1ZHBMV(1) BLAS routine ZHBMV(1)
2
6 ZHBMV - the matrix-vector operation y := alpha*A*x + beta*y,
7
9 SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
10 DOUBLE COMPLEX
12 ALPHA,BETA
13 INTEGER INCX,INCY,K,LDA,N
15 CHARACTER UPLO
17 DOUBLE COMPLEX
19 A(LDA,*),X(*),Y(*)
20
22 ZHBMV performs the matrix-vector operation
23 where alpha and beta are scalars, x and y are n element vectors and A
25 is an n by n hermitian band matrix, with k super-diagonals.
26
29 UPLO - CHARACTER*1.
30 On entry, UPLO specifies whether the upper or lower triangular
31 part of the band matrix A is being supplied as follows:
32 UPLO = 'U' or 'u' The upper triangular part of A is being sup‐
34 plied.
35 UPLO = 'L' or 'l' The lower triangular part of A is being sup‐
37 plied.
38 Unchanged on exit.
40 N - INTEGER.
42 On entry, N specifies the order of the matrix A. N must be at
43 least zero. Unchanged on exit.
44 K - INTEGER.
46 On entry, K specifies the number of super-diagonals of the
47 matrix A. K must satisfy 0 .le. K. Unchanged on exit.
48 ALPHA - COMPLEX*16 .
50 On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
51 A - COMPLEX*16 array of DIMENSION ( LDA, n ).
53 Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n
54 part of the array A must contain the upper triangular band part
55 of the hermitian matrix, supplied column by column, with the
56 leading diagonal of the matrix in row ( k + 1 ) of the array,
57 the first super-diagonal starting at position 2 in row k, and so
58 on. The top left k by k triangle of the array A is not refer‐
59 enced. The following program segment will transfer the upper
60 triangular part of a hermitian band matrix from conventional
61 full matrix storage to band storage:
62 DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J - K ), J A( M
64 + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE
65 Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n
67 part of the array A must contain the lower triangular band part
68 of the hermitian matrix, supplied column by column, with the
69 leading diagonal of the matrix in row 1 of the array, the first
70 sub-diagonal starting at position 1 in row 2, and so on. The
71 bottom right k by k triangle of the array A is not referenced.
72 The following program segment will transfer the lower triangular
73 part of a hermitian band matrix from conventional full matrix
74 storage to band storage:
75 DO 20, J = 1, N M = 1 - J DO 10, I = J, MIN( N, J + K ) A( M +
77 I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE
78 Note that the imaginary parts of the diagonal elements need not
80 be set and are assumed to be zero. Unchanged on exit.
81 LDA - INTEGER.
83 On entry, LDA specifies the first dimension of A as declared in
84 the calling (sub) program. LDA must be at least ( k + 1 ).
85 Unchanged on exit.
86 X - COMPLEX*16 array of DIMENSION at least
88 ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented
89 array X must contain the vector x. Unchanged on exit.
90 INCX - INTEGER.
92 On entry, INCX specifies the increment for the elements of X.
93 INCX must not be zero. Unchanged on exit.
94 BETA - COMPLEX*16 .
96 On entry, BETA specifies the scalar beta. Unchanged on exit.
97 Y - COMPLEX*16 array of DIMENSION at least
99 ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented
100 array Y must contain the vector y. On exit, Y is overwritten by
101 the updated vector y.
102 INCY - INTEGER.
104 On entry, INCY specifies the increment for the elements of Y.
105 INCY must not be zero. Unchanged on exit.
106 Level 2 Blas routine.
108 -- Written on 22-October-1986. Jack Dongarra, Argonne National
110 Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag
111 Central Office. Richard Hanson, Sandia National Labs.
112BLAS routine November 2006 ZHBMV(1)