LAPACK 3.3.1 Linear Algebra PACKage

# ztbtrs.f

Go to the documentation of this file.
```00001       SUBROUTINE ZTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
00002      \$                   LDB, INFO )
00003 *
00004 *  -- LAPACK routine (version 3.2) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *     November 2006
00008 *
00009 *     .. Scalar Arguments ..
00010       CHARACTER          DIAG, TRANS, UPLO
00011       INTEGER            INFO, KD, LDAB, LDB, N, NRHS
00012 *     ..
00013 *     .. Array Arguments ..
00014       COMPLEX*16         AB( LDAB, * ), B( LDB, * )
00015 *     ..
00016 *
00017 *  Purpose
00018 *  =======
00019 *
00020 *  ZTBTRS solves a triangular system of the form
00021 *
00022 *     A * X = B,  A**T * X = B,  or  A**H * X = B,
00023 *
00024 *  where A is a triangular band matrix of order N, and B is an
00025 *  N-by-NRHS matrix.  A check is made to verify that A is nonsingular.
00026 *
00027 *  Arguments
00028 *  =========
00029 *
00030 *  UPLO    (input) CHARACTER*1
00031 *          = 'U':  A is upper triangular;
00032 *          = 'L':  A is lower triangular.
00033 *
00034 *  TRANS   (input) CHARACTER*1
00035 *          Specifies the form of the system of equations:
00036 *          = 'N':  A * X = B     (No transpose)
00037 *          = 'T':  A**T * X = B  (Transpose)
00038 *          = 'C':  A**H * X = B  (Conjugate transpose)
00039 *
00040 *  DIAG    (input) CHARACTER*1
00041 *          = 'N':  A is non-unit triangular;
00042 *          = 'U':  A is unit triangular.
00043 *
00044 *  N       (input) INTEGER
00045 *          The order of the matrix A.  N >= 0.
00046 *
00047 *  KD      (input) INTEGER
00048 *          The number of superdiagonals or subdiagonals of the
00049 *          triangular band matrix A.  KD >= 0.
00050 *
00051 *  NRHS    (input) INTEGER
00052 *          The number of right hand sides, i.e., the number of columns
00053 *          of the matrix B.  NRHS >= 0.
00054 *
00055 *  AB      (input) COMPLEX*16 array, dimension (LDAB,N)
00056 *          The upper or lower triangular band matrix A, stored in the
00057 *          first kd+1 rows of AB.  The j-th column of A is stored
00058 *          in the j-th column of the array AB as follows:
00059 *          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
00060 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
00061 *          If DIAG = 'U', the diagonal elements of A are not referenced
00062 *          and are assumed to be 1.
00063 *
00064 *  LDAB    (input) INTEGER
00065 *          The leading dimension of the array AB.  LDAB >= KD+1.
00066 *
00067 *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
00068 *          On entry, the right hand side matrix B.
00069 *          On exit, if INFO = 0, the solution matrix X.
00070 *
00071 *  LDB     (input) INTEGER
00072 *          The leading dimension of the array B.  LDB >= max(1,N).
00073 *
00074 *  INFO    (output) INTEGER
00075 *          = 0:  successful exit
00076 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00077 *          > 0:  if INFO = i, the i-th diagonal element of A is zero,
00078 *                indicating that the matrix is singular and the
00079 *                solutions X have not been computed.
00080 *
00081 *  =====================================================================
00082 *
00083 *     .. Parameters ..
00084       COMPLEX*16         ZERO
00085       PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
00086 *     ..
00087 *     .. Local Scalars ..
00088       LOGICAL            NOUNIT, UPPER
00089       INTEGER            J
00090 *     ..
00091 *     .. External Functions ..
00092       LOGICAL            LSAME
00093       EXTERNAL           LSAME
00094 *     ..
00095 *     .. External Subroutines ..
00096       EXTERNAL           XERBLA, ZTBSV
00097 *     ..
00098 *     .. Intrinsic Functions ..
00099       INTRINSIC          MAX
00100 *     ..
00101 *     .. Executable Statements ..
00102 *
00103 *     Test the input parameters.
00104 *
00105       INFO = 0
00106       NOUNIT = LSAME( DIAG, 'N' )
00107       UPPER = LSAME( UPLO, 'U' )
00108       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00109          INFO = -1
00110       ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.
00111      \$         LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
00112          INFO = -2
00113       ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
00114          INFO = -3
00115       ELSE IF( N.LT.0 ) THEN
00116          INFO = -4
00117       ELSE IF( KD.LT.0 ) THEN
00118          INFO = -5
00119       ELSE IF( NRHS.LT.0 ) THEN
00120          INFO = -6
00121       ELSE IF( LDAB.LT.KD+1 ) THEN
00122          INFO = -8
00123       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00124          INFO = -10
00125       END IF
00126       IF( INFO.NE.0 ) THEN
00127          CALL XERBLA( 'ZTBTRS', -INFO )
00128          RETURN
00129       END IF
00130 *
00131 *     Quick return if possible
00132 *
00133       IF( N.EQ.0 )
00134      \$   RETURN
00135 *
00136 *     Check for singularity.
00137 *
00138       IF( NOUNIT ) THEN
00139          IF( UPPER ) THEN
00140             DO 10 INFO = 1, N
00141                IF( AB( KD+1, INFO ).EQ.ZERO )
00142      \$            RETURN
00143    10       CONTINUE
00144          ELSE
00145             DO 20 INFO = 1, N
00146                IF( AB( 1, INFO ).EQ.ZERO )
00147      \$            RETURN
00148    20       CONTINUE
00149          END IF
00150       END IF
00151       INFO = 0
00152 *
00153 *     Solve A * X = B,  A**T * X = B,  or  A**H * X = B.
00154 *
00155       DO 30 J = 1, NRHS
00156          CALL ZTBSV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, B( 1, J ), 1 )
00157    30 CONTINUE
00158 *
00159       RETURN
00160 *
00161 *     End of ZTBTRS
00162 *
00163       END
```