Annotation of rpl/lapack/lapack/dsycon.f, revision 1.10
1.10 ! bertrand 1: *> \brief \b DSYCON
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DSYCON + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsycon.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsycon.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsycon.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
! 22: * IWORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER UPLO
! 26: * INTEGER INFO, LDA, N
! 27: * DOUBLE PRECISION ANORM, RCOND
! 28: * ..
! 29: * .. Array Arguments ..
! 30: * INTEGER IPIV( * ), IWORK( * )
! 31: * DOUBLE PRECISION A( LDA, * ), WORK( * )
! 32: * ..
! 33: *
! 34: *
! 35: *> \par Purpose:
! 36: * =============
! 37: *>
! 38: *> \verbatim
! 39: *>
! 40: *> DSYCON estimates the reciprocal of the condition number (in the
! 41: *> 1-norm) of a real symmetric matrix A using the factorization
! 42: *> A = U*D*U**T or A = L*D*L**T computed by DSYTRF.
! 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] UPLO
! 52: *> \verbatim
! 53: *> UPLO is CHARACTER*1
! 54: *> Specifies whether the details of the factorization are stored
! 55: *> as an upper or lower triangular matrix.
! 56: *> = 'U': Upper triangular, form is A = U*D*U**T;
! 57: *> = 'L': Lower triangular, form is A = L*D*L**T.
! 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] A
! 67: *> \verbatim
! 68: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 69: *> The block diagonal matrix D and the multipliers used to
! 70: *> obtain the factor U or L as computed by DSYTRF.
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in] LDA
! 74: *> \verbatim
! 75: *> LDA is INTEGER
! 76: *> The leading dimension of the array A. LDA >= max(1,N).
! 77: *> \endverbatim
! 78: *>
! 79: *> \param[in] IPIV
! 80: *> \verbatim
! 81: *> IPIV is INTEGER array, dimension (N)
! 82: *> Details of the interchanges and the block structure of D
! 83: *> as determined by DSYTRF.
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[in] ANORM
! 87: *> \verbatim
! 88: *> ANORM is DOUBLE PRECISION
! 89: *> The 1-norm of the original matrix A.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[out] RCOND
! 93: *> \verbatim
! 94: *> RCOND is DOUBLE PRECISION
! 95: *> The reciprocal of the condition number of the matrix A,
! 96: *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
! 97: *> estimate of the 1-norm of inv(A) computed in this routine.
! 98: *> \endverbatim
! 99: *>
! 100: *> \param[out] WORK
! 101: *> \verbatim
! 102: *> WORK is DOUBLE PRECISION array, dimension (2*N)
! 103: *> \endverbatim
! 104: *>
! 105: *> \param[out] IWORK
! 106: *> \verbatim
! 107: *> IWORK is INTEGER array, dimension (N)
! 108: *> \endverbatim
! 109: *>
! 110: *> \param[out] INFO
! 111: *> \verbatim
! 112: *> INFO is INTEGER
! 113: *> = 0: successful exit
! 114: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 115: *> \endverbatim
! 116: *
! 117: * Authors:
! 118: * ========
! 119: *
! 120: *> \author Univ. of Tennessee
! 121: *> \author Univ. of California Berkeley
! 122: *> \author Univ. of Colorado Denver
! 123: *> \author NAG Ltd.
! 124: *
! 125: *> \date November 2011
! 126: *
! 127: *> \ingroup doubleSYcomputational
! 128: *
! 129: * =====================================================================
1.1 bertrand 130: SUBROUTINE DSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
131: $ IWORK, INFO )
132: *
1.10 ! bertrand 133: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 134: * -- LAPACK is a software package provided by Univ. of Tennessee, --
135: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.10 ! bertrand 136: * November 2011
1.1 bertrand 137: *
138: * .. Scalar Arguments ..
139: CHARACTER UPLO
140: INTEGER INFO, LDA, N
141: DOUBLE PRECISION ANORM, RCOND
142: * ..
143: * .. Array Arguments ..
144: INTEGER IPIV( * ), IWORK( * )
145: DOUBLE PRECISION A( LDA, * ), WORK( * )
146: * ..
147: *
148: * =====================================================================
149: *
150: * .. Parameters ..
151: DOUBLE PRECISION ONE, ZERO
152: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
153: * ..
154: * .. Local Scalars ..
155: LOGICAL UPPER
156: INTEGER I, KASE
157: DOUBLE PRECISION AINVNM
158: * ..
159: * .. Local Arrays ..
160: INTEGER ISAVE( 3 )
161: * ..
162: * .. External Functions ..
163: LOGICAL LSAME
164: EXTERNAL LSAME
165: * ..
166: * .. External Subroutines ..
167: EXTERNAL DLACN2, DSYTRS, XERBLA
168: * ..
169: * .. Intrinsic Functions ..
170: INTRINSIC MAX
171: * ..
172: * .. Executable Statements ..
173: *
174: * Test the input parameters.
175: *
176: INFO = 0
177: UPPER = LSAME( UPLO, 'U' )
178: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
179: INFO = -1
180: ELSE IF( N.LT.0 ) THEN
181: INFO = -2
182: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
183: INFO = -4
184: ELSE IF( ANORM.LT.ZERO ) THEN
185: INFO = -6
186: END IF
187: IF( INFO.NE.0 ) THEN
188: CALL XERBLA( 'DSYCON', -INFO )
189: RETURN
190: END IF
191: *
192: * Quick return if possible
193: *
194: RCOND = ZERO
195: IF( N.EQ.0 ) THEN
196: RCOND = ONE
197: RETURN
198: ELSE IF( ANORM.LE.ZERO ) THEN
199: RETURN
200: END IF
201: *
202: * Check that the diagonal matrix D is nonsingular.
203: *
204: IF( UPPER ) THEN
205: *
206: * Upper triangular storage: examine D from bottom to top
207: *
208: DO 10 I = N, 1, -1
209: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
210: $ RETURN
211: 10 CONTINUE
212: ELSE
213: *
214: * Lower triangular storage: examine D from top to bottom.
215: *
216: DO 20 I = 1, N
217: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
218: $ RETURN
219: 20 CONTINUE
220: END IF
221: *
222: * Estimate the 1-norm of the inverse.
223: *
224: KASE = 0
225: 30 CONTINUE
226: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
227: IF( KASE.NE.0 ) THEN
228: *
1.9 bertrand 229: * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
1.1 bertrand 230: *
231: CALL DSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
232: GO TO 30
233: END IF
234: *
235: * Compute the estimate of the reciprocal condition number.
236: *
237: IF( AINVNM.NE.ZERO )
238: $ RCOND = ( ONE / AINVNM ) / ANORM
239: *
240: RETURN
241: *
242: * End of DSYCON
243: *
244: END
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