| 1 | SUBROUTINE CHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) |
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| 2 | * .. Scalar Arguments .. |
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| 3 | COMPLEX ALPHA |
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| 4 | REAL BETA |
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| 5 | INTEGER K,LDA,LDB,LDC,N |
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| 6 | CHARACTER TRANS,UPLO |
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| 7 | * .. |
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| 8 | * .. Array Arguments .. |
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| 9 | COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) |
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| 10 | * .. |
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| 11 | * |
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| 12 | * Purpose |
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| 13 | * ======= |
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| 14 | * |
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| 15 | * CHER2K performs one of the hermitian rank 2k operations |
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| 16 | * |
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| 17 | * C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C, |
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| 18 | * |
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| 19 | * or |
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| 20 | * |
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| 21 | * C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C, |
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| 22 | * |
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| 23 | * where alpha and beta are scalars with beta real, C is an n by n |
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| 24 | * hermitian matrix and A and B are n by k matrices in the first case |
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| 25 | * and k by n matrices in the second case. |
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| 26 | * |
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| 27 | * Arguments |
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| 28 | * ========== |
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| 29 | * |
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| 30 | * UPLO - CHARACTER*1. |
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| 31 | * On entry, UPLO specifies whether the upper or lower |
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| 32 | * triangular part of the array C is to be referenced as |
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| 33 | * follows: |
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| 34 | * |
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| 35 | * UPLO = 'U' or 'u' Only the upper triangular part of C |
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| 36 | * is to be referenced. |
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| 37 | * |
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| 38 | * UPLO = 'L' or 'l' Only the lower triangular part of C |
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| 39 | * is to be referenced. |
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| 40 | * |
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| 41 | * Unchanged on exit. |
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| 42 | * |
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| 43 | * TRANS - CHARACTER*1. |
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| 44 | * On entry, TRANS specifies the operation to be performed as |
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| 45 | * follows: |
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| 46 | * |
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| 47 | * TRANS = 'N' or 'n' C := alpha*A*conjg( B' ) + |
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| 48 | * conjg( alpha )*B*conjg( A' ) + |
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| 49 | * beta*C. |
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| 50 | * |
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| 51 | * TRANS = 'C' or 'c' C := alpha*conjg( A' )*B + |
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| 52 | * conjg( alpha )*conjg( B' )*A + |
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| 53 | * beta*C. |
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| 54 | * |
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| 55 | * Unchanged on exit. |
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| 56 | * |
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| 57 | * N - INTEGER. |
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| 58 | * On entry, N specifies the order of the matrix C. N must be |
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| 59 | * at least zero. |
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| 60 | * Unchanged on exit. |
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| 61 | * |
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| 62 | * K - INTEGER. |
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| 63 | * On entry with TRANS = 'N' or 'n', K specifies the number |
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| 64 | * of columns of the matrices A and B, and on entry with |
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| 65 | * TRANS = 'C' or 'c', K specifies the number of rows of the |
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| 66 | * matrices A and B. K must be at least zero. |
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| 67 | * Unchanged on exit. |
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| 68 | * |
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| 69 | * ALPHA - COMPLEX . |
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| 70 | * On entry, ALPHA specifies the scalar alpha. |
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| 71 | * Unchanged on exit. |
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| 72 | * |
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| 73 | * A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is |
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| 74 | * k when TRANS = 'N' or 'n', and is n otherwise. |
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| 75 | * Before entry with TRANS = 'N' or 'n', the leading n by k |
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| 76 | * part of the array A must contain the matrix A, otherwise |
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| 77 | * the leading k by n part of the array A must contain the |
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| 78 | * matrix A. |
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| 79 | * Unchanged on exit. |
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| 80 | * |
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| 81 | * LDA - INTEGER. |
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| 82 | * On entry, LDA specifies the first dimension of A as declared |
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| 83 | * in the calling (sub) program. When TRANS = 'N' or 'n' |
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| 84 | * then LDA must be at least max( 1, n ), otherwise LDA must |
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| 85 | * be at least max( 1, k ). |
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| 86 | * Unchanged on exit. |
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| 87 | * |
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| 88 | * B - COMPLEX array of DIMENSION ( LDB, kb ), where kb is |
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| 89 | * k when TRANS = 'N' or 'n', and is n otherwise. |
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| 90 | * Before entry with TRANS = 'N' or 'n', the leading n by k |
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| 91 | * part of the array B must contain the matrix B, otherwise |
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| 92 | * the leading k by n part of the array B must contain the |
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| 93 | * matrix B. |
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| 94 | * Unchanged on exit. |
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| 95 | * |
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| 96 | * LDB - INTEGER. |
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| 97 | * On entry, LDB specifies the first dimension of B as declared |
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| 98 | * in the calling (sub) program. When TRANS = 'N' or 'n' |
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| 99 | * then LDB must be at least max( 1, n ), otherwise LDB must |
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| 100 | * be at least max( 1, k ). |
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| 101 | * Unchanged on exit. |
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| 102 | * |
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| 103 | * BETA - REAL . |
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| 104 | * On entry, BETA specifies the scalar beta. |
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| 105 | * Unchanged on exit. |
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| 106 | * |
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| 107 | * C - COMPLEX array of DIMENSION ( LDC, n ). |
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| 108 | * Before entry with UPLO = 'U' or 'u', the leading n by n |
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| 109 | * upper triangular part of the array C must contain the upper |
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| 110 | * triangular part of the hermitian matrix and the strictly |
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| 111 | * lower triangular part of C is not referenced. On exit, the |
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| 112 | * upper triangular part of the array C is overwritten by the |
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| 113 | * upper triangular part of the updated matrix. |
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| 114 | * Before entry with UPLO = 'L' or 'l', the leading n by n |
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| 115 | * lower triangular part of the array C must contain the lower |
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| 116 | * triangular part of the hermitian matrix and the strictly |
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| 117 | * upper triangular part of C is not referenced. On exit, the |
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| 118 | * lower triangular part of the array C is overwritten by the |
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| 119 | * lower triangular part of the updated matrix. |
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| 120 | * Note that the imaginary parts of the diagonal elements need |
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| 121 | * not be set, they are assumed to be zero, and on exit they |
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| 122 | * are set to zero. |
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| 123 | * |
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| 124 | * LDC - INTEGER. |
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| 125 | * On entry, LDC specifies the first dimension of C as declared |
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| 126 | * in the calling (sub) program. LDC must be at least |
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| 127 | * max( 1, n ). |
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| 128 | * Unchanged on exit. |
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| 129 | * |
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| 130 | * |
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| 131 | * Level 3 Blas routine. |
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| 132 | * |
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| 133 | * -- Written on 8-February-1989. |
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| 134 | * Jack Dongarra, Argonne National Laboratory. |
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| 135 | * Iain Duff, AERE Harwell. |
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| 136 | * Jeremy Du Croz, Numerical Algorithms Group Ltd. |
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| 137 | * Sven Hammarling, Numerical Algorithms Group Ltd. |
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| 138 | * |
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| 139 | * -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1. |
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| 140 | * Ed Anderson, Cray Research Inc. |
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| 141 | * |
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| 142 | * |
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| 143 | * .. External Functions .. |
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| 144 | LOGICAL LSAME |
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| 145 | EXTERNAL LSAME |
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| 146 | * .. |
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| 147 | * .. External Subroutines .. |
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| 148 | EXTERNAL XERBLA |
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| 149 | * .. |
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| 150 | * .. Intrinsic Functions .. |
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| 151 | INTRINSIC CONJG,MAX,REAL |
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| 152 | * .. |
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| 153 | * .. Local Scalars .. |
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| 154 | COMPLEX TEMP1,TEMP2 |
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| 155 | INTEGER I,INFO,J,L,NROWA |
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| 156 | LOGICAL UPPER |
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| 157 | * .. |
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| 158 | * .. Parameters .. |
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| 159 | REAL ONE |
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| 160 | PARAMETER (ONE=1.0E+0) |
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| 161 | COMPLEX ZERO |
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| 162 | PARAMETER (ZERO= (0.0E+0,0.0E+0)) |
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| 163 | * .. |
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| 164 | * |
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| 165 | * Test the input parameters. |
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| 166 | * |
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| 167 | IF (LSAME(TRANS,'N')) THEN |
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| 168 | NROWA = N |
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| 169 | ELSE |
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| 170 | NROWA = K |
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| 171 | END IF |
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| 172 | UPPER = LSAME(UPLO,'U') |
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| 173 | * |
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| 174 | INFO = 0 |
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| 175 | IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN |
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| 176 | INFO = 1 |
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| 177 | ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND. |
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| 178 | + (.NOT.LSAME(TRANS,'C'))) THEN |
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| 179 | INFO = 2 |
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| 180 | ELSE IF (N.LT.0) THEN |
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| 181 | INFO = 3 |
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| 182 | ELSE IF (K.LT.0) THEN |
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| 183 | INFO = 4 |
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| 184 | ELSE IF (LDA.LT.MAX(1,NROWA)) THEN |
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| 185 | INFO = 7 |
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| 186 | ELSE IF (LDB.LT.MAX(1,NROWA)) THEN |
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| 187 | INFO = 9 |
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| 188 | ELSE IF (LDC.LT.MAX(1,N)) THEN |
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| 189 | INFO = 12 |
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| 190 | END IF |
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| 191 | IF (INFO.NE.0) THEN |
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| 192 | CALL XERBLA('CHER2K',INFO) |
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| 193 | RETURN |
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| 194 | END IF |
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| 195 | * |
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| 196 | * Quick return if possible. |
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| 197 | * |
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| 198 | IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR. |
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| 199 | + (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN |
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| 200 | * |
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| 201 | * And when alpha.eq.zero. |
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| 202 | * |
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| 203 | IF (ALPHA.EQ.ZERO) THEN |
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| 204 | IF (UPPER) THEN |
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| 205 | IF (BETA.EQ.REAL(ZERO)) THEN |
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| 206 | DO 20 J = 1,N |
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| 207 | DO 10 I = 1,J |
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| 208 | C(I,J) = ZERO |
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| 209 | 10 CONTINUE |
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| 210 | 20 CONTINUE |
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| 211 | ELSE |
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| 212 | DO 40 J = 1,N |
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| 213 | DO 30 I = 1,J - 1 |
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| 214 | C(I,J) = BETA*C(I,J) |
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| 215 | 30 CONTINUE |
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| 216 | C(J,J) = BETA*REAL(C(J,J)) |
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| 217 | 40 CONTINUE |
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| 218 | END IF |
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| 219 | ELSE |
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| 220 | IF (BETA.EQ.REAL(ZERO)) THEN |
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| 221 | DO 60 J = 1,N |
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| 222 | DO 50 I = J,N |
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| 223 | C(I,J) = ZERO |
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| 224 | 50 CONTINUE |
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| 225 | 60 CONTINUE |
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| 226 | ELSE |
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| 227 | DO 80 J = 1,N |
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| 228 | C(J,J) = BETA*REAL(C(J,J)) |
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| 229 | DO 70 I = J + 1,N |
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| 230 | C(I,J) = BETA*C(I,J) |
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| 231 | 70 CONTINUE |
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| 232 | 80 CONTINUE |
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| 233 | END IF |
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| 234 | END IF |
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| 235 | RETURN |
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| 236 | END IF |
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| 237 | * |
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| 238 | * Start the operations. |
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| 239 | * |
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| 240 | IF (LSAME(TRANS,'N')) THEN |
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| 241 | * |
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| 242 | * Form C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + |
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| 243 | * C. |
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| 244 | * |
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| 245 | IF (UPPER) THEN |
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| 246 | DO 130 J = 1,N |
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| 247 | IF (BETA.EQ.REAL(ZERO)) THEN |
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| 248 | DO 90 I = 1,J |
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| 249 | C(I,J) = ZERO |
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| 250 | 90 CONTINUE |
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| 251 | ELSE IF (BETA.NE.ONE) THEN |
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| 252 | DO 100 I = 1,J - 1 |
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| 253 | C(I,J) = BETA*C(I,J) |
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| 254 | 100 CONTINUE |
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| 255 | C(J,J) = BETA*REAL(C(J,J)) |
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| 256 | ELSE |
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| 257 | C(J,J) = REAL(C(J,J)) |
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| 258 | END IF |
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| 259 | DO 120 L = 1,K |
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| 260 | IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN |
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| 261 | TEMP1 = ALPHA*CONJG(B(J,L)) |
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| 262 | TEMP2 = CONJG(ALPHA*A(J,L)) |
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| 263 | DO 110 I = 1,J - 1 |
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| 264 | C(I,J) = C(I,J) + A(I,L)*TEMP1 + |
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| 265 | + B(I,L)*TEMP2 |
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| 266 | 110 CONTINUE |
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| 267 | C(J,J) = REAL(C(J,J)) + |
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| 268 | + REAL(A(J,L)*TEMP1+B(J,L)*TEMP2) |
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| 269 | END IF |
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| 270 | 120 CONTINUE |
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| 271 | 130 CONTINUE |
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| 272 | ELSE |
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| 273 | DO 180 J = 1,N |
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| 274 | IF (BETA.EQ.REAL(ZERO)) THEN |
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| 275 | DO 140 I = J,N |
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| 276 | C(I,J) = ZERO |
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| 277 | 140 CONTINUE |
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| 278 | ELSE IF (BETA.NE.ONE) THEN |
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| 279 | DO 150 I = J + 1,N |
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| 280 | C(I,J) = BETA*C(I,J) |
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| 281 | 150 CONTINUE |
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| 282 | C(J,J) = BETA*REAL(C(J,J)) |
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| 283 | ELSE |
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| 284 | C(J,J) = REAL(C(J,J)) |
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| 285 | END IF |
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| 286 | DO 170 L = 1,K |
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| 287 | IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN |
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| 288 | TEMP1 = ALPHA*CONJG(B(J,L)) |
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| 289 | TEMP2 = CONJG(ALPHA*A(J,L)) |
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| 290 | DO 160 I = J + 1,N |
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| 291 | C(I,J) = C(I,J) + A(I,L)*TEMP1 + |
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| 292 | + B(I,L)*TEMP2 |
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| 293 | 160 CONTINUE |
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| 294 | C(J,J) = REAL(C(J,J)) + |
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| 295 | + REAL(A(J,L)*TEMP1+B(J,L)*TEMP2) |
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| 296 | END IF |
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| 297 | 170 CONTINUE |
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| 298 | 180 CONTINUE |
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| 299 | END IF |
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| 300 | ELSE |
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| 301 | * |
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| 302 | * Form C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + |
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| 303 | * C. |
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| 304 | * |
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| 305 | IF (UPPER) THEN |
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| 306 | DO 210 J = 1,N |
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| 307 | DO 200 I = 1,J |
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| 308 | TEMP1 = ZERO |
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| 309 | TEMP2 = ZERO |
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| 310 | DO 190 L = 1,K |
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| 311 | TEMP1 = TEMP1 + CONJG(A(L,I))*B(L,J) |
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| 312 | TEMP2 = TEMP2 + CONJG(B(L,I))*A(L,J) |
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| 313 | 190 CONTINUE |
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| 314 | IF (I.EQ.J) THEN |
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| 315 | IF (BETA.EQ.REAL(ZERO)) THEN |
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| 316 | C(J,J) = REAL(ALPHA*TEMP1+ |
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| 317 | + CONJG(ALPHA)*TEMP2) |
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| 318 | ELSE |
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| 319 | C(J,J) = BETA*REAL(C(J,J)) + |
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| 320 | + REAL(ALPHA*TEMP1+ |
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| 321 | + CONJG(ALPHA)*TEMP2) |
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| 322 | END IF |
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| 323 | ELSE |
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| 324 | IF (BETA.EQ.REAL(ZERO)) THEN |
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| 325 | C(I,J) = ALPHA*TEMP1 + CONJG(ALPHA)*TEMP2 |
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| 326 | ELSE |
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| 327 | C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 + |
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| 328 | + CONJG(ALPHA)*TEMP2 |
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| 329 | END IF |
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| 330 | END IF |
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| 331 | 200 CONTINUE |
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| 332 | 210 CONTINUE |
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| 333 | ELSE |
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| 334 | DO 240 J = 1,N |
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| 335 | DO 230 I = J,N |
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| 336 | TEMP1 = ZERO |
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| 337 | TEMP2 = ZERO |
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| 338 | DO 220 L = 1,K |
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| 339 | TEMP1 = TEMP1 + CONJG(A(L,I))*B(L,J) |
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| 340 | TEMP2 = TEMP2 + CONJG(B(L,I))*A(L,J) |
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| 341 | 220 CONTINUE |
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| 342 | IF (I.EQ.J) THEN |
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| 343 | IF (BETA.EQ.REAL(ZERO)) THEN |
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| 344 | C(J,J) = REAL(ALPHA*TEMP1+ |
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| 345 | + CONJG(ALPHA)*TEMP2) |
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| 346 | ELSE |
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| 347 | C(J,J) = BETA*REAL(C(J,J)) + |
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| 348 | + REAL(ALPHA*TEMP1+ |
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| 349 | + CONJG(ALPHA)*TEMP2) |
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| 350 | END IF |
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| 351 | ELSE |
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| 352 | IF (BETA.EQ.REAL(ZERO)) THEN |
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| 353 | C(I,J) = ALPHA*TEMP1 + CONJG(ALPHA)*TEMP2 |
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| 354 | ELSE |
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| 355 | C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 + |
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| 356 | + CONJG(ALPHA)*TEMP2 |
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| 357 | END IF |
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| 358 | END IF |
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| 359 | 230 CONTINUE |
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| 360 | 240 CONTINUE |
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| 361 | END IF |
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| 362 | END IF |
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| 363 | * |
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| 364 | RETURN |
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| 365 | * |
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| 366 | * End of CHER2K. |
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| 367 | * |
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| 368 | END |
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