1ZSYR2K(1) BLAS routine ZSYR2K(1)
2
6 ZSYR2K - one of the symmetric rank 2k operations C := alpha*A*B' +
7 alpha*B*A' + beta*C,
8
10 SUBROUTINE ZSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
11 DOUBLE COMPLEX
13 ALPHA,BETA
14 INTEGER K,LDA,LDB,LDC,N
16 CHARACTER TRANS,UPLO
18 DOUBLE COMPLEX
20 A(LDA,*),B(LDB,*),C(LDC,*)
21
23 ZSYR2K performs one of the symmetric rank 2k operations
24 or
26 C := alpha*A'*B + alpha*B'*A + beta*C,
28 where alpha and beta are scalars, C is an n by n symmetric matrix
30 and A and B are n by k matrices in the first case and k by n
31 matrices 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*B' + alpha*B*A' + beta*C.
53 TRANS = 'T' or 't' C := alpha*A'*B + alpha*B'*A + beta*C.
55 Unchanged on exit.
57 N - INTEGER.
59 On entry, N specifies the order of the matrix C. N must be at
60 least zero. Unchanged on exit.
61 K - INTEGER.
63 On entry with TRANS = 'N' or 'n', K specifies the number of
64 columns of the matrices A and B, and on entry with TRANS =
65 'T' or 't', K specifies the number of rows of the matrices A
66 and B. K must be at least zero. Unchanged on exit.
67 ALPHA - COMPLEX*16 .
69 On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
70 A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
72 k when TRANS = 'N' or 'n', and is n otherwise. Before
73 entry with TRANS = 'N' or 'n', the leading n by k part of
74 the array A must contain the matrix A, otherwise the leading
75 k by n part of the array A must contain the matrix A.
76 Unchanged on exit.
77 LDA - INTEGER.
79 On entry, LDA specifies the first dimension of A as declared in
80 the calling (sub) program. When TRANS = 'N' or 'n' then
81 LDA must be at least max( 1, n ), otherwise LDA must be at
82 least max( 1, k ). Unchanged on exit.
83 B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is
85 k when TRANS = 'N' or 'n', and is n otherwise. Before
86 entry with TRANS = 'N' or 'n', the leading n by k part of
87 the array B must contain the matrix B, otherwise the leading
88 k by n part of the array B must contain the matrix B.
89 Unchanged on exit.
90 LDB - INTEGER.
92 On entry, LDB specifies the first dimension of B as declared in
93 the calling (sub) program. When TRANS = 'N' or 'n' then
94 LDB must be at least max( 1, n ), otherwise LDB must be at
95 least max( 1, k ). Unchanged on exit.
96 BETA - COMPLEX*16 .
98 On entry, BETA specifies the scalar beta. Unchanged on exit.
99 C - COMPLEX*16 array of DIMENSION ( LDC, n ).
101 Before entry with UPLO = 'U' or 'u', the leading n by n
102 upper triangular part of the array C must contain the upper tri‐
103 angular part of the symmetric matrix and the strictly lower
104 triangular part of C is not referenced. On exit, the upper tri‐
105 angular part of the array C is overwritten by the upper trian‐
106 gular part of the updated matrix. Before entry with UPLO =
107 'L' or 'l', the leading n by n lower triangular part of the
108 array C must contain the lower triangular part of the symmet‐
109 ric matrix and the strictly upper triangular part of C is not
110 referenced. On exit, the lower triangular part of the array C
111 is overwritten by the lower triangular part of the updated
112 matrix.
113 LDC - INTEGER.
115 On entry, LDC specifies the first dimension of C as declared in
116 the calling (sub) program. LDC must be at least max( 1,
117 n ). Unchanged on exit.
118 Level 3 Blas routine.
120 -- Written on 8-February-1989. Jack Dongarra, Argonne National
122 Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical
123 Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms
124 Group Ltd.
125BLAS routine November 2006 ZSYR2K(1)