LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
dgesc2.f
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1 *> \brief \b DGESC2 solves a system of linear equations using the LU factorization with complete pivoting computed by sgetc2.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DGESC2( 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 * DOUBLE PRECISION A( LDA, * ), RHS( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> DGESC2 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 DGETC2.
44 *> \endverbatim
45 *
46 * Arguments:
47 * ==========
48 *
49 *> \param[in] N
50 *> \verbatim
51 *> N is INTEGER
52 *> The order of the matrix A.
53 *> \endverbatim
54 *>
55 *> \param[in] A
56 *> \verbatim
57 *> A is DOUBLE PRECISION array, dimension (LDA,N)
58 *> On entry, the LU part of the factorization of the n-by-n
59 *> matrix A computed by DGETC2: A = P * L * U * Q
60 *> \endverbatim
61 *>
62 *> \param[in] LDA
63 *> \verbatim
64 *> LDA is INTEGER
65 *> The leading dimension of the array A. LDA >= max(1, N).
66 *> \endverbatim
67 *>
68 *> \param[in,out] RHS
69 *> \verbatim
70 *> RHS is DOUBLE PRECISION array, dimension (N).
71 *> On entry, the right hand side vector b.
72 *> On exit, the solution vector X.
73 *> \endverbatim
74 *>
75 *> \param[in] IPIV
76 *> \verbatim
77 *> IPIV is INTEGER array, dimension (N).
78 *> The pivot indices; for 1 <= i <= N, row i of the
79 *> matrix has been interchanged with row IPIV(i).
80 *> \endverbatim
81 *>
82 *> \param[in] JPIV
83 *> \verbatim
84 *> JPIV is INTEGER array, dimension (N).
85 *> The pivot indices; for 1 <= j <= N, column j of the
86 *> matrix has been interchanged with column JPIV(j).
87 *> \endverbatim
88 *>
89 *> \param[out] SCALE
90 *> \verbatim
91 *> SCALE is DOUBLE PRECISION
92 *> On exit, SCALE contains the scale factor. SCALE is chosen
93 *> 0 <= SCALE <= 1 to prevent overflow in the solution.
94 *> \endverbatim
95 *
96 * Authors:
97 * ========
98 *
99 *> \author Univ. of Tennessee
100 *> \author Univ. of California Berkeley
101 *> \author Univ. of Colorado Denver
102 *> \author NAG Ltd.
103 *
104 *> \ingroup doubleGEauxiliary
105 *
106 *> \par Contributors:
107 * ==================
108 *>
109 *> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
110 *> Umea University, S-901 87 Umea, Sweden.
111 *
112 * =====================================================================
113  SUBROUTINE dgesc2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
114 *
115 * -- LAPACK auxiliary routine --
116 * -- LAPACK is a software package provided by Univ. of Tennessee, --
117 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118 *
119 * .. Scalar Arguments ..
120  INTEGER LDA, N
121  DOUBLE PRECISION SCALE
122 * ..
123 * .. Array Arguments ..
124  INTEGER IPIV( * ), JPIV( * )
125  DOUBLE PRECISION A( LDA, * ), RHS( * )
126 * ..
127 *
128 * =====================================================================
129 *
130 * .. Parameters ..
131  DOUBLE PRECISION ONE, TWO
132  parameter( one = 1.0d+0, two = 2.0d+0 )
133 * ..
134 * .. Local Scalars ..
135  INTEGER I, J
136  DOUBLE PRECISION BIGNUM, EPS, SMLNUM, TEMP
137 * ..
138 * .. External Subroutines ..
139  EXTERNAL dlaswp, dscal, dlabad
140 * ..
141 * .. External Functions ..
142  INTEGER IDAMAX
143  DOUBLE PRECISION DLAMCH
144  EXTERNAL idamax, dlamch
145 * ..
146 * .. Intrinsic Functions ..
147  INTRINSIC abs
148 * ..
149 * .. Executable Statements ..
150 *
151 * Set constant to control overflow
152 *
153  eps = dlamch( 'P' )
154  smlnum = dlamch( 'S' ) / eps
155  bignum = one / smlnum
156  CALL dlabad( smlnum, bignum )
157 *
158 * Apply permutations IPIV to RHS
159 *
160  CALL dlaswp( 1, rhs, lda, 1, n-1, ipiv, 1 )
161 *
162 * Solve for L part
163 *
164  DO 20 i = 1, n - 1
165  DO 10 j = i + 1, n
166  rhs( j ) = rhs( j ) - a( j, i )*rhs( i )
167  10 CONTINUE
168  20 CONTINUE
169 *
170 * Solve for U part
171 *
172  scale = one
173 *
174 * Check for scaling
175 *
176  i = idamax( n, rhs, 1 )
177  IF( two*smlnum*abs( rhs( i ) ).GT.abs( a( n, n ) ) ) THEN
178  temp = ( one / two ) / abs( rhs( i ) )
179  CALL dscal( n, temp, rhs( 1 ), 1 )
180  scale = scale*temp
181  END IF
182 *
183  DO 40 i = n, 1, -1
184  temp = one / a( i, i )
185  rhs( i ) = rhs( i )*temp
186  DO 30 j = i + 1, n
187  rhs( i ) = rhs( i ) - rhs( j )*( a( i, j )*temp )
188  30 CONTINUE
189  40 CONTINUE
190 *
191 * Apply permutations JPIV to the solution (RHS)
192 *
193  CALL dlaswp( 1, rhs, lda, 1, n-1, jpiv, -1 )
194  RETURN
195 *
196 * End of DGESC2
197 *
198  END
subroutine dlabad(SMALL, LARGE)
DLABAD
Definition: dlabad.f:74
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:79
subroutine dgesc2(N, A, LDA, RHS, IPIV, JPIV, SCALE)
DGESC2 solves a system of linear equations using the LU factorization with complete pivoting computed...
Definition: dgesc2.f:114
subroutine dlaswp(N, A, LDA, K1, K2, IPIV, INCX)
DLASWP performs a series of row interchanges on a general rectangular matrix.
Definition: dlaswp.f:115