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* @license Apache-2.0
*
* Copyright (c) 2025 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/* eslint-disable max-len, max-params */
'use strict';
// MODULES //
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
var dcovarmtk = require( '@stdlib/stats/strided/dcovarmtk' ).ndarray;
var dvarmtk = require( '@stdlib/stats/strided/dvarmtk' ).ndarray;
var dlacpy = require( '@stdlib/lapack/base/dlacpy' ).ndarray;
// MAIN //
/**
* Computes the covariance matrix for an `M` by `N` double-precision floating-point matrix `A` and assigns the results to a matrix `B` when provided known means and using a one-pass textbook algorithm.
*
* ## Notes
*
* - When `orient(A) = 'columns'`,
*
* - each column in `A` represents a variable and each row in `A` represents an observation.
* - `B` should be an `N` by `N` matrix.
* - the list of known means should be an `N` element vector.
*
* - When `orient(A) = 'rows'`,
*
* - each row in `A` represents a variable and each column in `A` represents an observation.
* - `B` should be an `M` by `M` matrix.
* - the list of known means should be an `M` element vector.
*
* @private
* @param {string} orient - specifies whether variables are stored along columns or along rows
* @param {string} uplo - specifies whether to overwrite the upper or lower triangular part of matrix `B`
* @param {NonNegativeInteger} M - number of rows in the matrix `A`
* @param {NonNegativeInteger} N - number of columns in the matrix `A`
* @param {number} correction - degrees of freedom adjustment
* @param {Float64Array} means - vector of known means
* @param {integer} strideM - stride length for `means`
* @param {NonNegativeInteger} offsetM - starting index for `means`
* @param {Float64Array} A - input matrix
* @param {integer} strideA1 - stride of the first dimension of `A`
* @param {integer} strideA2 - stride of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @param {Float64Array} B - output matrix
* @param {integer} strideB1 - stride of the first dimension of `B`
* @param {integer} strideB2 - stride of the second dimension of `B`
* @param {NonNegativeInteger} offsetB - starting index for `B`
* @returns {Float64Array} `B`
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* // Define a 2x3 matrix in which variables are stored along rows in row-major order:
* var A = new Float64Array([
* 1.0, -2.0, 2.0,
* 2.0, -2.0, 1.0
* ]);
*
* // Define a vector of known means:
* var means = new Float64Array( [ 1.0/3.0, 1.0/3.0 ] );
*
* // Allocate a 2x2 output matrix:
* var B = new Float64Array( [ 0.0, 0.0, 0.0, 0.0 ] );
*
* // Perform operation:
* var out = dcovmatmtk( 'rows', 'full', 2, 3, 1, means, 1, 0, A, 3, 1, 0, B, 2, 1, 0 );
* // returns <Float64Array>[ ~4.3333, ~3.8333, ~3.8333, ~4.3333 ]
*
* var bool = ( B === out );
* // returns true
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* // Define a 3x2 matrix in which variables are stored along columns in row-major order:
* var A = new Float64Array([
* 1.0, 2.0,
* -2.0, -2.0,
* 2.0, 1.0
* ]);
*
* // Define a vector of known means:
* var means = new Float64Array( [ 1.0/3.0, 1.0/3.0 ] );
*
* // Allocate a 2x2 output matrix:
* var B = new Float64Array( [ 0.0, 0.0, 0.0, 0.0 ] );
*
* // Perform operation:
* var out = dcovmatmtk( 'columns', 'full', 3, 2, 1, means, 1, 0, A, 2, 1, 0, B, 2, 1, 0 );
* // returns <Float64Array>[ ~4.3333, ~3.8333, ~3.8333, ~4.3333 ]
*
* var bool = ( B === out );
* // returns true
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* // Define a 2x3 matrix in which variables are stored along rows in column-major order:
* var A = new Float64Array( [ 1.0, 2.0, -2.0, -2.0, 2.0, 1.0 ] );
*
* // Define a vector of known means:
* var means = new Float64Array( [ 1.0/3.0, 1.0/3.0 ] );
*
* // Allocate a 2x2 output matrix:
* var B = new Float64Array( [ 0.0, 0.0, 0.0, 0.0 ] );
*
* // Perform operation:
* var out = dcovmatmtk( 'rows', 'full', 2, 3, 1, means, 1, 0, A, 1, 2, 0, B, 2, 1, 0 );
* // returns <Float64Array>[ ~4.3333, ~3.8333, ~3.8333, ~4.3333 ]
*
* var bool = ( B === out );
* // returns true
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* // Define a 3x2 matrix in which variables are stored along columns in column-major order:
* var A = new Float64Array( [ 1.0, -2.0, 2.0, 2.0, -2.0, 1.0 ] );
*
* // Define a vector of known means:
* var means = new Float64Array( [ 1.0/3.0, 1.0/3.0 ] );
*
* // Allocate a 2x2 output matrix:
* var B = new Float64Array( [ 0.0, 0.0, 0.0, 0.0 ] );
*
* // Perform operation:
* var out = dcovmatmtk( 'columns', 'full', 3, 2, 1, means, 1, 0, A, 1, 3, 0, B, 2, 1, 0 );
* // returns <Float64Array>[ ~4.3333, ~3.8333, ~3.8333, ~4.3333 ]
*
* var bool = ( B === out );
* // returns true
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* // Define a 4x3 matrix in which variables are stored along rows in row-major order:
* var A = new Float64Array([
* 1.0, -2.0, 2.0,
* 2.0, -2.0, 1.0,
* 2.0, -2.0, 1.0,
* 1.0, -2.0, 2.0
* ]);
*
* // Define a vector of known means:
* var means = new Float64Array( [ 1.0/3.0, 1.0/3.0, 1.0/3.0, 1.0/3.0 ] );
*
* // Allocate a 4x4 output matrix:
* var B = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
*
* // Perform operation:
* var out = dcovmatmtk( 'rows', 'full', 4, 3, 1, means, 1, 0, A, 3, 1, 0, B, 4, 1, 0 );
* // returns <Float64Array>[ ~4.33, ~3.83, ~3.83, ~4.33, ~3.83, ~4.33, ~4.33, ~3.83, ~3.83, ~4.33, ~4.33, ~3.83, ~4.33, ~3.83, ~3.83, ~4.33 ]
*
* var bool = ( B === out );
* // returns true
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* // Define a 3x4 matrix in which variables are stored along columns in column-major order:
* var A = new Float64Array( [ 1.0, -2.0, 2.0, 2.0, -2.0, 1.0, 2.0, -2.0, 1.0, 1.0, -2.0, 2.0 ] );
*
* // Define a vector of known means:
* var means = new Float64Array( [ 1.0/3.0, 1.0/3.0, 1.0/3.0, 1.0/3.0 ] );
*
* // Allocate a 4x4 output matrix:
* var B = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
*
* // Perform operation:
* var out = dcovmatmtk( 'columns', 'full', 3, 4, 1, means, 1, 0, A, 1, 3, 0, B, 4, 1, 0 );
* // returns <Float64Array>[ ~4.33, ~3.83, ~3.83, ~4.33, ~3.83, ~4.33, ~4.33, ~3.83, ~3.83, ~4.33, ~4.33, ~3.83, ~4.33, ~3.83, ~3.83, ~4.33 ]
*
* var bool = ( B === out );
* // returns true
*/
function dcovmatmtk( orient, uplo, M, N, correction, means, strideM, offsetM, A, strideA1, strideA2, offsetA, B, strideB1, strideB2, offsetB ) {
var nsamples;
var isrmb;
var full;
var nobs;
var sa1;
var sa0;
var sb1;
var sb0;
var sb;
var oa;
var om;
var ia;
var ib;
var im;
var i0;
var i1;
// Determine the memory layouts of `B`:
isrmb = isRowMajor( [ strideB1, strideB2 ] );
// Determine the outer and inner loop strides when writing to the upper or lower triangular part of `B`...
if ( uplo === 'upper') {
// Writing to the upper triangular part is cache optimal for a row-major `B`, but not for a column-major `B`...
sb0 = strideB2;
sb1 = strideB1;
} else if ( uplo === 'lower' ) {
// Writing to the lower triangular part is cache optimal for a column-major `B`, but not for a row-major `B`...
sb0 = strideB1;
sb1 = strideB2;
} else {
// When computing the full covariance matrix, write covariances in a manner which is cache optimal for the layout of `B`...
full = true;
if ( isrmb ) {
// For row-major matrices, the last dimension has the fastest changing index...
sb0 = strideB2;
sb1 = strideB1;
} else {
// For column-major matrices, the first dimension has the fastest changing index...
sb0 = strideB1;
sb1 = strideB2;
}
}
// Resolve loop variables...
if ( orient === 'rows' ) {
sa0 = strideA2;
sa1 = strideA1;
nsamples = M;
nobs = N;
} else { // orient === 'columns'
sa0 = strideA1;
sa1 = strideA2;
nsamples = N;
nobs = M;
}
// Compute the variances and set them along the diagonal...
sb = strideB1 + strideB2; // stride for elements along diagonal
ia = offsetA;
ib = offsetB;
im = offsetM;
for ( i0 = 0; i0 < nsamples; i0++ ) {
B[ ib ] = dvarmtk( nobs, correction, means[ im ], A, sa0, ia );
ia += sa1;
ib += sb;
im += strideM;
}
// Compute pairwise covariances...
oa = offsetA;
om = offsetM;
for ( i1 = 0; i1 < nsamples-1; i1++ ) {
ib = offsetB + ( sb1*i1 ) + ( sb0*i1 );
ia = oa;
im = om;
for ( i0 = i1+1; i0 < nsamples; i0++ ) {
im += strideM;
ia += sa1;
ib += sb0;
B[ ib ] = dcovarmtk( nobs, correction, means[ om ], A, sa0, oa, means[ im ], A, sa0, ia );
}
oa += sa1;
om += strideM;
}
// Copy the covariances to the other triangular part if the full covariance matrix is desired...
if ( full ) {
if ( isrmb ) {
// Copy the upper triangular part to the lower triangular part:
dlacpy( 'upper', nsamples, nsamples, B, sb1, sb0, offsetB, B, sb0, sb1, offsetB );
} else {
// Copy the lower triangular part to the upper triangular part:
dlacpy( 'lower', nsamples, nsamples, B, sb0, sb1, offsetB, B, sb1, sb0, offsetB );
}
}
return B;
}
// EXPORTS //
module.exports = dcovmatmtk;
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