1// Copyright ©2013 The Gonum Authors. All rights reserved. 2// Use of this source code is governed by a BSD-style 3// license that can be found in the LICENSE file. 4 5//go:generate ./conversions.bash 6 7package blas 8 9// Flag constants indicate Givens transformation H matrix state. 10type Flag int 11 12const ( 13 Identity Flag = -2 // H is the identity matrix; no rotation is needed. 14 Rescaling Flag = -1 // H specifies rescaling. 15 OffDiagonal Flag = 0 // Off-diagonal elements of H are non-unit. 16 Diagonal Flag = 1 // Diagonal elements of H are non-unit. 17) 18 19// SrotmParams contains Givens transformation parameters returned 20// by the Float32 Srotm method. 21type SrotmParams struct { 22 Flag 23 H [4]float32 // Column-major 2 by 2 matrix. 24} 25 26// DrotmParams contains Givens transformation parameters returned 27// by the Float64 Drotm method. 28type DrotmParams struct { 29 Flag 30 H [4]float64 // Column-major 2 by 2 matrix. 31} 32 33// Transpose specifies the transposition operation of a matrix. 34type Transpose byte 35 36const ( 37 NoTrans Transpose = 'N' 38 Trans Transpose = 'T' 39 ConjTrans Transpose = 'C' 40) 41 42// Uplo specifies whether a matrix is upper or lower triangular. 43type Uplo byte 44 45const ( 46 Upper Uplo = 'U' 47 Lower Uplo = 'L' 48 All Uplo = 'A' 49) 50 51// Diag specifies whether a matrix is unit triangular. 52type Diag byte 53 54const ( 55 NonUnit Diag = 'N' 56 Unit Diag = 'U' 57) 58 59// Side specifies from which side a multiplication operation is performed. 60type Side byte 61 62const ( 63 Left Side = 'L' 64 Right Side = 'R' 65) 66 67// Float32 implements the single precision real BLAS routines. 68type Float32 interface { 69 Float32Level1 70 Float32Level2 71 Float32Level3 72} 73 74// Float32Level1 implements the single precision real BLAS Level 1 routines. 75type Float32Level1 interface { 76 Sdsdot(n int, alpha float32, x []float32, incX int, y []float32, incY int) float32 77 Dsdot(n int, x []float32, incX int, y []float32, incY int) float64 78 Sdot(n int, x []float32, incX int, y []float32, incY int) float32 79 Snrm2(n int, x []float32, incX int) float32 80 Sasum(n int, x []float32, incX int) float32 81 Isamax(n int, x []float32, incX int) int 82 Sswap(n int, x []float32, incX int, y []float32, incY int) 83 Scopy(n int, x []float32, incX int, y []float32, incY int) 84 Saxpy(n int, alpha float32, x []float32, incX int, y []float32, incY int) 85 Srotg(a, b float32) (c, s, r, z float32) 86 Srotmg(d1, d2, b1, b2 float32) (p SrotmParams, rd1, rd2, rb1 float32) 87 Srot(n int, x []float32, incX int, y []float32, incY int, c, s float32) 88 Srotm(n int, x []float32, incX int, y []float32, incY int, p SrotmParams) 89 Sscal(n int, alpha float32, x []float32, incX int) 90} 91 92// Float32Level2 implements the single precision real BLAS Level 2 routines. 93type Float32Level2 interface { 94 Sgemv(tA Transpose, m, n int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int) 95 Sgbmv(tA Transpose, m, n, kL, kU int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int) 96 Strmv(ul Uplo, tA Transpose, d Diag, n int, a []float32, lda int, x []float32, incX int) 97 Stbmv(ul Uplo, tA Transpose, d Diag, n, k int, a []float32, lda int, x []float32, incX int) 98 Stpmv(ul Uplo, tA Transpose, d Diag, n int, ap []float32, x []float32, incX int) 99 Strsv(ul Uplo, tA Transpose, d Diag, n int, a []float32, lda int, x []float32, incX int) 100 Stbsv(ul Uplo, tA Transpose, d Diag, n, k int, a []float32, lda int, x []float32, incX int) 101 Stpsv(ul Uplo, tA Transpose, d Diag, n int, ap []float32, x []float32, incX int) 102 Ssymv(ul Uplo, n int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int) 103 Ssbmv(ul Uplo, n, k int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int) 104 Sspmv(ul Uplo, n int, alpha float32, ap []float32, x []float32, incX int, beta float32, y []float32, incY int) 105 Sger(m, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32, lda int) 106 Ssyr(ul Uplo, n int, alpha float32, x []float32, incX int, a []float32, lda int) 107 Sspr(ul Uplo, n int, alpha float32, x []float32, incX int, ap []float32) 108 Ssyr2(ul Uplo, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32, lda int) 109 Sspr2(ul Uplo, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32) 110} 111 112// Float32Level3 implements the single precision real BLAS Level 3 routines. 113type Float32Level3 interface { 114 Sgemm(tA, tB Transpose, m, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int) 115 Ssymm(s Side, ul Uplo, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int) 116 Ssyrk(ul Uplo, t Transpose, n, k int, alpha float32, a []float32, lda int, beta float32, c []float32, ldc int) 117 Ssyr2k(ul Uplo, t Transpose, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int) 118 Strmm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int) 119 Strsm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int) 120} 121 122// Float64 implements the single precision real BLAS routines. 123type Float64 interface { 124 Float64Level1 125 Float64Level2 126 Float64Level3 127} 128 129// Float64Level1 implements the double precision real BLAS Level 1 routines. 130type Float64Level1 interface { 131 Ddot(n int, x []float64, incX int, y []float64, incY int) float64 132 Dnrm2(n int, x []float64, incX int) float64 133 Dasum(n int, x []float64, incX int) float64 134 Idamax(n int, x []float64, incX int) int 135 Dswap(n int, x []float64, incX int, y []float64, incY int) 136 Dcopy(n int, x []float64, incX int, y []float64, incY int) 137 Daxpy(n int, alpha float64, x []float64, incX int, y []float64, incY int) 138 Drotg(a, b float64) (c, s, r, z float64) 139 Drotmg(d1, d2, b1, b2 float64) (p DrotmParams, rd1, rd2, rb1 float64) 140 Drot(n int, x []float64, incX int, y []float64, incY int, c float64, s float64) 141 Drotm(n int, x []float64, incX int, y []float64, incY int, p DrotmParams) 142 Dscal(n int, alpha float64, x []float64, incX int) 143} 144 145// Float64Level2 implements the double precision real BLAS Level 2 routines. 146type Float64Level2 interface { 147 Dgemv(tA Transpose, m, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int) 148 Dgbmv(tA Transpose, m, n, kL, kU int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int) 149 Dtrmv(ul Uplo, tA Transpose, d Diag, n int, a []float64, lda int, x []float64, incX int) 150 Dtbmv(ul Uplo, tA Transpose, d Diag, n, k int, a []float64, lda int, x []float64, incX int) 151 Dtpmv(ul Uplo, tA Transpose, d Diag, n int, ap []float64, x []float64, incX int) 152 Dtrsv(ul Uplo, tA Transpose, d Diag, n int, a []float64, lda int, x []float64, incX int) 153 Dtbsv(ul Uplo, tA Transpose, d Diag, n, k int, a []float64, lda int, x []float64, incX int) 154 Dtpsv(ul Uplo, tA Transpose, d Diag, n int, ap []float64, x []float64, incX int) 155 Dsymv(ul Uplo, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int) 156 Dsbmv(ul Uplo, n, k int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int) 157 Dspmv(ul Uplo, n int, alpha float64, ap []float64, x []float64, incX int, beta float64, y []float64, incY int) 158 Dger(m, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int) 159 Dsyr(ul Uplo, n int, alpha float64, x []float64, incX int, a []float64, lda int) 160 Dspr(ul Uplo, n int, alpha float64, x []float64, incX int, ap []float64) 161 Dsyr2(ul Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int) 162 Dspr2(ul Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64) 163} 164 165// Float64Level3 implements the double precision real BLAS Level 3 routines. 166type Float64Level3 interface { 167 Dgemm(tA, tB Transpose, m, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int) 168 Dsymm(s Side, ul Uplo, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int) 169 Dsyrk(ul Uplo, t Transpose, n, k int, alpha float64, a []float64, lda int, beta float64, c []float64, ldc int) 170 Dsyr2k(ul Uplo, t Transpose, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int) 171 Dtrmm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int) 172 Dtrsm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int) 173} 174 175// Complex64 implements the single precision complex BLAS routines. 176type Complex64 interface { 177 Complex64Level1 178 Complex64Level2 179 Complex64Level3 180} 181 182// Complex64Level1 implements the single precision complex BLAS Level 1 routines. 183type Complex64Level1 interface { 184 Cdotu(n int, x []complex64, incX int, y []complex64, incY int) (dotu complex64) 185 Cdotc(n int, x []complex64, incX int, y []complex64, incY int) (dotc complex64) 186 Scnrm2(n int, x []complex64, incX int) float32 187 Scasum(n int, x []complex64, incX int) float32 188 Icamax(n int, x []complex64, incX int) int 189 Cswap(n int, x []complex64, incX int, y []complex64, incY int) 190 Ccopy(n int, x []complex64, incX int, y []complex64, incY int) 191 Caxpy(n int, alpha complex64, x []complex64, incX int, y []complex64, incY int) 192 Cscal(n int, alpha complex64, x []complex64, incX int) 193 Csscal(n int, alpha float32, x []complex64, incX int) 194} 195 196// Complex64Level2 implements the single precision complex BLAS routines Level 2 routines. 197type Complex64Level2 interface { 198 Cgemv(tA Transpose, m, n int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int) 199 Cgbmv(tA Transpose, m, n, kL, kU int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int) 200 Ctrmv(ul Uplo, tA Transpose, d Diag, n int, a []complex64, lda int, x []complex64, incX int) 201 Ctbmv(ul Uplo, tA Transpose, d Diag, n, k int, a []complex64, lda int, x []complex64, incX int) 202 Ctpmv(ul Uplo, tA Transpose, d Diag, n int, ap []complex64, x []complex64, incX int) 203 Ctrsv(ul Uplo, tA Transpose, d Diag, n int, a []complex64, lda int, x []complex64, incX int) 204 Ctbsv(ul Uplo, tA Transpose, d Diag, n, k int, a []complex64, lda int, x []complex64, incX int) 205 Ctpsv(ul Uplo, tA Transpose, d Diag, n int, ap []complex64, x []complex64, incX int) 206 Chemv(ul Uplo, n int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int) 207 Chbmv(ul Uplo, n, k int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int) 208 Chpmv(ul Uplo, n int, alpha complex64, ap []complex64, x []complex64, incX int, beta complex64, y []complex64, incY int) 209 Cgeru(m, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int) 210 Cgerc(m, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int) 211 Cher(ul Uplo, n int, alpha float32, x []complex64, incX int, a []complex64, lda int) 212 Chpr(ul Uplo, n int, alpha float32, x []complex64, incX int, a []complex64) 213 Cher2(ul Uplo, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int) 214 Chpr2(ul Uplo, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, ap []complex64) 215} 216 217// Complex64Level3 implements the single precision complex BLAS Level 3 routines. 218type Complex64Level3 interface { 219 Cgemm(tA, tB Transpose, m, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int) 220 Csymm(s Side, ul Uplo, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int) 221 Csyrk(ul Uplo, t Transpose, n, k int, alpha complex64, a []complex64, lda int, beta complex64, c []complex64, ldc int) 222 Csyr2k(ul Uplo, t Transpose, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int) 223 Ctrmm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int) 224 Ctrsm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int) 225 Chemm(s Side, ul Uplo, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int) 226 Cherk(ul Uplo, t Transpose, n, k int, alpha float32, a []complex64, lda int, beta float32, c []complex64, ldc int) 227 Cher2k(ul Uplo, t Transpose, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta float32, c []complex64, ldc int) 228} 229 230// Complex128 implements the double precision complex BLAS routines. 231type Complex128 interface { 232 Complex128Level1 233 Complex128Level2 234 Complex128Level3 235} 236 237// Complex128Level1 implements the double precision complex BLAS Level 1 routines. 238type Complex128Level1 interface { 239 Zdotu(n int, x []complex128, incX int, y []complex128, incY int) (dotu complex128) 240 Zdotc(n int, x []complex128, incX int, y []complex128, incY int) (dotc complex128) 241 Dznrm2(n int, x []complex128, incX int) float64 242 Dzasum(n int, x []complex128, incX int) float64 243 Izamax(n int, x []complex128, incX int) int 244 Zswap(n int, x []complex128, incX int, y []complex128, incY int) 245 Zcopy(n int, x []complex128, incX int, y []complex128, incY int) 246 Zaxpy(n int, alpha complex128, x []complex128, incX int, y []complex128, incY int) 247 Zscal(n int, alpha complex128, x []complex128, incX int) 248 Zdscal(n int, alpha float64, x []complex128, incX int) 249} 250 251// Complex128Level2 implements the double precision complex BLAS Level 2 routines. 252type Complex128Level2 interface { 253 Zgemv(tA Transpose, m, n int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int) 254 Zgbmv(tA Transpose, m, n int, kL int, kU int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int) 255 Ztrmv(ul Uplo, tA Transpose, d Diag, n int, a []complex128, lda int, x []complex128, incX int) 256 Ztbmv(ul Uplo, tA Transpose, d Diag, n, k int, a []complex128, lda int, x []complex128, incX int) 257 Ztpmv(ul Uplo, tA Transpose, d Diag, n int, ap []complex128, x []complex128, incX int) 258 Ztrsv(ul Uplo, tA Transpose, d Diag, n int, a []complex128, lda int, x []complex128, incX int) 259 Ztbsv(ul Uplo, tA Transpose, d Diag, n, k int, a []complex128, lda int, x []complex128, incX int) 260 Ztpsv(ul Uplo, tA Transpose, d Diag, n int, ap []complex128, x []complex128, incX int) 261 Zhemv(ul Uplo, n int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int) 262 Zhbmv(ul Uplo, n, k int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int) 263 Zhpmv(ul Uplo, n int, alpha complex128, ap []complex128, x []complex128, incX int, beta complex128, y []complex128, incY int) 264 Zgeru(m, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int) 265 Zgerc(m, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int) 266 Zher(ul Uplo, n int, alpha float64, x []complex128, incX int, a []complex128, lda int) 267 Zhpr(ul Uplo, n int, alpha float64, x []complex128, incX int, a []complex128) 268 Zher2(ul Uplo, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int) 269 Zhpr2(ul Uplo, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, ap []complex128) 270} 271 272// Complex128Level3 implements the double precision complex BLAS Level 3 routines. 273type Complex128Level3 interface { 274 Zgemm(tA, tB Transpose, m, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int) 275 Zsymm(s Side, ul Uplo, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int) 276 Zsyrk(ul Uplo, t Transpose, n, k int, alpha complex128, a []complex128, lda int, beta complex128, c []complex128, ldc int) 277 Zsyr2k(ul Uplo, t Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int) 278 Ztrmm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int) 279 Ztrsm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int) 280 Zhemm(s Side, ul Uplo, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int) 281 Zherk(ul Uplo, t Transpose, n, k int, alpha float64, a []complex128, lda int, beta float64, c []complex128, ldc int) 282 Zher2k(ul Uplo, t Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta float64, c []complex128, ldc int) 283} 284