1DSYR2K(1) BLAS routine DSYR2K(1)
2
6 DSYR2K - one of the symmetric rank 2k operations C := alpha*A*B' +
7 alpha*B*A' + beta*C,
8
10 SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
11 DOUBLE PRECI‐
13 SION
14 ALPHA,BETA
15 INTEGER K,LDA,LDB,LDC,N
17 CHARACTER TRANS,UPLO
19 DOUBLE PRECI‐
21 SION
22 A(LDA,*),B(LDB,*),C(LDC,*)
23
25 DSYR2K performs one of the symmetric rank 2k operations
26 or
28 C := alpha*A'*B + alpha*B'*A + beta*C,
30 where alpha and beta are scalars, C is an n by n symmetric matrix
32 and A and B are n by k matrices in the first case and k by n
33 matrices in the second case.
34
37 UPLO - CHARACTER*1.
38 On entry, UPLO specifies whether the upper or lower
39 triangular part of the array C is to be referenced as
40 follows:
41 UPLO = 'U' or 'u' Only the upper triangular part of C is to
43 be referenced.
44 UPLO = 'L' or 'l' Only the lower triangular part of C is to
46 be referenced.
47 Unchanged on exit.
49 TRANS - CHARACTER*1.
51 On entry, TRANS specifies the operation to be performed as
52 follows:
53 TRANS = 'N' or 'n' C := alpha*A*B' + alpha*B*A' + beta*C.
55 TRANS = 'T' or 't' C := alpha*A'*B + alpha*B'*A + beta*C.
57 TRANS = 'C' or 'c' C := alpha*A'*B + alpha*B'*A + beta*C.
59 Unchanged on exit.
61 N - INTEGER.
63 On entry, N specifies the order of the matrix C. N must be at
64 least zero. Unchanged on exit.
65 K - INTEGER.
67 On entry with TRANS = 'N' or 'n', K specifies the number of
68 columns of the matrices A and B, and on entry with TRANS =
69 'T' or 't' or 'C' or 'c', K specifies the number of rows of
70 the matrices A and B. K must be at least zero. Unchanged on
71 exit.
72 ALPHA - DOUBLE PRECISION.
74 On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
75 A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
77 k when TRANS = 'N' or 'n', and is n otherwise. Before
78 entry with TRANS = 'N' or 'n', the leading n by k part of
79 the array A must contain the matrix A, otherwise the leading
80 k by n part of the array A must contain the matrix A.
81 Unchanged on exit.
82 LDA - INTEGER.
84 On entry, LDA specifies the first dimension of A as declared in
85 the calling (sub) program. When TRANS = 'N' or 'n' then
86 LDA must be at least max( 1, n ), otherwise LDA must be at
87 least max( 1, k ). Unchanged on exit.
88 B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
90 k when TRANS = 'N' or 'n', and is n otherwise. Before
91 entry with TRANS = 'N' or 'n', the leading n by k part of
92 the array B must contain the matrix B, otherwise the leading
93 k by n part of the array B must contain the matrix B.
94 Unchanged on exit.
95 LDB - INTEGER.
97 On entry, LDB specifies the first dimension of B as declared in
98 the calling (sub) program. When TRANS = 'N' or 'n' then
99 LDB must be at least max( 1, n ), otherwise LDB must be at
100 least max( 1, k ). Unchanged on exit.
101 BETA - DOUBLE PRECISION.
103 On entry, BETA specifies the scalar beta. Unchanged on exit.
104 C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
106 Before entry with UPLO = 'U' or 'u', the leading n by n
107 upper triangular part of the array C must contain the upper tri‐
108 angular part of the symmetric matrix and the strictly lower
109 triangular part of C is not referenced. On exit, the upper tri‐
110 angular part of the array C is overwritten by the upper trian‐
111 gular part of the updated matrix. Before entry with UPLO =
112 'L' or 'l', the leading n by n lower triangular part of the
113 array C must contain the lower triangular part of the symmet‐
114 ric matrix and the strictly upper triangular part of C is not
115 referenced. On exit, the lower triangular part of the array C
116 is overwritten by the lower triangular part of the updated
117 matrix.
118 LDC - INTEGER.
120 On entry, LDC specifies the first dimension of C as declared in
121 the calling (sub) program. LDC must be at least max( 1,
122 n ). Unchanged on exit.
123 Level 3 Blas routine.
125 -- Written on 8-February-1989. Jack Dongarra, Argonne National
127 Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical
128 Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms
129 Group Ltd.
130BLAS routine November 2006 DSYR2K(1)