summaryrefslogtreecommitdiff log msg author committer range
path: root/TESTING/MATGEN/dlahilb.f
 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 ``` ``````C> \brief \b DLAHILB * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DLAHILB( N, NRHS, A, LDA, X, LDX, B, LDB, WORK, INFO) * * .. Scalar Arguments .. * INTEGER N, NRHS, LDA, LDX, LDB, INFO * .. Array Arguments .. * DOUBLE PRECISION A(LDA, N), X(LDX, NRHS), B(LDB, NRHS), WORK(N) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAHILB generates an N by N scaled Hilbert matrix in A along with *> NRHS right-hand sides in B and solutions in X such that A*X=B. *> *> The Hilbert matrix is scaled by M = LCM(1, 2, ..., 2*N-1) so that all *> entries are integers. The right-hand sides are the first NRHS *> columns of M * the identity matrix, and the solutions are the *> first NRHS columns of the inverse Hilbert matrix. *> *> The condition number of the Hilbert matrix grows exponentially with *> its size, roughly as O(e ** (3.5*N)). Additionally, the inverse *> Hilbert matrices beyond a relatively small dimension cannot be *> generated exactly without extra precision. Precision is exhausted *> when the largest entry in the inverse Hilbert matrix is greater than *> 2 to the power of the number of bits in the fraction of the data type *> used plus one, which is 24 for single precision. *> *> In single, the generated solution is exact for N <= 6 and has *> small componentwise error for 7 <= N <= 11. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The dimension of the matrix A. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The requested number of right-hand sides. *> \endverbatim *> *> \param[out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA, N) *> The generated scaled Hilbert matrix. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= N. *> \endverbatim *> *> \param[out] X *> \verbatim *> X is DOUBLE PRECISION array, dimension (LDX, NRHS) *> The generated exact solutions. Currently, the first NRHS *> columns of the inverse Hilbert matrix. *> \endverbatim *> *> \param[in] LDX *> \verbatim *> LDX is INTEGER *> The leading dimension of the array X. LDX >= N. *> \endverbatim *> *> \param[out] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB, NRHS) *> The generated right-hand sides. Currently, the first NRHS *> columns of LCM(1, 2, ..., 2*N-1) * the identity matrix. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= N. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> = 1: N is too large; the data is still generated but may not *> be not exact. *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup double_matgen * * ===================================================================== SUBROUTINE DLAHILB( N, NRHS, A, LDA, X, LDX, B, LDB, WORK, INFO) * * -- LAPACK test routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER N, NRHS, LDA, LDX, LDB, INFO * .. Array Arguments .. DOUBLE PRECISION A(LDA, N), X(LDX, NRHS), B(LDB, NRHS), WORK(N) * .. * * ===================================================================== * .. Local Scalars .. INTEGER TM, TI, R INTEGER M INTEGER I, J * .. Parameters .. * NMAX_EXACT the largest dimension where the generated data is * exact. * NMAX_APPROX the largest dimension where the generated data has * a small componentwise relative error. INTEGER NMAX_EXACT, NMAX_APPROX PARAMETER (NMAX_EXACT = 6, NMAX_APPROX = 11) * .. * .. External Functions EXTERNAL DLASET INTRINSIC DBLE * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF (N .LT. 0 .OR. N .GT. NMAX_APPROX) THEN INFO = -1 ELSE IF (NRHS .LT. 0) THEN INFO = -2 ELSE IF (LDA .LT. N) THEN INFO = -4 ELSE IF (LDX .LT. N) THEN INFO = -6 ELSE IF (LDB .LT. N) THEN INFO = -8 END IF IF (INFO .LT. 0) THEN CALL XERBLA('DLAHILB', -INFO) RETURN END IF IF (N .GT. NMAX_EXACT) THEN INFO = 1 END IF * Compute M = the LCM of the integers [1, 2*N-1]. The largest * reasonable N is small enough that integers suffice (up to N = 11). M = 1 DO I = 2, (2*N-1) TM = M TI = I R = MOD(TM, TI) DO WHILE (R .NE. 0) TM = TI TI = R R = MOD(TM, TI) END DO M = (M / TI) * I END DO * Generate the scaled Hilbert matrix in A DO J = 1, N DO I = 1, N A(I, J) = DBLE(M) / (I + J - 1) END DO END DO * Generate matrix B as simply the first NRHS columns of M * the * identity. CALL DLASET('Full', N, NRHS, 0.0D+0, DBLE(M), B, LDB) * Generate the true solutions in X. Because B = the first NRHS * columns of M*I, the true solutions are just the first NRHS columns * of the inverse Hilbert matrix. WORK(1) = N DO J = 2, N WORK(J) = ( ( (WORK(J-1)/(J-1)) * (J-1 - N) ) /(J-1) ) \$ * (N +J -1) END DO DO J = 1, NRHS DO I = 1, N X(I, J) = (WORK(I)*WORK(J)) / (I + J - 1) END DO END DO END ``````