ext/nmatrix/math.cpp
/////////////////////////////////////////////////////////////////////
// = NMatrix
//
// A linear algebra library for scientific computation in Ruby.
// NMatrix is part of SciRuby.
//
// NMatrix was originally inspired by and derived from NArray, by
// Masahiro Tanaka: http://narray.rubyforge.org
//
// == Copyright Information
//
// SciRuby is Copyright (c) 2010 - present, Ruby Science Foundation
// NMatrix is Copyright (c) 2012 - present, John Woods and the Ruby Science Foundation
//
// Please see LICENSE.txt for additional copyright notices.
//
// == Contributing
//
// By contributing source code to SciRuby, you agree to be bound by
// our Contributor Agreement:
//
// * https://github.com/SciRuby/sciruby/wiki/Contributor-Agreement
//
// == math.cpp
//
// Ruby-exposed CBLAS and LAPACK functions that are available without
// an external library.
//
// === Procedure for adding CBLAS functions to math.cpp/math.h:
//
// This procedure is written as if for a fictional function with double
// version dbacon, which we'll say is from CBLAS.
//
// 1. Write a default templated version which probably returns a boolean.
// Call it bacon, and put it in math.h.
//
// template <typename DType>
// bool bacon(const CBLAS_TRANSPOSE trans, const int M, const int N, DType* A, ...) {
// rb_raise(rb_eNotImpError, "only implemented for ATLAS types (float32, float64, complex64, complex128)");
// }
//
// Make sure this is in namespace nm::math
//
// 2. In math.cpp, add a templated inline static version of the function which takes
// only void* pointers and uses static_cast to convert them to the
// proper dtype. This should also be in namespace nm::math
//
// This function may also need to switch m and n if these arguments are given.
//
// For an example, see cblas_gemm. This function should do nothing other than cast
// appropriately. If cblas_dbacon, cblas_sbacon, cblas_cbacon, and cblas_zbacon
// all take void* only, and no other pointers that vary between functions, you can skip
// this particular step -- as we can call them directly using a custom function pointer
// array (same function signature!).
//
// This version of the function will be the one exposed through NMatrix::BLAS. We
// want it to be as close to the actual BLAS version of the function as possible,
// and with as few checks as possible.
//
// You will probably need a forward declaration in the extern "C" block.
//
// Note: In that case, the function you wrote in Step 1 should also take exactly the
// same arguments as cblas_xbacon. Otherwise Bad Things will happen.
//
// 3. In cblas_templates_core.h, add a default template like in step 1 (which will just
// call nm::math::bacon()) and also
// inline specialized versions of bacon for the different BLAS types.
// This will allow both nmatrix-atlas and nmatrix-lapacke to use the optimized version
// of bacon from whatever external library is available, as well as the internal version
// if an external version is not available. These functions will end up in a namsespace
// like nm::math::atlas, but don't explicitly put them in a namespace, they will get
// put in the appropriate namespace when cblas_templates_core.h is included.
//
// template <typename DType>
// inline bool bacon(const CBLAS_TRANSPOSE trans, const int M, const int N, DType* A, ...) {
// nm::math::bacon(trans, M, N, A, ...);
// }
//
// template <>
// inline bool bacon(const CBLAS_TRANSPOSE trans, const int M, const int N, float* A, ...) {
// cblas_sbacon(trans, M, N, A, ...);
// return true;
// }
//
// Note that you should do everything in your power here to parse any return values
// cblas_sbacon may give you. We're not trying very hard in this example, but you might
// look at getrf to see how it might be done.
//
// 4. Write the C function nm_cblas_bacon, which is what Ruby will call. Use the example
// of nm_cblas_gemm below. Also you must add a similar function in math_atlas.cpp
// and math_lapacke.cpp
//
// 5. Expose the function in nm_math_init_blas(), in math.cpp:
//
// rb_define_singleton_method(cNMatrix_Internal_BLAS, "cblas_bacon", (METHOD)nm_cblas_bacon, 5);
//
// Do something similar in math_atlas.cpp and math_lapacke.cpp to add the function
// to the plugin gems.
//
// Here, we're telling Ruby that nm_cblas_bacon takes five arguments as a Ruby function.
//
// 6. In blas.rb, write a bacon function which accesses cblas_bacon, but does all the
// sanity checks we left out in step 2.
//
// 7. Write tests for NMatrix::BLAS::bacon, confirming that it works for the ATLAS dtypes.
//
// 8. After you get it working properly with CBLAS, download dbacon.f from NETLIB, and use
// f2c to convert it to C. Clean it up so it's readable. Remove the extra indices -- f2c
// inserts a lot of unnecessary stuff.
//
// Copy and paste the output into the default templated function you wrote in Step 1.
// Fix it so it works as a template instead of just for doubles.
//
// Because of step 3, this will automatically also work for the nmatrix-atlas
// and nmatrix-lapacke implementations.
//
// 9. Write tests to confirm that it works for all data types.
//
// 10. See about adding a Ruby-like interface, such as matrix_matrix_multiply for cblas_gemm,
// or matrix_vector_multiply for cblas_gemv. This step is not mandatory.
//
// 11. Pull request!
/*
* Project Includes
*/
#include <ruby.h>
#include <algorithm>
#include <limits>
#include <cmath>
#include "math/cblas_enums.h"
#include "data/data.h"
#include "math/magnitude.h"
#include "math/imax.h"
#include "math/scal.h"
#include "math/laswp.h"
#include "math/trsm.h"
#include "math/gemm.h"
#include "math/gemv.h"
#include "math/asum.h"
#include "math/nrm2.h"
#include "math/getrf.h"
#include "math/getrs.h"
#include "math/rot.h"
#include "math/rotg.h"
#include "math/math.h"
#include "math/util.h"
#include "storage/dense/dense.h"
#include "nmatrix.h"
#include "ruby_constants.h"
/*
* Forward Declarations
*/
extern "C" {
/* BLAS Level 1. */
static VALUE nm_cblas_scal(VALUE self, VALUE n, VALUE scale, VALUE vector, VALUE incx);
static VALUE nm_cblas_nrm2(VALUE self, VALUE n, VALUE x, VALUE incx);
static VALUE nm_cblas_asum(VALUE self, VALUE n, VALUE x, VALUE incx);
static VALUE nm_cblas_rot(VALUE self, VALUE n, VALUE x, VALUE incx, VALUE y, VALUE incy, VALUE c, VALUE s);
static VALUE nm_cblas_rotg(VALUE self, VALUE ab);
static VALUE nm_cblas_imax(VALUE self, VALUE n, VALUE x, VALUE incx);
/* BLAS Level 2. */
static VALUE nm_cblas_gemv(VALUE self, VALUE trans_a, VALUE m, VALUE n, VALUE vAlpha, VALUE a, VALUE lda,
VALUE x, VALUE incx, VALUE vBeta, VALUE y, VALUE incy);
/* BLAS Level 3. */
static VALUE nm_cblas_gemm(VALUE self, VALUE order, VALUE trans_a, VALUE trans_b, VALUE m, VALUE n, VALUE k, VALUE vAlpha,
VALUE a, VALUE lda, VALUE b, VALUE ldb, VALUE vBeta, VALUE c, VALUE ldc);
static VALUE nm_cblas_trsm(VALUE self, VALUE order, VALUE side, VALUE uplo, VALUE trans_a, VALUE diag, VALUE m, VALUE n,
VALUE vAlpha, VALUE a, VALUE lda, VALUE b, VALUE ldb);
/* LAPACK. */
static VALUE nm_has_clapack(VALUE self);
static VALUE nm_clapack_getrf(VALUE self, VALUE order, VALUE m, VALUE n, VALUE a, VALUE lda);
static VALUE nm_clapack_getrs(VALUE self, VALUE order, VALUE trans, VALUE n, VALUE nrhs, VALUE a, VALUE lda, VALUE ipiv, VALUE b, VALUE ldb);
static VALUE nm_clapack_laswp(VALUE self, VALUE n, VALUE a, VALUE lda, VALUE k1, VALUE k2, VALUE ipiv, VALUE incx);
} // end of extern "C" block
////////////////////
// Math Functions //
////////////////////
namespace nm {
namespace math {
/*
* Calculate the determinant for a dense matrix (A [elements]) of size 2 or 3. Return the result.
*/
template <typename DType>
void det_exact_from_dense(const int M, const void* A_elements, const int lda, void* result_arg) {
DType* result = reinterpret_cast<DType*>(result_arg);
const DType* A = reinterpret_cast<const DType*>(A_elements);
typename LongDType<DType>::type x, y;
if (M == 2) {
*result = A[0] * A[lda+1] - A[1] * A[lda];
} else if (M == 3) {
x = A[lda+1] * A[2*lda+2] - A[lda+2] * A[2*lda+1]; // ei - fh
y = A[lda] * A[2*lda+2] - A[lda+2] * A[2*lda]; // fg - di
x = A[0]*x - A[1]*y ; // a*(ei-fh) - b*(fg-di)
y = A[lda] * A[2*lda+1] - A[lda+1] * A[2*lda]; // dh - eg
*result = A[2]*y + x; // c*(dh-eg) + _
} else if (M < 2) {
rb_raise(rb_eArgError, "can only calculate exact determinant of a square matrix of size 2 or larger");
} else {
rb_raise(rb_eNotImpError, "exact determinant calculation needed for matrices larger than 3x3");
}
}
//we can't do det_exact on byte, because it will want to return a byte (unsigned), but determinants can be negative, even if all elements of the matrix are positive
template <>
void det_exact_from_dense<uint8_t>(const int M, const void* A_elements, const int lda, void* result_arg) {
rb_raise(nm_eDataTypeError, "cannot call det_exact on unsigned type");
}
/*
* Calculate the determinant for a yale matrix (storage) of size 2 or 3. Return the result.
*/
template <typename DType>
void det_exact_from_yale(const int M, const YALE_STORAGE* storage, const int lda, void* result_arg) {
DType* result = reinterpret_cast<DType*>(result_arg);
IType* ija = reinterpret_cast<IType *>(storage->ija);
DType* a = reinterpret_cast<DType*>(storage->a);
IType col_pos = storage->shape[0] + 1;
if (M == 2) {
if (ija[2] - ija[0] == 2) {
*result = a[0] * a[1] - a[col_pos] * a[col_pos+1];
}
else { *result = a[0] * a[1]; }
} else if (M == 3) {
DType m[3][3];
for (int i = 0; i < 3; ++i) {
m[i][i] = a[i];
switch(ija[i+1] - ija[i]) {
case 2:
m[i][ija[col_pos]] = a[col_pos];
m[i][ija[col_pos+1]] = a[col_pos+1];
col_pos += 2;
break;
case 1:
m[i][(i+1)%3] = m[i][(i+2)%3] = 0;
m[i][ija[col_pos]] = a[col_pos];
++col_pos;
break;
case 0:
m[i][(i+1)%3] = m[i][(i+2)%3] = 0;
break;
default:
rb_raise(rb_eArgError, "some value in IJA is incorrect!");
}
}
*result =
m[0][0] * m[1][1] * m[2][2] + m[0][1] * m[1][2] * m[2][0] + m[0][2] * m[1][0] * m[2][1]
- m[0][0] * m[1][2] * m[2][1] - m[0][1] * m[1][0] * m[2][2] - m[0][2] * m[1][1] * m[2][0];
} else if (M < 2) {
rb_raise(rb_eArgError, "can only calculate exact determinant of a square matrix of size 2 or larger");
} else {
rb_raise(rb_eNotImpError, "exact determinant calculation needed for matrices larger than 3x3");
}
}
/*
* Solve a system of linear equations using forward-substution followed by
* back substution from the LU factorization of the matrix of co-efficients.
* Replaces x_elements with the result. Works only with non-integer, non-object
* data types.
*
* args - r -> The number of rows of the matrix.
* lu_elements -> Elements of the LU decomposition of the co-efficients
* matrix, as a contiguos array.
* b_elements -> Elements of the the right hand sides, as a contiguous array.
* x_elements -> The array that will contain the results of the computation.
* pivot -> Positions of permuted rows.
*/
template <typename DType>
void solve(const int r, const void* lu_elements, const void* b_elements, void* x_elements, const int* pivot) {
int ii = 0, ip;
DType sum;
const DType* matrix = reinterpret_cast<const DType*>(lu_elements);
const DType* b = reinterpret_cast<const DType*>(b_elements);
DType* x = reinterpret_cast<DType*>(x_elements);
for (int i = 0; i < r; ++i) { x[i] = b[i]; }
for (int i = 0; i < r; ++i) { // forward substitution loop
ip = pivot[i];
sum = x[ip];
x[ip] = x[i];
if (ii != 0) {
for (int j = ii - 1;j < i; ++j) { sum = sum - matrix[i * r + j] * x[j]; }
}
else if (sum != 0.0) {
ii = i + 1;
}
x[i] = sum;
}
for (int i = r - 1; i >= 0; --i) { // back substitution loop
sum = x[i];
for (int j = i + 1; j < r; j++) { sum = sum - matrix[i * r + j] * x[j]; }
x[i] = sum/matrix[i * r + i];
}
}
/*
* Calculates in-place inverse of A_elements. Uses Gauss-Jordan elimination technique.
* In-place inversion of the matrix saves on memory and time.
*
* args - M - Shape of the matrix
* a_elements - A duplicate of the original expressed as a contiguos array
*/
template <typename DType>
void inverse(const int M, void* a_elements) {
DType* matrix = reinterpret_cast<DType*>(a_elements);
int row_index[M]; // arrays for keeping track of column scrambling
int col_index[M];
for (int k = 0;k < M; ++k) {
typename MagnitudeDType<DType>::type akk;
akk = magnitude( matrix[k * (M + 1)] ); // diagonal element
int interchange = k;
for (int row = k + 1; row < M; ++row) {
typename MagnitudeDType<DType>::type big;
big = magnitude( matrix[M*row + k] ); // element below the temp pivot
if ( big > akk ) {
interchange = row;
akk = big;
}
}
if (interchange != k) { // check if rows need flipping
DType temp;
for (int col = 0; col < M; ++col) {
NM_SWAP(matrix[interchange*M + col], matrix[k*M + col], temp);
}
}
row_index[k] = interchange;
col_index[k] = k;
if (matrix[k * (M + 1)] == (DType)(0)) {
rb_raise(rb_eZeroDivError, "Expected Non-Singular Matrix.");
}
DType pivot = matrix[k * (M + 1)];
matrix[k * (M + 1)] = (DType)(1); // set diagonal as 1 for in-place inversion
for (int col = 0; col < M; ++col) {
// divide each element in the kth row with the pivot
matrix[k*M + col] = matrix[k*M + col] / pivot;
}
for (int kk = 0; kk < M; ++kk) { // iterate and reduce all rows
if (kk == k) continue;
DType dum = matrix[k + M*kk];
matrix[k + M*kk] = (DType)(0); // prepare for inplace inversion
for (int col = 0; col < M; ++col) {
matrix[M*kk + col] = matrix[M*kk + col] - matrix[M*k + col] * dum;
}
}
}
// Unscramble columns
DType temp;
for (int k = M - 1; k >= 0; --k) {
if (row_index[k] != col_index[k]) {
for (int row = 0; row < M; ++row) {
NM_SWAP(matrix[row * M + row_index[k]], matrix[row * M + col_index[k]],
temp);
}
}
}
}
/*
* Reduce a square matrix to hessenberg form with householder transforms
*
* == Arguments
*
* nrows - The number of rows present in matrix a.
* a_elements - Elements of the matrix to be reduced in 1D array form.
*
* == References
*
* http://www.mymathlib.com/c_source/matrices/eigen/hessenberg_orthog.c
* This code has been included by permission of the author.
*/
template <typename DType>
void hessenberg(const int nrows, void* a_elements) {
DType* a = reinterpret_cast<DType*>(a_elements);
DType* u = new DType[nrows]; // auxillary storage for the chosen vector
DType sum_of_squares, *p_row, *psubdiag, *p_a, scale, innerproduct;
int i, k, col;
// For each column use a Householder transformation to zero all entries
// below the subdiagonal.
for (psubdiag = a + nrows, col = 0; col < nrows - 2; psubdiag += nrows + 1,
col++) {
// Calculate the signed square root of the sum of squares of the
// elements below the diagonal.
for (p_a = psubdiag, sum_of_squares = 0.0, i = col + 1; i < nrows;
p_a += nrows, i++) {
sum_of_squares += *p_a * *p_a;
}
if (sum_of_squares == 0.0) { continue; }
sum_of_squares = std::sqrt(sum_of_squares);
if ( *psubdiag >= 0.0 ) { sum_of_squares = -sum_of_squares; }
// Calculate the Householder transformation Q = I - 2uu'/u'u.
u[col + 1] = *psubdiag - sum_of_squares;
*psubdiag = sum_of_squares;
for (p_a = psubdiag + nrows, i = col + 2; i < nrows; p_a += nrows, i++) {
u[i] = *p_a;
*p_a = 0.0;
}
// Premultiply A by Q
scale = -1.0 / (sum_of_squares * u[col+1]);
for (p_row = psubdiag - col, i = col + 1; i < nrows; i++) {
p_a = a + nrows * (col + 1) + i;
for (innerproduct = 0.0, k = col + 1; k < nrows; p_a += nrows, k++) {
innerproduct += u[k] * *p_a;
}
innerproduct *= scale;
for (p_a = p_row + i, k = col + 1; k < nrows; p_a += nrows, k++) {
*p_a -= u[k] * innerproduct;
}
}
// Postmultiply QA by Q
for (p_row = a, i = 0; i < nrows; p_row += nrows, i++) {
for (innerproduct = 0.0, k = col + 1; k < nrows; k++) {
innerproduct += u[k] * *(p_row + k);
}
innerproduct *= scale;
for (k = col + 1; k < nrows; k++) {
*(p_row + k) -= u[k] * innerproduct;
}
}
}
delete[] u;
}
void raise_not_invertible_error() {
rb_raise(nm_eNotInvertibleError,
"matrix must have non-zero determinant to be invertible (not getting this error does not mean matrix is invertible if you're dealing with floating points)");
}
/*
* Calculate the exact inverse for a dense matrix (A [elements]) of size 2 or 3. Places the result in B_elements.
*/
template <typename DType>
void inverse_exact_from_dense(const int M, const void* A_elements,
const int lda, void* B_elements, const int ldb) {
const DType* A = reinterpret_cast<const DType*>(A_elements);
DType* B = reinterpret_cast<DType*>(B_elements);
if (M == 2) {
DType det = A[0] * A[lda+1] - A[1] * A[lda];
if (det == 0) { raise_not_invertible_error(); }
B[0] = A[lda+1] / det;
B[1] = -A[1] / det;
B[ldb] = -A[lda] / det;
B[ldb+1] = A[0] / det;
} else if (M == 3) {
// Calculate the exact determinant.
DType det;
det_exact_from_dense<DType>(M, A_elements, lda, reinterpret_cast<void*>(&det));
if (det == 0) { raise_not_invertible_error(); }
B[0] = ( A[lda+1] * A[2*lda+2] - A[lda+2] * A[2*lda+1]) / det; // A = ei - fh
B[1] = (- A[1] * A[2*lda+2] + A[2] * A[2*lda+1]) / det; // D = -bi + ch
B[2] = ( A[1] * A[lda+2] - A[2] * A[lda+1]) / det; // G = bf - ce
B[ldb] = (- A[lda] * A[2*lda+2] + A[lda+2] * A[2*lda]) / det; // B = -di + fg
B[ldb+1] = ( A[0] * A[2*lda+2] - A[2] * A[2*lda]) / det; // E = ai - cg
B[ldb+2] = (- A[0] * A[lda+2] + A[2] * A[lda]) / det; // H = -af + cd
B[2*ldb] = ( A[lda] * A[2*lda+1] - A[lda+1] * A[2*lda]) / det; // C = dh - eg
B[2*ldb+1]= ( -A[0] * A[2*lda+1] + A[1] * A[2*lda]) / det; // F = -ah + bg
B[2*ldb+2]= ( A[0] * A[lda+1] - A[1] * A[lda]) / det; // I = ae - bd
} else if (M == 1) {
B[0] = 1 / A[0];
} else {
rb_raise(rb_eNotImpError, "exact inverse calculation needed for matrices larger than 3x3");
}
}
template <typename DType>
void inverse_exact_from_yale(const int M, const YALE_STORAGE* storage,
const int lda, YALE_STORAGE* inverse, const int ldb) {
// inverse is a clone of storage
const DType* a = reinterpret_cast<const DType*>(storage->a);
const IType* ija = reinterpret_cast<const IType *>(storage->ija);
DType* b = reinterpret_cast<DType*>(inverse->a);
IType* ijb = reinterpret_cast<IType *>(inverse->ija);
IType col_pos = storage->shape[0] + 1;
// Calculate the exact determinant.
DType det;
if (M == 2) {
IType ndnz = ija[2] - ija[0];
if (ndnz == 2) {
det = a[0] * a[1] - a[col_pos] * a[col_pos+1];
}
else { det = a[0] * a[1]; }
if (det == 0) { raise_not_invertible_error(); }
b[0] = a[1] / det;
b[1] = a[0] / det;
if (ndnz == 2) {
b[col_pos] = -a[col_pos] / det;
b[col_pos+1] = -a[col_pos+1] / det;
}
else if (ndnz == 1) {
b[col_pos] = -a[col_pos] / det;
}
} else if (M == 3) {
DType *A = new DType[lda*3];
for (int i = 0; i < lda; ++i) {
A[i*3+i] = a[i];
switch (ija[i+1] - ija[i]) {
case 2:
A[i*3 + ija[col_pos]] = a[col_pos];
A[i*3 + ija[col_pos+1]] = a[col_pos+1];
col_pos += 2;
break;
case 1:
A[i*3 + (i+1)%3] = A[i*3 + (i+2)%3] = 0;
A[i*3 + ija[col_pos]] = a[col_pos];
col_pos += 1;
break;
case 0:
A[i*3 + (i+1)%3] = A[i*3 + (i+2)%3] = 0;
break;
default:
rb_raise(rb_eArgError, "some value in IJA is incorrect!");
}
}
det =
A[0] * A[lda+1] * A[2*lda+2] + A[1] * A[lda+2] * A[2*lda] + A[2] * A[lda] * A[2*lda+1]
- A[0] * A[lda+2] * A[2*lda+1] - A[1] * A[lda] * A[2*lda+2] - A[2] * A[lda+1] * A[2*lda];
if (det == 0) { raise_not_invertible_error(); }
DType *B = new DType[3*ldb];
B[0] = ( A[lda+1] * A[2*lda+2] - A[lda+2] * A[2*lda+1]) / det; // A = ei - fh
B[1] = (- A[1] * A[2*lda+2] + A[2] * A[2*lda+1]) / det; // D = -bi + ch
B[2] = ( A[1] * A[lda+2] - A[2] * A[lda+1]) / det; // G = bf - ce
B[ldb] = (- A[lda] * A[2*lda+2] + A[lda+2] * A[2*lda]) / det; // B = -di + fg
B[ldb+1] = ( A[0] * A[2*lda+2] - A[2] * A[2*lda]) / det; // E = ai - cg
B[ldb+2] = (- A[0] * A[lda+2] + A[2] * A[lda]) / det; // H = -af + cd
B[2*ldb] = ( A[lda] * A[2*lda+1] - A[lda+1] * A[2*lda]) / det; // C = dh - eg
B[2*ldb+1]= ( -A[0] * A[2*lda+1] + A[1] * A[2*lda]) / det; // F = -ah + bg
B[2*ldb+2]= ( A[0] * A[lda+1] - A[1] * A[lda]) / det; // I = ae - bd
// Calculate the size of ijb and b, then reallocate them.
IType ndnz = 0;
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
if (j != i && B[i*ldb + j] != 0) { ++ndnz; }
}
}
inverse->ndnz = ndnz;
col_pos = 4; // shape[0] + 1
inverse->capacity = 4 + ndnz;
NM_REALLOC_N(inverse->a, DType, 4 + ndnz);
NM_REALLOC_N(inverse->ija, IType, 4 + ndnz);
b = reinterpret_cast<DType*>(inverse->a);
ijb = reinterpret_cast<IType *>(inverse->ija);
for (int i = 0; i < 3; ++i) {
ijb[i] = col_pos;
for (int j = 0; j < 3; ++j) {
if (j == i) {
b[i] = B[i*ldb + j];
}
else if (B[i*ldb + j] != 0) {
b[col_pos] = B[i*ldb + j];
ijb[col_pos] = j;
++col_pos;
}
}
}
b[3] = 0;
ijb[3] = col_pos;
delete [] B;
delete [] A;
} else if (M == 1) {
b[0] = 1 / a[0];
} else {
rb_raise(rb_eNotImpError, "exact inverse calculation needed for matrices larger than 3x3");
}
}
/*
* Function signature conversion for calling CBLAS' gemm functions as directly as possible.
*
* For documentation: http://www.netlib.org/blas/dgemm.f
*/
template <typename DType>
inline static void cblas_gemm(const enum CBLAS_ORDER order,
const enum CBLAS_TRANSPOSE trans_a, const enum CBLAS_TRANSPOSE trans_b,
int m, int n, int k,
void* alpha,
void* a, int lda,
void* b, int ldb,
void* beta,
void* c, int ldc)
{
gemm<DType>(order, trans_a, trans_b, m, n, k, reinterpret_cast<DType*>(alpha),
reinterpret_cast<DType*>(a), lda,
reinterpret_cast<DType*>(b), ldb, reinterpret_cast<DType*>(beta),
reinterpret_cast<DType*>(c), ldc);
}
/*
* Function signature conversion for calling CBLAS's gemv functions as directly as possible.
*
* For documentation: http://www.netlib.org/lapack/double/dgetrf.f
*/
template <typename DType>
inline static bool cblas_gemv(const enum CBLAS_TRANSPOSE trans,
const int m, const int n,
const void* alpha,
const void* a, const int lda,
const void* x, const int incx,
const void* beta,
void* y, const int incy)
{
return gemv<DType>(trans,
m, n, reinterpret_cast<const DType*>(alpha),
reinterpret_cast<const DType*>(a), lda,
reinterpret_cast<const DType*>(x), incx, reinterpret_cast<const DType*>(beta),
reinterpret_cast<DType*>(y), incy);
}
/*
* Function signature conversion for calling CBLAS' trsm functions as directly as possible.
*
* For documentation: http://www.netlib.org/blas/dtrsm.f
*/
template <typename DType>
inline static void cblas_trsm(const enum CBLAS_ORDER order, const enum CBLAS_SIDE side, const enum CBLAS_UPLO uplo,
const enum CBLAS_TRANSPOSE trans_a, const enum CBLAS_DIAG diag,
const int m, const int n, const void* alpha, const void* a,
const int lda, void* b, const int ldb)
{
trsm<DType>(order, side, uplo, trans_a, diag, m, n, *reinterpret_cast<const DType*>(alpha),
reinterpret_cast<const DType*>(a), lda, reinterpret_cast<DType*>(b), ldb);
}
}
} // end of namespace nm::math
extern "C" {
///////////////////
// Ruby Bindings //
///////////////////
void nm_math_init_blas() {
VALUE cNMatrix_Internal = rb_define_module_under(cNMatrix, "Internal");
rb_define_singleton_method(cNMatrix, "has_clapack?", (METHOD)nm_has_clapack, 0);
VALUE cNMatrix_Internal_LAPACK = rb_define_module_under(cNMatrix_Internal, "LAPACK");
/* ATLAS-CLAPACK Functions that are implemented internally */
rb_define_singleton_method(cNMatrix_Internal_LAPACK, "clapack_getrf", (METHOD)nm_clapack_getrf, 5);
rb_define_singleton_method(cNMatrix_Internal_LAPACK, "clapack_getrs", (METHOD)nm_clapack_getrs, 9);
rb_define_singleton_method(cNMatrix_Internal_LAPACK, "clapack_laswp", (METHOD)nm_clapack_laswp, 7);
VALUE cNMatrix_Internal_BLAS = rb_define_module_under(cNMatrix_Internal, "BLAS");
rb_define_singleton_method(cNMatrix_Internal_BLAS, "cblas_scal", (METHOD)nm_cblas_scal, 4);
rb_define_singleton_method(cNMatrix_Internal_BLAS, "cblas_nrm2", (METHOD)nm_cblas_nrm2, 3);
rb_define_singleton_method(cNMatrix_Internal_BLAS, "cblas_asum", (METHOD)nm_cblas_asum, 3);
rb_define_singleton_method(cNMatrix_Internal_BLAS, "cblas_rot", (METHOD)nm_cblas_rot, 7);
rb_define_singleton_method(cNMatrix_Internal_BLAS, "cblas_rotg", (METHOD)nm_cblas_rotg, 1);
rb_define_singleton_method(cNMatrix_Internal_BLAS, "cblas_imax", (METHOD)nm_cblas_imax, 3);
rb_define_singleton_method(cNMatrix_Internal_BLAS, "cblas_gemm", (METHOD)nm_cblas_gemm, 14);
rb_define_singleton_method(cNMatrix_Internal_BLAS, "cblas_gemv", (METHOD)nm_cblas_gemv, 11);
rb_define_singleton_method(cNMatrix_Internal_BLAS, "cblas_trsm", (METHOD)nm_cblas_trsm, 12);
}
/*
* call-seq:
* NMatrix::BLAS.cblas_scal(n, alpha, vector, inc) -> NMatrix
*
* BLAS level 1 function +scal+. Works with all dtypes.
*
* Scale +vector+ in-place by +alpha+ and also return it. The operation is as
* follows:
* x <- alpha * x
*
* - +n+ -> Number of elements of +vector+.
* - +alpha+ -> Scalar value used in the operation.
* - +vector+ -> NMatrix of shape [n,1] or [1,n]. Modified in-place.
* - +inc+ -> Increment used in the scaling function. Should generally be 1.
*/
static VALUE nm_cblas_scal(VALUE self, VALUE n, VALUE alpha, VALUE vector, VALUE incx) {
nm::dtype_t dtype = NM_DTYPE(vector);
void* scalar = NM_ALLOCA_N(char, DTYPE_SIZES[dtype]);
rubyval_to_cval(alpha, dtype, scalar);
NAMED_DTYPE_TEMPLATE_TABLE(ttable, nm::math::cblas_scal, void, const int n,
const void* scalar, void* x, const int incx);
ttable[dtype](FIX2INT(n), scalar, NM_STORAGE_DENSE(vector)->elements,
FIX2INT(incx));
return vector;
}
/*
* Call any of the cblas_xrotg functions as directly as possible.
*
* xROTG computes the elements of a Givens plane rotation matrix such that:
*
* | c s | | a | | r |
* | -s c | * | b | = | 0 |
*
* where r = +- sqrt( a**2 + b**2 ) and c**2 + s**2 = 1.
*
* The Givens plane rotation can be used to introduce zero elements into a matrix selectively.
*
* This function differs from most of the other raw BLAS accessors. Instead of
* providing a, b, c, s as arguments, you should only provide a and b (the
* inputs), and you should provide them as the first two elements of any dense
* NMatrix type.
*
* The outputs [c,s] will be returned in a Ruby Array at the end; the input
* NMatrix will also be modified in-place.
*
* This function, like the other cblas_ functions, does minimal type-checking.
*/
static VALUE nm_cblas_rotg(VALUE self, VALUE ab) {
static void (*ttable[nm::NUM_DTYPES])(void* a, void* b, void* c, void* s) = {
NULL, NULL, NULL, NULL, NULL, // can't represent c and s as integers, so no point in having integer operations.
nm::math::cblas_rotg<float>,
nm::math::cblas_rotg<double>,
nm::math::cblas_rotg<nm::Complex64>,
nm::math::cblas_rotg<nm::Complex128>,
NULL //nm::math::cblas_rotg<nm::RubyObject>
};
nm::dtype_t dtype = NM_DTYPE(ab);
if (!ttable[dtype]) {
rb_raise(nm_eDataTypeError, "this operation undefined for integer vectors");
return Qnil;
} else {
NM_CONSERVATIVE(nm_register_value(&self));
NM_CONSERVATIVE(nm_register_value(&ab));
void *pC = NM_ALLOCA_N(char, DTYPE_SIZES[dtype]),
*pS = NM_ALLOCA_N(char, DTYPE_SIZES[dtype]);
// extract A and B from the NVector (first two elements)
void* pA = NM_STORAGE_DENSE(ab)->elements;
void* pB = (char*)(NM_STORAGE_DENSE(ab)->elements) + DTYPE_SIZES[dtype];
// c and s are output
ttable[dtype](pA, pB, pC, pS);
VALUE result = rb_ary_new2(2);
if (dtype == nm::RUBYOBJ) {
rb_ary_store(result, 0, *reinterpret_cast<VALUE*>(pC));
rb_ary_store(result, 1, *reinterpret_cast<VALUE*>(pS));
} else {
rb_ary_store(result, 0, nm::rubyobj_from_cval(pC, dtype).rval);
rb_ary_store(result, 1, nm::rubyobj_from_cval(pS, dtype).rval);
}
NM_CONSERVATIVE(nm_unregister_value(&ab));
NM_CONSERVATIVE(nm_unregister_value(&self));
return result;
}
}
/*
* Call any of the cblas_xrot functions as directly as possible.
*
* xROT is a BLAS level 1 routine (taking two vectors) which applies a plane rotation.
*
* It's tough to find documentation on xROT. Here are what we think the arguments are for:
* * n :: number of elements to consider in x and y
* * x :: a vector (expects an NVector)
* * incx :: stride of x
* * y :: a vector (expects an NVector)
* * incy :: stride of y
* * c :: cosine of the angle of rotation
* * s :: sine of the angle of rotation
*
* Note that c and s will be the same dtype as x and y, except when x and y are complex. If x and y are complex, c and s
* will be float for Complex64 or double for Complex128.
*
* You probably don't want to call this function. Instead, why don't you try rot, which is more flexible
* with its arguments?
*
* This function does almost no type checking. Seriously, be really careful when you call it! There's no exception
* handling, so you can easily crash Ruby!
*/
static VALUE nm_cblas_rot(VALUE self, VALUE n, VALUE x, VALUE incx, VALUE y, VALUE incy, VALUE c, VALUE s) {
static void (*ttable[nm::NUM_DTYPES])(const int N, void*, const int, void*, const int, const void*, const void*) = {
NULL, NULL, NULL, NULL, NULL, // can't represent c and s as integers, so no point in having integer operations.
nm::math::cblas_rot<float,float>,
nm::math::cblas_rot<double,double>,
nm::math::cblas_rot<nm::Complex64,float>,
nm::math::cblas_rot<nm::Complex128,double>,
nm::math::cblas_rot<nm::RubyObject,nm::RubyObject>
};
nm::dtype_t dtype = NM_DTYPE(x);
if (!ttable[dtype]) {
rb_raise(nm_eDataTypeError, "this operation undefined for integer vectors");
return Qfalse;
} else {
void *pC, *pS;
// We need to ensure the cosine and sine arguments are the correct dtype -- which may differ from the actual dtype.
if (dtype == nm::COMPLEX64) {
pC = NM_ALLOCA_N(float,1);
pS = NM_ALLOCA_N(float,1);
rubyval_to_cval(c, nm::FLOAT32, pC);
rubyval_to_cval(s, nm::FLOAT32, pS);
} else if (dtype == nm::COMPLEX128) {
pC = NM_ALLOCA_N(double,1);
pS = NM_ALLOCA_N(double,1);
rubyval_to_cval(c, nm::FLOAT64, pC);
rubyval_to_cval(s, nm::FLOAT64, pS);
} else {
pC = NM_ALLOCA_N(char, DTYPE_SIZES[dtype]);
pS = NM_ALLOCA_N(char, DTYPE_SIZES[dtype]);
rubyval_to_cval(c, dtype, pC);
rubyval_to_cval(s, dtype, pS);
}
ttable[dtype](FIX2INT(n), NM_STORAGE_DENSE(x)->elements, FIX2INT(incx), NM_STORAGE_DENSE(y)->elements, FIX2INT(incy), pC, pS);
return Qtrue;
}
}
/*
* Call any of the cblas_xnrm2 functions as directly as possible.
*
* xNRM2 is a BLAS level 1 routine which calculates the 2-norm of an n-vector x.
*
* Arguments:
* * n :: length of x, must be at least 0
* * x :: pointer to first entry of input vector
* * incx :: stride of x, must be POSITIVE (ATLAS says non-zero, but 3.8.4 code only allows positive)
*
* You probably don't want to call this function. Instead, why don't you try nrm2, which is more flexible
* with its arguments?
*
* This function does almost no type checking. Seriously, be really careful when you call it! There's no exception
* handling, so you can easily crash Ruby!
*/
static VALUE nm_cblas_nrm2(VALUE self, VALUE n, VALUE x, VALUE incx) {
static void (*ttable[nm::NUM_DTYPES])(const int N, const void* X, const int incX, void* sum) = {
NULL, NULL, NULL, NULL, NULL, // no help for integers
nm::math::cblas_nrm2<float32_t>,
nm::math::cblas_nrm2<float64_t>,
nm::math::cblas_nrm2<nm::Complex64>,
nm::math::cblas_nrm2<nm::Complex128>,
nm::math::cblas_nrm2<nm::RubyObject>
};
nm::dtype_t dtype = NM_DTYPE(x);
if (!ttable[dtype]) {
rb_raise(nm_eDataTypeError, "this operation undefined for integer vectors");
return Qnil;
} else {
// Determine the return dtype and allocate it
nm::dtype_t rdtype = dtype;
if (dtype == nm::COMPLEX64) rdtype = nm::FLOAT32;
else if (dtype == nm::COMPLEX128) rdtype = nm::FLOAT64;
void *Result = NM_ALLOCA_N(char, DTYPE_SIZES[rdtype]);
ttable[dtype](FIX2INT(n), NM_STORAGE_DENSE(x)->elements, FIX2INT(incx), Result);
return nm::rubyobj_from_cval(Result, rdtype).rval;
}
}
/*
* Call any of the cblas_xasum functions as directly as possible.
*
* xASUM is a BLAS level 1 routine which calculates the sum of absolute values of the entries
* of a vector x.
*
* Arguments:
* * n :: length of x, must be at least 0
* * x :: pointer to first entry of input vector
* * incx :: stride of x, must be POSITIVE (ATLAS says non-zero, but 3.8.4 code only allows positive)
*
* You probably don't want to call this function. Instead, why don't you try asum, which is more flexible
* with its arguments?
*
* This function does almost no type checking. Seriously, be really careful when you call it! There's no exception
* handling, so you can easily crash Ruby!
*/
static VALUE nm_cblas_asum(VALUE self, VALUE n, VALUE x, VALUE incx) {
static void (*ttable[nm::NUM_DTYPES])(const int N, const void* X, const int incX, void* sum) = {
nm::math::cblas_asum<uint8_t>,
nm::math::cblas_asum<int8_t>,
nm::math::cblas_asum<int16_t>,
nm::math::cblas_asum<int32_t>,
nm::math::cblas_asum<int64_t>,
nm::math::cblas_asum<float32_t>,
nm::math::cblas_asum<float64_t>,
nm::math::cblas_asum<nm::Complex64>,
nm::math::cblas_asum<nm::Complex128>,
nm::math::cblas_asum<nm::RubyObject>
};
nm::dtype_t dtype = NM_DTYPE(x);
// Determine the return dtype and allocate it
nm::dtype_t rdtype = dtype;
if (dtype == nm::COMPLEX64) rdtype = nm::FLOAT32;
else if (dtype == nm::COMPLEX128) rdtype = nm::FLOAT64;
void *Result = NM_ALLOCA_N(char, DTYPE_SIZES[rdtype]);
ttable[dtype](FIX2INT(n), NM_STORAGE_DENSE(x)->elements, FIX2INT(incx), Result);
return nm::rubyobj_from_cval(Result, rdtype).rval;
}
/*
* call-seq:
* NMatrix::BLAS.cblas_imax(n, vector, inc) -> Fixnum
*
* BLAS level 1 routine.
*
* Return the index of the largest element of +vector+.
*
* - +n+ -> Vector's size. Generally, you can use NMatrix#rows or NMatrix#cols.
* - +vector+ -> A NMatrix of shape [n,1] or [1,n] with any dtype.
* - +inc+ -> It's the increment used when searching. Use 1 except if you know
* what you're doing.
*/
static VALUE nm_cblas_imax(VALUE self, VALUE n, VALUE x, VALUE incx) {
NAMED_DTYPE_TEMPLATE_TABLE(ttable, nm::math::cblas_imax, int, const int n, const void* x, const int incx);
nm::dtype_t dtype = NM_DTYPE(x);
int index = ttable[dtype](FIX2INT(n), NM_STORAGE_DENSE(x)->elements, FIX2INT(incx));
// Convert to Ruby's Int value.
return INT2FIX(index);
}
/* Call any of the cblas_xgemm functions as directly as possible.
*
* The cblas_xgemm functions (dgemm, sgemm, cgemm, and zgemm) define the following operation:
*
* C = alpha*op(A)*op(B) + beta*C
*
* where op(X) is one of <tt>op(X) = X</tt>, <tt>op(X) = X**T</tt>, or the complex conjugate of X.
*
* Note that this will only work for dense matrices that are of types :float32, :float64, :complex64, and :complex128.
* Other types are not implemented in BLAS, and while they exist in NMatrix, this method is intended only to
* expose the ultra-optimized ATLAS versions.
*
* == Arguments
* See: http://www.netlib.org/blas/dgemm.f
*
* You probably don't want to call this function. Instead, why don't you try gemm, which is more flexible
* with its arguments?
*
* This function does almost no type checking. Seriously, be really careful when you call it! There's no exception
* handling, so you can easily crash Ruby!
*/
static VALUE nm_cblas_gemm(VALUE self,
VALUE order,
VALUE trans_a, VALUE trans_b,
VALUE m, VALUE n, VALUE k,
VALUE alpha,
VALUE a, VALUE lda,
VALUE b, VALUE ldb,
VALUE beta,
VALUE c, VALUE ldc)
{
NAMED_DTYPE_TEMPLATE_TABLE(ttable, nm::math::cblas_gemm, void, const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE trans_a, const enum CBLAS_TRANSPOSE trans_b, int m, int n, int k, void* alpha, void* a, int lda, void* b, int ldb, void* beta, void* c, int ldc);
nm::dtype_t dtype = NM_DTYPE(a);
void *pAlpha = NM_ALLOCA_N(char, DTYPE_SIZES[dtype]),
*pBeta = NM_ALLOCA_N(char, DTYPE_SIZES[dtype]);
rubyval_to_cval(alpha, dtype, pAlpha);
rubyval_to_cval(beta, dtype, pBeta);
ttable[dtype](blas_order_sym(order), blas_transpose_sym(trans_a), blas_transpose_sym(trans_b), FIX2INT(m), FIX2INT(n), FIX2INT(k), pAlpha, NM_STORAGE_DENSE(a)->elements, FIX2INT(lda), NM_STORAGE_DENSE(b)->elements, FIX2INT(ldb), pBeta, NM_STORAGE_DENSE(c)->elements, FIX2INT(ldc));
return c;
}
/* Call any of the cblas_xgemv functions as directly as possible.
*
* The cblas_xgemv functions (dgemv, sgemv, cgemv, and zgemv) define the following operation:
*
* y = alpha*op(A)*x + beta*y
*
* where op(A) is one of <tt>op(A) = A</tt>, <tt>op(A) = A**T</tt>, or the complex conjugate of A.
*
* Note that this will only work for dense matrices that are of types :float32, :float64, :complex64, and :complex128.
* Other types are not implemented in BLAS, and while they exist in NMatrix, this method is intended only to
* expose the ultra-optimized ATLAS versions.
*
* == Arguments
* See: http://www.netlib.org/blas/dgemm.f
*
* You probably don't want to call this function. Instead, why don't you try cblas_gemv, which is more flexible
* with its arguments?
*
* This function does almost no type checking. Seriously, be really careful when you call it! There's no exception
* handling, so you can easily crash Ruby!
*/
static VALUE nm_cblas_gemv(VALUE self,
VALUE trans_a,
VALUE m, VALUE n,
VALUE alpha,
VALUE a, VALUE lda,
VALUE x, VALUE incx,
VALUE beta,
VALUE y, VALUE incy)
{
NAMED_DTYPE_TEMPLATE_TABLE(ttable, nm::math::cblas_gemv, bool, const enum CBLAS_TRANSPOSE, const int, const int, const void*, const void*, const int, const void*, const int, const void*, void*, const int)
nm::dtype_t dtype = NM_DTYPE(a);
void *pAlpha = NM_ALLOCA_N(char, DTYPE_SIZES[dtype]),
*pBeta = NM_ALLOCA_N(char, DTYPE_SIZES[dtype]);
rubyval_to_cval(alpha, dtype, pAlpha);
rubyval_to_cval(beta, dtype, pBeta);
return ttable[dtype](blas_transpose_sym(trans_a), FIX2INT(m), FIX2INT(n), pAlpha, NM_STORAGE_DENSE(a)->elements, FIX2INT(lda), NM_STORAGE_DENSE(x)->elements, FIX2INT(incx), pBeta, NM_STORAGE_DENSE(y)->elements, FIX2INT(incy)) ? Qtrue : Qfalse;
}
static VALUE nm_cblas_trsm(VALUE self,
VALUE order,
VALUE side, VALUE uplo,
VALUE trans_a, VALUE diag,
VALUE m, VALUE n,
VALUE alpha,
VALUE a, VALUE lda,
VALUE b, VALUE ldb)
{
static void (*ttable[nm::NUM_DTYPES])(const enum CBLAS_ORDER, const enum CBLAS_SIDE, const enum CBLAS_UPLO,
const enum CBLAS_TRANSPOSE, const enum CBLAS_DIAG,
const int m, const int n, const void* alpha, const void* a,
const int lda, void* b, const int ldb) = {
NULL, NULL, NULL, NULL, NULL, // integers not allowed due to division
nm::math::cblas_trsm<float>,
nm::math::cblas_trsm<double>,
nm::math::cblas_trsm<nm::Complex64>,
nm::math::cblas_trsm<nm::Complex128>,
nm::math::cblas_trsm<nm::RubyObject>
};
nm::dtype_t dtype = NM_DTYPE(a);
if (!ttable[dtype]) {
rb_raise(nm_eDataTypeError, "this matrix operation undefined for integer matrices");
} else {
void *pAlpha = NM_ALLOCA_N(char, DTYPE_SIZES[dtype]);
rubyval_to_cval(alpha, dtype, pAlpha);
ttable[dtype](blas_order_sym(order), blas_side_sym(side), blas_uplo_sym(uplo), blas_transpose_sym(trans_a), blas_diag_sym(diag), FIX2INT(m), FIX2INT(n), pAlpha, NM_STORAGE_DENSE(a)->elements, FIX2INT(lda), NM_STORAGE_DENSE(b)->elements, FIX2INT(ldb));
}
return Qtrue;
}
/* Call any of the clapack_xgetrf functions as directly as possible.
*
* The clapack_getrf functions (dgetrf, sgetrf, cgetrf, and zgetrf) compute an LU factorization of a general M-by-N
* matrix A using partial pivoting with row interchanges.
*
* The factorization has the form:
* A = P * L * U
* where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n),
* and U is upper triangular (upper trapezoidal if m < n).
*
* This is the right-looking level 3 BLAS version of the algorithm.
*
* == Arguments
* See: http://www.netlib.org/lapack/double/dgetrf.f
* (You don't need argument 5; this is the value returned by this function.)
*
* You probably don't want to call this function. Instead, why don't you try clapack_getrf, which is more flexible
* with its arguments?
*
* This function does almost no type checking. Seriously, be really careful when you call it! There's no exception
* handling, so you can easily crash Ruby!
*
* Returns an array giving the pivot indices (normally these are argument #5).
*/
static VALUE nm_clapack_getrf(VALUE self, VALUE order, VALUE m, VALUE n, VALUE a, VALUE lda) {
static int (*ttable[nm::NUM_DTYPES])(const enum CBLAS_ORDER, const int m, const int n, void* a, const int lda, int* ipiv) = {
NULL, NULL, NULL, NULL, NULL, // integers not allowed due to division
nm::math::clapack_getrf<float>,
nm::math::clapack_getrf<double>,
nm::math::clapack_getrf<nm::Complex64>,
nm::math::clapack_getrf<nm::Complex128>,
nm::math::clapack_getrf<nm::RubyObject>
};
int M = FIX2INT(m),
N = FIX2INT(n);
// Allocate the pivot index array, which is of size MIN(M, N).
size_t ipiv_size = std::min(M,N);
int* ipiv = NM_ALLOCA_N(int, ipiv_size);
if (!ttable[NM_DTYPE(a)]) {
rb_raise(nm_eDataTypeError, "this matrix operation undefined for integer matrices");
} else {
// Call either our version of getrf or the LAPACK version.
ttable[NM_DTYPE(a)](blas_order_sym(order), M, N, NM_STORAGE_DENSE(a)->elements, FIX2INT(lda), ipiv);
}
// Result will be stored in a. We return ipiv as an array.
VALUE ipiv_array = rb_ary_new2(ipiv_size);
for (size_t i = 0; i < ipiv_size; ++i) {
rb_ary_store(ipiv_array, i, INT2FIX(ipiv[i]));
}
return ipiv_array;
}
/*
* Call any of the clapack_xgetrs functions as directly as possible.
*/
static VALUE nm_clapack_getrs(VALUE self, VALUE order, VALUE trans, VALUE n, VALUE nrhs, VALUE a, VALUE lda, VALUE ipiv, VALUE b, VALUE ldb) {
static int (*ttable[nm::NUM_DTYPES])(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE Trans, const int N,
const int NRHS, const void* A, const int lda, const int* ipiv, void* B,
const int ldb) = {
NULL, NULL, NULL, NULL, NULL, // integers not allowed due to division
nm::math::clapack_getrs<float>,
nm::math::clapack_getrs<double>,
nm::math::clapack_getrs<nm::Complex64>,
nm::math::clapack_getrs<nm::Complex128>,
nm::math::clapack_getrs<nm::RubyObject>
};
// Allocate the C version of the pivot index array
int* ipiv_;
if (!RB_TYPE_P(ipiv, T_ARRAY)) {
rb_raise(rb_eArgError, "ipiv must be of type Array");
} else {
ipiv_ = NM_ALLOCA_N(int, RARRAY_LEN(ipiv));
for (int index = 0; index < RARRAY_LEN(ipiv); ++index) {
ipiv_[index] = FIX2INT( RARRAY_AREF(ipiv, index) );
}
}
if (!ttable[NM_DTYPE(a)]) {
rb_raise(nm_eDataTypeError, "this matrix operation undefined for integer matrices");
} else {
// Call either our version of getrs or the LAPACK version.
ttable[NM_DTYPE(a)](blas_order_sym(order), blas_transpose_sym(trans), FIX2INT(n), FIX2INT(nrhs), NM_STORAGE_DENSE(a)->elements, FIX2INT(lda),
ipiv_, NM_STORAGE_DENSE(b)->elements, FIX2INT(ldb));
}
// b is both returned and modified directly in the argument list.
return b;
}
/*
* Simple way to check from within Ruby code if clapack functions are available, without
* having to wait around for an exception to be thrown.
*/
static VALUE nm_has_clapack(VALUE self) {
return Qfalse;
}
/*
* Call any of the clapack_xlaswp functions as directly as possible.
*
* Note that LAPACK's xlaswp functions accept a column-order matrix, but NMatrix uses row-order. Thus, n should be the
* number of rows and lda should be the number of columns, no matter what it says in the documentation for dlaswp.f.
*/
static VALUE nm_clapack_laswp(VALUE self, VALUE n, VALUE a, VALUE lda, VALUE k1, VALUE k2, VALUE ipiv, VALUE incx) {
static void (*ttable[nm::NUM_DTYPES])(const int n, void* a, const int lda, const int k1, const int k2, const int* ipiv, const int incx) = {
nm::math::clapack_laswp<uint8_t>,
nm::math::clapack_laswp<int8_t>,
nm::math::clapack_laswp<int16_t>,
nm::math::clapack_laswp<int32_t>,
nm::math::clapack_laswp<int64_t>,
nm::math::clapack_laswp<float>,
nm::math::clapack_laswp<double>,
nm::math::clapack_laswp<nm::Complex64>,
nm::math::clapack_laswp<nm::Complex128>,
nm::math::clapack_laswp<nm::RubyObject>
};
// Allocate the C version of the pivot index array
int* ipiv_;
if (!RB_TYPE_P(ipiv, T_ARRAY)) {
rb_raise(rb_eArgError, "ipiv must be of type Array");
} else {
ipiv_ = NM_ALLOCA_N(int, RARRAY_LEN(ipiv));
for (int index = 0; index < RARRAY_LEN(ipiv); ++index) {
ipiv_[index] = FIX2INT( RARRAY_AREF(ipiv, index) );
}
}
// Call either our version of laswp or the LAPACK version.
ttable[NM_DTYPE(a)](FIX2INT(n), NM_STORAGE_DENSE(a)->elements, FIX2INT(lda), FIX2INT(k1), FIX2INT(k2), ipiv_, FIX2INT(incx));
// a is both returned and modified directly in the argument list.
return a;
}
/*
* C accessor for calculating an exact determinant. Dense matrix version.
*/
void nm_math_det_exact_from_dense(const int M, const void* elements, const int lda,
nm::dtype_t dtype, void* result) {
NAMED_DTYPE_TEMPLATE_TABLE(ttable, nm::math::det_exact_from_dense, void, const int M,
const void* A_elements, const int lda, void* result_arg);
ttable[dtype](M, elements, lda, result);
}
/*
* C accessor for calculating an exact determinant. Yale matrix version.
*/
void nm_math_det_exact_from_yale(const int M, const YALE_STORAGE* storage, const int lda,
nm::dtype_t dtype, void* result) {
NAMED_DTYPE_TEMPLATE_TABLE(ttable, nm::math::det_exact_from_yale, void, const int M,
const YALE_STORAGE* storage, const int lda, void* result_arg);
ttable[dtype](M, storage, lda, result);
}
/*
* C accessor for solving a system of linear equations.
*/
void nm_math_solve(VALUE lu, VALUE b, VALUE x, VALUE ipiv) {
int* pivot = new int[RARRAY_LEN(ipiv)];
for (int i = 0; i < RARRAY_LEN(ipiv); ++i) {
pivot[i] = FIX2INT(rb_ary_entry(ipiv, i));
}
NAMED_DTYPE_TEMPLATE_TABLE(ttable, nm::math::solve, void, const int, const void*, const void*, void*, const int*);
ttable[NM_DTYPE(x)](NM_SHAPE0(b), NM_STORAGE_DENSE(lu)->elements,
NM_STORAGE_DENSE(b)->elements, NM_STORAGE_DENSE(x)->elements, pivot);
}
/*
* C accessor for reducing a matrix to hessenberg form.
*/
void nm_math_hessenberg(VALUE a) {
static void (*ttable[nm::NUM_DTYPES])(const int, void*) = {
NULL, NULL, NULL, NULL, NULL, // does not support ints
nm::math::hessenberg<float>,
nm::math::hessenberg<double>,
NULL, NULL, // does not support Complex
NULL // no support for Ruby Object
};
ttable[NM_DTYPE(a)](NM_SHAPE0(a), NM_STORAGE_DENSE(a)->elements);
}
/*
* C accessor for calculating an in-place inverse.
*/
void nm_math_inverse(const int M, void* a_elements, nm::dtype_t dtype) {
NAMED_DTYPE_TEMPLATE_TABLE(ttable, nm::math::inverse, void, const int, void*);
ttable[dtype](M, a_elements);
}
/*
* C accessor for calculating an exact inverse. Dense matrix version.
*/
void nm_math_inverse_exact_from_dense(const int M, const void* A_elements,
const int lda, void* B_elements, const int ldb, nm::dtype_t dtype) {
NAMED_DTYPE_TEMPLATE_TABLE(ttable, nm::math::inverse_exact_from_dense, void,
const int, const void*, const int, void*, const int);
ttable[dtype](M, A_elements, lda, B_elements, ldb);
}
/*
* C accessor for calculating an exact inverse. Yale matrix version.
*/
void nm_math_inverse_exact_from_yale(const int M, const YALE_STORAGE* storage,
const int lda, YALE_STORAGE* inverse, const int ldb, nm::dtype_t dtype) {
NAMED_DTYPE_TEMPLATE_TABLE(ttable, nm::math::inverse_exact_from_yale, void,
const int, const YALE_STORAGE*, const int, YALE_STORAGE*, const int);
ttable[dtype](M, storage, lda, inverse, ldb);
}
/*
* Transpose an array of elements that represent a row-major dense matrix. Does not allocate anything, only does an memcpy.
*/
void nm_math_transpose_generic(const size_t M, const size_t N, const void* A, const int lda, void* B, const int ldb, size_t element_size) {
for (size_t i = 0; i < N; ++i) {
for (size_t j = 0; j < M; ++j) {
memcpy(reinterpret_cast<char*>(B) + (i*ldb+j)*element_size,
reinterpret_cast<const char*>(A) + (j*lda+i)*element_size,
element_size);
}
}
}
} // end of extern "C" block