89 lines
3.4 KiB
Go
89 lines
3.4 KiB
Go
|
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
|||
|
|
// Use of this source code is governed by a BSD-style
|
|||
|
|
// license that can be found in the LICENSE file.
|
|||
|
|
|
|||
|
|
// Ensure changes made to blas/native are reflected in blas/cgo where relevant.
|
|||
|
|
|
|||
|
|
/*
|
|||
|
|
Package gonum is a Go implementation of the BLAS API. This implementation
|
|||
|
|
panics when the input arguments are invalid as per the standard, for example
|
|||
|
|
if a vector increment is zero. Note that the treatment of NaN values
|
|||
|
|
is not specified, and differs among the BLAS implementations.
|
|||
|
|
gonum.org/v1/gonum/blas/blas64 provides helpful wrapper functions to the BLAS
|
|||
|
|
interface. The rest of this text describes the layout of the data for the input types.
|
|||
|
|
|
|||
|
|
Note that in the function documentation, x[i] refers to the i^th element
|
|||
|
|
of the vector, which will be different from the i^th element of the slice if
|
|||
|
|
incX != 1.
|
|||
|
|
|
|||
|
|
See http://www.netlib.org/lapack/explore-html/d4/de1/_l_i_c_e_n_s_e_source.html
|
|||
|
|
for more license information.
|
|||
|
|
|
|||
|
|
Vector arguments are effectively strided slices. They have two input arguments,
|
|||
|
|
a number of elements, n, and an increment, incX. The increment specifies the
|
|||
|
|
distance between elements of the vector. The actual Go slice may be longer
|
|||
|
|
than necessary.
|
|||
|
|
The increment may be positive or negative, except in functions with only
|
|||
|
|
a single vector argument where the increment may only be positive. If the increment
|
|||
|
|
is negative, s[0] is the last element in the slice. Note that this is not the same
|
|||
|
|
as counting backward from the end of the slice, as len(s) may be longer than
|
|||
|
|
necessary. So, for example, if n = 5 and incX = 3, the elements of s are
|
|||
|
|
[0 * * 1 * * 2 * * 3 * * 4 * * * ...]
|
|||
|
|
where ∗ elements are never accessed. If incX = -3, the same elements are
|
|||
|
|
accessed, just in reverse order (4, 3, 2, 1, 0).
|
|||
|
|
|
|||
|
|
Dense matrices are specified by a number of rows, a number of columns, and a stride.
|
|||
|
|
The stride specifies the number of entries in the slice between the first element
|
|||
|
|
of successive rows. The stride must be at least as large as the number of columns
|
|||
|
|
but may be longer.
|
|||
|
|
[a00 ... a0n a0* ... a1stride-1 a21 ... amn am* ... amstride-1]
|
|||
|
|
Thus, dense[i*ld + j] refers to the {i, j}th element of the matrix.
|
|||
|
|
|
|||
|
|
Symmetric and triangular matrices (non-packed) are stored identically to Dense,
|
|||
|
|
except that only elements in one triangle of the matrix are accessed.
|
|||
|
|
|
|||
|
|
Packed symmetric and packed triangular matrices are laid out with the entries
|
|||
|
|
condensed such that all of the unreferenced elements are removed. So, the upper triangular
|
|||
|
|
matrix
|
|||
|
|
[
|
|||
|
|
1 2 3
|
|||
|
|
0 4 5
|
|||
|
|
0 0 6
|
|||
|
|
]
|
|||
|
|
and the lower-triangular matrix
|
|||
|
|
[
|
|||
|
|
1 0 0
|
|||
|
|
2 3 0
|
|||
|
|
4 5 6
|
|||
|
|
]
|
|||
|
|
will both be compacted as [1 2 3 4 5 6]. The (i, j) element of the original
|
|||
|
|
dense matrix can be found at element i*n - (i-1)*i/2 + j for upper triangular,
|
|||
|
|
and at element i * (i+1) /2 + j for lower triangular.
|
|||
|
|
|
|||
|
|
Banded matrices are laid out in a compact format, constructed by removing the
|
|||
|
|
zeros in the rows and aligning the diagonals. For example, the matrix
|
|||
|
|
[
|
|||
|
|
1 2 3 0 0 0
|
|||
|
|
4 5 6 7 0 0
|
|||
|
|
0 8 9 10 11 0
|
|||
|
|
0 0 12 13 14 15
|
|||
|
|
0 0 0 16 17 18
|
|||
|
|
0 0 0 0 19 20
|
|||
|
|
]
|
|||
|
|
|
|||
|
|
implicitly becomes (∗ entries are never accessed)
|
|||
|
|
[
|
|||
|
|
* 1 2 3
|
|||
|
|
4 5 6 7
|
|||
|
|
8 9 10 11
|
|||
|
|
12 13 14 15
|
|||
|
|
16 17 18 *
|
|||
|
|
19 20 * *
|
|||
|
|
]
|
|||
|
|
which is given to the BLAS routine as [∗ 1 2 3 4 ...].
|
|||
|
|
|
|||
|
|
See http://www.crest.iu.edu/research/mtl/reference/html/banded.html
|
|||
|
|
for more information
|
|||
|
|
*/
|
|||
|
|
package gonum // import "gonum.org/v1/gonum/blas/gonum"
|