SUBROUTINE STBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, \$ LDB, INFO ) * * -- LAPACK routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. CHARACTER DIAG, TRANS, UPLO INTEGER INFO, KD, LDAB, LDB, N, NRHS * .. * .. Array Arguments .. REAL AB( LDAB, * ), B( LDB, * ) * .. * * Purpose * ======= * * STBTRS solves a triangular system of the form * * A * X = B or A**T * X = B, * * where A is a triangular band matrix of order N, and B is an * N-by NRHS matrix. A check is made to verify that A is nonsingular. * * Arguments * ========= * * UPLO (input) CHARACTER*1 * = 'U': A is upper triangular; * = 'L': A is lower triangular. * * TRANS (input) CHARACTER*1 * Specifies the form the system of equations: * = 'N': A * X = B (No transpose) * = 'T': A**T * X = B (Transpose) * = 'C': A**H * X = B (Conjugate transpose = Transpose) * * DIAG (input) CHARACTER*1 * = 'N': A is non-unit triangular; * = 'U': A is unit triangular. * * N (input) INTEGER * The order of the matrix A. N >= 0. * * KD (input) INTEGER * The number of superdiagonals or subdiagonals of the * triangular band matrix A. 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 upper or lower triangular band matrix A, stored in the * first kd+1 rows of AB. The j-th column of A is stored * in the j-th column of the array AB as follows: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). * If DIAG = 'U', the diagonal elements of A are not referenced * and are assumed to be 1. * * 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, if INFO = 0, 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 * > 0: if INFO = i, the i-th diagonal element of A is zero, * indicating that the matrix is singular and the * solutions X have not been computed. * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. * .. Local Scalars .. LOGICAL NOUNIT, 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 NOUNIT = LSAME( DIAG, 'N' ) UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT. \$ LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN INFO = -2 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( KD.LT.0 ) THEN INFO = -5 ELSE IF( NRHS.LT.0 ) THEN INFO = -6 ELSE IF( LDAB.LT.KD+1 ) THEN INFO = -8 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'STBTRS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * * Check for singularity. * IF( NOUNIT ) THEN IF( UPPER ) THEN DO 10 INFO = 1, N IF( AB( KD+1, INFO ).EQ.ZERO ) \$ RETURN 10 CONTINUE ELSE DO 20 INFO = 1, N IF( AB( 1, INFO ).EQ.ZERO ) \$ RETURN 20 CONTINUE END IF END IF INFO = 0 * * Solve A * X = B or A**T * X = B. * DO 30 J = 1, NRHS CALL STBSV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, B( 1, J ), 1 ) 30 CONTINUE * RETURN * * End of STBTRS * END