Annotation of rpl/lapack/lapack/zspcon.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZSPCON
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZSPCON + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zspcon.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zspcon.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zspcon.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER UPLO
! 25: * INTEGER INFO, N
! 26: * DOUBLE PRECISION ANORM, RCOND
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * INTEGER IPIV( * )
! 30: * COMPLEX*16 AP( * ), WORK( * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> ZSPCON estimates the reciprocal of the condition number (in the
! 40: *> 1-norm) of a complex symmetric packed matrix A using the
! 41: *> factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF.
! 42: *>
! 43: *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
! 44: *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
! 45: *> \endverbatim
! 46: *
! 47: * Arguments:
! 48: * ==========
! 49: *
! 50: *> \param[in] UPLO
! 51: *> \verbatim
! 52: *> UPLO is CHARACTER*1
! 53: *> Specifies whether the details of the factorization are stored
! 54: *> as an upper or lower triangular matrix.
! 55: *> = 'U': Upper triangular, form is A = U*D*U**T;
! 56: *> = 'L': Lower triangular, form is A = L*D*L**T.
! 57: *> \endverbatim
! 58: *>
! 59: *> \param[in] N
! 60: *> \verbatim
! 61: *> N is INTEGER
! 62: *> The order of the matrix A. N >= 0.
! 63: *> \endverbatim
! 64: *>
! 65: *> \param[in] AP
! 66: *> \verbatim
! 67: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
! 68: *> The block diagonal matrix D and the multipliers used to
! 69: *> obtain the factor U or L as computed by ZSPTRF, stored as a
! 70: *> packed triangular matrix.
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in] IPIV
! 74: *> \verbatim
! 75: *> IPIV is INTEGER array, dimension (N)
! 76: *> Details of the interchanges and the block structure of D
! 77: *> as determined by ZSPTRF.
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] ANORM
! 81: *> \verbatim
! 82: *> ANORM is DOUBLE PRECISION
! 83: *> The 1-norm of the original matrix A.
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[out] RCOND
! 87: *> \verbatim
! 88: *> RCOND is DOUBLE PRECISION
! 89: *> The reciprocal of the condition number of the matrix A,
! 90: *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
! 91: *> estimate of the 1-norm of inv(A) computed in this routine.
! 92: *> \endverbatim
! 93: *>
! 94: *> \param[out] WORK
! 95: *> \verbatim
! 96: *> WORK is COMPLEX*16 array, dimension (2*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 ZSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, 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: INTEGER IPIV( * )
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: INTEGER I, IP, KASE
145: DOUBLE PRECISION AINVNM
146: * ..
147: * .. Local Arrays ..
148: INTEGER ISAVE( 3 )
149: * ..
150: * .. External Functions ..
151: LOGICAL LSAME
152: EXTERNAL LSAME
153: * ..
154: * .. External Subroutines ..
155: EXTERNAL XERBLA, ZLACN2, ZSPTRS
156: * ..
157: * .. Executable Statements ..
158: *
159: * Test the input parameters.
160: *
161: INFO = 0
162: UPPER = LSAME( UPLO, 'U' )
163: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
164: INFO = -1
165: ELSE IF( N.LT.0 ) THEN
166: INFO = -2
167: ELSE IF( ANORM.LT.ZERO ) THEN
168: INFO = -5
169: END IF
170: IF( INFO.NE.0 ) THEN
171: CALL XERBLA( 'ZSPCON', -INFO )
172: RETURN
173: END IF
174: *
175: * Quick return if possible
176: *
177: RCOND = ZERO
178: IF( N.EQ.0 ) THEN
179: RCOND = ONE
180: RETURN
181: ELSE IF( ANORM.LE.ZERO ) THEN
182: RETURN
183: END IF
184: *
185: * Check that the diagonal matrix D is nonsingular.
186: *
187: IF( UPPER ) THEN
188: *
189: * Upper triangular storage: examine D from bottom to top
190: *
191: IP = N*( N+1 ) / 2
192: DO 10 I = N, 1, -1
193: IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
194: $ RETURN
195: IP = IP - I
196: 10 CONTINUE
197: ELSE
198: *
199: * Lower triangular storage: examine D from top to bottom.
200: *
201: IP = 1
202: DO 20 I = 1, N
203: IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
204: $ RETURN
205: IP = IP + N - I + 1
206: 20 CONTINUE
207: END IF
208: *
209: * Estimate the 1-norm of the inverse.
210: *
211: KASE = 0
212: 30 CONTINUE
213: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
214: IF( KASE.NE.0 ) THEN
215: *
1.8 bertrand 216: * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
1.1 bertrand 217: *
218: CALL ZSPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
219: GO TO 30
220: END IF
221: *
222: * Compute the estimate of the reciprocal condition number.
223: *
224: IF( AINVNM.NE.ZERO )
225: $ RCOND = ( ONE / AINVNM ) / ANORM
226: *
227: RETURN
228: *
229: * End of ZSPCON
230: *
231: END
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