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SUBROUTINE SPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
*
* -- LAPACK routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, KD, LDAB, LDB, N, NRHS
* ..
* .. Array Arguments ..
REAL AB( LDAB, * ), B( LDB, * )
* ..
*
* 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.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* = 'U': Upper triangular factor stored in AB;
* = 'L': Lower triangular factor stored in AB.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* KD (input) INTEGER
* The number of superdiagonals of the matrix A if UPLO = 'U',
* or the number of subdiagonals if UPLO = 'L'. KD >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the matrix B. NRHS >= 0.
*
* AB (input) 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).
*
* LDAB (input) INTEGER
* The leading dimension of the array AB. LDAB >= KD+1.
*
* B (input/output) REAL array, dimension (LDB,NRHS)
* On entry, the right hand side matrix B.
* On exit, the solution matrix X.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL UPPER
INTEGER J
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL STBSV, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( KD.LT.0 ) THEN
INFO = -3
ELSE IF( NRHS.LT.0 ) THEN
INFO = -4
ELSE IF( LDAB.LT.KD+1 ) THEN
INFO = -6
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SPBTRS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 )
$ RETURN
*
IF( UPPER ) THEN
*
* Solve A*X = B where A = U'*U.
*
DO 10 J = 1, NRHS
*
* Solve U'*X = B, overwriting B with X.
*
CALL STBSV( 'Upper', 'Transpose', 'Non-unit', N, KD, AB,
$ LDAB, B( 1, J ), 1 )
*
* Solve U*X = B, overwriting B with X.
*
CALL STBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB,
$ LDAB, B( 1, J ), 1 )
10 CONTINUE
ELSE
*
* Solve A*X = B where A = L*L'.
*
DO 20 J = 1, NRHS
*
* Solve L*X = B, overwriting B with X.
*
CALL STBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
$ LDAB, B( 1, J ), 1 )
*
* Solve L'*X = B, overwriting B with X.
*
CALL STBSV( 'Lower', 'Transpose', 'Non-unit', N, KD, AB,
$ LDAB, B( 1, J ), 1 )
20 CONTINUE
END IF
*
RETURN
*
* End of SPBTRS
*
END
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