Annotation of rpl/lapack/lapack/zppcon.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZPPCON
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZPPCON + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zppcon.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zppcon.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zppcon.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZPPCON( UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER UPLO
! 25: * INTEGER INFO, N
! 26: * DOUBLE PRECISION ANORM, RCOND
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * DOUBLE PRECISION RWORK( * )
! 30: * COMPLEX*16 AP( * ), WORK( * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> ZPPCON estimates the reciprocal of the condition number (in the
! 40: *> 1-norm) of a complex Hermitian positive definite packed matrix using
! 41: *> the Cholesky factorization A = U**H*U or A = L*L**H computed by
! 42: *> ZPPTRF.
! 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] AP
! 65: *> \verbatim
! 66: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
! 67: *> The triangular factor U or L from the Cholesky factorization
! 68: *> A = U**H*U or A = L*L**H, packed columnwise in a linear
! 69: *> array. The j-th column of U or L is stored in the array AP
! 70: *> as follows:
! 71: *> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
! 72: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] ANORM
! 76: *> \verbatim
! 77: *> ANORM is DOUBLE PRECISION
! 78: *> The 1-norm (or infinity-norm) of the Hermitian matrix A.
! 79: *> \endverbatim
! 80: *>
! 81: *> \param[out] RCOND
! 82: *> \verbatim
! 83: *> RCOND is DOUBLE PRECISION
! 84: *> The reciprocal of the condition number of the matrix A,
! 85: *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
! 86: *> estimate of the 1-norm of inv(A) computed in this routine.
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[out] WORK
! 90: *> \verbatim
! 91: *> WORK is COMPLEX*16 array, dimension (2*N)
! 92: *> \endverbatim
! 93: *>
! 94: *> \param[out] RWORK
! 95: *> \verbatim
! 96: *> RWORK is DOUBLE PRECISION array, dimension (N)
! 97: *> \endverbatim
! 98: *>
! 99: *> \param[out] INFO
! 100: *> \verbatim
! 101: *> INFO is INTEGER
! 102: *> = 0: successful exit
! 103: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 104: *> \endverbatim
! 105: *
! 106: * Authors:
! 107: * ========
! 108: *
! 109: *> \author Univ. of Tennessee
! 110: *> \author Univ. of California Berkeley
! 111: *> \author Univ. of Colorado Denver
! 112: *> \author NAG Ltd.
! 113: *
! 114: *> \date November 2011
! 115: *
! 116: *> \ingroup complex16OTHERcomputational
! 117: *
! 118: * =====================================================================
1.1 bertrand 119: SUBROUTINE ZPPCON( UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO )
120: *
1.9 ! bertrand 121: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 122: * -- LAPACK is a software package provided by Univ. of Tennessee, --
123: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 124: * November 2011
1.1 bertrand 125: *
126: * .. Scalar Arguments ..
127: CHARACTER UPLO
128: INTEGER INFO, N
129: DOUBLE PRECISION ANORM, RCOND
130: * ..
131: * .. Array Arguments ..
132: DOUBLE PRECISION RWORK( * )
133: COMPLEX*16 AP( * ), WORK( * )
134: * ..
135: *
136: * =====================================================================
137: *
138: * .. Parameters ..
139: DOUBLE PRECISION ONE, ZERO
140: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
141: * ..
142: * .. Local Scalars ..
143: LOGICAL UPPER
144: CHARACTER NORMIN
145: INTEGER IX, KASE
146: DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
147: COMPLEX*16 ZDUM
148: * ..
149: * .. Local Arrays ..
150: INTEGER ISAVE( 3 )
151: * ..
152: * .. External Functions ..
153: LOGICAL LSAME
154: INTEGER IZAMAX
155: DOUBLE PRECISION DLAMCH
156: EXTERNAL LSAME, IZAMAX, DLAMCH
157: * ..
158: * .. External Subroutines ..
159: EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATPS
160: * ..
161: * .. Intrinsic Functions ..
162: INTRINSIC ABS, DBLE, DIMAG
163: * ..
164: * .. Statement Functions ..
165: DOUBLE PRECISION CABS1
166: * ..
167: * .. Statement Function definitions ..
168: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
169: * ..
170: * .. Executable Statements ..
171: *
172: * Test the input parameters.
173: *
174: INFO = 0
175: UPPER = LSAME( UPLO, 'U' )
176: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
177: INFO = -1
178: ELSE IF( N.LT.0 ) THEN
179: INFO = -2
180: ELSE IF( ANORM.LT.ZERO ) THEN
181: INFO = -4
182: END IF
183: IF( INFO.NE.0 ) THEN
184: CALL XERBLA( 'ZPPCON', -INFO )
185: RETURN
186: END IF
187: *
188: * Quick return if possible
189: *
190: RCOND = ZERO
191: IF( N.EQ.0 ) THEN
192: RCOND = ONE
193: RETURN
194: ELSE IF( ANORM.EQ.ZERO ) THEN
195: RETURN
196: END IF
197: *
198: SMLNUM = DLAMCH( 'Safe minimum' )
199: *
200: * Estimate the 1-norm of the inverse.
201: *
202: KASE = 0
203: NORMIN = 'N'
204: 10 CONTINUE
205: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
206: IF( KASE.NE.0 ) THEN
207: IF( UPPER ) THEN
208: *
1.8 bertrand 209: * Multiply by inv(U**H).
1.1 bertrand 210: *
211: CALL ZLATPS( 'Upper', 'Conjugate transpose', 'Non-unit',
212: $ NORMIN, N, AP, WORK, SCALEL, RWORK, INFO )
213: NORMIN = 'Y'
214: *
215: * Multiply by inv(U).
216: *
217: CALL ZLATPS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
218: $ AP, WORK, SCALEU, RWORK, INFO )
219: ELSE
220: *
221: * Multiply by inv(L).
222: *
223: CALL ZLATPS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
224: $ AP, WORK, SCALEL, RWORK, INFO )
225: NORMIN = 'Y'
226: *
1.8 bertrand 227: * Multiply by inv(L**H).
1.1 bertrand 228: *
229: CALL ZLATPS( 'Lower', 'Conjugate transpose', 'Non-unit',
230: $ NORMIN, N, AP, WORK, SCALEU, RWORK, INFO )
231: END IF
232: *
233: * Multiply by 1/SCALE if doing so will not cause overflow.
234: *
235: SCALE = SCALEL*SCALEU
236: IF( SCALE.NE.ONE ) THEN
237: IX = IZAMAX( N, WORK, 1 )
238: IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
239: $ GO TO 20
240: CALL ZDRSCL( N, SCALE, WORK, 1 )
241: END IF
242: GO TO 10
243: END IF
244: *
245: * Compute the estimate of the reciprocal condition number.
246: *
247: IF( AINVNM.NE.ZERO )
248: $ RCOND = ( ONE / AINVNM ) / ANORM
249: *
250: 20 CONTINUE
251: RETURN
252: *
253: * End of ZPPCON
254: *
255: END
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