1SGBMV(1) BLAS routine SGBMV(1)
2
6 SGBMV - performs one of the matrix-vector operations y := alpha*A*x +
7 beta*y, or y := alpha*A'*x + beta*y,
8
10 SUBROUTINE SGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
11 REAL ALPHA,BETA
13 INTEGER INCX,INCY,KL,KU,LDA,M,N
15 CHARACTER TRANS
17 REAL A(LDA,*),X(*),Y(*)
19
21 SGBMV performs one of the matrix-vector operations
22 where alpha and beta are scalars, x and y are vectors and A is an m by
24 n band matrix, with kl sub-diagonals and ku super-diagonals.
25
28 TRANS - CHARACTER*1.
29 On entry, TRANS specifies the operation to be performed as fol‐
30 lows:
31 TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
33 TRANS = 'T' or 't' y := alpha*A'*x + beta*y.
35 TRANS = 'C' or 'c' y := alpha*A'*x + beta*y.
37 Unchanged on exit.
39 M - INTEGER.
41 On entry, M specifies the number of rows of the matrix A. M
42 must be at least zero. Unchanged on exit.
43 N - INTEGER.
45 On entry, N specifies the number of columns of the matrix A. N
46 must be at least zero. Unchanged on exit.
47 KL - INTEGER.
49 On entry, KL specifies the number of sub-diagonals of the matrix
50 A. KL must satisfy 0 .le. KL. Unchanged on exit.
51 KU - INTEGER.
53 On entry, KU specifies the number of super-diagonals of the
54 matrix A. KU must satisfy 0 .le. KU. Unchanged on exit.
55 ALPHA - REAL .
57 On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
58 A - REAL array of DIMENSION ( LDA, n ).
60 Before entry, the leading ( kl + ku + 1 ) by n part of the array
61 A must contain the matrix of coefficients, supplied column by
62 column, with the leading diagonal of the matrix in row ( ku + 1
63 ) of the array, the first super-diagonal starting at position 2
64 in row ku, the first sub-diagonal starting at position 1 in row
65 ( ku + 2 ), and so on. Elements in the array A that do not cor‐
66 respond to elements in the band matrix (such as the top left ku
67 by ku triangle) are not referenced. The following program seg‐
68 ment will transfer a band matrix from conventional full matrix
69 storage to band storage:
70 DO 20, J = 1, N K = KU + 1 - J DO 10, I = MAX( 1, J - KU ), MIN(
72 M, J + KL ) A( K + I, J ) = matrix( I, J ) 10 CONTINUE 20
73 CONTINUE
74 Unchanged on exit.
76 LDA - INTEGER.
78 On entry, LDA specifies the first dimension of A as declared in
79 the calling (sub) program. LDA must be at least ( kl + ku + 1 ).
80 Unchanged on exit.
81 X - REAL array of DIMENSION at least
83 ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at
84 least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry,
85 the incremented array X must contain the vector x. Unchanged on
86 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. When BETA is supplied
94 as zero then Y need not be set on input. Unchanged on exit.
95 Y - REAL array of DIMENSION at least
97 ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at
98 least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. Before entry,
99 the incremented array Y must contain the vector y. On exit, Y is
100 overwritten by the updated vector y.
101 INCY - INTEGER.
103 On entry, INCY specifies the increment for the elements of Y.
104 INCY must not be zero. Unchanged on exit.
105
107 Level 2 Blas routine.
108 -- Written on 22-October-1986.
110 Jack Dongarra, Argonne National Lab.
111 Jeremy Du Croz, Nag Central Office.
112 Sven Hammarling, Nag Central Office.
113 Richard Hanson, Sandia National Labs.
114BLAS routine November 2008 SGBMV(1)