LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ spbt01()

 subroutine spbt01 ( character uplo, integer n, integer kd, real, dimension( lda, * ) a, integer lda, real, dimension( ldafac, * ) afac, integer ldafac, real, dimension( * ) rwork, real resid )

SPBT01

Purpose:
``` SPBT01 reconstructs a symmetric positive definite band matrix A from
its L*L' or U'*U factorization and computes the residual
norm( L*L' - A ) / ( N * norm(A) * EPS ) or
norm( U'*U - A ) / ( N * norm(A) * EPS ),
where EPS is the machine epsilon, L' is the conjugate transpose of
L, and U' is the conjugate transpose of U.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular``` [in] N ``` N is INTEGER The number of rows and columns of the matrix A. N >= 0.``` [in] KD ``` KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.``` [in] A ``` A is REAL array, dimension (LDA,N) The original symmetric band matrix A. If UPLO = 'U', the upper triangular part of A is stored as a band matrix; if UPLO = 'L', the lower triangular part of A is stored. The columns of the appropriate triangle are stored in the columns of A and the diagonals of the triangle are stored in the rows of A. See SPBTRF for further details.``` [in] LDA ``` LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).``` [in] AFAC ``` AFAC is REAL array, dimension (LDAFAC,N) The factored form of the matrix A. AFAC contains the factor L or U from the L*L' or U'*U factorization in band storage format, as computed by SPBTRF.``` [in] LDAFAC ``` LDAFAC is INTEGER The leading dimension of the array AFAC. LDAFAC >= max(1,KD+1).``` [out] RWORK ` RWORK is REAL array, dimension (N)` [out] RESID ``` RESID is REAL If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ) If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )```

Definition at line 117 of file spbt01.f.

119*
120* -- LAPACK test routine --
121* -- LAPACK is a software package provided by Univ. of Tennessee, --
122* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
123*
124* .. Scalar Arguments ..
125 CHARACTER UPLO
126 INTEGER KD, LDA, LDAFAC, N
127 REAL RESID
128* ..
129* .. Array Arguments ..
130 REAL A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
131* ..
132*
133* =====================================================================
134*
135*
136* .. Parameters ..
137 REAL ZERO, ONE
138 parameter( zero = 0.0e+0, one = 1.0e+0 )
139* ..
140* .. Local Scalars ..
141 INTEGER I, J, K, KC, KLEN, ML, MU
142 REAL ANORM, EPS, T
143* ..
144* .. External Functions ..
145 LOGICAL LSAME
146 REAL SDOT, SLAMCH, SLANSB
147 EXTERNAL lsame, sdot, slamch, slansb
148* ..
149* .. External Subroutines ..
150 EXTERNAL sscal, ssyr, strmv
151* ..
152* .. Intrinsic Functions ..
153 INTRINSIC max, min, real
154* ..
155* .. Executable Statements ..
156*
157* Quick exit if N = 0.
158*
159 IF( n.LE.0 ) THEN
160 resid = zero
161 RETURN
162 END IF
163*
164* Exit with RESID = 1/EPS if ANORM = 0.
165*
166 eps = slamch( 'Epsilon' )
167 anorm = slansb( '1', uplo, n, kd, a, lda, rwork )
168 IF( anorm.LE.zero ) THEN
169 resid = one / eps
170 RETURN
171 END IF
172*
173* Compute the product U'*U, overwriting U.
174*
175 IF( lsame( uplo, 'U' ) ) THEN
176 DO 10 k = n, 1, -1
177 kc = max( 1, kd+2-k )
178 klen = kd + 1 - kc
179*
180* Compute the (K,K) element of the result.
181*
182 t = sdot( klen+1, afac( kc, k ), 1, afac( kc, k ), 1 )
183 afac( kd+1, k ) = t
184*
185* Compute the rest of column K.
186*
187 IF( klen.GT.0 )
188 \$ CALL strmv( 'Upper', 'Transpose', 'Non-unit', klen,
189 \$ afac( kd+1, k-klen ), ldafac-1,
190 \$ afac( kc, k ), 1 )
191*
192 10 CONTINUE
193*
194* UPLO = 'L': Compute the product L*L', overwriting L.
195*
196 ELSE
197 DO 20 k = n, 1, -1
198 klen = min( kd, n-k )
199*
200* Add a multiple of column K of the factor L to each of
201* columns K+1 through N.
202*
203 IF( klen.GT.0 )
204 \$ CALL ssyr( 'Lower', klen, one, afac( 2, k ), 1,
205 \$ afac( 1, k+1 ), ldafac-1 )
206*
207* Scale column K by the diagonal element.
208*
209 t = afac( 1, k )
210 CALL sscal( klen+1, t, afac( 1, k ), 1 )
211*
212 20 CONTINUE
213 END IF
214*
215* Compute the difference L*L' - A or U'*U - A.
216*
217 IF( lsame( uplo, 'U' ) ) THEN
218 DO 40 j = 1, n
219 mu = max( 1, kd+2-j )
220 DO 30 i = mu, kd + 1
221 afac( i, j ) = afac( i, j ) - a( i, j )
222 30 CONTINUE
223 40 CONTINUE
224 ELSE
225 DO 60 j = 1, n
226 ml = min( kd+1, n-j+1 )
227 DO 50 i = 1, ml
228 afac( i, j ) = afac( i, j ) - a( i, j )
229 50 CONTINUE
230 60 CONTINUE
231 END IF
232*
233* Compute norm( L*L' - A ) / ( N * norm(A) * EPS )
234*
235 resid = slansb( 'I', uplo, n, kd, afac, ldafac, rwork )
236*
237 resid = ( ( resid / real( n ) ) / anorm ) / eps
238*
239 RETURN
240*
241* End of SPBT01
242*
real function sdot(n, sx, incx, sy, incy)
SDOT
Definition sdot.f:82
subroutine ssyr(uplo, n, alpha, x, incx, a, lda)
SSYR
Definition ssyr.f:132
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
real function slansb(norm, uplo, n, k, ab, ldab, work)
SLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition slansb.f:129
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine sscal(n, sa, sx, incx)
SSCAL
Definition sscal.f:79
subroutine strmv(uplo, trans, diag, n, a, lda, x, incx)
STRMV
Definition strmv.f:147
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