Annotation of rpl/lapack/lapack/dla_syrcond.f, revision 1.6
1.6 ! bertrand 1: *> \brief \b DLA_SYRCOND
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLA_SYRCOND + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_syrcond.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_syrcond.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_syrcond.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * DOUBLE PRECISION FUNCTION DLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF,
! 22: * IPIV, CMODE, C, INFO, WORK,
! 23: * IWORK )
! 24: *
! 25: * .. Scalar Arguments ..
! 26: * CHARACTER UPLO
! 27: * INTEGER N, LDA, LDAF, INFO, CMODE
! 28: * ..
! 29: * .. Array Arguments
! 30: * INTEGER IWORK( * ), IPIV( * )
! 31: * DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * )
! 32: * ..
! 33: *
! 34: *
! 35: *> \par Purpose:
! 36: * =============
! 37: *>
! 38: *> \verbatim
! 39: *>
! 40: *> DLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C)
! 41: *> where op2 is determined by CMODE as follows
! 42: *> CMODE = 1 op2(C) = C
! 43: *> CMODE = 0 op2(C) = I
! 44: *> CMODE = -1 op2(C) = inv(C)
! 45: *> The Skeel condition number cond(A) = norminf( |inv(A)||A| )
! 46: *> is computed by computing scaling factors R such that
! 47: *> diag(R)*A*op2(C) is row equilibrated and computing the standard
! 48: *> infinity-norm condition number.
! 49: *> \endverbatim
! 50: *
! 51: * Arguments:
! 52: * ==========
! 53: *
! 54: *> \param[in] UPLO
! 55: *> \verbatim
! 56: *> UPLO is CHARACTER*1
! 57: *> = 'U': Upper triangle of A is stored;
! 58: *> = 'L': Lower triangle of A is stored.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in] N
! 62: *> \verbatim
! 63: *> N is INTEGER
! 64: *> The number of linear equations, i.e., the order of the
! 65: *> matrix A. N >= 0.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] A
! 69: *> \verbatim
! 70: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 71: *> On entry, the N-by-N matrix A.
! 72: *> \endverbatim
! 73: *>
! 74: *> \param[in] LDA
! 75: *> \verbatim
! 76: *> LDA is INTEGER
! 77: *> The leading dimension of the array A. LDA >= max(1,N).
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] AF
! 81: *> \verbatim
! 82: *> AF is DOUBLE PRECISION array, dimension (LDAF,N)
! 83: *> The block diagonal matrix D and the multipliers used to
! 84: *> obtain the factor U or L as computed by DSYTRF.
! 85: *> \endverbatim
! 86: *>
! 87: *> \param[in] LDAF
! 88: *> \verbatim
! 89: *> LDAF is INTEGER
! 90: *> The leading dimension of the array AF. LDAF >= max(1,N).
! 91: *> \endverbatim
! 92: *>
! 93: *> \param[in] IPIV
! 94: *> \verbatim
! 95: *> IPIV is INTEGER array, dimension (N)
! 96: *> Details of the interchanges and the block structure of D
! 97: *> as determined by DSYTRF.
! 98: *> \endverbatim
! 99: *>
! 100: *> \param[in] CMODE
! 101: *> \verbatim
! 102: *> CMODE is INTEGER
! 103: *> Determines op2(C) in the formula op(A) * op2(C) as follows:
! 104: *> CMODE = 1 op2(C) = C
! 105: *> CMODE = 0 op2(C) = I
! 106: *> CMODE = -1 op2(C) = inv(C)
! 107: *> \endverbatim
! 108: *>
! 109: *> \param[in] C
! 110: *> \verbatim
! 111: *> C is DOUBLE PRECISION array, dimension (N)
! 112: *> The vector C in the formula op(A) * op2(C).
! 113: *> \endverbatim
! 114: *>
! 115: *> \param[out] INFO
! 116: *> \verbatim
! 117: *> INFO is INTEGER
! 118: *> = 0: Successful exit.
! 119: *> i > 0: The ith argument is invalid.
! 120: *> \endverbatim
! 121: *>
! 122: *> \param[in] WORK
! 123: *> \verbatim
! 124: *> WORK is DOUBLE PRECISION array, dimension (3*N).
! 125: *> Workspace.
! 126: *> \endverbatim
! 127: *>
! 128: *> \param[in] IWORK
! 129: *> \verbatim
! 130: *> IWORK is INTEGER array, dimension (N).
! 131: *> Workspace.
! 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 doubleSYcomputational
! 145: *
! 146: * =====================================================================
1.1 bertrand 147: DOUBLE PRECISION FUNCTION DLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF,
148: $ IPIV, CMODE, C, INFO, WORK,
149: $ IWORK )
150: *
1.6 ! bertrand 151: * -- LAPACK computational routine (version 3.4.0) --
! 152: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 153: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 154: * November 2011
1.1 bertrand 155: *
156: * .. Scalar Arguments ..
157: CHARACTER UPLO
158: INTEGER N, LDA, LDAF, INFO, CMODE
159: * ..
160: * .. Array Arguments
161: INTEGER IWORK( * ), IPIV( * )
162: DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * )
163: * ..
164: *
165: * =====================================================================
166: *
167: * .. Local Scalars ..
168: CHARACTER NORMIN
169: INTEGER KASE, I, J
170: DOUBLE PRECISION AINVNM, SMLNUM, TMP
171: LOGICAL UP
172: * ..
173: * .. Local Arrays ..
174: INTEGER ISAVE( 3 )
175: * ..
176: * .. External Functions ..
177: LOGICAL LSAME
178: INTEGER IDAMAX
179: DOUBLE PRECISION DLAMCH
180: EXTERNAL LSAME, IDAMAX, DLAMCH
181: * ..
182: * .. External Subroutines ..
183: EXTERNAL DLACN2, DLATRS, DRSCL, XERBLA, DSYTRS
184: * ..
185: * .. Intrinsic Functions ..
186: INTRINSIC ABS, MAX
187: * ..
188: * .. Executable Statements ..
189: *
190: DLA_SYRCOND = 0.0D+0
191: *
192: INFO = 0
193: IF( N.LT.0 ) THEN
194: INFO = -2
195: END IF
196: IF( INFO.NE.0 ) THEN
197: CALL XERBLA( 'DLA_SYRCOND', -INFO )
198: RETURN
199: END IF
200: IF( N.EQ.0 ) THEN
201: DLA_SYRCOND = 1.0D+0
202: RETURN
203: END IF
204: UP = .FALSE.
205: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
206: *
207: * Compute the equilibration matrix R such that
208: * inv(R)*A*C has unit 1-norm.
209: *
210: IF ( UP ) THEN
211: DO I = 1, N
212: TMP = 0.0D+0
213: IF ( CMODE .EQ. 1 ) THEN
214: DO J = 1, I
215: TMP = TMP + ABS( A( J, I ) * C( J ) )
216: END DO
217: DO J = I+1, N
218: TMP = TMP + ABS( A( I, J ) * C( J ) )
219: END DO
220: ELSE IF ( CMODE .EQ. 0 ) THEN
221: DO J = 1, I
222: TMP = TMP + ABS( A( J, I ) )
223: END DO
224: DO J = I+1, N
225: TMP = TMP + ABS( A( I, J ) )
226: END DO
227: ELSE
228: DO J = 1, I
229: TMP = TMP + ABS( A( J, I ) / C( J ) )
230: END DO
231: DO J = I+1, N
232: TMP = TMP + ABS( A( I, J ) / C( J ) )
233: END DO
234: END IF
235: WORK( 2*N+I ) = TMP
236: END DO
237: ELSE
238: DO I = 1, N
239: TMP = 0.0D+0
240: IF ( CMODE .EQ. 1 ) THEN
241: DO J = 1, I
242: TMP = TMP + ABS( A( I, J ) * C( J ) )
243: END DO
244: DO J = I+1, N
245: TMP = TMP + ABS( A( J, I ) * C( J ) )
246: END DO
247: ELSE IF ( CMODE .EQ. 0 ) THEN
248: DO J = 1, I
249: TMP = TMP + ABS( A( I, J ) )
250: END DO
251: DO J = I+1, N
252: TMP = TMP + ABS( A( J, I ) )
253: END DO
254: ELSE
255: DO J = 1, I
256: TMP = TMP + ABS( A( I, J) / C( J ) )
257: END DO
258: DO J = I+1, N
259: TMP = TMP + ABS( A( J, I) / C( J ) )
260: END DO
261: END IF
262: WORK( 2*N+I ) = TMP
263: END DO
264: ENDIF
265: *
266: * Estimate the norm of inv(op(A)).
267: *
268: SMLNUM = DLAMCH( 'Safe minimum' )
269: AINVNM = 0.0D+0
270: NORMIN = 'N'
271:
272: KASE = 0
273: 10 CONTINUE
274: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
275: IF( KASE.NE.0 ) THEN
276: IF( KASE.EQ.2 ) THEN
277: *
278: * Multiply by R.
279: *
280: DO I = 1, N
281: WORK( I ) = WORK( I ) * WORK( 2*N+I )
282: END DO
283:
284: IF ( UP ) THEN
285: CALL DSYTRS( 'U', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
286: ELSE
287: CALL DSYTRS( 'L', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
288: ENDIF
289: *
290: * Multiply by inv(C).
291: *
292: IF ( CMODE .EQ. 1 ) THEN
293: DO I = 1, N
294: WORK( I ) = WORK( I ) / C( I )
295: END DO
296: ELSE IF ( CMODE .EQ. -1 ) THEN
297: DO I = 1, N
298: WORK( I ) = WORK( I ) * C( I )
299: END DO
300: END IF
301: ELSE
302: *
1.5 bertrand 303: * Multiply by inv(C**T).
1.1 bertrand 304: *
305: IF ( CMODE .EQ. 1 ) THEN
306: DO I = 1, N
307: WORK( I ) = WORK( I ) / C( I )
308: END DO
309: ELSE IF ( CMODE .EQ. -1 ) THEN
310: DO I = 1, N
311: WORK( I ) = WORK( I ) * C( I )
312: END DO
313: END IF
314:
315: IF ( UP ) THEN
316: CALL DSYTRS( 'U', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
317: ELSE
318: CALL DSYTRS( 'L', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
319: ENDIF
320: *
321: * Multiply by R.
322: *
323: DO I = 1, N
324: WORK( I ) = WORK( I ) * WORK( 2*N+I )
325: END DO
326: END IF
327: *
328: GO TO 10
329: END IF
330: *
331: * Compute the estimate of the reciprocal condition number.
332: *
333: IF( AINVNM .NE. 0.0D+0 )
334: $ DLA_SYRCOND = ( 1.0D+0 / AINVNM )
335: *
336: RETURN
337: *
338: END
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