1SSBMV(1) BLAS routine SSBMV(1)
2
6 SSBMV - the matrix-vector operation y := alpha*A*x + beta*y,
7
9 SUBROUTINE SSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
10 REAL ALPHA,BETA
12 INTEGER INCX,INCY,K,LDA,N
14 CHARACTER UPLO
16 REAL A(LDA,*),X(*),Y(*)
18
20 SSBMV performs the matrix-vector operation
21 where alpha and beta are scalars, x and y are n element vectors and A
23 is an n by n symmetric band matrix, with k super-diagonals.
24
27 UPLO - CHARACTER*1.
28 On entry, UPLO specifies whether the upper or lower triangular
29 part of the band matrix A is being supplied as follows:
30 UPLO = 'U' or 'u' The upper triangular part of A is being sup‐
32 plied.
33 UPLO = 'L' or 'l' The lower triangular part of A is being sup‐
35 plied.
36 Unchanged on exit.
38 N - INTEGER.
40 On entry, N specifies the order of the matrix A. N must be at
41 least zero. Unchanged on exit.
42 K - INTEGER.
44 On entry, K specifies the number of super-diagonals of the
45 matrix A. K must satisfy 0 .le. K. Unchanged on exit.
46 ALPHA - REAL .
48 On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
49 A - REAL array of DIMENSION ( LDA, n ).
51 Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n
52 part of the array A must contain the upper triangular band part
53 of the symmetric matrix, supplied column by column, with the
54 leading diagonal of the matrix in row ( k + 1 ) of the array,
55 the first super-diagonal starting at position 2 in row k, and so
56 on. The top left k by k triangle of the array A is not refer‐
57 enced. The following program segment will transfer the upper
58 triangular part of a symmetric band matrix from conventional
59 full matrix storage to band storage:
60 DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J - K ), J A( M
62 + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE
63 Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n
65 part of the array A must contain the lower triangular band part
66 of the symmetric matrix, supplied column by column, with the
67 leading diagonal of the matrix in row 1 of the array, the first
68 sub-diagonal starting at position 1 in row 2, and so on. The
69 bottom right k by k triangle of the array A is not referenced.
70 The following program segment will transfer the lower triangular
71 part of a symmetric band matrix from conventional full matrix
72 storage to band storage:
73 DO 20, J = 1, N M = 1 - J DO 10, I = J, MIN( N, J + K ) A( M +
75 I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE
76 Unchanged on exit.
78 LDA - INTEGER.
80 On entry, LDA specifies the first dimension of A as declared in
81 the calling (sub) program. LDA must be at least ( k + 1 ).
82 Unchanged on exit.
83 X - REAL array of DIMENSION at least
85 ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented
86 array X must contain the vector x. Unchanged on exit.
87 INCX - INTEGER.
89 On entry, INCX specifies the increment for the elements of X.
90 INCX must not be zero. Unchanged on exit.
91 BETA - REAL .
93 On entry, BETA specifies the scalar beta. Unchanged on exit.
94 Y - REAL array of DIMENSION at least
96 ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented
97 array Y must contain the vector y. On exit, Y is overwritten by
98 the updated vector y.
99 INCY - INTEGER.
101 On entry, INCY specifies the increment for the elements of Y.
102 INCY must not be zero. Unchanged on exit.
103 Level 2 Blas routine.
105 -- Written on 22-October-1986. Jack Dongarra, Argonne National
107 Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag
108 Central Office. Richard Hanson, Sandia National Labs.
109BLAS routine November 2006 SSBMV(1)