| 1 | SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP) |
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| 2 | * .. Scalar Arguments .. |
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| 3 | REAL ALPHA |
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| 4 | INTEGER INCX,N |
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| 5 | CHARACTER UPLO |
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| 6 | * .. |
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| 7 | * .. Array Arguments .. |
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| 8 | COMPLEX AP(*),X(*) |
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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 | * CHPR performs the hermitian rank 1 operation |
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| 15 | * |
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| 16 | * A := alpha*x*conjg( x' ) + A, |
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| 17 | * |
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| 18 | * where alpha is a real scalar, x is an n element vector and A is an |
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| 19 | * n by n hermitian matrix, supplied in packed form. |
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| 20 | * |
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| 21 | * Arguments |
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| 22 | * ========== |
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| 23 | * |
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| 24 | * UPLO - CHARACTER*1. |
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| 25 | * On entry, UPLO specifies whether the upper or lower |
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| 26 | * triangular part of the matrix A is supplied in the packed |
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| 27 | * array AP as follows: |
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| 28 | * |
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| 29 | * UPLO = 'U' or 'u' The upper triangular part of A is |
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| 30 | * supplied in AP. |
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| 31 | * |
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| 32 | * UPLO = 'L' or 'l' The lower triangular part of A is |
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| 33 | * supplied in AP. |
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| 34 | * |
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| 35 | * Unchanged on exit. |
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| 36 | * |
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| 37 | * N - INTEGER. |
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| 38 | * On entry, N specifies the order of the matrix A. |
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| 39 | * N must be at least zero. |
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| 40 | * Unchanged on exit. |
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| 41 | * |
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| 42 | * ALPHA - REAL . |
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| 43 | * On entry, ALPHA specifies the scalar alpha. |
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| 44 | * Unchanged on exit. |
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| 45 | * |
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| 46 | * X - COMPLEX array of dimension at least |
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| 47 | * ( 1 + ( n - 1 )*abs( INCX ) ). |
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| 48 | * Before entry, the incremented array X must contain the n |
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| 49 | * element vector x. |
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| 50 | * Unchanged on exit. |
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| 51 | * |
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| 52 | * INCX - INTEGER. |
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| 53 | * On entry, INCX specifies the increment for the elements of |
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| 54 | * X. INCX must not be zero. |
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| 55 | * Unchanged on exit. |
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| 56 | * |
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| 57 | * AP - COMPLEX array of DIMENSION at least |
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| 58 | * ( ( n*( n + 1 ) )/2 ). |
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| 59 | * Before entry with UPLO = 'U' or 'u', the array AP must |
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| 60 | * contain the upper triangular part of the hermitian matrix |
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| 61 | * packed sequentially, column by column, so that AP( 1 ) |
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| 62 | * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) |
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| 63 | * and a( 2, 2 ) respectively, and so on. On exit, the array |
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| 64 | * AP is overwritten by the upper triangular part of the |
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| 65 | * updated matrix. |
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| 66 | * Before entry with UPLO = 'L' or 'l', the array AP must |
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| 67 | * contain the lower triangular part of the hermitian matrix |
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| 68 | * packed sequentially, column by column, so that AP( 1 ) |
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| 69 | * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) |
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| 70 | * and a( 3, 1 ) respectively, and so on. On exit, the array |
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| 71 | * AP is overwritten by the lower triangular part of the |
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| 72 | * updated matrix. |
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| 73 | * Note that the imaginary parts of the diagonal elements need |
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| 74 | * not be set, they are assumed to be zero, and on exit they |
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| 75 | * are set to zero. |
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| 76 | * |
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| 77 | * |
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| 78 | * Level 2 Blas routine. |
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| 79 | * |
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| 80 | * -- Written on 22-October-1986. |
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| 81 | * Jack Dongarra, Argonne National Lab. |
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| 82 | * Jeremy Du Croz, Nag Central Office. |
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| 83 | * Sven Hammarling, Nag Central Office. |
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| 84 | * Richard Hanson, Sandia National Labs. |
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| 85 | * |
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| 86 | * |
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| 87 | * .. Parameters .. |
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| 88 | COMPLEX ZERO |
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| 89 | PARAMETER (ZERO= (0.0E+0,0.0E+0)) |
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| 90 | * .. |
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| 91 | * .. Local Scalars .. |
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| 92 | COMPLEX TEMP |
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| 93 | INTEGER I,INFO,IX,J,JX,K,KK,KX |
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| 94 | * .. |
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| 95 | * .. External Functions .. |
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| 96 | LOGICAL LSAME |
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| 97 | EXTERNAL LSAME |
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| 98 | * .. |
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| 99 | * .. External Subroutines .. |
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| 100 | EXTERNAL XERBLA |
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| 101 | * .. |
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| 102 | * .. Intrinsic Functions .. |
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| 103 | INTRINSIC CONJG,REAL |
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| 104 | * .. |
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| 105 | * |
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| 106 | * Test the input parameters. |
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| 107 | * |
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| 108 | INFO = 0 |
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| 109 | IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN |
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| 110 | INFO = 1 |
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| 111 | ELSE IF (N.LT.0) THEN |
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| 112 | INFO = 2 |
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| 113 | ELSE IF (INCX.EQ.0) THEN |
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| 114 | INFO = 5 |
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| 115 | END IF |
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| 116 | IF (INFO.NE.0) THEN |
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| 117 | CALL XERBLA('CHPR ',INFO) |
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| 118 | RETURN |
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| 119 | END IF |
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| 120 | * |
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| 121 | * Quick return if possible. |
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| 122 | * |
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| 123 | IF ((N.EQ.0) .OR. (ALPHA.EQ.REAL(ZERO))) RETURN |
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| 124 | * |
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| 125 | * Set the start point in X if the increment is not unity. |
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| 126 | * |
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| 127 | IF (INCX.LE.0) THEN |
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| 128 | KX = 1 - (N-1)*INCX |
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| 129 | ELSE IF (INCX.NE.1) THEN |
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| 130 | KX = 1 |
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| 131 | END IF |
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| 132 | * |
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| 133 | * Start the operations. In this version the elements of the array AP |
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| 134 | * are accessed sequentially with one pass through AP. |
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| 135 | * |
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| 136 | KK = 1 |
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| 137 | IF (LSAME(UPLO,'U')) THEN |
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| 138 | * |
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| 139 | * Form A when upper triangle is stored in AP. |
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| 140 | * |
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| 141 | IF (INCX.EQ.1) THEN |
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| 142 | DO 20 J = 1,N |
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| 143 | IF (X(J).NE.ZERO) THEN |
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| 144 | TEMP = ALPHA*CONJG(X(J)) |
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| 145 | K = KK |
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| 146 | DO 10 I = 1,J - 1 |
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| 147 | AP(K) = AP(K) + X(I)*TEMP |
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| 148 | K = K + 1 |
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| 149 | 10 CONTINUE |
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| 150 | AP(KK+J-1) = REAL(AP(KK+J-1)) + REAL(X(J)*TEMP) |
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| 151 | ELSE |
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| 152 | AP(KK+J-1) = REAL(AP(KK+J-1)) |
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| 153 | END IF |
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| 154 | KK = KK + J |
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| 155 | 20 CONTINUE |
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| 156 | ELSE |
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| 157 | JX = KX |
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| 158 | DO 40 J = 1,N |
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| 159 | IF (X(JX).NE.ZERO) THEN |
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| 160 | TEMP = ALPHA*CONJG(X(JX)) |
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| 161 | IX = KX |
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| 162 | DO 30 K = KK,KK + J - 2 |
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| 163 | AP(K) = AP(K) + X(IX)*TEMP |
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| 164 | IX = IX + INCX |
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| 165 | 30 CONTINUE |
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| 166 | AP(KK+J-1) = REAL(AP(KK+J-1)) + REAL(X(JX)*TEMP) |
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| 167 | ELSE |
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| 168 | AP(KK+J-1) = REAL(AP(KK+J-1)) |
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| 169 | END IF |
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| 170 | JX = JX + INCX |
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| 171 | KK = KK + J |
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| 172 | 40 CONTINUE |
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| 173 | END IF |
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| 174 | ELSE |
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| 175 | * |
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| 176 | * Form A when lower triangle is stored in AP. |
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| 177 | * |
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| 178 | IF (INCX.EQ.1) THEN |
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| 179 | DO 60 J = 1,N |
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| 180 | IF (X(J).NE.ZERO) THEN |
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| 181 | TEMP = ALPHA*CONJG(X(J)) |
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| 182 | AP(KK) = REAL(AP(KK)) + REAL(TEMP*X(J)) |
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| 183 | K = KK + 1 |
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| 184 | DO 50 I = J + 1,N |
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| 185 | AP(K) = AP(K) + X(I)*TEMP |
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| 186 | K = K + 1 |
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| 187 | 50 CONTINUE |
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| 188 | ELSE |
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| 189 | AP(KK) = REAL(AP(KK)) |
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| 190 | END IF |
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| 191 | KK = KK + N - J + 1 |
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| 192 | 60 CONTINUE |
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| 193 | ELSE |
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| 194 | JX = KX |
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| 195 | DO 80 J = 1,N |
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| 196 | IF (X(JX).NE.ZERO) THEN |
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| 197 | TEMP = ALPHA*CONJG(X(JX)) |
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| 198 | AP(KK) = REAL(AP(KK)) + REAL(TEMP*X(JX)) |
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| 199 | IX = JX |
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| 200 | DO 70 K = KK + 1,KK + N - J |
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| 201 | IX = IX + INCX |
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| 202 | AP(K) = AP(K) + X(IX)*TEMP |
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| 203 | 70 CONTINUE |
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| 204 | ELSE |
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| 205 | AP(KK) = REAL(AP(KK)) |
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| 206 | END IF |
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| 207 | JX = JX + INCX |
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| 208 | KK = KK + N - J + 1 |
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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 | * |
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| 213 | RETURN |
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| 214 | * |
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| 215 | * End of CHPR . |
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| 216 | * |
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| 217 | END |
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