 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine dgesc2 ( integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) RHS, integer, dimension( * ) IPIV, integer, dimension( * ) JPIV, double precision SCALE )

DGESC2 solves a system of linear equations using the LU factorization with complete pivoting computed by sgetc2.

Purpose:
``` DGESC2 solves a system of linear equations

A * X = scale* RHS

with a general N-by-N matrix A using the LU factorization with
complete pivoting computed by DGETC2.```
Parameters
 [in] N ``` N is INTEGER The order of the matrix A.``` [in] A ``` A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the LU part of the factorization of the n-by-n matrix A computed by DGETC2: A = P * L * U * Q``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1, N).``` [in,out] RHS ``` RHS is DOUBLE PRECISION array, dimension (N). On entry, the right hand side vector b. On exit, the solution vector X.``` [in] IPIV ``` IPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= i <= N, row i of the matrix has been interchanged with row IPIV(i).``` [in] JPIV ``` JPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= j <= N, column j of the matrix has been interchanged with column JPIV(j).``` [out] SCALE ``` SCALE is DOUBLE PRECISION On exit, SCALE contains the scale factor. SCALE is chosen 0 <= SCALE <= 1 to prevent owerflow in the solution.```
Date
September 2012
Contributors:
Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

Definition at line 116 of file dgesc2.f.

116 *
117 * -- LAPACK auxiliary routine (version 3.4.2) --
118 * -- LAPACK is a software package provided by Univ. of Tennessee, --
119 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120 * September 2012
121 *
122 * .. Scalar Arguments ..
123  INTEGER lda, n
124  DOUBLE PRECISION scale
125 * ..
126 * .. Array Arguments ..
127  INTEGER ipiv( * ), jpiv( * )
128  DOUBLE PRECISION a( lda, * ), rhs( * )
129 * ..
130 *
131 * =====================================================================
132 *
133 * .. Parameters ..
134  DOUBLE PRECISION one, two
135  parameter ( one = 1.0d+0, two = 2.0d+0 )
136 * ..
137 * .. Local Scalars ..
138  INTEGER i, j
139  DOUBLE PRECISION bignum, eps, smlnum, temp
140 * ..
141 * .. External Subroutines ..
142  EXTERNAL dlaswp, dscal
143 * ..
144 * .. External Functions ..
145  INTEGER idamax
146  DOUBLE PRECISION dlamch
147  EXTERNAL idamax, dlamch
148 * ..
149 * .. Intrinsic Functions ..
150  INTRINSIC abs
151 * ..
152 * .. Executable Statements ..
153 *
154 * Set constant to control owerflow
155 *
156  eps = dlamch( 'P' )
157  smlnum = dlamch( 'S' ) / eps
158  bignum = one / smlnum
159  CALL dlabad( smlnum, bignum )
160 *
161 * Apply permutations IPIV to RHS
162 *
163  CALL dlaswp( 1, rhs, lda, 1, n-1, ipiv, 1 )
164 *
165 * Solve for L part
166 *
167  DO 20 i = 1, n - 1
168  DO 10 j = i + 1, n
169  rhs( j ) = rhs( j ) - a( j, i )*rhs( i )
170  10 CONTINUE
171  20 CONTINUE
172 *
173 * Solve for U part
174 *
175  scale = one
176 *
177 * Check for scaling
178 *
179  i = idamax( n, rhs, 1 )
180  IF( two*smlnum*abs( rhs( i ) ).GT.abs( a( n, n ) ) ) THEN
181  temp = ( one / two ) / abs( rhs( i ) )
182  CALL dscal( n, temp, rhs( 1 ), 1 )
183  scale = scale*temp
184  END IF
185 *
186  DO 40 i = n, 1, -1
187  temp = one / a( i, i )
188  rhs( i ) = rhs( i )*temp
189  DO 30 j = i + 1, n
190  rhs( i ) = rhs( i ) - rhs( j )*( a( i, j )*temp )
191  30 CONTINUE
192  40 CONTINUE
193 *
194 * Apply permutations JPIV to the solution (RHS)
195 *
196  CALL dlaswp( 1, rhs, lda, 1, n-1, jpiv, -1 )
197  RETURN
198 *
199 * End of DGESC2
200 *
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:53
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65