1ZTBSV(1) BLAS routine ZTBSV(1)
2
6 ZTBSV - solves one of the systems of equations A*x = b, or A'*x = b,
7 or conjg( A' )*x = b,
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10 SUBROUTINE ZTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
11 INTEGER INCX,K,LDA,N
13 CHARACTER DIAG,TRANS,UPLO
15 DOUBLE COMPLEX
17 A(LDA,*),X(*)
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20 ZTBSV solves one of the systems of equations
21 where b and x are n element vectors and A is an n by n unit, or non-
23 unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals.
24 No test for singularity or near-singularity is included in this rou‐
26 tine. Such tests must be performed before calling this routine.
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30 UPLO - CHARACTER*1.
31 On entry, UPLO specifies whether the matrix is an upper or lower
32 triangular matrix as follows:
33 UPLO = 'U' or 'u' A is an upper triangular matrix.
35 UPLO = 'L' or 'l' A is a lower triangular matrix.
37 Unchanged on exit.
39 TRANS - CHARACTER*1.
41 On entry, TRANS specifies the equations to be solved as follows:
42 TRANS = 'N' or 'n' A*x = b.
44 TRANS = 'T' or 't' A'*x = b.
46 TRANS = 'C' or 'c' conjg( A' )*x = b.
48 Unchanged on exit.
50 DIAG - CHARACTER*1.
52 On entry, DIAG specifies whether or not A is unit triangular as
53 follows:
54 DIAG = 'U' or 'u' A is assumed to be unit triangular.
56 DIAG = 'N' or 'n' A is not assumed to be unit triangular.
58 Unchanged on exit.
60 N - INTEGER.
62 On entry, N specifies the order of the matrix A. N must be at
63 least zero. Unchanged on exit.
64 K - INTEGER.
66 On entry with UPLO = 'U' or 'u', K specifies the number of
67 super-diagonals of the matrix A. On entry with UPLO = 'L' or
68 'l', K specifies the number of sub-diagonals of the matrix A. K
69 must satisfy 0 .le. K. Unchanged on exit.
70 A - COMPLEX*16 array of DIMENSION ( LDA, n ).
72 Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n
73 part of the array A must contain the upper triangular band part
74 of the matrix of coefficients, supplied column by column, with
75 the leading diagonal of the matrix in row ( k + 1 ) of the
76 array, the first super-diagonal starting at position 2 in row k,
77 and so on. The top left k by k triangle of the array A is not
78 referenced. The following program segment will transfer an
79 upper triangular band matrix from conventional full matrix stor‐
80 age to band storage:
81 DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J - K ), J A( M
83 + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE
84 Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n
86 part of the array A must contain the lower triangular band part
87 of the matrix of coefficients, supplied column by column, with
88 the leading diagonal of the matrix in row 1 of the array, the
89 first sub-diagonal starting at position 1 in row 2, and so on.
90 The bottom right k by k triangle of the array A is not refer‐
91 enced. The following program segment will transfer a lower tri‐
92 angular band matrix from conventional full matrix storage to
93 band storage:
94 DO 20, J = 1, N M = 1 - J DO 10, I = J, MIN( N, J + K ) A( M +
96 I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE
97 Note that when DIAG = 'U' or 'u' the elements of the array A
99 corresponding to the diagonal elements of the matrix are not
100 referenced, but are assumed to be unity. Unchanged on exit.
101 LDA - INTEGER.
103 On entry, LDA specifies the first dimension of A as declared in
104 the calling (sub) program. LDA must be at least ( k + 1 ).
105 Unchanged on exit.
106 X - COMPLEX*16 array of dimension at least
108 ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented
109 array X must contain the n element right-hand side vector b. On
110 exit, X is overwritten with the solution vector x.
111 INCX - INTEGER.
113 On entry, INCX specifies the increment for the elements of X.
114 INCX must not be zero. Unchanged on exit.
115
117 Level 2 Blas routine.
118 -- Written on 22-October-1986.
120 Jack Dongarra, Argonne National Lab.
121 Jeremy Du Croz, Nag Central Office.
122 Sven Hammarling, Nag Central Office.
123 Richard Hanson, Sandia National Labs.
124BLAS routine November 2008 ZTBSV(1)