 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ cgesc2()

 subroutine cgesc2 ( integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) RHS, integer, dimension( * ) IPIV, integer, dimension( * ) JPIV, real SCALE )

CGESC2 solves a system of linear equations using the LU factorization with complete pivoting computed by sgetc2.

Purpose:
``` CGESC2 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 CGETC2.```
Parameters
 [in] N ``` N is INTEGER The number of columns of the matrix A.``` [in] A ``` A is COMPLEX array, dimension (LDA, N) On entry, the LU part of the factorization of the n-by-n matrix A computed by CGETC2: 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 COMPLEX 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 REAL On exit, SCALE contains the scale factor. SCALE is chosen 0 <= SCALE <= 1 to prevent overflow in the solution.```
Contributors:
Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

Definition at line 114 of file cgesc2.f.

115 *
116 * -- LAPACK auxiliary routine --
117 * -- LAPACK is a software package provided by Univ. of Tennessee, --
118 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119 *
120 * .. Scalar Arguments ..
121  INTEGER LDA, N
122  REAL SCALE
123 * ..
124 * .. Array Arguments ..
125  INTEGER IPIV( * ), JPIV( * )
126  COMPLEX A( LDA, * ), RHS( * )
127 * ..
128 *
129 * =====================================================================
130 *
131 * .. Parameters ..
132  REAL ZERO, ONE, TWO
133  parameter( zero = 0.0e+0, one = 1.0e+0, two = 2.0e+0 )
134 * ..
135 * .. Local Scalars ..
136  INTEGER I, J
137  REAL BIGNUM, EPS, SMLNUM
138  COMPLEX TEMP
139 * ..
140 * .. External Subroutines ..
142 * ..
143 * .. External Functions ..
144  INTEGER ICAMAX
145  REAL SLAMCH
146  EXTERNAL icamax, slamch
147 * ..
148 * .. Intrinsic Functions ..
149  INTRINSIC abs, cmplx, real
150 * ..
151 * .. Executable Statements ..
152 *
153 * Set constant to control overflow
154 *
155  eps = slamch( 'P' )
156  smlnum = slamch( 'S' ) / eps
157  bignum = one / smlnum
158  CALL slabad( smlnum, bignum )
159 *
160 * Apply permutations IPIV to RHS
161 *
162  CALL claswp( 1, rhs, lda, 1, n-1, ipiv, 1 )
163 *
164 * Solve for L part
165 *
166  DO 20 i = 1, n - 1
167  DO 10 j = i + 1, n
168  rhs( j ) = rhs( j ) - a( j, i )*rhs( i )
169  10 CONTINUE
170  20 CONTINUE
171 *
172 * Solve for U part
173 *
174  scale = one
175 *
176 * Check for scaling
177 *
178  i = icamax( n, rhs, 1 )
179  IF( two*smlnum*abs( rhs( i ) ).GT.abs( a( n, n ) ) ) THEN
180  temp = cmplx( one / two, zero ) / abs( rhs( i ) )
181  CALL cscal( n, temp, rhs( 1 ), 1 )
182  scale = scale*real( temp )
183  END IF
184  DO 40 i = n, 1, -1
185  temp = cmplx( one, zero ) / a( i, i )
186  rhs( i ) = rhs( i )*temp
187  DO 30 j = i + 1, n
188  rhs( i ) = rhs( i ) - rhs( j )*( a( i, j )*temp )
189  30 CONTINUE
190  40 CONTINUE
191 *
192 * Apply permutations JPIV to the solution (RHS)
193 *
194  CALL claswp( 1, rhs, lda, 1, n-1, jpiv, -1 )
195  RETURN
196 *
197 * End of CGESC2
198 *
integer function icamax(N, CX, INCX)
ICAMAX
Definition: icamax.f:71
subroutine cscal(N, CA, CX, INCX)
CSCAL
Definition: cscal.f:78
subroutine claswp(N, A, LDA, K1, K2, IPIV, INCX)
CLASWP performs a series of row interchanges on a general rectangular matrix.
Definition: claswp.f:115
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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