| 1 | SUBROUTINE CGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) |
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| 2 | * .. Scalar Arguments .. |
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| 3 | COMPLEX ALPHA,BETA |
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| 4 | INTEGER INCX,INCY,KL,KU,LDA,M,N |
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| 5 | CHARACTER TRANS |
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| 6 | * .. |
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| 7 | * .. Array Arguments .. |
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| 8 | COMPLEX 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 | * CGBMV performs one of the matrix-vector operations |
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| 15 | * |
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| 16 | * y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or |
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| 17 | * |
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| 18 | * y := alpha*conjg( A' )*x + beta*y, |
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| 19 | * |
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| 20 | * where alpha and beta are scalars, x and y are vectors and A is an |
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| 21 | * m by n band matrix, with kl sub-diagonals and ku super-diagonals. |
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| 22 | * |
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| 23 | * Arguments |
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| 24 | * ========== |
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| 25 | * |
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| 26 | * TRANS - CHARACTER*1. |
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| 27 | * On entry, TRANS specifies the operation to be performed as |
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| 28 | * follows: |
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| 29 | * |
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| 30 | * TRANS = 'N' or 'n' y := alpha*A*x + beta*y. |
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| 31 | * |
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| 32 | * TRANS = 'T' or 't' y := alpha*A'*x + beta*y. |
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| 33 | * |
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| 34 | * TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y. |
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| 35 | * |
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| 36 | * Unchanged on exit. |
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| 37 | * |
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| 38 | * M - INTEGER. |
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| 39 | * On entry, M specifies the number of rows of the matrix A. |
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| 40 | * M must be at least zero. |
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| 41 | * Unchanged on exit. |
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| 42 | * |
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| 43 | * N - INTEGER. |
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| 44 | * On entry, N specifies the number of columns of the matrix A. |
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| 45 | * N must be at least zero. |
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| 46 | * Unchanged on exit. |
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| 47 | * |
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| 48 | * KL - INTEGER. |
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| 49 | * On entry, KL specifies the number of sub-diagonals of the |
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| 50 | * matrix A. KL must satisfy 0 .le. KL. |
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| 51 | * Unchanged on exit. |
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| 52 | * |
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| 53 | * KU - INTEGER. |
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| 54 | * On entry, KU specifies the number of super-diagonals of the |
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| 55 | * matrix A. KU must satisfy 0 .le. KU. |
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| 56 | * Unchanged on exit. |
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| 57 | * |
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| 58 | * ALPHA - COMPLEX . |
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| 59 | * On entry, ALPHA specifies the scalar alpha. |
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| 60 | * Unchanged on exit. |
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| 61 | * |
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| 62 | * A - COMPLEX array of DIMENSION ( LDA, n ). |
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| 63 | * Before entry, the leading ( kl + ku + 1 ) by n part of the |
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| 64 | * array A must contain the matrix of coefficients, supplied |
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| 65 | * column by column, with the leading diagonal of the matrix in |
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| 66 | * row ( ku + 1 ) of the array, the first super-diagonal |
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| 67 | * starting at position 2 in row ku, the first sub-diagonal |
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| 68 | * starting at position 1 in row ( ku + 2 ), and so on. |
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| 69 | * Elements in the array A that do not correspond to elements |
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| 70 | * in the band matrix (such as the top left ku by ku triangle) |
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| 71 | * are not referenced. |
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| 72 | * The following program segment will transfer a band matrix |
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| 73 | * from conventional full matrix storage to band storage: |
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| 74 | * |
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| 75 | * DO 20, J = 1, N |
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| 76 | * K = KU + 1 - J |
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| 77 | * DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) |
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| 78 | * A( K + I, J ) = matrix( I, J ) |
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| 79 | * 10 CONTINUE |
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| 80 | * 20 CONTINUE |
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| 81 | * |
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| 82 | * Unchanged on exit. |
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| 83 | * |
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| 84 | * LDA - INTEGER. |
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| 85 | * On entry, LDA specifies the first dimension of A as declared |
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| 86 | * in the calling (sub) program. LDA must be at least |
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| 87 | * ( kl + ku + 1 ). |
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| 88 | * Unchanged on exit. |
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| 89 | * |
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| 90 | * X - COMPLEX array of DIMENSION at least |
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| 91 | * ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' |
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| 92 | * and at least |
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| 93 | * ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. |
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| 94 | * Before entry, the incremented array X must contain the |
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| 95 | * vector x. |
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| 96 | * Unchanged on exit. |
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| 97 | * |
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| 98 | * INCX - INTEGER. |
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| 99 | * On entry, INCX specifies the increment for the elements of |
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| 100 | * X. INCX must not be zero. |
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| 101 | * Unchanged on exit. |
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| 102 | * |
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| 103 | * BETA - COMPLEX . |
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| 104 | * On entry, BETA specifies the scalar beta. When BETA is |
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| 105 | * supplied as zero then Y need not be set on input. |
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| 106 | * Unchanged on exit. |
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| 107 | * |
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| 108 | * Y - COMPLEX array of DIMENSION at least |
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| 109 | * ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' |
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| 110 | * and at least |
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| 111 | * ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. |
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| 112 | * Before entry, the incremented array Y must contain the |
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| 113 | * vector y. On exit, Y is overwritten by the updated vector y. |
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| 114 | * |
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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 | COMPLEX ONE |
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| 133 | PARAMETER (ONE= (1.0E+0,0.0E+0)) |
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| 134 | COMPLEX ZERO |
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| 135 | PARAMETER (ZERO= (0.0E+0,0.0E+0)) |
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| 136 | * .. |
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| 137 | * .. Local Scalars .. |
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| 138 | COMPLEX TEMP |
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| 139 | INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY |
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| 140 | LOGICAL NOCONJ |
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| 141 | * .. |
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| 142 | * .. External Functions .. |
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| 143 | LOGICAL LSAME |
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| 144 | EXTERNAL LSAME |
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| 145 | * .. |
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| 146 | * .. External Subroutines .. |
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| 147 | EXTERNAL XERBLA |
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| 148 | * .. |
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| 149 | * .. Intrinsic Functions .. |
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| 150 | INTRINSIC CONJG,MAX,MIN |
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| 151 | * .. |
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| 152 | * |
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| 153 | * Test the input parameters. |
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| 154 | * |
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| 155 | INFO = 0 |
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| 156 | IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. |
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| 157 | + .NOT.LSAME(TRANS,'C')) THEN |
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| 158 | INFO = 1 |
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| 159 | ELSE IF (M.LT.0) THEN |
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| 160 | INFO = 2 |
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| 161 | ELSE IF (N.LT.0) THEN |
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| 162 | INFO = 3 |
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| 163 | ELSE IF (KL.LT.0) THEN |
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| 164 | INFO = 4 |
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| 165 | ELSE IF (KU.LT.0) THEN |
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| 166 | INFO = 5 |
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| 167 | ELSE IF (LDA.LT. (KL+KU+1)) THEN |
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| 168 | INFO = 8 |
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| 169 | ELSE IF (INCX.EQ.0) THEN |
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| 170 | INFO = 10 |
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| 171 | ELSE IF (INCY.EQ.0) THEN |
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| 172 | INFO = 13 |
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| 173 | END IF |
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| 174 | IF (INFO.NE.0) THEN |
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| 175 | CALL XERBLA('CGBMV ',INFO) |
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| 176 | RETURN |
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| 177 | END IF |
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| 178 | * |
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| 179 | * Quick return if possible. |
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| 180 | * |
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| 181 | IF ((M.EQ.0) .OR. (N.EQ.0) .OR. |
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| 182 | + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN |
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| 183 | * |
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| 184 | NOCONJ = LSAME(TRANS,'T') |
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| 185 | * |
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| 186 | * Set LENX and LENY, the lengths of the vectors x and y, and set |
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| 187 | * up the start points in X and Y. |
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| 188 | * |
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| 189 | IF (LSAME(TRANS,'N')) THEN |
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| 190 | LENX = N |
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| 191 | LENY = M |
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| 192 | ELSE |
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| 193 | LENX = M |
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| 194 | LENY = N |
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| 195 | END IF |
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| 196 | IF (INCX.GT.0) THEN |
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| 197 | KX = 1 |
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| 198 | ELSE |
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| 199 | KX = 1 - (LENX-1)*INCX |
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| 200 | END IF |
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| 201 | IF (INCY.GT.0) THEN |
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| 202 | KY = 1 |
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| 203 | ELSE |
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| 204 | KY = 1 - (LENY-1)*INCY |
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| 205 | END IF |
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| 206 | * |
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| 207 | * Start the operations. In this version the elements of A are |
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| 208 | * accessed sequentially with one pass through the band part of A. |
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| 209 | * |
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| 210 | * First form y := beta*y. |
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| 211 | * |
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| 212 | IF (BETA.NE.ONE) THEN |
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| 213 | IF (INCY.EQ.1) THEN |
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| 214 | IF (BETA.EQ.ZERO) THEN |
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| 215 | DO 10 I = 1,LENY |
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| 216 | Y(I) = ZERO |
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| 217 | 10 CONTINUE |
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| 218 | ELSE |
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| 219 | DO 20 I = 1,LENY |
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| 220 | Y(I) = BETA*Y(I) |
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| 221 | 20 CONTINUE |
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| 222 | END IF |
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| 223 | ELSE |
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| 224 | IY = KY |
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| 225 | IF (BETA.EQ.ZERO) THEN |
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| 226 | DO 30 I = 1,LENY |
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| 227 | Y(IY) = ZERO |
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| 228 | IY = IY + INCY |
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| 229 | 30 CONTINUE |
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| 230 | ELSE |
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| 231 | DO 40 I = 1,LENY |
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| 232 | Y(IY) = BETA*Y(IY) |
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| 233 | IY = IY + INCY |
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| 234 | 40 CONTINUE |
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| 235 | END IF |
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| 236 | END IF |
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| 237 | END IF |
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| 238 | IF (ALPHA.EQ.ZERO) RETURN |
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| 239 | KUP1 = KU + 1 |
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| 240 | IF (LSAME(TRANS,'N')) THEN |
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| 241 | * |
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| 242 | * Form y := alpha*A*x + y. |
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| 243 | * |
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| 244 | JX = KX |
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| 245 | IF (INCY.EQ.1) THEN |
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| 246 | DO 60 J = 1,N |
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| 247 | IF (X(JX).NE.ZERO) THEN |
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| 248 | TEMP = ALPHA*X(JX) |
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| 249 | K = KUP1 - J |
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| 250 | DO 50 I = MAX(1,J-KU),MIN(M,J+KL) |
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| 251 | Y(I) = Y(I) + TEMP*A(K+I,J) |
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| 252 | 50 CONTINUE |
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| 253 | END IF |
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| 254 | JX = JX + INCX |
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| 255 | 60 CONTINUE |
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| 256 | ELSE |
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| 257 | DO 80 J = 1,N |
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| 258 | IF (X(JX).NE.ZERO) THEN |
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| 259 | TEMP = ALPHA*X(JX) |
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| 260 | IY = KY |
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| 261 | K = KUP1 - J |
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| 262 | DO 70 I = MAX(1,J-KU),MIN(M,J+KL) |
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| 263 | Y(IY) = Y(IY) + TEMP*A(K+I,J) |
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| 264 | IY = IY + INCY |
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| 265 | 70 CONTINUE |
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| 266 | END IF |
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| 267 | JX = JX + INCX |
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| 268 | IF (J.GT.KU) KY = KY + INCY |
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| 269 | 80 CONTINUE |
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| 270 | END IF |
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| 271 | ELSE |
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| 272 | * |
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| 273 | * Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. |
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| 274 | * |
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| 275 | JY = KY |
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| 276 | IF (INCX.EQ.1) THEN |
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| 277 | DO 110 J = 1,N |
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| 278 | TEMP = ZERO |
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| 279 | K = KUP1 - J |
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| 280 | IF (NOCONJ) THEN |
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| 281 | DO 90 I = MAX(1,J-KU),MIN(M,J+KL) |
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| 282 | TEMP = TEMP + A(K+I,J)*X(I) |
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| 283 | 90 CONTINUE |
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| 284 | ELSE |
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| 285 | DO 100 I = MAX(1,J-KU),MIN(M,J+KL) |
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| 286 | TEMP = TEMP + CONJG(A(K+I,J))*X(I) |
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| 287 | 100 CONTINUE |
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| 288 | END IF |
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| 289 | Y(JY) = Y(JY) + ALPHA*TEMP |
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| 290 | JY = JY + INCY |
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| 291 | 110 CONTINUE |
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| 292 | ELSE |
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| 293 | DO 140 J = 1,N |
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| 294 | TEMP = ZERO |
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| 295 | IX = KX |
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| 296 | K = KUP1 - J |
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| 297 | IF (NOCONJ) THEN |
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| 298 | DO 120 I = MAX(1,J-KU),MIN(M,J+KL) |
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| 299 | TEMP = TEMP + A(K+I,J)*X(IX) |
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| 300 | IX = IX + INCX |
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| 301 | 120 CONTINUE |
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| 302 | ELSE |
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| 303 | DO 130 I = MAX(1,J-KU),MIN(M,J+KL) |
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| 304 | TEMP = TEMP + CONJG(A(K+I,J))*X(IX) |
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| 305 | IX = IX + INCX |
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| 306 | 130 CONTINUE |
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| 307 | END IF |
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| 308 | Y(JY) = Y(JY) + ALPHA*TEMP |
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| 309 | JY = JY + INCY |
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| 310 | IF (J.GT.KU) KX = KX + INCX |
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| 311 | 140 CONTINUE |
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| 312 | END IF |
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| 313 | END IF |
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| 314 | * |
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| 315 | RETURN |
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| 316 | * |
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| 317 | * End of CGBMV . |
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| 318 | * |
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| 319 | END |
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