
! 61: * On exit, the corresponding sum of squares updated with the
! 62: * contributions from the current sub-system.
! 63: * If TRANS = 'T' RDSUM is not touched.
! 64: * NOTE: RDSUM only makes sense when DTGSY2 is called by STGSYL.
! 65: *
! 66: * RDSCAL (input/output) DOUBLE PRECISION
! 67: * On entry, scaling factor used to prevent overflow in RDSUM.
! 68: * On exit, RDSCAL is updated w.r.t. the current contributions
! 69: * in RDSUM.
! 70: * If TRANS = 'T', RDSCAL is not touched.
! 71: * NOTE: RDSCAL only makes sense when DTGSY2 is called by
! 72: * DTGSYL.
! 73: *
! 74: * IPIV (input) INTEGER array, dimension (N).
! 75: * The pivot indices; for 1 <= i <= N, row i of the
! 76: * matrix has been interchanged with row IPIV(i).
! 77: *
! 78: * JPIV (input) INTEGER array, dimension (N).
! 79: * The pivot indices; for 1 <= j <= N, column j of the
! 80: * matrix has been interchanged with column JPIV(j).
! 81: *
! 82: * Further Details
! 83: * ===============
! 84: *
! 85: * Based on contributions by
! 86: * Bo Kagstrom and Peter Poromaa, Department of Computing Science,
! 87: * Umea University, S-901 87 Umea, Sweden.
! 88: *
! 89: * This routine is a further developed implementation of algorithm
! 90: * BSOLVE in [1] using complete pivoting in the LU factorization.
! 91: *
! 92: * [1] Bo Kagstrom and Lars Westin,
! 93: * Generalized Schur Methods with Condition Estimators for
! 94: * Solving the Generalized Sylvester Equation, IEEE Transactions
! 95: * on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751.
! 96: *
! 97: * [2] Peter Poromaa,
! 98: * On Efficient and Robust Estimators for the Separation
! 99: * between two Regular Matrix Pairs with Applications in
! 100: * Condition Estimation. Report IMINF-95.05, Departement of
! 101: * Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.
! 102: *
! 103: * =====================================================================
! 104: *
! 105: * .. Parameters ..
! 106: INTEGER MAXDIM
! 107: PARAMETER ( MAXDIM = 8 )
! 108: DOUBLE PRECISION ZERO, ONE
! 109: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 110: * ..
! 111: * .. Local Scalars ..
! 112: INTEGER I, INFO, J, K
! 113: DOUBLE PRECISION BM, BP, PMONE, SMINU, SPLUS, TEMP
! 114: * ..
! 115: * .. Local Arrays ..
! 116: INTEGER IWORK( MAXDIM )
! 117: DOUBLE PRECISION WORK( 4*MAXDIM ), XM( MAXDIM ), XP( MAXDIM )
! 118: * ..
! 119: * .. External Subroutines ..
! 120: EXTERNAL DAXPY, DCOPY, DGECON, DGESC2, DLASSQ, DLASWP,
! 121: $ DSCAL
! 122: * ..
! 123: * .. External Functions ..
! 124: DOUBLE PRECISION DASUM, DDOT
! 125: EXTERNAL DASUM, DDOT
! 126: * ..
! 127: * .. Intrinsic Functions ..
! 128: INTRINSIC ABS, SQRT
! 129: * ..
! 130: * .. Executable Statements ..
! 131: *
! 132: IF( IJOB.NE.2 ) THEN
! 133: *
! 134: * Apply permutations IPIV to RHS
! 135: *
! 136: CALL DLASWP( 1, RHS, LDZ, 1, N-1, IPIV, 1 )
! 137: *
! 138: * Solve for L-part choosing RHS either to +1 or -1.
! 139: *
! 140: PMONE = -ONE
! 141: *
! 142: DO 10 J = 1, N - 1
! 143: BP = RHS( J ) + ONE
! 144: BM = RHS( J ) - ONE
! 145: SPLUS = ONE
! 146: *
! 147: * Look-ahead for L-part RHS(1:N-1) = + or -1, SPLUS and
! 148: * SMIN computed more efficiently than in BSOLVE [1].
! 149: *
! 150: SPLUS = SPLUS + DDOT( N-J, Z( J+1, J ), 1, Z( J+1, J ), 1 )
! 151: SMINU = DDOT( N-J, Z( J+1, J ), 1, RHS( J+1 ), 1 )
! 152: SPLUS = SPLUS*RHS( J )
! 153: IF( SPLUS.GT.SMINU ) THEN
! 154: RHS( J ) = BP
! 155: ELSE IF( SMINU.GT.SPLUS ) THEN
! 156: RHS( J ) = BM
! 157: ELSE
! 158: *
! 159: * In this case the updating sums are equal and we can
! 160: * choose RHS(J) +1 or -1. The first time this happens
! 161: * we choose -1, thereafter +1. This is a simple way to
! 162: * get good estimates of matrices like Byers well-known
! 163: * example (see [1]). (Not done in BSOLVE.)
! 164: *
! 165: RHS( J ) = RHS( J ) + PMONE
! 166: PMONE = ONE
! 167: END IF
! 168: *
! 169: * Compute the remaining r.h.s.
! 170: *
! 171: TEMP = -RHS( J )
! 172: CALL DAXPY( N-J, TEMP, Z( J+1, J ), 1, RHS( J+1 ), 1 )
! 173: *
! 174: 10 CONTINUE
! 175: *
! 176: * Solve for U-part, look-ahead for RHS(N) = +-1. This is not done
! 177: * in BSOLVE and will hopefully give us a better estimate because
! 178: * any ill-conditioning of the original matrix is transfered to U
! 179: * and not to L. U(N, N) is an approximation to sigma_min(LU).
! 180: *
! 181: CALL DCOPY( N-1, RHS, 1, XP, 1 )
! 182: XP( N ) = RHS( N ) + ONE
! 183: RHS( N ) = RHS( N ) - ONE
! 184: SPLUS = ZERO
! 185: SMINU = ZERO
! 186: DO 30 I = N, 1, -1
! 187: TEMP = ONE / Z( I, I )
! 188: XP( I ) = XP( I )*TEMP
! 189: RHS( I ) = RHS( I )*TEMP
! 190: DO 20 K = I + 1, N
! 191: XP( I ) = XP( I ) - XP( K )*( Z( I, K )*TEMP )
! 192: RHS( I ) = RHS( I ) - RHS( K )*( Z( I, K )*TEMP )
! 193: 20 CONTINUE
! 194: SPLUS = SPLUS + ABS( XP( I ) )
! 195: SMINU = SMINU + ABS( RHS( I ) )
! 196: 30 CONTINUE
! 197: IF( SPLUS.GT.SMINU )
! 198: $ CALL DCOPY( N, XP, 1, RHS, 1 )
! 199: *
! 200: * Apply the permutations JPIV to the computed solution (RHS)
! 201: *
! 202: CALL DLASWP( 1, RHS, LDZ, 1, N-1, JPIV, -1 )
! 203: *
! 204: * Compute the sum of squares
! 205: *
! 206: CALL DLASSQ( N, RHS, 1, RDSCAL, RDSUM )
! 207: *
! 208: ELSE
! 209: *
! 210: * IJOB = 2, Compute approximate nullvector XM of Z
! 211: *
! 212: CALL DGECON( 'I', N, Z, LDZ, ONE, TEMP, WORK, IWORK, INFO )
! 213: CALL DCOPY( N, WORK( N+1 ), 1, XM, 1 )
! 214: *
! 215: * Compute RHS
! 216: *
! 217: CALL DLASWP( 1, XM, LDZ, 1, N-1, IPIV, -1 )
! 218: TEMP = ONE / SQRT( DDOT( N, XM, 1, XM, 1 ) )
! 219: CALL DSCAL( N, TEMP, XM, 1 )
! 220: CALL DCOPY( N, XM, 1, XP, 1 )
! 221: CALL DAXPY( N, ONE, RHS, 1, XP, 1 )
! 222: CALL DAXPY( N, -ONE, XM, 1, RHS, 1 )
! 223: CALL DGESC2( N, Z, LDZ, RHS, IPIV, JPIV, TEMP )
! 224: CALL DGESC2( N, Z, LDZ, XP, IPIV, JPIV, TEMP )
! 225: IF( DASUM( N, XP, 1 ).GT.DASUM( N, RHS, 1 ) )
! 226: $ CALL DCOPY( N, XP, 1, RHS, 1 )
! 227: *
! 228: * Compute the sum of squares
! 229: *
! 230: CALL DLASSQ( N, RHS, 1, RDSCAL, RDSUM )
! 231: *
! 232: END IF
! 233: *
! 234: RETURN
! 235: *
! 236: * End of DLATDF
! 237: *
! 238: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dlatdf.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack