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