1CSYR2K(1) BLAS routine CSYR2K(1)
2
6 CSYR2K - one of the symmetric rank 2k operations C := alpha*A*B' +
7 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 Level 3 Blas routine.
118 -- Written on 8-February-1989. Jack Dongarra, Argonne National
120 Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical
121 Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms
122 Group Ltd.
123BLAS routine November 2006 CSYR2K(1)