1ZHERK(1) BLAS routine ZHERK(1)
2
6 ZHERK - one of the hermitian rank k operations C := alpha*A*conjg( A'
7 ) + beta*C,
8
10 SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
11 DOUBLE PRECISION
13 ALPHA,BETA
14 INTEGER K,LDA,LDC,N
16 CHARACTER TRANS,UPLO
18 DOUBLE COMPLEX
20 A(LDA,*),C(LDC,*)
21
23 ZHERK performs one of the hermitian rank k operations
24 or
26 C := alpha*conjg( A' )*A + beta*C,
28 where alpha and beta are real scalars, C is an n by n hermitian
30 matrix and A is an n by k matrix in the first case and a k by n
31 matrix 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*conjg( A' ) + beta*C.
53 TRANS = 'C' or 'c' C := alpha*conjg( A' )*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 matrix A, and on entry with TRANS =
65 'C' or 'c', K specifies the number of rows of the matrix A.
66 K must be at least zero. Unchanged on exit.
67 ALPHA - DOUBLE PRECISION .
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 BETA - DOUBLE PRECISION.
85 On entry, BETA specifies the scalar beta. Unchanged on exit.
86 C - COMPLEX*16 array of DIMENSION ( LDC, n ).
88 Before entry with UPLO = 'U' or 'u', the leading n by n
89 upper triangular part of the array C must contain the upper tri‐
90 angular part of the hermitian matrix and the strictly lower
91 triangular part of C is not referenced. On exit, the upper tri‐
92 angular part of the array C is overwritten by the upper trian‐
93 gular part of the updated matrix. Before entry with UPLO =
94 'L' or 'l', the leading n by n lower triangular part of the
95 array C must contain the lower triangular part of the hermit‐
96 ian matrix and the strictly upper triangular part of C is not
97 referenced. On exit, the lower triangular part of the array C
98 is overwritten by the lower triangular part of the updated
99 matrix. Note that the imaginary parts of the diagonal elements
100 need not be set, they are assumed to be zero, and on exit they
101 are set to zero.
102 LDC - INTEGER.
104 On entry, LDC specifies the first dimension of C as declared in
105 the calling (sub) program. LDC must be at least max( 1,
106 n ). Unchanged on exit.
107 Level 3 Blas routine.
109 -- Written on 8-February-1989. Jack Dongarra, Argonne National
111 Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical
112 Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms
113 Group Ltd.
114 -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA =
116 1. Ed Anderson, Cray Research Inc.
117BLAS routine November 2006 ZHERK(1)