Annotation of rpl/lapack/lapack/dla_porpvgrw.f, revision 1.5
1.5 ! bertrand 1: *> \brief \b DLA_PORPVGRW
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLA_PORPVGRW + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_porpvgrw.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_porpvgrw.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_porpvgrw.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * DOUBLE PRECISION FUNCTION DLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF,
! 22: * LDAF, WORK )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER*1 UPLO
! 26: * INTEGER NCOLS, LDA, LDAF
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *>
! 39: *> DLA_PORPVGRW computes the reciprocal pivot growth factor
! 40: *> norm(A)/norm(U). The "max absolute element" norm is used. If this is
! 41: *> much less than 1, the stability of the LU factorization of the
! 42: *> (equilibrated) matrix A could be poor. This also means that the
! 43: *> solution X, estimated condition numbers, and error bounds could be
! 44: *> unreliable.
! 45: *> \endverbatim
! 46: *
! 47: * Arguments:
! 48: * ==========
! 49: *
! 50: *> \param[in] UPLO
! 51: *> \verbatim
! 52: *> UPLO is CHARACTER*1
! 53: *> = 'U': Upper triangle of A is stored;
! 54: *> = 'L': Lower triangle of A is stored.
! 55: *> \endverbatim
! 56: *>
! 57: *> \param[in] NCOLS
! 58: *> \verbatim
! 59: *> NCOLS is INTEGER
! 60: *> The number of columns of the matrix A. NCOLS >= 0.
! 61: *> \endverbatim
! 62: *>
! 63: *> \param[in] A
! 64: *> \verbatim
! 65: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 66: *> On entry, the N-by-N matrix A.
! 67: *> \endverbatim
! 68: *>
! 69: *> \param[in] LDA
! 70: *> \verbatim
! 71: *> LDA is INTEGER
! 72: *> The leading dimension of the array A. LDA >= max(1,N).
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] AF
! 76: *> \verbatim
! 77: *> AF is DOUBLE PRECISION array, dimension (LDAF,N)
! 78: *> The triangular factor U or L from the Cholesky factorization
! 79: *> A = U**T*U or A = L*L**T, as computed by DPOTRF.
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in] LDAF
! 83: *> \verbatim
! 84: *> LDAF is INTEGER
! 85: *> The leading dimension of the array AF. LDAF >= max(1,N).
! 86: *> \endverbatim
! 87: *>
! 88: *> \param[in] WORK
! 89: *> \verbatim
! 90: *> WORK is DOUBLE PRECISION array, dimension (2*N)
! 91: *> \endverbatim
! 92: *
! 93: * Authors:
! 94: * ========
! 95: *
! 96: *> \author Univ. of Tennessee
! 97: *> \author Univ. of California Berkeley
! 98: *> \author Univ. of Colorado Denver
! 99: *> \author NAG Ltd.
! 100: *
! 101: *> \date November 2011
! 102: *
! 103: *> \ingroup doublePOcomputational
! 104: *
! 105: * =====================================================================
1.1 bertrand 106: DOUBLE PRECISION FUNCTION DLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF,
107: $ LDAF, WORK )
108: *
1.5 ! bertrand 109: * -- LAPACK computational routine (version 3.4.0) --
! 110: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 111: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 112: * November 2011
1.1 bertrand 113: *
114: * .. Scalar Arguments ..
115: CHARACTER*1 UPLO
116: INTEGER NCOLS, LDA, LDAF
117: * ..
118: * .. Array Arguments ..
119: DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * )
120: * ..
121: *
122: * =====================================================================
123: *
124: * .. Local Scalars ..
125: INTEGER I, J
126: DOUBLE PRECISION AMAX, UMAX, RPVGRW
127: LOGICAL UPPER
128: * ..
129: * .. Intrinsic Functions ..
130: INTRINSIC ABS, MAX, MIN
131: * ..
132: * .. External Functions ..
133: EXTERNAL LSAME, DLASET
134: LOGICAL LSAME
135: * ..
136: * .. Executable Statements ..
137: *
138: UPPER = LSAME( 'Upper', UPLO )
139: *
140: * DPOTRF will have factored only the NCOLSxNCOLS leading minor, so
141: * we restrict the growth search to that minor and use only the first
142: * 2*NCOLS workspace entries.
143: *
144: RPVGRW = 1.0D+0
145: DO I = 1, 2*NCOLS
146: WORK( I ) = 0.0D+0
147: END DO
148: *
149: * Find the max magnitude entry of each column.
150: *
151: IF ( UPPER ) THEN
152: DO J = 1, NCOLS
153: DO I = 1, J
154: WORK( NCOLS+J ) =
155: $ MAX( ABS( A( I, J ) ), WORK( NCOLS+J ) )
156: END DO
157: END DO
158: ELSE
159: DO J = 1, NCOLS
160: DO I = J, NCOLS
161: WORK( NCOLS+J ) =
162: $ MAX( ABS( A( I, J ) ), WORK( NCOLS+J ) )
163: END DO
164: END DO
165: END IF
166: *
167: * Now find the max magnitude entry of each column of the factor in
168: * AF. No pivoting, so no permutations.
169: *
170: IF ( LSAME( 'Upper', UPLO ) ) THEN
171: DO J = 1, NCOLS
172: DO I = 1, J
173: WORK( J ) = MAX( ABS( AF( I, J ) ), WORK( J ) )
174: END DO
175: END DO
176: ELSE
177: DO J = 1, NCOLS
178: DO I = J, NCOLS
179: WORK( J ) = MAX( ABS( AF( I, J ) ), WORK( J ) )
180: END DO
181: END DO
182: END IF
183: *
184: * Compute the *inverse* of the max element growth factor. Dividing
185: * by zero would imply the largest entry of the factor's column is
186: * zero. Than can happen when either the column of A is zero or
187: * massive pivots made the factor underflow to zero. Neither counts
188: * as growth in itself, so simply ignore terms with zero
189: * denominators.
190: *
191: IF ( LSAME( 'Upper', UPLO ) ) THEN
192: DO I = 1, NCOLS
193: UMAX = WORK( I )
194: AMAX = WORK( NCOLS+I )
195: IF ( UMAX /= 0.0D+0 ) THEN
196: RPVGRW = MIN( AMAX / UMAX, RPVGRW )
197: END IF
198: END DO
199: ELSE
200: DO I = 1, NCOLS
201: UMAX = WORK( I )
202: AMAX = WORK( NCOLS+I )
203: IF ( UMAX /= 0.0D+0 ) THEN
204: RPVGRW = MIN( AMAX / UMAX, RPVGRW )
205: END IF
206: END DO
207: END IF
208:
209: DLA_PORPVGRW = RPVGRW
210: END
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