1DSYRK(1) BLAS routine DSYRK(1)
2
6 DSYRK - performs one of the symmetric rank k operations C :=
7 alpha*A*A' + 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
109 Level 3 Blas routine.
110 -- Written on 8-February-1989.
112 Jack Dongarra, Argonne National Laboratory.
113 Iain Duff, AERE Harwell.
114 Jeremy Du Croz, Numerical Algorithms Group Ltd.
115 Sven Hammarling, Numerical Algorithms Group Ltd.
116BLAS routine November 2008 DSYRK(1)