Annotation of rpl/lapack/lapack/dtbcon.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DTBCON
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DTBCON + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtbcon.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtbcon.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtbcon.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
! 22: * IWORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER DIAG, NORM, UPLO
! 26: * INTEGER INFO, KD, LDAB, N
! 27: * DOUBLE PRECISION RCOND
! 28: * ..
! 29: * .. Array Arguments ..
! 30: * INTEGER IWORK( * )
! 31: * DOUBLE PRECISION AB( LDAB, * ), WORK( * )
! 32: * ..
! 33: *
! 34: *
! 35: *> \par Purpose:
! 36: * =============
! 37: *>
! 38: *> \verbatim
! 39: *>
! 40: *> DTBCON estimates the reciprocal of the condition number of a
! 41: *> triangular band 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] KD
! 82: *> \verbatim
! 83: *> KD is INTEGER
! 84: *> The number of superdiagonals or subdiagonals of the
! 85: *> triangular band matrix A. KD >= 0.
! 86: *> \endverbatim
! 87: *>
! 88: *> \param[in] AB
! 89: *> \verbatim
! 90: *> AB is DOUBLE PRECISION array, dimension (LDAB,N)
! 91: *> The upper or lower triangular band matrix A, stored in the
! 92: *> first kd+1 rows of the array. The j-th column of A is stored
! 93: *> in the j-th column of the array AB as follows:
! 94: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
! 95: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
! 96: *> If DIAG = 'U', the diagonal elements of A are not referenced
! 97: *> and are assumed to be 1.
! 98: *> \endverbatim
! 99: *>
! 100: *> \param[in] LDAB
! 101: *> \verbatim
! 102: *> LDAB is INTEGER
! 103: *> The leading dimension of the array AB. LDAB >= KD+1.
! 104: *> \endverbatim
! 105: *>
! 106: *> \param[out] RCOND
! 107: *> \verbatim
! 108: *> RCOND is DOUBLE PRECISION
! 109: *> The reciprocal of the condition number of the matrix A,
! 110: *> computed as RCOND = 1/(norm(A) * norm(inv(A))).
! 111: *> \endverbatim
! 112: *>
! 113: *> \param[out] WORK
! 114: *> \verbatim
! 115: *> WORK is DOUBLE PRECISION array, dimension (3*N)
! 116: *> \endverbatim
! 117: *>
! 118: *> \param[out] IWORK
! 119: *> \verbatim
! 120: *> IWORK is INTEGER array, dimension (N)
! 121: *> \endverbatim
! 122: *>
! 123: *> \param[out] INFO
! 124: *> \verbatim
! 125: *> INFO is INTEGER
! 126: *> = 0: successful exit
! 127: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 128: *> \endverbatim
! 129: *
! 130: * Authors:
! 131: * ========
! 132: *
! 133: *> \author Univ. of Tennessee
! 134: *> \author Univ. of California Berkeley
! 135: *> \author Univ. of Colorado Denver
! 136: *> \author NAG Ltd.
! 137: *
! 138: *> \date November 2011
! 139: *
! 140: *> \ingroup doubleOTHERcomputational
! 141: *
! 142: * =====================================================================
1.1 bertrand 143: SUBROUTINE DTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
144: $ IWORK, INFO )
145: *
1.9 ! bertrand 146: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 147: * -- LAPACK is a software package provided by Univ. of Tennessee, --
148: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 149: * November 2011
1.1 bertrand 150: *
151: * .. Scalar Arguments ..
152: CHARACTER DIAG, NORM, UPLO
153: INTEGER INFO, KD, LDAB, N
154: DOUBLE PRECISION RCOND
155: * ..
156: * .. Array Arguments ..
157: INTEGER IWORK( * )
158: DOUBLE PRECISION AB( LDAB, * ), WORK( * )
159: * ..
160: *
161: * =====================================================================
162: *
163: * .. Parameters ..
164: DOUBLE PRECISION ONE, ZERO
165: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
166: * ..
167: * .. Local Scalars ..
168: LOGICAL NOUNIT, ONENRM, UPPER
169: CHARACTER NORMIN
170: INTEGER IX, KASE, KASE1
171: DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
172: * ..
173: * .. Local Arrays ..
174: INTEGER ISAVE( 3 )
175: * ..
176: * .. External Functions ..
177: LOGICAL LSAME
178: INTEGER IDAMAX
179: DOUBLE PRECISION DLAMCH, DLANTB
180: EXTERNAL LSAME, IDAMAX, DLAMCH, DLANTB
181: * ..
182: * .. External Subroutines ..
183: EXTERNAL DLACN2, DLATBS, DRSCL, XERBLA
184: * ..
185: * .. Intrinsic Functions ..
186: INTRINSIC ABS, DBLE, MAX
187: * ..
188: * .. Executable Statements ..
189: *
190: * Test the input parameters.
191: *
192: INFO = 0
193: UPPER = LSAME( UPLO, 'U' )
194: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
195: NOUNIT = LSAME( DIAG, 'N' )
196: *
197: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
198: INFO = -1
199: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
200: INFO = -2
201: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
202: INFO = -3
203: ELSE IF( N.LT.0 ) THEN
204: INFO = -4
205: ELSE IF( KD.LT.0 ) THEN
206: INFO = -5
207: ELSE IF( LDAB.LT.KD+1 ) THEN
208: INFO = -7
209: END IF
210: IF( INFO.NE.0 ) THEN
211: CALL XERBLA( 'DTBCON', -INFO )
212: RETURN
213: END IF
214: *
215: * Quick return if possible
216: *
217: IF( N.EQ.0 ) THEN
218: RCOND = ONE
219: RETURN
220: END IF
221: *
222: RCOND = ZERO
223: SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( 1, N ) )
224: *
225: * Compute the norm of the triangular matrix A.
226: *
227: ANORM = DLANTB( NORM, UPLO, DIAG, N, KD, AB, LDAB, WORK )
228: *
229: * Continue only if ANORM > 0.
230: *
231: IF( ANORM.GT.ZERO ) THEN
232: *
233: * Estimate the norm of the inverse of A.
234: *
235: AINVNM = ZERO
236: NORMIN = 'N'
237: IF( ONENRM ) THEN
238: KASE1 = 1
239: ELSE
240: KASE1 = 2
241: END IF
242: KASE = 0
243: 10 CONTINUE
244: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
245: IF( KASE.NE.0 ) THEN
246: IF( KASE.EQ.KASE1 ) THEN
247: *
248: * Multiply by inv(A).
249: *
250: CALL DLATBS( UPLO, 'No transpose', DIAG, NORMIN, N, KD,
251: $ AB, LDAB, WORK, SCALE, WORK( 2*N+1 ), INFO )
252: ELSE
253: *
1.8 bertrand 254: * Multiply by inv(A**T).
1.1 bertrand 255: *
256: CALL DLATBS( UPLO, 'Transpose', DIAG, NORMIN, N, KD, AB,
257: $ LDAB, WORK, SCALE, WORK( 2*N+1 ), INFO )
258: END IF
259: NORMIN = 'Y'
260: *
261: * Multiply by 1/SCALE if doing so will not cause overflow.
262: *
263: IF( SCALE.NE.ONE ) THEN
264: IX = IDAMAX( N, WORK, 1 )
265: XNORM = ABS( WORK( IX ) )
266: IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
267: $ GO TO 20
268: CALL DRSCL( N, SCALE, WORK, 1 )
269: END IF
270: GO TO 10
271: END IF
272: *
273: * Compute the estimate of the reciprocal condition number.
274: *
275: IF( AINVNM.NE.ZERO )
276: $ RCOND = ( ONE / ANORM ) / AINVNM
277: END IF
278: *
279: 20 CONTINUE
280: RETURN
281: *
282: * End of DTBCON
283: *
284: END
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