Annotation of rpl/lapack/lapack/zgbcon.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZGBCON
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZGBCON + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgbcon.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgbcon.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgbcon.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
! 22: * WORK, RWORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER NORM
! 26: * INTEGER INFO, KL, KU, LDAB, N
! 27: * DOUBLE PRECISION ANORM, RCOND
! 28: * ..
! 29: * .. Array Arguments ..
! 30: * INTEGER IPIV( * )
! 31: * DOUBLE PRECISION RWORK( * )
! 32: * COMPLEX*16 AB( LDAB, * ), WORK( * )
! 33: * ..
! 34: *
! 35: *
! 36: *> \par Purpose:
! 37: * =============
! 38: *>
! 39: *> \verbatim
! 40: *>
! 41: *> ZGBCON estimates the reciprocal of the condition number of a complex
! 42: *> general band matrix A, in either the 1-norm or the infinity-norm,
! 43: *> using the LU factorization computed by ZGBTRF.
! 44: *>
! 45: *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
! 46: *> condition number is computed as
! 47: *> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
! 48: *> \endverbatim
! 49: *
! 50: * Arguments:
! 51: * ==========
! 52: *
! 53: *> \param[in] NORM
! 54: *> \verbatim
! 55: *> NORM is CHARACTER*1
! 56: *> Specifies whether the 1-norm condition number or the
! 57: *> infinity-norm condition number is required:
! 58: *> = '1' or 'O': 1-norm;
! 59: *> = 'I': Infinity-norm.
! 60: *> \endverbatim
! 61: *>
! 62: *> \param[in] N
! 63: *> \verbatim
! 64: *> N is INTEGER
! 65: *> The order of the matrix A. N >= 0.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] KL
! 69: *> \verbatim
! 70: *> KL is INTEGER
! 71: *> The number of subdiagonals within the band of A. KL >= 0.
! 72: *> \endverbatim
! 73: *>
! 74: *> \param[in] KU
! 75: *> \verbatim
! 76: *> KU is INTEGER
! 77: *> The number of superdiagonals within the band of A. KU >= 0.
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] AB
! 81: *> \verbatim
! 82: *> AB is COMPLEX*16 array, dimension (LDAB,N)
! 83: *> Details of the LU factorization of the band matrix A, as
! 84: *> computed by ZGBTRF. U is stored as an upper triangular band
! 85: *> matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
! 86: *> the multipliers used during the factorization are stored in
! 87: *> rows KL+KU+2 to 2*KL+KU+1.
! 88: *> \endverbatim
! 89: *>
! 90: *> \param[in] LDAB
! 91: *> \verbatim
! 92: *> LDAB is INTEGER
! 93: *> The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[in] IPIV
! 97: *> \verbatim
! 98: *> IPIV is INTEGER array, dimension (N)
! 99: *> The pivot indices; for 1 <= i <= N, row i of the matrix was
! 100: *> interchanged with row IPIV(i).
! 101: *> \endverbatim
! 102: *>
! 103: *> \param[in] ANORM
! 104: *> \verbatim
! 105: *> ANORM is DOUBLE PRECISION
! 106: *> If NORM = '1' or 'O', the 1-norm of the original matrix A.
! 107: *> If NORM = 'I', the infinity-norm of the original matrix A.
! 108: *> \endverbatim
! 109: *>
! 110: *> \param[out] RCOND
! 111: *> \verbatim
! 112: *> RCOND is DOUBLE PRECISION
! 113: *> The reciprocal of the condition number of the matrix A,
! 114: *> computed as RCOND = 1/(norm(A) * norm(inv(A))).
! 115: *> \endverbatim
! 116: *>
! 117: *> \param[out] WORK
! 118: *> \verbatim
! 119: *> WORK is COMPLEX*16 array, dimension (2*N)
! 120: *> \endverbatim
! 121: *>
! 122: *> \param[out] RWORK
! 123: *> \verbatim
! 124: *> RWORK is DOUBLE PRECISION array, dimension (N)
! 125: *> \endverbatim
! 126: *>
! 127: *> \param[out] INFO
! 128: *> \verbatim
! 129: *> INFO is INTEGER
! 130: *> = 0: successful exit
! 131: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 132: *> \endverbatim
! 133: *
! 134: * Authors:
! 135: * ========
! 136: *
! 137: *> \author Univ. of Tennessee
! 138: *> \author Univ. of California Berkeley
! 139: *> \author Univ. of Colorado Denver
! 140: *> \author NAG Ltd.
! 141: *
! 142: *> \date November 2011
! 143: *
! 144: *> \ingroup complex16GBcomputational
! 145: *
! 146: * =====================================================================
1.1 bertrand 147: SUBROUTINE ZGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
148: $ WORK, RWORK, INFO )
149: *
1.9 ! bertrand 150: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 151: * -- LAPACK is a software package provided by Univ. of Tennessee, --
152: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 153: * November 2011
1.1 bertrand 154: *
155: * .. Scalar Arguments ..
156: CHARACTER NORM
157: INTEGER INFO, KL, KU, LDAB, N
158: DOUBLE PRECISION ANORM, RCOND
159: * ..
160: * .. Array Arguments ..
161: INTEGER IPIV( * )
162: DOUBLE PRECISION RWORK( * )
163: COMPLEX*16 AB( LDAB, * ), WORK( * )
164: * ..
165: *
166: * =====================================================================
167: *
168: * .. Parameters ..
169: DOUBLE PRECISION ONE, ZERO
170: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
171: * ..
172: * .. Local Scalars ..
173: LOGICAL LNOTI, ONENRM
174: CHARACTER NORMIN
175: INTEGER IX, J, JP, KASE, KASE1, KD, LM
176: DOUBLE PRECISION AINVNM, SCALE, SMLNUM
177: COMPLEX*16 T, ZDUM
178: * ..
179: * .. Local Arrays ..
180: INTEGER ISAVE( 3 )
181: * ..
182: * .. External Functions ..
183: LOGICAL LSAME
184: INTEGER IZAMAX
185: DOUBLE PRECISION DLAMCH
186: COMPLEX*16 ZDOTC
187: EXTERNAL LSAME, IZAMAX, DLAMCH, ZDOTC
188: * ..
189: * .. External Subroutines ..
190: EXTERNAL XERBLA, ZAXPY, ZDRSCL, ZLACN2, ZLATBS
191: * ..
192: * .. Intrinsic Functions ..
193: INTRINSIC ABS, DBLE, DIMAG, MIN
194: * ..
195: * .. Statement Functions ..
196: DOUBLE PRECISION CABS1
197: * ..
198: * .. Statement Function definitions ..
199: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
200: * ..
201: * .. Executable Statements ..
202: *
203: * Test the input parameters.
204: *
205: INFO = 0
206: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
207: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
208: INFO = -1
209: ELSE IF( N.LT.0 ) THEN
210: INFO = -2
211: ELSE IF( KL.LT.0 ) THEN
212: INFO = -3
213: ELSE IF( KU.LT.0 ) THEN
214: INFO = -4
215: ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
216: INFO = -6
217: ELSE IF( ANORM.LT.ZERO ) THEN
218: INFO = -8
219: END IF
220: IF( INFO.NE.0 ) THEN
221: CALL XERBLA( 'ZGBCON', -INFO )
222: RETURN
223: END IF
224: *
225: * Quick return if possible
226: *
227: RCOND = ZERO
228: IF( N.EQ.0 ) THEN
229: RCOND = ONE
230: RETURN
231: ELSE IF( ANORM.EQ.ZERO ) THEN
232: RETURN
233: END IF
234: *
235: SMLNUM = DLAMCH( 'Safe minimum' )
236: *
237: * Estimate the norm of inv(A).
238: *
239: AINVNM = ZERO
240: NORMIN = 'N'
241: IF( ONENRM ) THEN
242: KASE1 = 1
243: ELSE
244: KASE1 = 2
245: END IF
246: KD = KL + KU + 1
247: LNOTI = KL.GT.0
248: KASE = 0
249: 10 CONTINUE
250: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
251: IF( KASE.NE.0 ) THEN
252: IF( KASE.EQ.KASE1 ) THEN
253: *
254: * Multiply by inv(L).
255: *
256: IF( LNOTI ) THEN
257: DO 20 J = 1, N - 1
258: LM = MIN( KL, N-J )
259: JP = IPIV( J )
260: T = WORK( JP )
261: IF( JP.NE.J ) THEN
262: WORK( JP ) = WORK( J )
263: WORK( J ) = T
264: END IF
265: CALL ZAXPY( LM, -T, AB( KD+1, J ), 1, WORK( J+1 ), 1 )
266: 20 CONTINUE
267: END IF
268: *
269: * Multiply by inv(U).
270: *
271: CALL ZLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
272: $ KL+KU, AB, LDAB, WORK, SCALE, RWORK, INFO )
273: ELSE
274: *
1.8 bertrand 275: * Multiply by inv(U**H).
1.1 bertrand 276: *
277: CALL ZLATBS( 'Upper', 'Conjugate transpose', 'Non-unit',
278: $ NORMIN, N, KL+KU, AB, LDAB, WORK, SCALE, RWORK,
279: $ INFO )
280: *
1.8 bertrand 281: * Multiply by inv(L**H).
1.1 bertrand 282: *
283: IF( LNOTI ) THEN
284: DO 30 J = N - 1, 1, -1
285: LM = MIN( KL, N-J )
286: WORK( J ) = WORK( J ) - ZDOTC( LM, AB( KD+1, J ), 1,
287: $ WORK( J+1 ), 1 )
288: JP = IPIV( J )
289: IF( JP.NE.J ) THEN
290: T = WORK( JP )
291: WORK( JP ) = WORK( J )
292: WORK( J ) = T
293: END IF
294: 30 CONTINUE
295: END IF
296: END IF
297: *
298: * Divide X by 1/SCALE if doing so will not cause overflow.
299: *
300: NORMIN = 'Y'
301: IF( SCALE.NE.ONE ) THEN
302: IX = IZAMAX( N, WORK, 1 )
303: IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
304: $ GO TO 40
305: CALL ZDRSCL( N, SCALE, WORK, 1 )
306: END IF
307: GO TO 10
308: END IF
309: *
310: * Compute the estimate of the reciprocal condition number.
311: *
312: IF( AINVNM.NE.ZERO )
313: $ RCOND = ( ONE / AINVNM ) / ANORM
314: *
315: 40 CONTINUE
316: RETURN
317: *
318: * End of ZGBCON
319: *
320: END
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