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

 subroutine spbtrs ( character UPLO, integer N, integer KD, integer NRHS, real, dimension( ldab, * ) AB, integer LDAB, real, dimension( ldb, * ) B, integer LDB, integer INFO )

SPBTRS

Purpose:
``` SPBTRS solves a system of linear equations A*X = B with a symmetric
positive definite band matrix A using the Cholesky factorization
A = U**T*U or A = L*L**T computed by SPBTRF.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangular factor stored in AB; = 'L': Lower triangular factor stored in AB.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] KD ``` KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.``` [in] AB ``` AB is REAL array, dimension (LDAB,N) The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).``` [in] LDAB ``` LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.``` [in,out] B ``` B is REAL array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 120 of file spbtrs.f.

121*
122* -- LAPACK computational routine --
123* -- LAPACK is a software package provided by Univ. of Tennessee, --
124* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125*
126* .. Scalar Arguments ..
127 CHARACTER UPLO
128 INTEGER INFO, KD, LDAB, LDB, N, NRHS
129* ..
130* .. Array Arguments ..
131 REAL AB( LDAB, * ), B( LDB, * )
132* ..
133*
134* =====================================================================
135*
136* .. Local Scalars ..
137 LOGICAL UPPER
138 INTEGER J
139* ..
140* .. External Functions ..
141 LOGICAL LSAME
142 EXTERNAL lsame
143* ..
144* .. External Subroutines ..
145 EXTERNAL stbsv, xerbla
146* ..
147* .. Intrinsic Functions ..
148 INTRINSIC max
149* ..
150* .. Executable Statements ..
151*
152* Test the input parameters.
153*
154 info = 0
155 upper = lsame( uplo, 'U' )
156 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
157 info = -1
158 ELSE IF( n.LT.0 ) THEN
159 info = -2
160 ELSE IF( kd.LT.0 ) THEN
161 info = -3
162 ELSE IF( nrhs.LT.0 ) THEN
163 info = -4
164 ELSE IF( ldab.LT.kd+1 ) THEN
165 info = -6
166 ELSE IF( ldb.LT.max( 1, n ) ) THEN
167 info = -8
168 END IF
169 IF( info.NE.0 ) THEN
170 CALL xerbla( 'SPBTRS', -info )
171 RETURN
172 END IF
173*
174* Quick return if possible
175*
176 IF( n.EQ.0 .OR. nrhs.EQ.0 )
177 \$ RETURN
178*
179 IF( upper ) THEN
180*
181* Solve A*X = B where A = U**T *U.
182*
183 DO 10 j = 1, nrhs
184*
185* Solve U**T *X = B, overwriting B with X.
186*
187 CALL stbsv( 'Upper', 'Transpose', 'Non-unit', n, kd, ab,
188 \$ ldab, b( 1, j ), 1 )
189*
190* Solve U*X = B, overwriting B with X.
191*
192 CALL stbsv( 'Upper', 'No transpose', 'Non-unit', n, kd, ab,
193 \$ ldab, b( 1, j ), 1 )
194 10 CONTINUE
195 ELSE
196*
197* Solve A*X = B where A = L*L**T.
198*
199 DO 20 j = 1, nrhs
200*
201* Solve L*X = B, overwriting B with X.
202*
203 CALL stbsv( 'Lower', 'No transpose', 'Non-unit', n, kd, ab,
204 \$ ldab, b( 1, j ), 1 )
205*
206* Solve L**T *X = B, overwriting B with X.
207*
208 CALL stbsv( 'Lower', 'Transpose', 'Non-unit', n, kd, ab,
209 \$ ldab, b( 1, j ), 1 )
210 20 CONTINUE
211 END IF
212*
213 RETURN
214*
215* End of SPBTRS
216*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine stbsv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
STBSV
Definition: stbsv.f:189
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