1CSYR2K(1) BLAS routine CSYR2K(1)
2
6 CSYR2K - performs one of the symmetric rank 2k operations C :=
7 alpha*A*B' + alpha*B*A' + beta*C,
8
10 SUBROUTINE CSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
11 COMPLEX ALPHA,BETA
13 INTEGER K,LDA,LDB,LDC,N
15 CHARACTER TRANS,UPLO
17 COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
19
21 CSYR2K performs one of the symmetric rank 2k operations
22 or
24 C := alpha*A'*B + alpha*B'*A + beta*C,
26 where alpha and beta are scalars, C is an n by n symmetric matrix
28 and A and B are n by k matrices in the first case and k by n
29 matrices in the second case.
30
33 UPLO - CHARACTER*1.
34 On entry, UPLO specifies whether the upper or lower
35 triangular part of the array C is to be referenced as
36 follows:
37 UPLO = 'U' or 'u' Only the upper triangular part of C is to
39 be referenced.
40 UPLO = 'L' or 'l' Only the lower triangular part of C is to
42 be referenced.
43 Unchanged on exit.
45 TRANS - CHARACTER*1.
47 On entry, TRANS specifies the operation to be performed as
48 follows:
49 TRANS = 'N' or 'n' C := alpha*A*B' + alpha*B*A' + beta*C.
51 TRANS = 'T' or 't' C := alpha*A'*B + alpha*B'*A + beta*C.
53 Unchanged on exit.
55 N - INTEGER.
57 On entry, N specifies the order of the matrix C. N must be at
58 least zero. Unchanged on exit.
59 K - INTEGER.
61 On entry with TRANS = 'N' or 'n', K specifies the number of
62 columns of the matrices A and B, and on entry with TRANS =
63 'T' or 't', K specifies the number of rows of the matrices A
64 and B. K must be at least zero. Unchanged on exit.
65 ALPHA - COMPLEX .
67 On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
68 A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is
70 k when TRANS = 'N' or 'n', and is n otherwise. Before
71 entry with TRANS = 'N' or 'n', the leading n by k part of
72 the array A must contain the matrix A, otherwise the leading
73 k by n part of the array A must contain the matrix A.
74 Unchanged on exit.
75 LDA - INTEGER.
77 On entry, LDA specifies the first dimension of A as declared in
78 the calling (sub) program. When TRANS = 'N' or 'n' then
79 LDA must be at least max( 1, n ), otherwise LDA must be at
80 least max( 1, k ). Unchanged on exit.
81 B - COMPLEX array of DIMENSION ( LDB, kb ), where kb is
83 k when TRANS = 'N' or 'n', and is n otherwise. Before
84 entry with TRANS = 'N' or 'n', the leading n by k part of
85 the array B must contain the matrix B, otherwise the leading
86 k by n part of the array B must contain the matrix B.
87 Unchanged on exit.
88 LDB - INTEGER.
90 On entry, LDB specifies the first dimension of B as declared in
91 the calling (sub) program. When TRANS = 'N' or 'n' then
92 LDB must be at least max( 1, n ), otherwise LDB must be at
93 least max( 1, k ). Unchanged on exit.
94 BETA - COMPLEX .
96 On entry, BETA specifies the scalar beta. Unchanged on exit.
97 C - COMPLEX array of DIMENSION ( LDC, n ).
99 Before entry with UPLO = 'U' or 'u', the leading n by n
100 upper triangular part of the array C must contain the upper tri‐
101 angular part of the symmetric matrix and the strictly lower
102 triangular part of C is not referenced. On exit, the upper tri‐
103 angular part of the array C is overwritten by the upper trian‐
104 gular part of the updated matrix. Before entry with UPLO =
105 'L' or 'l', the leading n by n lower triangular part of the
106 array C must contain the lower triangular part of the symmet‐
107 ric matrix and the strictly upper triangular part of C is not
108 referenced. On exit, the lower triangular part of the array C
109 is overwritten by the lower triangular part of the updated
110 matrix.
111 LDC - INTEGER.
113 On entry, LDC specifies the first dimension of C as declared in
114 the calling (sub) program. LDC must be at least max( 1,
115 n ). Unchanged on exit.
116
118 Level 3 Blas routine.
119 -- Written on 8-February-1989.
121 Jack Dongarra, Argonne National Laboratory.
122 Iain Duff, AERE Harwell.
123 Jeremy Du Croz, Numerical Algorithms Group Ltd.
124 Sven Hammarling, Numerical Algorithms Group Ltd.
125BLAS routine November 2008 CSYR2K(1)