1ZSYR2K(1) BLAS routine ZSYR2K(1)
2
6 ZSYR2K - performs one of the symmetric rank 2k operations C :=
7 alpha*A*B' + 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
120 Level 3 Blas routine.
121 -- Written on 8-February-1989.
123 Jack Dongarra, Argonne National Laboratory.
124 Iain Duff, AERE Harwell.
125 Jeremy Du Croz, Numerical Algorithms Group Ltd.
126 Sven Hammarling, Numerical Algorithms Group Ltd.
127BLAS routine November 2008 ZSYR2K(1)