Annotation of rpl/lapack/lapack/dtpcon.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DTPCON
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DTPCON + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtpcon.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtpcon.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtpcon.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, IWORK,
! 22: * INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER DIAG, NORM, UPLO
! 26: * INTEGER INFO, N
! 27: * DOUBLE PRECISION RCOND
! 28: * ..
! 29: * .. Array Arguments ..
! 30: * INTEGER IWORK( * )
! 31: * DOUBLE PRECISION AP( * ), WORK( * )
! 32: * ..
! 33: *
! 34: *
! 35: *> \par Purpose:
! 36: * =============
! 37: *>
! 38: *> \verbatim
! 39: *>
! 40: *> DTPCON estimates the reciprocal of the condition number of a packed
! 41: *> triangular matrix A, in either the 1-norm or the infinity-norm.
! 42: *>
! 43: *> The norm of A is computed and an estimate is obtained for
! 44: *> norm(inv(A)), then the reciprocal of the condition number is
! 45: *> computed as
! 46: *> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
! 47: *> \endverbatim
! 48: *
! 49: * Arguments:
! 50: * ==========
! 51: *
! 52: *> \param[in] NORM
! 53: *> \verbatim
! 54: *> NORM is CHARACTER*1
! 55: *> Specifies whether the 1-norm condition number or the
! 56: *> infinity-norm condition number is required:
! 57: *> = '1' or 'O': 1-norm;
! 58: *> = 'I': Infinity-norm.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in] UPLO
! 62: *> \verbatim
! 63: *> UPLO is CHARACTER*1
! 64: *> = 'U': A is upper triangular;
! 65: *> = 'L': A is lower triangular.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] DIAG
! 69: *> \verbatim
! 70: *> DIAG is CHARACTER*1
! 71: *> = 'N': A is non-unit triangular;
! 72: *> = 'U': A is unit triangular.
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] N
! 76: *> \verbatim
! 77: *> N is INTEGER
! 78: *> The order of the matrix A. N >= 0.
! 79: *> \endverbatim
! 80: *>
! 81: *> \param[in] AP
! 82: *> \verbatim
! 83: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 84: *> The upper or lower triangular matrix A, packed columnwise in
! 85: *> a linear array. The j-th column of A is stored in the array
! 86: *> AP as follows:
! 87: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 88: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
! 89: *> If DIAG = 'U', the diagonal elements of A are not referenced
! 90: *> and are assumed to be 1.
! 91: *> \endverbatim
! 92: *>
! 93: *> \param[out] RCOND
! 94: *> \verbatim
! 95: *> RCOND is DOUBLE PRECISION
! 96: *> The reciprocal of the condition number of the matrix A,
! 97: *> computed as RCOND = 1/(norm(A) * norm(inv(A))).
! 98: *> \endverbatim
! 99: *>
! 100: *> \param[out] WORK
! 101: *> \verbatim
! 102: *> WORK is DOUBLE PRECISION array, dimension (3*N)
! 103: *> \endverbatim
! 104: *>
! 105: *> \param[out] IWORK
! 106: *> \verbatim
! 107: *> IWORK is INTEGER array, dimension (N)
! 108: *> \endverbatim
! 109: *>
! 110: *> \param[out] INFO
! 111: *> \verbatim
! 112: *> INFO is INTEGER
! 113: *> = 0: successful exit
! 114: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 115: *> \endverbatim
! 116: *
! 117: * Authors:
! 118: * ========
! 119: *
! 120: *> \author Univ. of Tennessee
! 121: *> \author Univ. of California Berkeley
! 122: *> \author Univ. of Colorado Denver
! 123: *> \author NAG Ltd.
! 124: *
! 125: *> \date November 2011
! 126: *
! 127: *> \ingroup doubleOTHERcomputational
! 128: *
! 129: * =====================================================================
1.1 bertrand 130: SUBROUTINE DTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, IWORK,
131: $ INFO )
132: *
1.9 ! bertrand 133: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 134: * -- LAPACK is a software package provided by Univ. of Tennessee, --
135: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 136: * November 2011
1.1 bertrand 137: *
138: * .. Scalar Arguments ..
139: CHARACTER DIAG, NORM, UPLO
140: INTEGER INFO, N
141: DOUBLE PRECISION RCOND
142: * ..
143: * .. Array Arguments ..
144: INTEGER IWORK( * )
145: DOUBLE PRECISION AP( * ), WORK( * )
146: * ..
147: *
148: * =====================================================================
149: *
150: * .. Parameters ..
151: DOUBLE PRECISION ONE, ZERO
152: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
153: * ..
154: * .. Local Scalars ..
155: LOGICAL NOUNIT, ONENRM, UPPER
156: CHARACTER NORMIN
157: INTEGER IX, KASE, KASE1
158: DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
159: * ..
160: * .. Local Arrays ..
161: INTEGER ISAVE( 3 )
162: * ..
163: * .. External Functions ..
164: LOGICAL LSAME
165: INTEGER IDAMAX
166: DOUBLE PRECISION DLAMCH, DLANTP
167: EXTERNAL LSAME, IDAMAX, DLAMCH, DLANTP
168: * ..
169: * .. External Subroutines ..
170: EXTERNAL DLACN2, DLATPS, DRSCL, XERBLA
171: * ..
172: * .. Intrinsic Functions ..
173: INTRINSIC ABS, DBLE, MAX
174: * ..
175: * .. Executable Statements ..
176: *
177: * Test the input parameters.
178: *
179: INFO = 0
180: UPPER = LSAME( UPLO, 'U' )
181: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
182: NOUNIT = LSAME( DIAG, 'N' )
183: *
184: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
185: INFO = -1
186: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
187: INFO = -2
188: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
189: INFO = -3
190: ELSE IF( N.LT.0 ) THEN
191: INFO = -4
192: END IF
193: IF( INFO.NE.0 ) THEN
194: CALL XERBLA( 'DTPCON', -INFO )
195: RETURN
196: END IF
197: *
198: * Quick return if possible
199: *
200: IF( N.EQ.0 ) THEN
201: RCOND = ONE
202: RETURN
203: END IF
204: *
205: RCOND = ZERO
206: SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( 1, N ) )
207: *
208: * Compute the norm of the triangular matrix A.
209: *
210: ANORM = DLANTP( NORM, UPLO, DIAG, N, AP, WORK )
211: *
212: * Continue only if ANORM > 0.
213: *
214: IF( ANORM.GT.ZERO ) THEN
215: *
216: * Estimate the norm of the inverse of A.
217: *
218: AINVNM = ZERO
219: NORMIN = 'N'
220: IF( ONENRM ) THEN
221: KASE1 = 1
222: ELSE
223: KASE1 = 2
224: END IF
225: KASE = 0
226: 10 CONTINUE
227: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
228: IF( KASE.NE.0 ) THEN
229: IF( KASE.EQ.KASE1 ) THEN
230: *
231: * Multiply by inv(A).
232: *
233: CALL DLATPS( UPLO, 'No transpose', DIAG, NORMIN, N, AP,
234: $ WORK, SCALE, WORK( 2*N+1 ), INFO )
235: ELSE
236: *
1.8 bertrand 237: * Multiply by inv(A**T).
1.1 bertrand 238: *
239: CALL DLATPS( UPLO, 'Transpose', DIAG, NORMIN, N, AP,
240: $ WORK, SCALE, WORK( 2*N+1 ), INFO )
241: END IF
242: NORMIN = 'Y'
243: *
244: * Multiply by 1/SCALE if doing so will not cause overflow.
245: *
246: IF( SCALE.NE.ONE ) THEN
247: IX = IDAMAX( N, WORK, 1 )
248: XNORM = ABS( WORK( IX ) )
249: IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
250: $ GO TO 20
251: CALL DRSCL( N, SCALE, WORK, 1 )
252: END IF
253: GO TO 10
254: END IF
255: *
256: * Compute the estimate of the reciprocal condition number.
257: *
258: IF( AINVNM.NE.ZERO )
259: $ RCOND = ( ONE / ANORM ) / AINVNM
260: END IF
261: *
262: 20 CONTINUE
263: RETURN
264: *
265: * End of DTPCON
266: *
267: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dtpcon.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack