Annotation of rpl/lapack/lapack/dgtcon.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DGTCON
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DGTCON + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgtcon.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgtcon.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgtcon.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
! 22: * WORK, IWORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER NORM
! 26: * INTEGER INFO, N
! 27: * DOUBLE PRECISION ANORM, RCOND
! 28: * ..
! 29: * .. Array Arguments ..
! 30: * INTEGER IPIV( * ), IWORK( * )
! 31: * DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
! 32: * ..
! 33: *
! 34: *
! 35: *> \par Purpose:
! 36: * =============
! 37: *>
! 38: *> \verbatim
! 39: *>
! 40: *> DGTCON estimates the reciprocal of the condition number of a real
! 41: *> tridiagonal matrix A using the LU factorization as computed by
! 42: *> DGTTRF.
! 43: *>
! 44: *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
! 45: *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
! 46: *> \endverbatim
! 47: *
! 48: * Arguments:
! 49: * ==========
! 50: *
! 51: *> \param[in] NORM
! 52: *> \verbatim
! 53: *> NORM is CHARACTER*1
! 54: *> Specifies whether the 1-norm condition number or the
! 55: *> infinity-norm condition number is required:
! 56: *> = '1' or 'O': 1-norm;
! 57: *> = 'I': Infinity-norm.
! 58: *> \endverbatim
! 59: *>
! 60: *> \param[in] N
! 61: *> \verbatim
! 62: *> N is INTEGER
! 63: *> The order of the matrix A. N >= 0.
! 64: *> \endverbatim
! 65: *>
! 66: *> \param[in] DL
! 67: *> \verbatim
! 68: *> DL is DOUBLE PRECISION array, dimension (N-1)
! 69: *> The (n-1) multipliers that define the matrix L from the
! 70: *> LU factorization of A as computed by DGTTRF.
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in] D
! 74: *> \verbatim
! 75: *> D is DOUBLE PRECISION array, dimension (N)
! 76: *> The n diagonal elements of the upper triangular matrix U from
! 77: *> the LU factorization of A.
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] DU
! 81: *> \verbatim
! 82: *> DU is DOUBLE PRECISION array, dimension (N-1)
! 83: *> The (n-1) elements of the first superdiagonal of U.
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[in] DU2
! 87: *> \verbatim
! 88: *> DU2 is DOUBLE PRECISION array, dimension (N-2)
! 89: *> The (n-2) elements of the second superdiagonal of U.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[in] IPIV
! 93: *> \verbatim
! 94: *> IPIV is INTEGER array, dimension (N)
! 95: *> The pivot indices; for 1 <= i <= n, row i of the matrix was
! 96: *> interchanged with row IPIV(i). IPIV(i) will always be either
! 97: *> i or i+1; IPIV(i) = i indicates a row interchange was not
! 98: *> required.
! 99: *> \endverbatim
! 100: *>
! 101: *> \param[in] ANORM
! 102: *> \verbatim
! 103: *> ANORM is DOUBLE PRECISION
! 104: *> If NORM = '1' or 'O', the 1-norm of the original matrix A.
! 105: *> If NORM = 'I', the infinity-norm of the original matrix A.
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[out] RCOND
! 109: *> \verbatim
! 110: *> RCOND is DOUBLE PRECISION
! 111: *> The reciprocal of the condition number of the matrix A,
! 112: *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
! 113: *> estimate of the 1-norm of inv(A) computed in this routine.
! 114: *> \endverbatim
! 115: *>
! 116: *> \param[out] WORK
! 117: *> \verbatim
! 118: *> WORK is DOUBLE PRECISION array, dimension (2*N)
! 119: *> \endverbatim
! 120: *>
! 121: *> \param[out] IWORK
! 122: *> \verbatim
! 123: *> IWORK is INTEGER array, dimension (N)
! 124: *> \endverbatim
! 125: *>
! 126: *> \param[out] INFO
! 127: *> \verbatim
! 128: *> INFO is INTEGER
! 129: *> = 0: successful exit
! 130: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 131: *> \endverbatim
! 132: *
! 133: * Authors:
! 134: * ========
! 135: *
! 136: *> \author Univ. of Tennessee
! 137: *> \author Univ. of California Berkeley
! 138: *> \author Univ. of Colorado Denver
! 139: *> \author NAG Ltd.
! 140: *
! 141: *> \date November 2011
! 142: *
! 143: *> \ingroup doubleOTHERcomputational
! 144: *
! 145: * =====================================================================
1.1 bertrand 146: SUBROUTINE DGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
147: $ WORK, IWORK, INFO )
148: *
1.9 ! bertrand 149: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 150: * -- LAPACK is a software package provided by Univ. of Tennessee, --
151: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 152: * November 2011
1.1 bertrand 153: *
154: * .. Scalar Arguments ..
155: CHARACTER NORM
156: INTEGER INFO, N
157: DOUBLE PRECISION ANORM, RCOND
158: * ..
159: * .. Array Arguments ..
160: INTEGER IPIV( * ), IWORK( * )
161: DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
162: * ..
163: *
164: * =====================================================================
165: *
166: * .. Parameters ..
167: DOUBLE PRECISION ONE, ZERO
168: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
169: * ..
170: * .. Local Scalars ..
171: LOGICAL ONENRM
172: INTEGER I, KASE, KASE1
173: DOUBLE PRECISION AINVNM
174: * ..
175: * .. Local Arrays ..
176: INTEGER ISAVE( 3 )
177: * ..
178: * .. External Functions ..
179: LOGICAL LSAME
180: EXTERNAL LSAME
181: * ..
182: * .. External Subroutines ..
183: EXTERNAL DGTTRS, DLACN2, XERBLA
184: * ..
185: * .. Executable Statements ..
186: *
187: * Test the input arguments.
188: *
189: INFO = 0
190: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
191: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
192: INFO = -1
193: ELSE IF( N.LT.0 ) THEN
194: INFO = -2
195: ELSE IF( ANORM.LT.ZERO ) THEN
196: INFO = -8
197: END IF
198: IF( INFO.NE.0 ) THEN
199: CALL XERBLA( 'DGTCON', -INFO )
200: RETURN
201: END IF
202: *
203: * Quick return if possible
204: *
205: RCOND = ZERO
206: IF( N.EQ.0 ) THEN
207: RCOND = ONE
208: RETURN
209: ELSE IF( ANORM.EQ.ZERO ) THEN
210: RETURN
211: END IF
212: *
213: * Check that D(1:N) is non-zero.
214: *
215: DO 10 I = 1, N
216: IF( D( I ).EQ.ZERO )
217: $ RETURN
218: 10 CONTINUE
219: *
220: AINVNM = ZERO
221: IF( ONENRM ) THEN
222: KASE1 = 1
223: ELSE
224: KASE1 = 2
225: END IF
226: KASE = 0
227: 20 CONTINUE
228: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
229: IF( KASE.NE.0 ) THEN
230: IF( KASE.EQ.KASE1 ) THEN
231: *
232: * Multiply by inv(U)*inv(L).
233: *
234: CALL DGTTRS( 'No transpose', N, 1, DL, D, DU, DU2, IPIV,
235: $ WORK, N, INFO )
236: ELSE
237: *
1.8 bertrand 238: * Multiply by inv(L**T)*inv(U**T).
1.1 bertrand 239: *
240: CALL DGTTRS( 'Transpose', N, 1, DL, D, DU, DU2, IPIV, WORK,
241: $ N, INFO )
242: END IF
243: GO TO 20
244: END IF
245: *
246: * Compute the estimate of the reciprocal condition number.
247: *
248: IF( AINVNM.NE.ZERO )
249: $ RCOND = ( ONE / AINVNM ) / ANORM
250: *
251: RETURN
252: *
253: * End of DGTCON
254: *
255: END
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