Annotation of rpl/lapack/lapack/zla_gbrcond_x.f, revision 1.6
1.6 ! bertrand 1: *> \brief \b ZLA_GBRCOND_X
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLA_GBRCOND_X + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_gbrcond_x.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_gbrcond_x.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gbrcond_x.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X( TRANS, N, KL, KU, AB,
! 22: * LDAB, AFB, LDAFB, IPIV,
! 23: * X, INFO, WORK, RWORK )
! 24: *
! 25: * .. Scalar Arguments ..
! 26: * CHARACTER TRANS
! 27: * INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
! 28: * ..
! 29: * .. Array Arguments ..
! 30: * INTEGER IPIV( * )
! 31: * COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ),
! 32: * $ X( * )
! 33: * DOUBLE PRECISION RWORK( * )
! 34: *
! 35: *
! 36: *
! 37: *> \par Purpose:
! 38: * =============
! 39: *>
! 40: *> \verbatim
! 41: *>
! 42: *> ZLA_GBRCOND_X Computes the infinity norm condition number of
! 43: *> op(A) * diag(X) where X is a COMPLEX*16 vector.
! 44: *> \endverbatim
! 45: *
! 46: * Arguments:
! 47: * ==========
! 48: *
! 49: *> \param[in] TRANS
! 50: *> \verbatim
! 51: *> TRANS is CHARACTER*1
! 52: *> Specifies the form of the system of equations:
! 53: *> = 'N': A * X = B (No transpose)
! 54: *> = 'T': A**T * X = B (Transpose)
! 55: *> = 'C': A**H * X = B (Conjugate Transpose = Transpose)
! 56: *> \endverbatim
! 57: *>
! 58: *> \param[in] N
! 59: *> \verbatim
! 60: *> N is INTEGER
! 61: *> The number of linear equations, i.e., the order of the
! 62: *> matrix A. N >= 0.
! 63: *> \endverbatim
! 64: *>
! 65: *> \param[in] KL
! 66: *> \verbatim
! 67: *> KL is INTEGER
! 68: *> The number of subdiagonals within the band of A. KL >= 0.
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[in] KU
! 72: *> \verbatim
! 73: *> KU is INTEGER
! 74: *> The number of superdiagonals within the band of A. KU >= 0.
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[in] AB
! 78: *> \verbatim
! 79: *> AB is COMPLEX*16 array, dimension (LDAB,N)
! 80: *> On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
! 81: *> The j-th column of A is stored in the j-th column of the
! 82: *> array AB as follows:
! 83: *> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[in] LDAB
! 87: *> \verbatim
! 88: *> LDAB is INTEGER
! 89: *> The leading dimension of the array AB. LDAB >= KL+KU+1.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[in] AFB
! 93: *> \verbatim
! 94: *> AFB is COMPLEX*16 array, dimension (LDAFB,N)
! 95: *> Details of the LU factorization of the band matrix A, as
! 96: *> computed by ZGBTRF. U is stored as an upper triangular
! 97: *> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
! 98: *> and the multipliers used during the factorization are stored
! 99: *> in rows KL+KU+2 to 2*KL+KU+1.
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[in] LDAFB
! 103: *> \verbatim
! 104: *> LDAFB is INTEGER
! 105: *> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[in] IPIV
! 109: *> \verbatim
! 110: *> IPIV is INTEGER array, dimension (N)
! 111: *> The pivot indices from the factorization A = P*L*U
! 112: *> as computed by ZGBTRF; row i of the matrix was interchanged
! 113: *> with row IPIV(i).
! 114: *> \endverbatim
! 115: *>
! 116: *> \param[in] X
! 117: *> \verbatim
! 118: *> X is COMPLEX*16 array, dimension (N)
! 119: *> The vector X in the formula op(A) * diag(X).
! 120: *> \endverbatim
! 121: *>
! 122: *> \param[out] INFO
! 123: *> \verbatim
! 124: *> INFO is INTEGER
! 125: *> = 0: Successful exit.
! 126: *> i > 0: The ith argument is invalid.
! 127: *> \endverbatim
! 128: *>
! 129: *> \param[in] WORK
! 130: *> \verbatim
! 131: *> WORK is COMPLEX*16 array, dimension (2*N).
! 132: *> Workspace.
! 133: *> \endverbatim
! 134: *>
! 135: *> \param[in] RWORK
! 136: *> \verbatim
! 137: *> RWORK is DOUBLE PRECISION array, dimension (N).
! 138: *> Workspace.
! 139: *> \endverbatim
! 140: *
! 141: * Authors:
! 142: * ========
! 143: *
! 144: *> \author Univ. of Tennessee
! 145: *> \author Univ. of California Berkeley
! 146: *> \author Univ. of Colorado Denver
! 147: *> \author NAG Ltd.
! 148: *
! 149: *> \date November 2011
! 150: *
! 151: *> \ingroup complex16GBcomputational
! 152: *
! 153: * =====================================================================
1.1 bertrand 154: DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X( TRANS, N, KL, KU, AB,
155: $ LDAB, AFB, LDAFB, IPIV,
156: $ X, INFO, WORK, RWORK )
157: *
1.6 ! bertrand 158: * -- LAPACK computational routine (version 3.4.0) --
! 159: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 160: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 161: * November 2011
1.1 bertrand 162: *
163: * .. Scalar Arguments ..
164: CHARACTER TRANS
165: INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
166: * ..
167: * .. Array Arguments ..
168: INTEGER IPIV( * )
169: COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ),
170: $ X( * )
171: DOUBLE PRECISION RWORK( * )
172: *
173: *
174: * =====================================================================
175: *
176: * .. Local Scalars ..
177: LOGICAL NOTRANS
178: INTEGER KASE, I, J
179: DOUBLE PRECISION AINVNM, ANORM, TMP
180: COMPLEX*16 ZDUM
181: * ..
182: * .. Local Arrays ..
183: INTEGER ISAVE( 3 )
184: * ..
185: * .. External Functions ..
186: LOGICAL LSAME
187: EXTERNAL LSAME
188: * ..
189: * .. External Subroutines ..
190: EXTERNAL ZLACN2, ZGBTRS, XERBLA
191: * ..
192: * .. Intrinsic Functions ..
193: INTRINSIC ABS, MAX
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: ZLA_GBRCOND_X = 0.0D+0
204: *
205: INFO = 0
206: NOTRANS = LSAME( TRANS, 'N' )
207: IF ( .NOT. NOTRANS .AND. .NOT. LSAME(TRANS, 'T') .AND. .NOT.
208: $ LSAME( TRANS, 'C' ) ) THEN
209: INFO = -1
210: ELSE IF( N.LT.0 ) THEN
211: INFO = -2
212: ELSE IF( KL.LT.0 .OR. KL.GT.N-1 ) THEN
213: INFO = -3
214: ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
215: INFO = -4
216: ELSE IF( LDAB.LT.KL+KU+1 ) THEN
217: INFO = -6
218: ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
219: INFO = -8
220: END IF
221: IF( INFO.NE.0 ) THEN
222: CALL XERBLA( 'ZLA_GBRCOND_X', -INFO )
223: RETURN
224: END IF
225: *
226: * Compute norm of op(A)*op2(C).
227: *
228: KD = KU + 1
229: KE = KL + 1
230: ANORM = 0.0D+0
231: IF ( NOTRANS ) THEN
232: DO I = 1, N
233: TMP = 0.0D+0
234: DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
235: TMP = TMP + CABS1( AB( KD+I-J, J) * X( J ) )
236: END DO
237: RWORK( I ) = TMP
238: ANORM = MAX( ANORM, TMP )
239: END DO
240: ELSE
241: DO I = 1, N
242: TMP = 0.0D+0
243: DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
244: TMP = TMP + CABS1( AB( KE-I+J, I ) * X( J ) )
245: END DO
246: RWORK( I ) = TMP
247: ANORM = MAX( ANORM, TMP )
248: END DO
249: END IF
250: *
251: * Quick return if possible.
252: *
253: IF( N.EQ.0 ) THEN
254: ZLA_GBRCOND_X = 1.0D+0
255: RETURN
256: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
257: RETURN
258: END IF
259: *
260: * Estimate the norm of inv(op(A)).
261: *
262: AINVNM = 0.0D+0
263: *
264: KASE = 0
265: 10 CONTINUE
266: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
267: IF( KASE.NE.0 ) THEN
268: IF( KASE.EQ.2 ) THEN
269: *
270: * Multiply by R.
271: *
272: DO I = 1, N
273: WORK( I ) = WORK( I ) * RWORK( I )
274: END DO
275: *
276: IF ( NOTRANS ) THEN
277: CALL ZGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
278: $ IPIV, WORK, N, INFO )
279: ELSE
280: CALL ZGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
281: $ LDAFB, IPIV, WORK, N, INFO )
282: ENDIF
283: *
284: * Multiply by inv(X).
285: *
286: DO I = 1, N
287: WORK( I ) = WORK( I ) / X( I )
288: END DO
289: ELSE
290: *
1.5 bertrand 291: * Multiply by inv(X**H).
1.1 bertrand 292: *
293: DO I = 1, N
294: WORK( I ) = WORK( I ) / X( I )
295: END DO
296: *
297: IF ( NOTRANS ) THEN
298: CALL ZGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
299: $ LDAFB, IPIV, WORK, N, INFO )
300: ELSE
301: CALL ZGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
302: $ IPIV, WORK, N, INFO )
303: END IF
304: *
305: * Multiply by R.
306: *
307: DO I = 1, N
308: WORK( I ) = WORK( I ) * RWORK( I )
309: END DO
310: END IF
311: GO TO 10
312: END IF
313: *
314: * Compute the estimate of the reciprocal condition number.
315: *
316: IF( AINVNM .NE. 0.0D+0 )
317: $ ZLA_GBRCOND_X = 1.0D+0 / AINVNM
318: *
319: RETURN
320: *
321: END
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