| 1 | SUBROUTINE DTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
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| 2 | * .. Scalar Arguments ..
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| 3 | INTEGER INCX,K,LDA,N
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| 4 | CHARACTER DIAG,TRANS,UPLO
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| 5 | * ..
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| 6 | * .. Array Arguments ..
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| 7 | DOUBLE PRECISION A(LDA,*),X(*)
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| 8 | * ..
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| 9 | *
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| 10 | * Purpose
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| 11 | * =======
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| 12 | *
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| 13 | * DTBMV performs one of the matrix-vector operations
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| 14 | *
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| 15 | * x := A*x, or x := A'*x,
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| 16 | *
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| 17 | * where x is an n element vector and A is an n by n unit, or non-unit,
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| 18 | * upper or lower triangular band matrix, with ( k + 1 ) diagonals.
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| 19 | *
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| 20 | * Arguments
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| 21 | * ==========
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| 22 | *
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| 23 | * UPLO - CHARACTER*1.
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| 24 | * On entry, UPLO specifies whether the matrix is an upper or
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| 25 | * lower triangular matrix as follows:
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| 26 | *
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| 27 | * UPLO = 'U' or 'u' A is an upper triangular matrix.
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| 28 | *
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| 29 | * UPLO = 'L' or 'l' A is a lower triangular matrix.
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| 30 | *
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| 31 | * Unchanged on exit.
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| 32 | *
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| 33 | * TRANS - CHARACTER*1.
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| 34 | * On entry, TRANS specifies the operation to be performed as
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| 35 | * follows:
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| 36 | *
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| 37 | * TRANS = 'N' or 'n' x := A*x.
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| 38 | *
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| 39 | * TRANS = 'T' or 't' x := A'*x.
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| 40 | *
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| 41 | * TRANS = 'C' or 'c' x := A'*x.
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| 42 | *
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| 43 | * Unchanged on exit.
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| 44 | *
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| 45 | * DIAG - CHARACTER*1.
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| 46 | * On entry, DIAG specifies whether or not A is unit
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| 47 | * triangular as follows:
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| 48 | *
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| 49 | * DIAG = 'U' or 'u' A is assumed to be unit triangular.
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| 50 | *
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| 51 | * DIAG = 'N' or 'n' A is not assumed to be unit
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| 52 | * triangular.
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| 53 | *
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| 54 | * Unchanged on exit.
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| 55 | *
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| 56 | * N - INTEGER.
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| 57 | * On entry, N specifies the order of the matrix A.
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| 58 | * N must be at least zero.
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| 59 | * Unchanged on exit.
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| 60 | *
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| 61 | * K - INTEGER.
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| 62 | * On entry with UPLO = 'U' or 'u', K specifies the number of
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| 63 | * super-diagonals of the matrix A.
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| 64 | * On entry with UPLO = 'L' or 'l', K specifies the number of
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| 65 | * sub-diagonals of the matrix A.
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| 66 | * K must satisfy 0 .le. K.
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| 67 | * Unchanged on exit.
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| 68 | *
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| 69 | * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
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| 70 | * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
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| 71 | * by n part of the array A must contain the upper triangular
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| 72 | * band part of the matrix of coefficients, supplied column by
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| 73 | * column, with the leading diagonal of the matrix in row
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| 74 | * ( k + 1 ) of the array, the first super-diagonal starting at
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| 75 | * position 2 in row k, and so on. The top left k by k triangle
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| 76 | * of the array A is not referenced.
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| 77 | * The following program segment will transfer an upper
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| 78 | * triangular band matrix from conventional full matrix storage
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| 79 | * to band storage:
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| 80 | *
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| 81 | * DO 20, J = 1, N
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| 82 | * M = K + 1 - J
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| 83 | * DO 10, I = MAX( 1, J - K ), J
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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 | * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
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| 89 | * by n part of the array A must contain the lower triangular
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| 90 | * band part of the matrix of coefficients, supplied column by
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| 91 | * column, with the leading diagonal of the matrix in row 1 of
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| 92 | * the array, the first sub-diagonal starting at position 1 in
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| 93 | * row 2, and so on. The bottom right k by k triangle of the
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| 94 | * array A is not referenced.
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| 95 | * The following program segment will transfer a lower
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| 96 | * triangular band matrix from conventional full matrix storage
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| 97 | * to band storage:
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| 98 | *
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| 99 | * DO 20, J = 1, N
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| 100 | * M = 1 - J
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| 101 | * DO 10, I = J, MIN( N, J + K )
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| 102 | * A( M + I, J ) = matrix( I, J )
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| 103 | * 10 CONTINUE
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| 104 | * 20 CONTINUE
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| 105 | *
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| 106 | * Note that when DIAG = 'U' or 'u' the elements of the array A
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| 107 | * corresponding to the diagonal elements of the matrix are not
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| 108 | * referenced, but are assumed to be unity.
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| 109 | * Unchanged on exit.
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| 110 | *
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| 111 | * LDA - INTEGER.
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| 112 | * On entry, LDA specifies the first dimension of A as declared
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| 113 | * in the calling (sub) program. LDA must be at least
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| 114 | * ( k + 1 ).
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| 115 | * Unchanged on exit.
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| 116 | *
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| 117 | * X - DOUBLE PRECISION array of dimension at least
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| 118 | * ( 1 + ( n - 1 )*abs( INCX ) ).
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| 119 | * Before entry, the incremented array X must contain the n
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| 120 | * element vector x. On exit, X is overwritten with the
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| 121 | * tranformed vector x.
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| 122 | *
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| 123 | * INCX - INTEGER.
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| 124 | * On entry, INCX specifies the increment for the elements of
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| 125 | * X. INCX must not be zero.
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| 126 | * Unchanged on exit.
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| 127 | *
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| 128 | * Further Details
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| 129 | * ===============
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| 130 | *
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| 131 | * Level 2 Blas routine.
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| 132 | *
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| 133 | * -- Written on 22-October-1986.
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| 134 | * Jack Dongarra, Argonne National Lab.
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| 135 | * Jeremy Du Croz, Nag Central Office.
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| 136 | * Sven Hammarling, Nag Central Office.
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| 137 | * Richard Hanson, Sandia National Labs.
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| 138 | *
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| 139 | * =====================================================================
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| 140 | *
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| 141 | * .. Parameters ..
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| 142 | DOUBLE PRECISION ZERO
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| 143 | PARAMETER (ZERO=0.0D+0)
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| 144 | * ..
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| 145 | * .. Local Scalars ..
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| 146 | DOUBLE PRECISION TEMP
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| 147 | INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
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| 148 | LOGICAL NOUNIT
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| 149 | * ..
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| 150 | * .. External Functions ..
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| 151 | LOGICAL LSAME
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| 152 | EXTERNAL LSAME
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| 153 | * ..
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| 154 | * .. External Subroutines ..
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| 155 | EXTERNAL XERBLA
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| 156 | * ..
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| 157 | * .. Intrinsic Functions ..
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| 158 | INTRINSIC MAX,MIN
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| 159 | * ..
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| 160 | *
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| 161 | * Test the input parameters.
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| 162 | *
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| 163 | INFO = 0
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| 164 | IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
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| 165 | INFO = 1
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| 166 | ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
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| 167 | + .NOT.LSAME(TRANS,'C')) THEN
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| 168 | INFO = 2
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| 169 | ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
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| 170 | INFO = 3
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| 171 | ELSE IF (N.LT.0) THEN
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| 172 | INFO = 4
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| 173 | ELSE IF (K.LT.0) THEN
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| 174 | INFO = 5
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| 175 | ELSE IF (LDA.LT. (K+1)) THEN
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| 176 | INFO = 7
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| 177 | ELSE IF (INCX.EQ.0) THEN
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| 178 | INFO = 9
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| 179 | END IF
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| 180 | IF (INFO.NE.0) THEN
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| 181 | CALL XERBLA('DTBMV ',INFO)
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| 182 | RETURN
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| 183 | END IF
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| 184 | *
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| 185 | * Quick return if possible.
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| 186 | *
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| 187 | IF (N.EQ.0) RETURN
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| 188 | *
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| 189 | NOUNIT = LSAME(DIAG,'N')
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| 190 | *
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| 191 | * Set up the start point in X if the increment is not unity. This
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| 192 | * will be ( N - 1 )*INCX too small for descending loops.
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| 193 | *
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| 194 | IF (INCX.LE.0) THEN
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| 195 | KX = 1 - (N-1)*INCX
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| 196 | ELSE IF (INCX.NE.1) THEN
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| 197 | KX = 1
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| 198 | END IF
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| 199 | *
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| 200 | * Start the operations. In this version the elements of A are
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| 201 | * accessed sequentially with one pass through A.
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| 202 | *
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| 203 | IF (LSAME(TRANS,'N')) THEN
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| 204 | *
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| 205 | * Form x := A*x.
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| 206 | *
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| 207 | IF (LSAME(UPLO,'U')) THEN
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| 208 | KPLUS1 = K + 1
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| 209 | IF (INCX.EQ.1) THEN
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| 210 | DO 20 J = 1,N
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| 211 | IF (X(J).NE.ZERO) THEN
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| 212 | TEMP = X(J)
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| 213 | L = KPLUS1 - J
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| 214 | DO 10 I = MAX(1,J-K),J - 1
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| 215 | X(I) = X(I) + TEMP*A(L+I,J)
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| 216 | 10 CONTINUE
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| 217 | IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J)
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| 218 | END IF
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| 219 | 20 CONTINUE
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| 220 | ELSE
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| 221 | JX = KX
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| 222 | DO 40 J = 1,N
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| 223 | IF (X(JX).NE.ZERO) THEN
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| 224 | TEMP = X(JX)
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| 225 | IX = KX
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| 226 | L = KPLUS1 - J
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| 227 | DO 30 I = MAX(1,J-K),J - 1
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| 228 | X(IX) = X(IX) + TEMP*A(L+I,J)
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| 229 | IX = IX + INCX
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| 230 | 30 CONTINUE
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| 231 | IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J)
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| 232 | END IF
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| 233 | JX = JX + INCX
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| 234 | IF (J.GT.K) KX = KX + INCX
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| 235 | 40 CONTINUE
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| 236 | END IF
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| 237 | ELSE
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| 238 | IF (INCX.EQ.1) THEN
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| 239 | DO 60 J = N,1,-1
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| 240 | IF (X(J).NE.ZERO) THEN
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| 241 | TEMP = X(J)
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| 242 | L = 1 - J
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| 243 | DO 50 I = MIN(N,J+K),J + 1,-1
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| 244 | X(I) = X(I) + TEMP*A(L+I,J)
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| 245 | 50 CONTINUE
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| 246 | IF (NOUNIT) X(J) = X(J)*A(1,J)
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| 247 | END IF
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| 248 | 60 CONTINUE
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| 249 | ELSE
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| 250 | KX = KX + (N-1)*INCX
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| 251 | JX = KX
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| 252 | DO 80 J = N,1,-1
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| 253 | IF (X(JX).NE.ZERO) THEN
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| 254 | TEMP = X(JX)
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| 255 | IX = KX
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| 256 | L = 1 - J
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| 257 | DO 70 I = MIN(N,J+K),J + 1,-1
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| 258 | X(IX) = X(IX) + TEMP*A(L+I,J)
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| 259 | IX = IX - INCX
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| 260 | 70 CONTINUE
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| 261 | IF (NOUNIT) X(JX) = X(JX)*A(1,J)
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| 262 | END IF
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| 263 | JX = JX - INCX
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| 264 | IF ((N-J).GE.K) KX = KX - INCX
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| 265 | 80 CONTINUE
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| 266 | END IF
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| 267 | END IF
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| 268 | ELSE
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| 269 | *
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| 270 | * Form x := A'*x.
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| 271 | *
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| 272 | IF (LSAME(UPLO,'U')) THEN
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| 273 | KPLUS1 = K + 1
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| 274 | IF (INCX.EQ.1) THEN
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| 275 | DO 100 J = N,1,-1
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| 276 | TEMP = X(J)
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| 277 | L = KPLUS1 - J
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| 278 | IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
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| 279 | DO 90 I = J - 1,MAX(1,J-K),-1
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| 280 | TEMP = TEMP + A(L+I,J)*X(I)
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| 281 | 90 CONTINUE
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| 282 | X(J) = TEMP
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| 283 | 100 CONTINUE
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| 284 | ELSE
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| 285 | KX = KX + (N-1)*INCX
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| 286 | JX = KX
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| 287 | DO 120 J = N,1,-1
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| 288 | TEMP = X(JX)
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| 289 | KX = KX - INCX
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| 290 | IX = KX
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| 291 | L = KPLUS1 - J
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| 292 | IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
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| 293 | DO 110 I = J - 1,MAX(1,J-K),-1
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| 294 | TEMP = TEMP + A(L+I,J)*X(IX)
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| 295 | IX = IX - INCX
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| 296 | 110 CONTINUE
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| 297 | X(JX) = TEMP
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| 298 | JX = JX - INCX
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| 299 | 120 CONTINUE
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| 300 | END IF
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| 301 | ELSE
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| 302 | IF (INCX.EQ.1) THEN
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| 303 | DO 140 J = 1,N
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| 304 | TEMP = X(J)
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| 305 | L = 1 - J
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| 306 | IF (NOUNIT) TEMP = TEMP*A(1,J)
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| 307 | DO 130 I = J + 1,MIN(N,J+K)
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| 308 | TEMP = TEMP + A(L+I,J)*X(I)
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| 309 | 130 CONTINUE
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| 310 | X(J) = TEMP
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| 311 | 140 CONTINUE
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| 312 | ELSE
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| 313 | JX = KX
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| 314 | DO 160 J = 1,N
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| 315 | TEMP = X(JX)
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| 316 | KX = KX + INCX
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| 317 | IX = KX
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| 318 | L = 1 - J
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| 319 | IF (NOUNIT) TEMP = TEMP*A(1,J)
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| 320 | DO 150 I = J + 1,MIN(N,J+K)
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| 321 | TEMP = TEMP + A(L+I,J)*X(IX)
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| 322 | IX = IX + INCX
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| 323 | 150 CONTINUE
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| 324 | X(JX) = TEMP
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| 325 | JX = JX + INCX
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| 326 | 160 CONTINUE
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| 327 | END IF
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| 328 | END IF
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| 329 | END IF
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| 330 | *
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| 331 | RETURN
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| 332 | *
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| 333 | * End of DTBMV .
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| 334 | *
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| 335 | END
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