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SUBROUTINE SGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, 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
* March 31, 1993
*
* .. Scalar Arguments ..
CHARACTER TRANS
INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
REAL AB( LDAB, * ), B( LDB, * )
* ..
*
* Purpose
* =======
*
* SGBTRS solves a system of linear equations
* A * X = B or A' * X = B
* with a general band matrix A using the LU factorization computed
* by SGBTRF.
*
* Arguments
* =========
*
* TRANS (input) CHARACTER*1
* Specifies the form of the system of equations.
* = 'N': A * X = B (No transpose)
* = 'T': A'* X = B (Transpose)
* = 'C': A'* X = B (Conjugate transpose = Transpose)
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* KL (input) INTEGER
* The number of subdiagonals within the band of A. KL >= 0.
*
* KU (input) INTEGER
* The number of superdiagonals within the band of A. KU >= 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)
* Details of the LU factorization of the band matrix A, as
* computed by SGBTRF. 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.
*
* LDAB (input) INTEGER
* The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
*
* IPIV (input) INTEGER array, dimension (N)
* The pivot indices; for 1 <= i <= N, row i of the matrix was
* interchanged with row IPIV(i).
*
* 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
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL LNOTI, NOTRAN
INTEGER I, J, KD, L, LM
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL SGEMV, SGER, SSWAP, STBSV, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
NOTRAN = LSAME( TRANS, 'N' )
IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT.
$ LSAME( TRANS, 'C' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( KL.LT.0 ) THEN
INFO = -3
ELSE IF( KU.LT.0 ) THEN
INFO = -4
ELSE IF( NRHS.LT.0 ) THEN
INFO = -5
ELSE IF( LDAB.LT.( 2*KL+KU+1 ) ) THEN
INFO = -7
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SGBTRS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 )
$ RETURN
*
KD = KU + KL + 1
LNOTI = KL.GT.0
*
IF( NOTRAN ) THEN
*
* Solve A*X = B.
*
* Solve L*X = B, overwriting B with X.
*
* L is represented as a product of permutations and unit lower
* triangular matrices L = P(1) * L(1) * ... * P(n-1) * L(n-1),
* where each transformation L(i) is a rank-one modification of
* the identity matrix.
*
IF( LNOTI ) THEN
DO 10 J = 1, N - 1
LM = MIN( KL, N-J )
L = IPIV( J )
IF( L.NE.J )
$ CALL SSWAP( NRHS, B( L, 1 ), LDB, B( J, 1 ), LDB )
CALL SGER( LM, NRHS, -ONE, AB( KD+1, J ), 1, B( J, 1 ),
$ LDB, B( J+1, 1 ), LDB )
10 CONTINUE
END IF
*
DO 20 I = 1, NRHS
*
* Solve U*X = B, overwriting B with X.
*
CALL STBSV( 'Upper', 'No transpose', 'Non-unit', N, KL+KU,
$ AB, LDAB, B( 1, I ), 1 )
20 CONTINUE
*
ELSE
*
* Solve A'*X = B.
*
DO 30 I = 1, NRHS
*
* Solve U'*X = B, overwriting B with X.
*
CALL STBSV( 'Upper', 'Transpose', 'Non-unit', N, KL+KU, AB,
$ LDAB, B( 1, I ), 1 )
30 CONTINUE
*
* Solve L'*X = B, overwriting B with X.
*
IF( LNOTI ) THEN
DO 40 J = N - 1, 1, -1
LM = MIN( KL, N-J )
CALL SGEMV( 'Transpose', LM, NRHS, -ONE, B( J+1, 1 ),
$ LDB, AB( KD+1, J ), 1, ONE, B( J, 1 ), LDB )
L = IPIV( J )
IF( L.NE.J )
$ CALL SSWAP( NRHS, B( L, 1 ), LDB, B( J, 1 ), LDB )
40 CONTINUE
END IF
END IF
RETURN
*
* End of SGBTRS
*
END
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