1ZTBTRS(1)                LAPACK routine (version 3.2)                ZTBTRS(1)
2
3
4

NAME

6       ZTBTRS - solves a triangular system of the form   A * X = B, A**T * X =
7       B, or A**H * X = B,
8

SYNOPSIS

10       SUBROUTINE ZTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB,  LDAB,  B,  LDB,
11                          INFO )
12
13           CHARACTER      DIAG, TRANS, UPLO
14
15           INTEGER        INFO, KD, LDAB, LDB, N, NRHS
16
17           COMPLEX*16     AB( LDAB, * ), B( LDB, * )
18

PURPOSE

20       ZTBTRS  solves  a triangular system of the form where A is a triangular
21       band matrix of order N, and B is an N-by-NRHS matrix.  A check is  made
22       to verify that A is nonsingular.
23

ARGUMENTS

25       UPLO    (input) CHARACTER*1
26               = 'U':  A is upper triangular;
27               = 'L':  A is lower triangular.
28
29       TRANS   (input) CHARACTER*1
30               Specifies the form of the system of equations:
31               = 'N':  A * X = B     (No transpose)
32               = 'T':  A**T * X = B  (Transpose)
33               = 'C':  A**H * X = B  (Conjugate transpose)
34
35       DIAG    (input) CHARACTER*1
36               = 'N':  A is non-unit triangular;
37               = 'U':  A is unit triangular.
38
39       N       (input) INTEGER
40               The order of the matrix A.  N >= 0.
41
42       KD      (input) INTEGER
43               The  number of superdiagonals or subdiagonals of the triangular
44               band matrix A.  KD >= 0.
45
46       NRHS    (input) INTEGER
47               The number of right hand sides, i.e., the number of columns  of
48               the matrix B.  NRHS >= 0.
49
50       AB      (input) COMPLEX*16 array, dimension (LDAB,N)
51               The  upper  or  lower  triangular  band matrix A, stored in the
52               first kd+1 rows of AB.  The j-th column of A is stored  in  the
53               j-th  column  of  the  array  AB  as  follows:  if  UPLO = 'U',
54               AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO  =  'L',
55               AB(1+i-j,j)     = A(i,j) for j<=i<=min(n,j+kd).  If DIAG = 'U',
56               the diagonal elements of A are not referenced and  are  assumed
57               to be 1.
58
59       LDAB    (input) INTEGER
60               The leading dimension of the array AB.  LDAB >= KD+1.
61
62       B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
63               On  entry, the right hand side matrix B.  On exit, if INFO = 0,
64               the solution matrix X.
65
66       LDB     (input) INTEGER
67               The leading dimension of the array B.  LDB >= max(1,N).
68
69       INFO    (output) INTEGER
70               = 0:  successful exit
71               < 0:  if INFO = -i, the i-th argument had an illegal value
72               > 0:  if INFO = i, the i-th diagonal  element  of  A  is  zero,
73               indicating that the matrix is singular and the solutions X have
74               not been computed.
75
76
77
78 LAPACK routine (version 3.2)    November 2008                       ZTBTRS(1)
Impressum