Annotation of rpl/lapack/lapack/zhecon.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZHECON
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZHECON + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhecon.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhecon.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhecon.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
! 22: * 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( * )
! 31: * COMPLEX*16 A( LDA, * ), WORK( * )
! 32: * ..
! 33: *
! 34: *
! 35: *> \par Purpose:
! 36: * =============
! 37: *>
! 38: *> \verbatim
! 39: *>
! 40: *> ZHECON estimates the reciprocal of the condition number of a complex
! 41: *> Hermitian matrix A using the factorization A = U*D*U**H or
! 42: *> A = L*D*L**H computed by ZHETRF.
! 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**H;
! 57: *> = 'L': Lower triangular, form is A = L*D*L**H.
! 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 COMPLEX*16 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 ZHETRF.
! 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 ZHETRF.
! 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 COMPLEX*16 array, dimension (2*N)
! 103: *> \endverbatim
! 104: *>
! 105: *> \param[out] INFO
! 106: *> \verbatim
! 107: *> INFO is INTEGER
! 108: *> = 0: successful exit
! 109: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 110: *> \endverbatim
! 111: *
! 112: * Authors:
! 113: * ========
! 114: *
! 115: *> \author Univ. of Tennessee
! 116: *> \author Univ. of California Berkeley
! 117: *> \author Univ. of Colorado Denver
! 118: *> \author NAG Ltd.
! 119: *
! 120: *> \date November 2011
! 121: *
! 122: *> \ingroup complex16HEcomputational
! 123: *
! 124: * =====================================================================
1.1 bertrand 125: SUBROUTINE ZHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
126: $ INFO )
127: *
1.9 ! bertrand 128: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 129: * -- LAPACK is a software package provided by Univ. of Tennessee, --
130: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 131: * November 2011
1.1 bertrand 132: *
133: * .. Scalar Arguments ..
134: CHARACTER UPLO
135: INTEGER INFO, LDA, N
136: DOUBLE PRECISION ANORM, RCOND
137: * ..
138: * .. Array Arguments ..
139: INTEGER IPIV( * )
140: COMPLEX*16 A( LDA, * ), WORK( * )
141: * ..
142: *
143: * =====================================================================
144: *
145: * .. Parameters ..
146: DOUBLE PRECISION ONE, ZERO
147: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
148: * ..
149: * .. Local Scalars ..
150: LOGICAL UPPER
151: INTEGER I, KASE
152: DOUBLE PRECISION AINVNM
153: * ..
154: * .. Local Arrays ..
155: INTEGER ISAVE( 3 )
156: * ..
157: * .. External Functions ..
158: LOGICAL LSAME
159: EXTERNAL LSAME
160: * ..
161: * .. External Subroutines ..
162: EXTERNAL XERBLA, ZHETRS, ZLACN2
163: * ..
164: * .. Intrinsic Functions ..
165: INTRINSIC MAX
166: * ..
167: * .. Executable Statements ..
168: *
169: * Test the input parameters.
170: *
171: INFO = 0
172: UPPER = LSAME( UPLO, 'U' )
173: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
174: INFO = -1
175: ELSE IF( N.LT.0 ) THEN
176: INFO = -2
177: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
178: INFO = -4
179: ELSE IF( ANORM.LT.ZERO ) THEN
180: INFO = -6
181: END IF
182: IF( INFO.NE.0 ) THEN
183: CALL XERBLA( 'ZHECON', -INFO )
184: RETURN
185: END IF
186: *
187: * Quick return if possible
188: *
189: RCOND = ZERO
190: IF( N.EQ.0 ) THEN
191: RCOND = ONE
192: RETURN
193: ELSE IF( ANORM.LE.ZERO ) THEN
194: RETURN
195: END IF
196: *
197: * Check that the diagonal matrix D is nonsingular.
198: *
199: IF( UPPER ) THEN
200: *
201: * Upper triangular storage: examine D from bottom to top
202: *
203: DO 10 I = N, 1, -1
204: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
205: $ RETURN
206: 10 CONTINUE
207: ELSE
208: *
209: * Lower triangular storage: examine D from top to bottom.
210: *
211: DO 20 I = 1, N
212: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
213: $ RETURN
214: 20 CONTINUE
215: END IF
216: *
217: * Estimate the 1-norm of the inverse.
218: *
219: KASE = 0
220: 30 CONTINUE
221: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
222: IF( KASE.NE.0 ) THEN
223: *
1.8 bertrand 224: * Multiply by inv(L*D*L**H) or inv(U*D*U**H).
1.1 bertrand 225: *
226: CALL ZHETRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
227: GO TO 30
228: END IF
229: *
230: * Compute the estimate of the reciprocal condition number.
231: *
232: IF( AINVNM.NE.ZERO )
233: $ RCOND = ( ONE / AINVNM ) / ANORM
234: *
235: RETURN
236: *
237: * End of ZHECON
238: *
239: END
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