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