| 1 | SUBROUTINE SSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) |
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| 2 | * .. Scalar Arguments .. |
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| 3 | REAL ALPHA,BETA |
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| 4 | INTEGER INCX,INCY,K,LDA,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 | REAL A(LDA,*),X(*),Y(*) |
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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 | * SSBMV performs the matrix-vector operation |
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| 15 | * |
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| 16 | * y := alpha*A*x + beta*y, |
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| 17 | * |
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| 18 | * where alpha and beta are scalars, x and y are n element vectors and |
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| 19 | * A is an n by n symmetric band matrix, with k super-diagonals. |
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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 band matrix A is being supplied as |
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| 27 | * 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 | * being supplied. |
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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 | * being supplied. |
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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 | * K - INTEGER. |
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| 43 | * On entry, K specifies the number of super-diagonals of the |
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| 44 | * matrix A. K must satisfy 0 .le. K. |
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| 45 | * Unchanged on exit. |
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| 46 | * |
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| 47 | * ALPHA - REAL . |
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| 48 | * On entry, ALPHA specifies the scalar alpha. |
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| 49 | * Unchanged on exit. |
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| 50 | * |
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| 51 | * A - REAL array of DIMENSION ( LDA, n ). |
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| 52 | * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) |
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| 53 | * by n part of the array A must contain the upper triangular |
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| 54 | * band part of the symmetric matrix, supplied column by |
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| 55 | * column, with the leading diagonal of the matrix in row |
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| 56 | * ( k + 1 ) of the array, the first super-diagonal starting at |
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| 57 | * position 2 in row k, and so on. The top left k by k triangle |
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| 58 | * of the array A is not referenced. |
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| 59 | * The following program segment will transfer the upper |
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| 60 | * triangular part of a symmetric band matrix from conventional |
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| 61 | * full matrix storage to band storage: |
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| 62 | * |
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| 63 | * DO 20, J = 1, N |
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| 64 | * M = K + 1 - J |
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| 65 | * DO 10, I = MAX( 1, J - K ), J |
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| 66 | * A( M + I, J ) = matrix( I, J ) |
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| 67 | * 10 CONTINUE |
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| 68 | * 20 CONTINUE |
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| 69 | * |
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| 70 | * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) |
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| 71 | * by n part of the array A must contain the lower triangular |
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| 72 | * band part of the symmetric matrix, supplied column by |
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| 73 | * column, with the leading diagonal of the matrix in row 1 of |
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| 74 | * the array, the first sub-diagonal starting at position 1 in |
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| 75 | * row 2, and so on. The bottom right k by k triangle of the |
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| 76 | * array A is not referenced. |
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| 77 | * The following program segment will transfer the lower |
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| 78 | * triangular part of a symmetric band matrix from conventional |
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| 79 | * full matrix storage to band storage: |
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| 80 | * |
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| 81 | * DO 20, J = 1, N |
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| 82 | * M = 1 - J |
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| 83 | * DO 10, I = J, MIN( N, J + K ) |
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| 84 | * A( M + I, J ) = matrix( I, J ) |
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| 85 | * 10 CONTINUE |
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| 86 | * 20 CONTINUE |
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| 87 | * |
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| 88 | * Unchanged on exit. |
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| 89 | * |
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| 90 | * LDA - INTEGER. |
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| 91 | * On entry, LDA specifies the first dimension of A as declared |
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| 92 | * in the calling (sub) program. LDA must be at least |
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| 93 | * ( k + 1 ). |
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| 94 | * Unchanged on exit. |
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| 95 | * |
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| 96 | * X - REAL array of DIMENSION at least |
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| 97 | * ( 1 + ( n - 1 )*abs( INCX ) ). |
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| 98 | * Before entry, the incremented array X must contain the |
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| 99 | * vector x. |
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| 100 | * Unchanged on exit. |
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| 101 | * |
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| 102 | * INCX - INTEGER. |
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| 103 | * On entry, INCX specifies the increment for the elements of |
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| 104 | * X. INCX must not be zero. |
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| 105 | * Unchanged on exit. |
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| 106 | * |
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| 107 | * BETA - REAL . |
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| 108 | * On entry, BETA specifies the scalar beta. |
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| 109 | * Unchanged on exit. |
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| 110 | * |
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| 111 | * Y - REAL array of DIMENSION at least |
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| 112 | * ( 1 + ( n - 1 )*abs( INCY ) ). |
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| 113 | * Before entry, the incremented array Y must contain the |
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| 114 | * vector y. On exit, Y is overwritten by the updated vector y. |
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| 115 | * |
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| 116 | * INCY - INTEGER. |
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| 117 | * On entry, INCY specifies the increment for the elements of |
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| 118 | * Y. INCY must not be zero. |
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| 119 | * Unchanged on exit. |
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| 120 | * |
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| 121 | * |
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| 122 | * Level 2 Blas routine. |
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| 123 | * |
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| 124 | * -- Written on 22-October-1986. |
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| 125 | * Jack Dongarra, Argonne National Lab. |
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| 126 | * Jeremy Du Croz, Nag Central Office. |
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| 127 | * Sven Hammarling, Nag Central Office. |
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| 128 | * Richard Hanson, Sandia National Labs. |
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| 129 | * |
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| 130 | * |
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| 131 | * .. Parameters .. |
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| 132 | REAL ONE,ZERO |
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| 133 | PARAMETER (ONE=1.0E+0,ZERO=0.0E+0) |
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| 134 | * .. |
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| 135 | * .. Local Scalars .. |
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| 136 | REAL TEMP1,TEMP2 |
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| 137 | INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L |
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| 138 | * .. |
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| 139 | * .. External Functions .. |
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| 140 | LOGICAL LSAME |
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| 141 | EXTERNAL LSAME |
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| 142 | * .. |
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| 143 | * .. External Subroutines .. |
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| 144 | EXTERNAL XERBLA |
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| 145 | * .. |
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| 146 | * .. Intrinsic Functions .. |
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| 147 | INTRINSIC MAX,MIN |
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| 148 | * .. |
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| 149 | * |
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| 150 | * Test the input parameters. |
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| 151 | * |
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| 152 | INFO = 0 |
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| 153 | IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN |
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| 154 | INFO = 1 |
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| 155 | ELSE IF (N.LT.0) THEN |
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| 156 | INFO = 2 |
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| 157 | ELSE IF (K.LT.0) THEN |
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| 158 | INFO = 3 |
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| 159 | ELSE IF (LDA.LT. (K+1)) THEN |
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| 160 | INFO = 6 |
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| 161 | ELSE IF (INCX.EQ.0) THEN |
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| 162 | INFO = 8 |
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| 163 | ELSE IF (INCY.EQ.0) THEN |
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| 164 | INFO = 11 |
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| 165 | END IF |
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| 166 | IF (INFO.NE.0) THEN |
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| 167 | CALL XERBLA('SSBMV ',INFO) |
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| 168 | RETURN |
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| 169 | END IF |
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| 170 | * |
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| 171 | * Quick return if possible. |
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| 172 | * |
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| 173 | IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN |
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| 174 | * |
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| 175 | * Set up the start points in X and Y. |
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| 176 | * |
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| 177 | IF (INCX.GT.0) THEN |
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| 178 | KX = 1 |
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| 179 | ELSE |
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| 180 | KX = 1 - (N-1)*INCX |
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| 181 | END IF |
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| 182 | IF (INCY.GT.0) THEN |
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| 183 | KY = 1 |
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| 184 | ELSE |
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| 185 | KY = 1 - (N-1)*INCY |
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| 186 | END IF |
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| 187 | * |
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| 188 | * Start the operations. In this version the elements of the array A |
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| 189 | * are accessed sequentially with one pass through A. |
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| 190 | * |
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| 191 | * First form y := beta*y. |
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| 192 | * |
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| 193 | IF (BETA.NE.ONE) THEN |
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| 194 | IF (INCY.EQ.1) THEN |
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| 195 | IF (BETA.EQ.ZERO) THEN |
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| 196 | DO 10 I = 1,N |
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| 197 | Y(I) = ZERO |
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| 198 | 10 CONTINUE |
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| 199 | ELSE |
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| 200 | DO 20 I = 1,N |
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| 201 | Y(I) = BETA*Y(I) |
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| 202 | 20 CONTINUE |
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| 203 | END IF |
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| 204 | ELSE |
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| 205 | IY = KY |
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| 206 | IF (BETA.EQ.ZERO) THEN |
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| 207 | DO 30 I = 1,N |
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| 208 | Y(IY) = ZERO |
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| 209 | IY = IY + INCY |
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| 210 | 30 CONTINUE |
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| 211 | ELSE |
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| 212 | DO 40 I = 1,N |
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| 213 | Y(IY) = BETA*Y(IY) |
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| 214 | IY = IY + INCY |
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| 215 | 40 CONTINUE |
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| 216 | END IF |
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| 217 | END IF |
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| 218 | END IF |
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| 219 | IF (ALPHA.EQ.ZERO) RETURN |
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| 220 | IF (LSAME(UPLO,'U')) THEN |
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| 221 | * |
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| 222 | * Form y when upper triangle of A is stored. |
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| 223 | * |
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| 224 | KPLUS1 = K + 1 |
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| 225 | IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN |
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| 226 | DO 60 J = 1,N |
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| 227 | TEMP1 = ALPHA*X(J) |
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| 228 | TEMP2 = ZERO |
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| 229 | L = KPLUS1 - J |
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| 230 | DO 50 I = MAX(1,J-K),J - 1 |
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| 231 | Y(I) = Y(I) + TEMP1*A(L+I,J) |
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| 232 | TEMP2 = TEMP2 + A(L+I,J)*X(I) |
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| 233 | 50 CONTINUE |
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| 234 | Y(J) = Y(J) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2 |
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| 235 | 60 CONTINUE |
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| 236 | ELSE |
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| 237 | JX = KX |
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| 238 | JY = KY |
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| 239 | DO 80 J = 1,N |
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| 240 | TEMP1 = ALPHA*X(JX) |
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| 241 | TEMP2 = ZERO |
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| 242 | IX = KX |
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| 243 | IY = KY |
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| 244 | L = KPLUS1 - J |
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| 245 | DO 70 I = MAX(1,J-K),J - 1 |
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| 246 | Y(IY) = Y(IY) + TEMP1*A(L+I,J) |
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| 247 | TEMP2 = TEMP2 + A(L+I,J)*X(IX) |
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| 248 | IX = IX + INCX |
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| 249 | IY = IY + INCY |
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| 250 | 70 CONTINUE |
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| 251 | Y(JY) = Y(JY) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2 |
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| 252 | JX = JX + INCX |
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| 253 | JY = JY + INCY |
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| 254 | IF (J.GT.K) THEN |
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| 255 | KX = KX + INCX |
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| 256 | KY = KY + INCY |
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| 257 | END IF |
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| 258 | 80 CONTINUE |
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| 259 | END IF |
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| 260 | ELSE |
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| 261 | * |
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| 262 | * Form y when lower triangle of A is stored. |
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| 263 | * |
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| 264 | IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN |
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| 265 | DO 100 J = 1,N |
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| 266 | TEMP1 = ALPHA*X(J) |
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| 267 | TEMP2 = ZERO |
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| 268 | Y(J) = Y(J) + TEMP1*A(1,J) |
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| 269 | L = 1 - J |
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| 270 | DO 90 I = J + 1,MIN(N,J+K) |
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| 271 | Y(I) = Y(I) + TEMP1*A(L+I,J) |
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| 272 | TEMP2 = TEMP2 + A(L+I,J)*X(I) |
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| 273 | 90 CONTINUE |
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| 274 | Y(J) = Y(J) + ALPHA*TEMP2 |
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| 275 | 100 CONTINUE |
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| 276 | ELSE |
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| 277 | JX = KX |
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| 278 | JY = KY |
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| 279 | DO 120 J = 1,N |
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| 280 | TEMP1 = ALPHA*X(JX) |
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| 281 | TEMP2 = ZERO |
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| 282 | Y(JY) = Y(JY) + TEMP1*A(1,J) |
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| 283 | L = 1 - J |
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| 284 | IX = JX |
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| 285 | IY = JY |
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| 286 | DO 110 I = J + 1,MIN(N,J+K) |
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| 287 | IX = IX + INCX |
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| 288 | IY = IY + INCY |
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| 289 | Y(IY) = Y(IY) + TEMP1*A(L+I,J) |
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| 290 | TEMP2 = TEMP2 + A(L+I,J)*X(IX) |
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| 291 | 110 CONTINUE |
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| 292 | Y(JY) = Y(JY) + ALPHA*TEMP2 |
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| 293 | JX = JX + INCX |
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| 294 | JY = JY + INCY |
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| 295 | 120 CONTINUE |
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| 296 | END IF |
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| 297 | END IF |
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| 298 | * |
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| 299 | RETURN |
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| 300 | * |
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| 301 | * End of SSBMV . |
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| 302 | * |
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| 303 | END |
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