Annotation of rpl/lapack/lapack/zgetc2.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZGETC2
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZGETC2 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgetc2.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgetc2.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgetc2.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INFO, LDA, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * INTEGER IPIV( * ), JPIV( * )
! 28: * COMPLEX*16 A( LDA, * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> ZGETC2 computes an LU factorization, using complete pivoting, of the
! 38: *> n-by-n matrix A. The factorization has the form A = P * L * U * Q,
! 39: *> where P and Q are permutation matrices, L is lower triangular with
! 40: *> unit diagonal elements and U is upper triangular.
! 41: *>
! 42: *> This is a level 1 BLAS version of the algorithm.
! 43: *> \endverbatim
! 44: *
! 45: * Arguments:
! 46: * ==========
! 47: *
! 48: *> \param[in] N
! 49: *> \verbatim
! 50: *> N is INTEGER
! 51: *> The order of the matrix A. N >= 0.
! 52: *> \endverbatim
! 53: *>
! 54: *> \param[in,out] A
! 55: *> \verbatim
! 56: *> A is COMPLEX*16 array, dimension (LDA, N)
! 57: *> On entry, the n-by-n matrix to be factored.
! 58: *> On exit, the factors L and U from the factorization
! 59: *> A = P*L*U*Q; the unit diagonal elements of L are not stored.
! 60: *> If U(k, k) appears to be less than SMIN, U(k, k) is given the
! 61: *> value of SMIN, giving a nonsingular perturbed system.
! 62: *> \endverbatim
! 63: *>
! 64: *> \param[in] LDA
! 65: *> \verbatim
! 66: *> LDA is INTEGER
! 67: *> The leading dimension of the array A. LDA >= max(1, N).
! 68: *> \endverbatim
! 69: *>
! 70: *> \param[out] IPIV
! 71: *> \verbatim
! 72: *> IPIV is INTEGER array, dimension (N).
! 73: *> The pivot indices; for 1 <= i <= N, row i of the
! 74: *> matrix has been interchanged with row IPIV(i).
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[out] JPIV
! 78: *> \verbatim
! 79: *> JPIV is INTEGER array, dimension (N).
! 80: *> The pivot indices; for 1 <= j <= N, column j of the
! 81: *> matrix has been interchanged with column JPIV(j).
! 82: *> \endverbatim
! 83: *>
! 84: *> \param[out] INFO
! 85: *> \verbatim
! 86: *> INFO is INTEGER
! 87: *> = 0: successful exit
! 88: *> > 0: if INFO = k, U(k, k) is likely to produce overflow if
! 89: *> one tries to solve for x in Ax = b. So U is perturbed
! 90: *> to avoid the overflow.
! 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 complex16GEauxiliary
! 104: *
! 105: *> \par Contributors:
! 106: * ==================
! 107: *>
! 108: *> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
! 109: *> Umea University, S-901 87 Umea, Sweden.
! 110: *
! 111: * =====================================================================
1.1 bertrand 112: SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO )
113: *
1.8 ! bertrand 114: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 115: * -- LAPACK is a software package provided by Univ. of Tennessee, --
116: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 117: * November 2011
1.1 bertrand 118: *
119: * .. Scalar Arguments ..
120: INTEGER INFO, LDA, N
121: * ..
122: * .. Array Arguments ..
123: INTEGER IPIV( * ), JPIV( * )
124: COMPLEX*16 A( LDA, * )
125: * ..
126: *
127: * =====================================================================
128: *
129: * .. Parameters ..
130: DOUBLE PRECISION ZERO, ONE
131: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
132: * ..
133: * .. Local Scalars ..
134: INTEGER I, IP, IPV, J, JP, JPV
135: DOUBLE PRECISION BIGNUM, EPS, SMIN, SMLNUM, XMAX
136: * ..
137: * .. External Subroutines ..
138: EXTERNAL ZGERU, ZSWAP
139: * ..
140: * .. External Functions ..
141: DOUBLE PRECISION DLAMCH
142: EXTERNAL DLAMCH
143: * ..
144: * .. Intrinsic Functions ..
145: INTRINSIC ABS, DCMPLX, MAX
146: * ..
147: * .. Executable Statements ..
148: *
149: * Set constants to control overflow
150: *
151: INFO = 0
152: EPS = DLAMCH( 'P' )
153: SMLNUM = DLAMCH( 'S' ) / EPS
154: BIGNUM = ONE / SMLNUM
155: CALL DLABAD( SMLNUM, BIGNUM )
156: *
157: * Factorize A using complete pivoting.
158: * Set pivots less than SMIN to SMIN
159: *
160: DO 40 I = 1, N - 1
161: *
162: * Find max element in matrix A
163: *
164: XMAX = ZERO
165: DO 20 IP = I, N
166: DO 10 JP = I, N
167: IF( ABS( A( IP, JP ) ).GE.XMAX ) THEN
168: XMAX = ABS( A( IP, JP ) )
169: IPV = IP
170: JPV = JP
171: END IF
172: 10 CONTINUE
173: 20 CONTINUE
174: IF( I.EQ.1 )
175: $ SMIN = MAX( EPS*XMAX, SMLNUM )
176: *
177: * Swap rows
178: *
179: IF( IPV.NE.I )
180: $ CALL ZSWAP( N, A( IPV, 1 ), LDA, A( I, 1 ), LDA )
181: IPIV( I ) = IPV
182: *
183: * Swap columns
184: *
185: IF( JPV.NE.I )
186: $ CALL ZSWAP( N, A( 1, JPV ), 1, A( 1, I ), 1 )
187: JPIV( I ) = JPV
188: *
189: * Check for singularity
190: *
191: IF( ABS( A( I, I ) ).LT.SMIN ) THEN
192: INFO = I
193: A( I, I ) = DCMPLX( SMIN, ZERO )
194: END IF
195: DO 30 J = I + 1, N
196: A( J, I ) = A( J, I ) / A( I, I )
197: 30 CONTINUE
198: CALL ZGERU( N-I, N-I, -DCMPLX( ONE ), A( I+1, I ), 1,
199: $ A( I, I+1 ), LDA, A( I+1, I+1 ), LDA )
200: 40 CONTINUE
201: *
202: IF( ABS( A( N, N ) ).LT.SMIN ) THEN
203: INFO = N
204: A( N, N ) = DCMPLX( SMIN, ZERO )
205: END IF
206: RETURN
207: *
208: * End of ZGETC2
209: *
210: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zgetc2.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack