1DSYRK(1) BLAS routine DSYRK(1)
2
6 DSYRK - one of the symmetric rank k operations C := alpha*A*A' +
7 beta*C,
8
10 SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
11 DOUBLE PRECISION
13 ALPHA,BETA
14 INTEGER K,LDA,LDC,N
16 CHARACTER TRANS,UPLO
18 DOUBLE PRECISION
20 A(LDA,*),C(LDC,*)
21
23 DSYRK performs one of the symmetric rank k operations
24 or
26 C := alpha*A'*A + beta*C,
28 where alpha and beta are scalars, C is an n by n symmetric matrix
30 and A is an n by k matrix in the first case and a k by n matrix
31 in the second case.
32
35 UPLO - CHARACTER*1.
36 On entry, UPLO specifies whether the upper or lower
37 triangular part of the array C is to be referenced as
38 follows:
39 UPLO = 'U' or 'u' Only the upper triangular part of C is to
41 be referenced.
42 UPLO = 'L' or 'l' Only the lower triangular part of C is to
44 be referenced.
45 Unchanged on exit.
47 TRANS - CHARACTER*1.
49 On entry, TRANS specifies the operation to be performed as
50 follows:
51 TRANS = 'N' or 'n' C := alpha*A*A' + beta*C.
53 TRANS = 'T' or 't' C := alpha*A'*A + beta*C.
55 TRANS = 'C' or 'c' C := alpha*A'*A + beta*C.
57 Unchanged on exit.
59 N - INTEGER.
61 On entry, N specifies the order of the matrix C. N must be at
62 least zero. Unchanged on exit.
63 K - INTEGER.
65 On entry with TRANS = 'N' or 'n', K specifies the number of
66 columns of the matrix A, and on entry with TRANS =
67 'T' or 't' or 'C' or 'c', K specifies the number of rows of
68 the matrix A. K must be at least zero. Unchanged on exit.
69 ALPHA - DOUBLE PRECISION.
71 On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
72 A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
74 k when TRANS = 'N' or 'n', and is n otherwise. Before
75 entry with TRANS = 'N' or 'n', the leading n by k part of
76 the array A must contain the matrix A, otherwise the leading
77 k by n part of the array A must contain the matrix A.
78 Unchanged on exit.
79 LDA - INTEGER.
81 On entry, LDA specifies the first dimension of A as declared in
82 the calling (sub) program. When TRANS = 'N' or 'n' then
83 LDA must be at least max( 1, n ), otherwise LDA must be at
84 least max( 1, k ). Unchanged on exit.
85 BETA - DOUBLE PRECISION.
87 On entry, BETA specifies the scalar beta. Unchanged on exit.
88 C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
90 Before entry with UPLO = 'U' or 'u', the leading n by n
91 upper triangular part of the array C must contain the upper tri‐
92 angular part of the symmetric matrix and the strictly lower
93 triangular part of C is not referenced. On exit, the upper tri‐
94 angular part of the array C is overwritten by the upper trian‐
95 gular part of the updated matrix. Before entry with UPLO =
96 'L' or 'l', the leading n by n lower triangular part of the
97 array C must contain the lower triangular part of the symmet‐
98 ric matrix and the strictly upper triangular part of C is not
99 referenced. On exit, the lower triangular part of the array C
100 is overwritten by the lower triangular part of the updated
101 matrix.
102 LDC - INTEGER.
104 On entry, LDC specifies the first dimension of C as declared in
105 the calling (sub) program. LDC must be at least max( 1,
106 n ). Unchanged on exit.
107 Level 3 Blas routine.
109 -- Written on 8-February-1989. Jack Dongarra, Argonne National
111 Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical
112 Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms
113 Group Ltd.
114BLAS routine November 2006 DSYRK(1)