Annotation of rpl/lapack/lapack/zgesc2.f, revision 1.12
1.11 bertrand 1: *> \brief \b ZGESC2 solves a system of linear equations using the LU factorization with complete pivoting computed by sgetc2.
1.8 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZGESC2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgesc2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgesc2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgesc2.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER LDA, N
25: * DOUBLE PRECISION SCALE
26: * ..
27: * .. Array Arguments ..
28: * INTEGER IPIV( * ), JPIV( * )
29: * COMPLEX*16 A( LDA, * ), RHS( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZGESC2 solves a system of linear equations
39: *>
40: *> A * X = scale* RHS
41: *>
42: *> with a general N-by-N matrix A using the LU factorization with
43: *> complete pivoting computed by ZGETC2.
44: *>
45: *> \endverbatim
46: *
47: * Arguments:
48: * ==========
49: *
50: *> \param[in] N
51: *> \verbatim
52: *> N is INTEGER
53: *> The number of columns of the matrix A.
54: *> \endverbatim
55: *>
56: *> \param[in] A
57: *> \verbatim
58: *> A is COMPLEX*16 array, dimension (LDA, N)
59: *> On entry, the LU part of the factorization of the n-by-n
60: *> matrix A computed by ZGETC2: A = P * L * U * Q
61: *> \endverbatim
62: *>
63: *> \param[in] LDA
64: *> \verbatim
65: *> LDA is INTEGER
66: *> The leading dimension of the array A. LDA >= max(1, N).
67: *> \endverbatim
68: *>
69: *> \param[in,out] RHS
70: *> \verbatim
71: *> RHS is COMPLEX*16 array, dimension N.
72: *> On entry, the right hand side vector b.
73: *> On exit, the solution vector X.
74: *> \endverbatim
75: *>
76: *> \param[in] IPIV
77: *> \verbatim
78: *> IPIV is INTEGER array, dimension (N).
79: *> The pivot indices; for 1 <= i <= N, row i of the
80: *> matrix has been interchanged with row IPIV(i).
81: *> \endverbatim
82: *>
83: *> \param[in] JPIV
84: *> \verbatim
85: *> JPIV is INTEGER array, dimension (N).
86: *> The pivot indices; for 1 <= j <= N, column j of the
87: *> matrix has been interchanged with column JPIV(j).
88: *> \endverbatim
89: *>
90: *> \param[out] SCALE
91: *> \verbatim
92: *> SCALE is DOUBLE PRECISION
93: *> On exit, SCALE contains the scale factor. SCALE is chosen
94: *> 0 <= SCALE <= 1 to prevent owerflow in the solution.
95: *> \endverbatim
96: *
97: * Authors:
98: * ========
99: *
100: *> \author Univ. of Tennessee
101: *> \author Univ. of California Berkeley
102: *> \author Univ. of Colorado Denver
103: *> \author NAG Ltd.
104: *
1.11 bertrand 105: *> \date September 2012
1.8 bertrand 106: *
107: *> \ingroup complex16GEauxiliary
108: *
109: *> \par Contributors:
110: * ==================
111: *>
112: *> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
113: *> Umea University, S-901 87 Umea, Sweden.
114: *
115: * =====================================================================
1.1 bertrand 116: SUBROUTINE ZGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
117: *
1.11 bertrand 118: * -- LAPACK auxiliary routine (version 3.4.2) --
1.1 bertrand 119: * -- LAPACK is a software package provided by Univ. of Tennessee, --
120: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.11 bertrand 121: * September 2012
1.1 bertrand 122: *
123: * .. Scalar Arguments ..
124: INTEGER LDA, N
125: DOUBLE PRECISION SCALE
126: * ..
127: * .. Array Arguments ..
128: INTEGER IPIV( * ), JPIV( * )
129: COMPLEX*16 A( LDA, * ), RHS( * )
130: * ..
131: *
132: * =====================================================================
133: *
134: * .. Parameters ..
135: DOUBLE PRECISION ZERO, ONE, TWO
136: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
137: * ..
138: * .. Local Scalars ..
139: INTEGER I, J
140: DOUBLE PRECISION BIGNUM, EPS, SMLNUM
141: COMPLEX*16 TEMP
142: * ..
143: * .. External Subroutines ..
144: EXTERNAL ZLASWP, ZSCAL
145: * ..
146: * .. External Functions ..
147: INTEGER IZAMAX
148: DOUBLE PRECISION DLAMCH
149: EXTERNAL IZAMAX, DLAMCH
150: * ..
151: * .. Intrinsic Functions ..
152: INTRINSIC ABS, DBLE, DCMPLX
153: * ..
154: * .. Executable Statements ..
155: *
156: * Set constant to control overflow
157: *
158: EPS = DLAMCH( 'P' )
159: SMLNUM = DLAMCH( 'S' ) / EPS
160: BIGNUM = ONE / SMLNUM
161: CALL DLABAD( SMLNUM, BIGNUM )
162: *
163: * Apply permutations IPIV to RHS
164: *
165: CALL ZLASWP( 1, RHS, LDA, 1, N-1, IPIV, 1 )
166: *
167: * Solve for L part
168: *
169: DO 20 I = 1, N - 1
170: DO 10 J = I + 1, N
171: RHS( J ) = RHS( J ) - A( J, I )*RHS( I )
172: 10 CONTINUE
173: 20 CONTINUE
174: *
175: * Solve for U part
176: *
177: SCALE = ONE
178: *
179: * Check for scaling
180: *
181: I = IZAMAX( N, RHS, 1 )
182: IF( TWO*SMLNUM*ABS( RHS( I ) ).GT.ABS( A( N, N ) ) ) THEN
183: TEMP = DCMPLX( ONE / TWO, ZERO ) / ABS( RHS( I ) )
184: CALL ZSCAL( N, TEMP, RHS( 1 ), 1 )
185: SCALE = SCALE*DBLE( TEMP )
186: END IF
187: DO 40 I = N, 1, -1
188: TEMP = DCMPLX( ONE, ZERO ) / A( I, I )
189: RHS( I ) = RHS( I )*TEMP
190: DO 30 J = I + 1, N
191: RHS( I ) = RHS( I ) - RHS( J )*( A( I, J )*TEMP )
192: 30 CONTINUE
193: 40 CONTINUE
194: *
195: * Apply permutations JPIV to the solution (RHS)
196: *
197: CALL ZLASWP( 1, RHS, LDA, 1, N-1, JPIV, -1 )
198: RETURN
199: *
200: * End of ZGESC2
201: *
202: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zgesc2.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack