Annotation of rpl/lapack/lapack/zpocon.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZPOCON
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZPOCON + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpocon.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpocon.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpocon.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK,
! 22: * INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER UPLO
! 26: * INTEGER INFO, LDA, N
! 27: * DOUBLE PRECISION ANORM, RCOND
! 28: * ..
! 29: * .. Array Arguments ..
! 30: * DOUBLE PRECISION RWORK( * )
! 31: * COMPLEX*16 A( LDA, * ), WORK( * )
! 32: * ..
! 33: *
! 34: *
! 35: *> \par Purpose:
! 36: * =============
! 37: *>
! 38: *> \verbatim
! 39: *>
! 40: *> ZPOCON estimates the reciprocal of the condition number (in the
! 41: *> 1-norm) of a complex Hermitian positive definite matrix using the
! 42: *> Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.
! 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: *> = 'U': Upper triangle of A is stored;
! 55: *> = 'L': Lower triangle of A is stored.
! 56: *> \endverbatim
! 57: *>
! 58: *> \param[in] N
! 59: *> \verbatim
! 60: *> N is INTEGER
! 61: *> The order of the matrix A. N >= 0.
! 62: *> \endverbatim
! 63: *>
! 64: *> \param[in] A
! 65: *> \verbatim
! 66: *> A is COMPLEX*16 array, dimension (LDA,N)
! 67: *> The triangular factor U or L from the Cholesky factorization
! 68: *> A = U**H*U or A = L*L**H, as computed by ZPOTRF.
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[in] LDA
! 72: *> \verbatim
! 73: *> LDA is INTEGER
! 74: *> The leading dimension of the array A. LDA >= max(1,N).
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[in] ANORM
! 78: *> \verbatim
! 79: *> ANORM is DOUBLE PRECISION
! 80: *> The 1-norm (or infinity-norm) of the Hermitian matrix A.
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[out] RCOND
! 84: *> \verbatim
! 85: *> RCOND is DOUBLE PRECISION
! 86: *> The reciprocal of the condition number of the matrix A,
! 87: *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
! 88: *> estimate of the 1-norm of inv(A) computed in this routine.
! 89: *> \endverbatim
! 90: *>
! 91: *> \param[out] WORK
! 92: *> \verbatim
! 93: *> WORK is COMPLEX*16 array, dimension (2*N)
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[out] RWORK
! 97: *> \verbatim
! 98: *> RWORK is DOUBLE PRECISION array, dimension (N)
! 99: *> \endverbatim
! 100: *>
! 101: *> \param[out] INFO
! 102: *> \verbatim
! 103: *> INFO is INTEGER
! 104: *> = 0: successful exit
! 105: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 106: *> \endverbatim
! 107: *
! 108: * Authors:
! 109: * ========
! 110: *
! 111: *> \author Univ. of Tennessee
! 112: *> \author Univ. of California Berkeley
! 113: *> \author Univ. of Colorado Denver
! 114: *> \author NAG Ltd.
! 115: *
! 116: *> \date November 2011
! 117: *
! 118: *> \ingroup complex16POcomputational
! 119: *
! 120: * =====================================================================
1.1 bertrand 121: SUBROUTINE ZPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK,
122: $ INFO )
123: *
1.9 ! bertrand 124: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 125: * -- LAPACK is a software package provided by Univ. of Tennessee, --
126: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 127: * November 2011
1.1 bertrand 128: *
129: * .. Scalar Arguments ..
130: CHARACTER UPLO
131: INTEGER INFO, LDA, N
132: DOUBLE PRECISION ANORM, RCOND
133: * ..
134: * .. Array Arguments ..
135: DOUBLE PRECISION RWORK( * )
136: COMPLEX*16 A( LDA, * ), WORK( * )
137: * ..
138: *
139: * =====================================================================
140: *
141: * .. Parameters ..
142: DOUBLE PRECISION ONE, ZERO
143: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
144: * ..
145: * .. Local Scalars ..
146: LOGICAL UPPER
147: CHARACTER NORMIN
148: INTEGER IX, KASE
149: DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
150: COMPLEX*16 ZDUM
151: * ..
152: * .. Local Arrays ..
153: INTEGER ISAVE( 3 )
154: * ..
155: * .. External Functions ..
156: LOGICAL LSAME
157: INTEGER IZAMAX
158: DOUBLE PRECISION DLAMCH
159: EXTERNAL LSAME, IZAMAX, DLAMCH
160: * ..
161: * .. External Subroutines ..
162: EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATRS
163: * ..
164: * .. Intrinsic Functions ..
165: INTRINSIC ABS, DBLE, DIMAG, MAX
166: * ..
167: * .. Statement Functions ..
168: DOUBLE PRECISION CABS1
169: * ..
170: * .. Statement Function definitions ..
171: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
172: * ..
173: * .. Executable Statements ..
174: *
175: * Test the input parameters.
176: *
177: INFO = 0
178: UPPER = LSAME( UPLO, 'U' )
179: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
180: INFO = -1
181: ELSE IF( N.LT.0 ) THEN
182: INFO = -2
183: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
184: INFO = -4
185: ELSE IF( ANORM.LT.ZERO ) THEN
186: INFO = -5
187: END IF
188: IF( INFO.NE.0 ) THEN
189: CALL XERBLA( 'ZPOCON', -INFO )
190: RETURN
191: END IF
192: *
193: * Quick return if possible
194: *
195: RCOND = ZERO
196: IF( N.EQ.0 ) THEN
197: RCOND = ONE
198: RETURN
199: ELSE IF( ANORM.EQ.ZERO ) THEN
200: RETURN
201: END IF
202: *
203: SMLNUM = DLAMCH( 'Safe minimum' )
204: *
205: * Estimate the 1-norm of inv(A).
206: *
207: KASE = 0
208: NORMIN = 'N'
209: 10 CONTINUE
210: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
211: IF( KASE.NE.0 ) THEN
212: IF( UPPER ) THEN
213: *
1.8 bertrand 214: * Multiply by inv(U**H).
1.1 bertrand 215: *
216: CALL ZLATRS( 'Upper', 'Conjugate transpose', 'Non-unit',
217: $ NORMIN, N, A, LDA, WORK, SCALEL, RWORK, INFO )
218: NORMIN = 'Y'
219: *
220: * Multiply by inv(U).
221: *
222: CALL ZLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
223: $ A, LDA, WORK, SCALEU, RWORK, INFO )
224: ELSE
225: *
226: * Multiply by inv(L).
227: *
228: CALL ZLATRS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
229: $ A, LDA, WORK, SCALEL, RWORK, INFO )
230: NORMIN = 'Y'
231: *
1.8 bertrand 232: * Multiply by inv(L**H).
1.1 bertrand 233: *
234: CALL ZLATRS( 'Lower', 'Conjugate transpose', 'Non-unit',
235: $ NORMIN, N, A, LDA, WORK, SCALEU, RWORK, INFO )
236: END IF
237: *
238: * Multiply by 1/SCALE if doing so will not cause overflow.
239: *
240: SCALE = SCALEL*SCALEU
241: IF( SCALE.NE.ONE ) THEN
242: IX = IZAMAX( N, WORK, 1 )
243: IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
244: $ GO TO 20
245: CALL ZDRSCL( N, SCALE, WORK, 1 )
246: END IF
247: GO TO 10
248: END IF
249: *
250: * Compute the estimate of the reciprocal condition number.
251: *
252: IF( AINVNM.NE.ZERO )
253: $ RCOND = ( ONE / AINVNM ) / ANORM
254: *
255: 20 CONTINUE
256: RETURN
257: *
258: * End of ZPOCON
259: *
260: END
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