Annotation of rpl/lapack/lapack/zgetc2.f, revision 1.17
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: *
1.15 bertrand 101: *> \date June 2016
1.8 bertrand 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: *
1.17 ! bertrand 114: * -- LAPACK auxiliary routine (version 3.7.0) --
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..--
1.15 bertrand 117: * June 2016
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: *
1.15 bertrand 149: INFO = 0
150: *
151: * Quick return if possible
152: *
153: IF( N.EQ.0 )
154: $ RETURN
155: *
1.1 bertrand 156: * Set constants to control overflow
157: *
158: EPS = DLAMCH( 'P' )
159: SMLNUM = DLAMCH( 'S' ) / EPS
160: BIGNUM = ONE / SMLNUM
161: CALL DLABAD( SMLNUM, BIGNUM )
162: *
1.15 bertrand 163: * Handle the case N=1 by itself
164: *
165: IF( N.EQ.1 ) THEN
166: IPIV( 1 ) = 1
167: JPIV( 1 ) = 1
168: IF( ABS( A( 1, 1 ) ).LT.SMLNUM ) THEN
169: INFO = 1
170: A( 1, 1 ) = DCMPLX( SMLNUM, ZERO )
171: END IF
172: RETURN
173: END IF
174: *
1.1 bertrand 175: * Factorize A using complete pivoting.
176: * Set pivots less than SMIN to SMIN
177: *
178: DO 40 I = 1, N - 1
179: *
180: * Find max element in matrix A
181: *
182: XMAX = ZERO
183: DO 20 IP = I, N
184: DO 10 JP = I, N
185: IF( ABS( A( IP, JP ) ).GE.XMAX ) THEN
186: XMAX = ABS( A( IP, JP ) )
187: IPV = IP
188: JPV = JP
189: END IF
190: 10 CONTINUE
191: 20 CONTINUE
192: IF( I.EQ.1 )
193: $ SMIN = MAX( EPS*XMAX, SMLNUM )
194: *
195: * Swap rows
196: *
197: IF( IPV.NE.I )
198: $ CALL ZSWAP( N, A( IPV, 1 ), LDA, A( I, 1 ), LDA )
199: IPIV( I ) = IPV
200: *
201: * Swap columns
202: *
203: IF( JPV.NE.I )
204: $ CALL ZSWAP( N, A( 1, JPV ), 1, A( 1, I ), 1 )
205: JPIV( I ) = JPV
206: *
207: * Check for singularity
208: *
209: IF( ABS( A( I, I ) ).LT.SMIN ) THEN
210: INFO = I
211: A( I, I ) = DCMPLX( SMIN, ZERO )
212: END IF
213: DO 30 J = I + 1, N
214: A( J, I ) = A( J, I ) / A( I, I )
215: 30 CONTINUE
216: CALL ZGERU( N-I, N-I, -DCMPLX( ONE ), A( I+1, I ), 1,
217: $ A( I, I+1 ), LDA, A( I+1, I+1 ), LDA )
218: 40 CONTINUE
219: *
220: IF( ABS( A( N, N ) ).LT.SMIN ) THEN
221: INFO = N
222: A( N, N ) = DCMPLX( SMIN, ZERO )
223: END IF
1.13 bertrand 224: *
225: * Set last pivots to N
226: *
227: IPIV( N ) = N
228: JPIV( N ) = N
229: *
1.1 bertrand 230: RETURN
231: *
232: * End of ZGETC2
233: *
234: END
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