1ZTBMV(1) BLAS routine ZTBMV(1)
2
6 ZTBMV - one of the matrix-vector operations x := A*x, or x := A'*x,
7 or x := conjg( A' )*x,
8
10 SUBROUTINE ZTBMV(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(*)
18
20 ZTBMV performs one of the matrix-vector operations
21 where x is an n element vector and A is an n by n unit, or non-unit,
23 upper or lower triangular band matrix, with ( k + 1 ) diagonals.
24
27 UPLO - CHARACTER*1.
28 On entry, UPLO specifies whether the matrix is an upper or lower
29 triangular matrix as follows:
30 UPLO = 'U' or 'u' A is an upper triangular matrix.
32 UPLO = 'L' or 'l' A is a lower triangular matrix.
34 Unchanged on exit.
36 TRANS - CHARACTER*1.
38 On entry, TRANS specifies the operation to be performed as fol‐
39 lows:
40 TRANS = 'N' or 'n' x := A*x.
42 TRANS = 'T' or 't' x := A'*x.
44 TRANS = 'C' or 'c' x := conjg( A' )*x.
46 Unchanged on exit.
48 DIAG - CHARACTER*1.
50 On entry, DIAG specifies whether or not A is unit triangular as
51 follows:
52 DIAG = 'U' or 'u' A is assumed to be unit triangular.
54 DIAG = 'N' or 'n' A is not assumed to be unit triangular.
56 Unchanged on exit.
58 N - INTEGER.
60 On entry, N specifies the order of the matrix A. N must be at
61 least zero. Unchanged on exit.
62 K - INTEGER.
64 On entry with UPLO = 'U' or 'u', K specifies the number of
65 super-diagonals of the matrix A. On entry with UPLO = 'L' or
66 'l', K specifies the number of sub-diagonals of the matrix A. K
67 must satisfy 0 .le. K. Unchanged on exit.
68 A - COMPLEX*16 array of DIMENSION ( LDA, n ).
70 Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n
71 part of the array A must contain the upper triangular band part
72 of the matrix of coefficients, supplied column by column, with
73 the leading diagonal of the matrix in row ( k + 1 ) of the
74 array, the first super-diagonal starting at position 2 in row k,
75 and so on. The top left k by k triangle of the array A is not
76 referenced. The following program segment will transfer an
77 upper triangular band matrix from conventional full matrix stor‐
78 age to band storage:
79 DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J - K ), J A( M
81 + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE
82 Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n
84 part of the array A must contain the lower triangular band part
85 of the matrix of coefficients, supplied column by column, with
86 the leading diagonal of the matrix in row 1 of the array, the
87 first sub-diagonal starting at position 1 in row 2, and so on.
88 The bottom right k by k triangle of the array A is not refer‐
89 enced. The following program segment will transfer a lower tri‐
90 angular band matrix from conventional full matrix storage to
91 band storage:
92 DO 20, J = 1, N M = 1 - J DO 10, I = J, MIN( N, J + K ) A( M +
94 I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE
95 Note that when DIAG = 'U' or 'u' the elements of the array A
97 corresponding to the diagonal elements of the matrix are not
98 referenced, but are assumed to be unity. Unchanged on exit.
99 LDA - INTEGER.
101 On entry, LDA specifies the first dimension of A as declared in
102 the calling (sub) program. LDA must be at least ( k + 1 ).
103 Unchanged on exit.
104 X - COMPLEX*16 array of dimension at least
106 ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented
107 array X must contain the n element vector x. On exit, X is over‐
108 written with the tranformed vector x.
109 INCX - INTEGER.
111 On entry, INCX specifies the increment for the elements of X.
112 INCX must not be zero. Unchanged on exit.
113 Level 2 Blas routine.
115 -- Written on 22-October-1986. Jack Dongarra, Argonne National
117 Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag
118 Central Office. Richard Hanson, Sandia National Labs.
119BLAS routine November 2006 ZTBMV(1)