 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cgbt01()

 subroutine cgbt01 ( integer M, integer N, integer KL, integer KU, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, complex, dimension( * ) WORK, real RESID )

CGBT01

Purpose:
``` CGBT01 reconstructs a band matrix A from its L*U factorization and
computes the residual:
norm(L*U - A) / ( N * norm(A) * EPS ),
where EPS is the machine epsilon.

The expression L*U - A is computed one column at a time, so A and
AFAC are not modified.```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrix A. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix A. N >= 0.``` [in] KL ``` KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.``` [in] KU ``` KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.``` [in,out] A ``` A is COMPLEX array, dimension (LDA,N) The original matrix A in band storage, stored in rows 1 to KL+KU+1.``` [in] LDA ``` LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KL+KU+1).``` [in] AFAC ``` AFAC is COMPLEX array, dimension (LDAFAC,N) The factored form of the matrix A. AFAC contains the banded factors L and U from the L*U factorization, as computed by CGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1. See CGBTRF for further details.``` [in] LDAFAC ``` LDAFAC is INTEGER The leading dimension of the array AFAC. LDAFAC >= max(1,2*KL*KU+1).``` [in] IPIV ``` IPIV is INTEGER array, dimension (min(M,N)) The pivot indices from CGBTRF.``` [out] WORK ` WORK is COMPLEX array, dimension (2*KL+KU+1)` [out] RESID ``` RESID is REAL norm(L*U - A) / ( N * norm(A) * EPS )```

Definition at line 124 of file cgbt01.f.

126*
127* -- LAPACK test routine --
128* -- LAPACK is a software package provided by Univ. of Tennessee, --
129* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130*
131* .. Scalar Arguments ..
132 INTEGER KL, KU, LDA, LDAFAC, M, N
133 REAL RESID
134* ..
135* .. Array Arguments ..
136 INTEGER IPIV( * )
137 COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), WORK( * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 REAL ZERO, ONE
144 parameter( zero = 0.0e+0, one = 1.0e+0 )
145* ..
146* .. Local Scalars ..
147 INTEGER I, I1, I2, IL, IP, IW, J, JL, JU, JUA, KD, LENJ
148 REAL ANORM, EPS
149 COMPLEX T
150* ..
151* .. External Functions ..
152 REAL SCASUM, SLAMCH
153 EXTERNAL scasum, slamch
154* ..
155* .. External Subroutines ..
156 EXTERNAL caxpy, ccopy
157* ..
158* .. Intrinsic Functions ..
159 INTRINSIC cmplx, max, min, real
160* ..
161* .. Executable Statements ..
162*
163* Quick exit if M = 0 or N = 0.
164*
165 resid = zero
166 IF( m.LE.0 .OR. n.LE.0 )
167 \$ RETURN
168*
169* Determine EPS and the norm of A.
170*
171 eps = slamch( 'Epsilon' )
172 kd = ku + 1
173 anorm = zero
174 DO 10 j = 1, n
175 i1 = max( kd+1-j, 1 )
176 i2 = min( kd+m-j, kl+kd )
177 IF( i2.GE.i1 )
178 \$ anorm = max( anorm, scasum( i2-i1+1, a( i1, j ), 1 ) )
179 10 CONTINUE
180*
181* Compute one column at a time of L*U - A.
182*
183 kd = kl + ku + 1
184 DO 40 j = 1, n
185*
186* Copy the J-th column of U to WORK.
187*
188 ju = min( kl+ku, j-1 )
189 jl = min( kl, m-j )
190 lenj = min( m, j ) - j + ju + 1
191 IF( lenj.GT.0 ) THEN
192 CALL ccopy( lenj, afac( kd-ju, j ), 1, work, 1 )
193 DO 20 i = lenj + 1, ju + jl + 1
194 work( i ) = zero
195 20 CONTINUE
196*
197* Multiply by the unit lower triangular matrix L. Note that L
198* is stored as a product of transformations and permutations.
199*
200 DO 30 i = min( m-1, j ), j - ju, -1
201 il = min( kl, m-i )
202 IF( il.GT.0 ) THEN
203 iw = i - j + ju + 1
204 t = work( iw )
205 CALL caxpy( il, t, afac( kd+1, i ), 1, work( iw+1 ),
206 \$ 1 )
207 ip = ipiv( i )
208 IF( i.NE.ip ) THEN
209 ip = ip - j + ju + 1
210 work( iw ) = work( ip )
211 work( ip ) = t
212 END IF
213 END IF
214 30 CONTINUE
215*
216* Subtract the corresponding column of A.
217*
218 jua = min( ju, ku )
219 IF( jua+jl+1.GT.0 )
220 \$ CALL caxpy( jua+jl+1, -cmplx( one ), a( ku+1-jua, j ), 1,
221 \$ work( ju+1-jua ), 1 )
222*
223* Compute the 1-norm of the column.
224*
225 resid = max( resid, scasum( ju+jl+1, work, 1 ) )
226 END IF
227 40 CONTINUE
228*
229* Compute norm(L*U - A) / ( N * norm(A) * EPS )
230*
231 IF( anorm.LE.zero ) THEN
232 IF( resid.NE.zero )
233 \$ resid = one / eps
234 ELSE
235 resid = ( ( resid / real( n ) ) / anorm ) / eps
236 END IF
237*
238 RETURN
239*
240* End of CGBT01
241*
subroutine ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:81
subroutine caxpy(N, CA, CX, INCX, CY, INCY)
CAXPY
Definition: caxpy.f:88
real function scasum(N, CX, INCX)
SCASUM
Definition: scasum.f:72
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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