Annotation of rpl/lapack/lapack/zgetc2.f, revision 1.21
1.11 bertrand 1: *> \brief \b ZGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix.
1.8 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.17 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.17 bertrand 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">
1.8 bertrand 15: *> [TXT]</a>
1.17 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO )
1.17 bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * INTEGER INFO, LDA, N
25: * ..
26: * .. Array Arguments ..
27: * INTEGER IPIV( * ), JPIV( * )
28: * COMPLEX*16 A( LDA, * )
29: * ..
1.17 bertrand 30: *
1.8 bertrand 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: *
1.17 bertrand 96: *> \author Univ. of Tennessee
97: *> \author Univ. of California Berkeley
98: *> \author Univ. of Colorado Denver
99: *> \author NAG Ltd.
1.8 bertrand 100: *
101: *> \ingroup complex16GEauxiliary
102: *
103: *> \par Contributors:
104: * ==================
105: *>
106: *> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
107: *> Umea University, S-901 87 Umea, Sweden.
108: *
109: * =====================================================================
1.1 bertrand 110: SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO )
111: *
1.21 ! bertrand 112: * -- LAPACK auxiliary routine --
1.1 bertrand 113: * -- LAPACK is a software package provided by Univ. of Tennessee, --
114: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115: *
116: * .. Scalar Arguments ..
117: INTEGER INFO, LDA, N
118: * ..
119: * .. Array Arguments ..
120: INTEGER IPIV( * ), JPIV( * )
121: COMPLEX*16 A( LDA, * )
122: * ..
123: *
124: * =====================================================================
125: *
126: * .. Parameters ..
127: DOUBLE PRECISION ZERO, ONE
128: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
129: * ..
130: * .. Local Scalars ..
131: INTEGER I, IP, IPV, J, JP, JPV
132: DOUBLE PRECISION BIGNUM, EPS, SMIN, SMLNUM, XMAX
133: * ..
134: * .. External Subroutines ..
1.19 bertrand 135: EXTERNAL ZGERU, ZSWAP, DLABAD
1.1 bertrand 136: * ..
137: * .. External Functions ..
138: DOUBLE PRECISION DLAMCH
139: EXTERNAL DLAMCH
140: * ..
141: * .. Intrinsic Functions ..
142: INTRINSIC ABS, DCMPLX, MAX
143: * ..
144: * .. Executable Statements ..
145: *
1.15 bertrand 146: INFO = 0
147: *
148: * Quick return if possible
149: *
150: IF( N.EQ.0 )
151: $ RETURN
152: *
1.1 bertrand 153: * Set constants to control overflow
154: *
155: EPS = DLAMCH( 'P' )
156: SMLNUM = DLAMCH( 'S' ) / EPS
157: BIGNUM = ONE / SMLNUM
158: CALL DLABAD( SMLNUM, BIGNUM )
159: *
1.15 bertrand 160: * Handle the case N=1 by itself
161: *
162: IF( N.EQ.1 ) THEN
163: IPIV( 1 ) = 1
164: JPIV( 1 ) = 1
165: IF( ABS( A( 1, 1 ) ).LT.SMLNUM ) THEN
166: INFO = 1
167: A( 1, 1 ) = DCMPLX( SMLNUM, ZERO )
168: END IF
169: RETURN
170: END IF
171: *
1.1 bertrand 172: * Factorize A using complete pivoting.
173: * Set pivots less than SMIN to SMIN
174: *
175: DO 40 I = 1, N - 1
176: *
177: * Find max element in matrix A
178: *
179: XMAX = ZERO
180: DO 20 IP = I, N
181: DO 10 JP = I, N
182: IF( ABS( A( IP, JP ) ).GE.XMAX ) THEN
183: XMAX = ABS( A( IP, JP ) )
184: IPV = IP
185: JPV = JP
186: END IF
187: 10 CONTINUE
188: 20 CONTINUE
189: IF( I.EQ.1 )
190: $ SMIN = MAX( EPS*XMAX, SMLNUM )
191: *
192: * Swap rows
193: *
194: IF( IPV.NE.I )
195: $ CALL ZSWAP( N, A( IPV, 1 ), LDA, A( I, 1 ), LDA )
196: IPIV( I ) = IPV
197: *
198: * Swap columns
199: *
200: IF( JPV.NE.I )
201: $ CALL ZSWAP( N, A( 1, JPV ), 1, A( 1, I ), 1 )
202: JPIV( I ) = JPV
203: *
204: * Check for singularity
205: *
206: IF( ABS( A( I, I ) ).LT.SMIN ) THEN
207: INFO = I
208: A( I, I ) = DCMPLX( SMIN, ZERO )
209: END IF
210: DO 30 J = I + 1, N
211: A( J, I ) = A( J, I ) / A( I, I )
212: 30 CONTINUE
213: CALL ZGERU( N-I, N-I, -DCMPLX( ONE ), A( I+1, I ), 1,
214: $ A( I, I+1 ), LDA, A( I+1, I+1 ), LDA )
215: 40 CONTINUE
216: *
217: IF( ABS( A( N, N ) ).LT.SMIN ) THEN
218: INFO = N
219: A( N, N ) = DCMPLX( SMIN, ZERO )
220: END IF
1.13 bertrand 221: *
222: * Set last pivots to N
223: *
224: IPIV( N ) = N
225: JPIV( N ) = N
226: *
1.1 bertrand 227: RETURN
228: *
229: * End of ZGETC2
230: *
231: 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