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