1CTBMV(1) BLAS routine CTBMV(1)
2
6 CTBMV - one of the matrix-vector operations x := A*x, or x := A'*x,
7 or x := conjg( A' )*x,
8
10 SUBROUTINE CTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
11 INTEGER INCX,K,LDA,N
13 CHARACTER DIAG,TRANS,UPLO
15 COMPLEX A(LDA,*),X(*)
17
19 CTBMV performs one of the matrix-vector operations
20 where x is an n element vector and A is an n by n unit, or non-unit,
22 upper or lower triangular band matrix, with ( k + 1 ) diagonals.
23
26 UPLO - CHARACTER*1.
27 On entry, UPLO specifies whether the matrix is an upper or lower
28 triangular matrix as follows:
29 UPLO = 'U' or 'u' A is an upper triangular matrix.
31 UPLO = 'L' or 'l' A is a lower triangular matrix.
33 Unchanged on exit.
35 TRANS - CHARACTER*1.
37 On entry, TRANS specifies the operation to be performed as fol‐
38 lows:
39 TRANS = 'N' or 'n' x := A*x.
41 TRANS = 'T' or 't' x := A'*x.
43 TRANS = 'C' or 'c' x := conjg( A' )*x.
45 Unchanged on exit.
47 DIAG - CHARACTER*1.
49 On entry, DIAG specifies whether or not A is unit triangular as
50 follows:
51 DIAG = 'U' or 'u' A is assumed to be unit triangular.
53 DIAG = 'N' or 'n' A is not assumed to be unit triangular.
55 Unchanged on exit.
57 N - INTEGER.
59 On entry, N specifies the order of the matrix A. N must be at
60 least zero. Unchanged on exit.
61 K - INTEGER.
63 On entry with UPLO = 'U' or 'u', K specifies the number of
64 super-diagonals of the matrix A. On entry with UPLO = 'L' or
65 'l', K specifies the number of sub-diagonals of the matrix A. K
66 must satisfy 0 .le. K. Unchanged on exit.
67 A - COMPLEX array of DIMENSION ( LDA, n ).
69 Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n
70 part of the array A must contain the upper triangular band part
71 of the matrix of coefficients, supplied column by column, with
72 the leading diagonal of the matrix in row ( k + 1 ) of the
73 array, the first super-diagonal starting at position 2 in row k,
74 and so on. The top left k by k triangle of the array A is not
75 referenced. The following program segment will transfer an
76 upper triangular band matrix from conventional full matrix stor‐
77 age to band storage:
78 DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J - K ), J A( M
80 + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE
81 Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n
83 part of the array A must contain the lower triangular band part
84 of the matrix of coefficients, supplied column by column, with
85 the leading diagonal of the matrix in row 1 of the array, the
86 first sub-diagonal starting at position 1 in row 2, and so on.
87 The bottom right k by k triangle of the array A is not refer‐
88 enced. The following program segment will transfer a lower tri‐
89 angular band matrix from conventional full matrix storage to
90 band storage:
91 DO 20, J = 1, N M = 1 - J DO 10, I = J, MIN( N, J + K ) A( M +
93 I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE
94 Note that when DIAG = 'U' or 'u' the elements of the array A
96 corresponding to the diagonal elements of the matrix are not
97 referenced, but are assumed to be unity. Unchanged on exit.
98 LDA - INTEGER.
100 On entry, LDA specifies the first dimension of A as declared in
101 the calling (sub) program. LDA must be at least ( k + 1 ).
102 Unchanged on exit.
103 X - COMPLEX array of dimension at least
105 ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented
106 array X must contain the n element vector x. On exit, X is over‐
107 written with the tranformed vector x.
108 INCX - INTEGER.
110 On entry, INCX specifies the increment for the elements of X.
111 INCX must not be zero. Unchanged on exit.
112 Level 2 Blas routine.
114 -- Written on 22-October-1986. Jack Dongarra, Argonne National
116 Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag
117 Central Office. Richard Hanson, Sandia National Labs.
118BLAS routine November 2006 CTBMV(1)