Annotation of rpl/lapack/lapack/zptcon.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZPTCON( N, D, E, ANORM, RCOND, RWORK, INFO )
! 2: *
! 3: * -- LAPACK 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 INFO, N
! 10: DOUBLE PRECISION ANORM, RCOND
! 11: * ..
! 12: * .. Array Arguments ..
! 13: DOUBLE PRECISION D( * ), RWORK( * )
! 14: COMPLEX*16 E( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZPTCON computes the reciprocal of the condition number (in the
! 21: * 1-norm) of a complex Hermitian positive definite tridiagonal matrix
! 22: * using the factorization A = L*D*L**H or A = U**H*D*U computed by
! 23: * ZPTTRF.
! 24: *
! 25: * Norm(inv(A)) is computed by a direct method, and the reciprocal of
! 26: * the condition number is computed as
! 27: * RCOND = 1 / (ANORM * norm(inv(A))).
! 28: *
! 29: * Arguments
! 30: * =========
! 31: *
! 32: * N (input) INTEGER
! 33: * The order of the matrix A. N >= 0.
! 34: *
! 35: * D (input) DOUBLE PRECISION array, dimension (N)
! 36: * The n diagonal elements of the diagonal matrix D from the
! 37: * factorization of A, as computed by ZPTTRF.
! 38: *
! 39: * E (input) COMPLEX*16 array, dimension (N-1)
! 40: * The (n-1) off-diagonal elements of the unit bidiagonal factor
! 41: * U or L from the factorization of A, as computed by ZPTTRF.
! 42: *
! 43: * ANORM (input) DOUBLE PRECISION
! 44: * The 1-norm of the original matrix A.
! 45: *
! 46: * RCOND (output) DOUBLE PRECISION
! 47: * The reciprocal of the condition number of the matrix A,
! 48: * computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the
! 49: * 1-norm of inv(A) computed in this routine.
! 50: *
! 51: * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
! 52: *
! 53: * INFO (output) INTEGER
! 54: * = 0: successful exit
! 55: * < 0: if INFO = -i, the i-th argument had an illegal value
! 56: *
! 57: * Further Details
! 58: * ===============
! 59: *
! 60: * The method used is described in Nicholas J. Higham, "Efficient
! 61: * Algorithms for Computing the Condition Number of a Tridiagonal
! 62: * Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
! 63: *
! 64: * =====================================================================
! 65: *
! 66: * .. Parameters ..
! 67: DOUBLE PRECISION ONE, ZERO
! 68: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 69: * ..
! 70: * .. Local Scalars ..
! 71: INTEGER I, IX
! 72: DOUBLE PRECISION AINVNM
! 73: * ..
! 74: * .. External Functions ..
! 75: INTEGER IDAMAX
! 76: EXTERNAL IDAMAX
! 77: * ..
! 78: * .. External Subroutines ..
! 79: EXTERNAL XERBLA
! 80: * ..
! 81: * .. Intrinsic Functions ..
! 82: INTRINSIC ABS
! 83: * ..
! 84: * .. Executable Statements ..
! 85: *
! 86: * Test the input arguments.
! 87: *
! 88: INFO = 0
! 89: IF( N.LT.0 ) THEN
! 90: INFO = -1
! 91: ELSE IF( ANORM.LT.ZERO ) THEN
! 92: INFO = -4
! 93: END IF
! 94: IF( INFO.NE.0 ) THEN
! 95: CALL XERBLA( 'ZPTCON', -INFO )
! 96: RETURN
! 97: END IF
! 98: *
! 99: * Quick return if possible
! 100: *
! 101: RCOND = ZERO
! 102: IF( N.EQ.0 ) THEN
! 103: RCOND = ONE
! 104: RETURN
! 105: ELSE IF( ANORM.EQ.ZERO ) THEN
! 106: RETURN
! 107: END IF
! 108: *
! 109: * Check that D(1:N) is positive.
! 110: *
! 111: DO 10 I = 1, N
! 112: IF( D( I ).LE.ZERO )
! 113: $ RETURN
! 114: 10 CONTINUE
! 115: *
! 116: * Solve M(A) * x = e, where M(A) = (m(i,j)) is given by
! 117: *
! 118: * m(i,j) = abs(A(i,j)), i = j,
! 119: * m(i,j) = -abs(A(i,j)), i .ne. j,
! 120: *
! 121: * and e = [ 1, 1, ..., 1 ]'. Note M(A) = M(L)*D*M(L)'.
! 122: *
! 123: * Solve M(L) * x = e.
! 124: *
! 125: RWORK( 1 ) = ONE
! 126: DO 20 I = 2, N
! 127: RWORK( I ) = ONE + RWORK( I-1 )*ABS( E( I-1 ) )
! 128: 20 CONTINUE
! 129: *
! 130: * Solve D * M(L)' * x = b.
! 131: *
! 132: RWORK( N ) = RWORK( N ) / D( N )
! 133: DO 30 I = N - 1, 1, -1
! 134: RWORK( I ) = RWORK( I ) / D( I ) + RWORK( I+1 )*ABS( E( I ) )
! 135: 30 CONTINUE
! 136: *
! 137: * Compute AINVNM = max(x(i)), 1<=i<=n.
! 138: *
! 139: IX = IDAMAX( N, RWORK, 1 )
! 140: AINVNM = ABS( RWORK( IX ) )
! 141: *
! 142: * Compute the reciprocal condition number.
! 143: *
! 144: IF( AINVNM.NE.ZERO )
! 145: $ RCOND = ( ONE / AINVNM ) / ANORM
! 146: *
! 147: RETURN
! 148: *
! 149: * End of ZPTCON
! 150: *
! 151: END
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