1CHERK(1) BLAS routine CHERK(1)
2
6 CHERK - performs one of the hermitian rank k operations C :=
7 alpha*A*conjg( A' ) + beta*C,
8
10 SUBROUTINE CHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
11 REAL ALPHA,BETA
13 INTEGER K,LDA,LDC,N
15 CHARACTER TRANS,UPLO
17 COMPLEX A(LDA,*),C(LDC,*)
19
21 CHERK performs one of the hermitian rank k operations
22 or
24 C := alpha*conjg( A' )*A + beta*C,
26 where alpha and beta are real scalars, C is an n by n hermitian
28 matrix and A is an n by k matrix in the first case and a k by n
29 matrix 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*conjg( A' ) + beta*C.
51 TRANS = 'C' or 'c' C := alpha*conjg( A' )*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 matrix A, and on entry with TRANS =
63 'C' or 'c', K specifies the number of rows of the matrix A.
64 K must be at least zero. Unchanged on exit.
65 ALPHA - REAL .
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 BETA - REAL .
83 On entry, BETA specifies the scalar beta. Unchanged on exit.
84 C - COMPLEX array of DIMENSION ( LDC, n ).
86 Before entry with UPLO = 'U' or 'u', the leading n by n
87 upper triangular part of the array C must contain the upper tri‐
88 angular part of the hermitian matrix and the strictly lower
89 triangular part of C is not referenced. On exit, the upper tri‐
90 angular part of the array C is overwritten by the upper trian‐
91 gular part of the updated matrix. Before entry with UPLO =
92 'L' or 'l', the leading n by n lower triangular part of the
93 array C must contain the lower triangular part of the hermit‐
94 ian matrix and the strictly upper triangular part of C is not
95 referenced. On exit, the lower triangular part of the array C
96 is overwritten by the lower triangular part of the updated
97 matrix. Note that the imaginary parts of the diagonal elements
98 need not be set, they are assumed to be zero, and on exit they
99 are set to zero.
100 LDC - INTEGER.
102 On entry, LDC specifies the first dimension of C as declared in
103 the calling (sub) program. LDC must be at least max( 1,
104 n ). Unchanged on exit.
105
107 Level 3 Blas routine.
108 -- Written on 8-February-1989.
110 Jack Dongarra, Argonne National Laboratory.
111 Iain Duff, AERE Harwell.
112 Jeremy Du Croz, Numerical Algorithms Group Ltd.
113 Sven Hammarling, Numerical Algorithms Group Ltd.
114 -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1.
116 Ed Anderson, Cray Research Inc.
117BLAS routine November 2008 CHERK(1)