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‎lapack/base/iladlr/base.js.html‎

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// MODULES //
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&nbsp;
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var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
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var max = require( '@stdlib/math/base/special/max' );
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&nbsp;
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&nbsp;
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// MAIN //
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&nbsp;
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/**
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* Finds the index of the last non-zero row in a matrix `A`.
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*
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* ## Notes
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*
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* - If provided an empty matrix or a matrix containing only zeros, the function returns `-1` (i.e., an invalid index).
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*
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* @private
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* @param {PositiveInteger} M - number of rows in `A`
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* @param {PositiveInteger} N - number of columns in `A`
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*
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* var out = iladlr( 3, 2, A, 2, 1, 0 );
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* // returns 1
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*
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* @example
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* var Float64array = require( '@stdlib/array/float64' );
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*
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* var A = new Float64array( [ 1.0, 3.0, 0.0, 2.0, 4.0, 0.0 ] ); // =&gt; [ [ 1.0, 2.0 ], [ 3.0, 4.0 ], [ 0.0, 0.0 ] ]
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*
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* var out = iladlr( 3, 2, A, 1, 3, 0 );
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* // returns 1
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*/
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function iladlr( M, N, A, strideA1, strideA2, offsetA ) {
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var iladlr;
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var ia1;
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var ia2;
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var i;
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var j;
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var last;
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var da0;
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var da1;
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var S0;
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var S1;
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var ia;
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var i0;
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var i1;
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var k;
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&nbsp;
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if ( M === 0 || N === 0 ) {
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return -1; // Invalid index
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// Check whether the matrix is an empty matrix...
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if ( M &lt;= 0 || N &lt;= 0 ) {
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return -1;
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}
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// Compute the index of the first element in the last row:
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ia = offsetA + ( (M-1) * strideA1 );
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&nbsp;
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ia1 = offsetA + ( (M-1) * strideA1 ); // A( M, 1 )
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ia2 = ia1 + ( (N-1) * strideA2 ); // A( M, N )
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// Compute the index offset for the last element in the last row:
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last = ( N-1 ) * strideA2;
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&nbsp;
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// Quick test for common case where corners are non-zero:
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if ( A[ ia1 ] !== 0.0 || A[ ia2 ] !== 0.0 ) <span class="branch-0 cbranch-no" title="branch not covered" >{</span>
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// Check for the common case where the first and last elements in the last row are non-zero...
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if ( A[ ia ] !== 0.0 || A[ ia+last ] !== 0.0 ) <span class="branch-0 cbranch-no" title="branch not covered" >{</span>
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<span class="cstat-no" title="statement not covered" > }</span>
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&nbsp;
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// Search for the last row containing at least one non-zero element...
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if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
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ia1 = offsetA + ( (M-1) * strideA1 ); // Tracks rows
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for ( i = M - 1; i &gt;= 0; i-- ) {
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ia2 = 0; // Tracks columns
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for ( j = 0; j &lt; N; j++ ) {
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if ( A[ ia1 + ia2 ] !== 0.0 ) { // Find the last row with a non-zero entry
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return i;
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S0 = N;
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S1 = M;
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&nbsp;
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// Resolve loop offset (pointer) increments:
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da0 = strideA2;
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da1 = strideA1 - ( S0*strideA2 );
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&nbsp;
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// Scan a row-major linear buffer from the last indexed element to the first indexed element, always moving in the same direction when both strides are the same sign, thus ensuring cache optimal traversal...
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ia += last;
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for ( i1 = S1-1; i1 &gt;= 0; i1-- ) {
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for ( i0 = 0; i0 &lt; S0; i0++ ) {
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if ( A[ ia ] !== 0.0 ) {
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// We found a row with a non-zero element!
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return i1;
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}
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ia2 += strideA2;
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ia -= da0;
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}
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ia1 -= strideA1;
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ia -= da1;
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}
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&nbsp;
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// If we reach here, then all entries in the matrix are zero, return -1 (invalid index)
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// If we've made it here, then all entries in the matrix are zero:
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return -1;
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}
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// Column-major...
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S0 = M;
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S1 = N;
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&nbsp;
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// Resolve loop offset (pointer) increments:
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da0 = strideA1;
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da1 = strideA2;
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&nbsp;
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// Column major
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ia2 = offsetA; // Tracks columns
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iladlr = -1; // initialize iladlr, will return -1 (invalid index) if all entries are zero
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// Compute the index offset for the last element in each row:
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last = offsetA + ( (S0-1)*da0 );
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&nbsp;
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for ( j = 0; j &lt; N; j++ ) {
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i = M - 1;
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ia1 = (M-1) * strideA1; // Tracks rows
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while ( A[ ia1 + ia2 ] === 0.0 &amp;&amp; i &gt;= 0 ) {
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i -= 1;
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ia1 -= strideA1;
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// Initialize an index of the last row in which a non-zero element was seen:
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k = -1;
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&nbsp;
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// Finding the last non-zero row when a matrix is stored in column-major order requires effectively performing a full linear scan. In order to ensure cache-efficient traversal, scan up each column (otherwise, if we went row-by-row, we'd hop around linear memory, resulting in poor cache behavior)...
477+
for ( i1 = 0; i1 &lt; S1; i1++ ) {
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// Reset the pointer to point to the last element in the current column:
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ia = last + ( i1*da1 );
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&nbsp;
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// Scan up the rows in a column looking for a non-zero element...
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for ( i0 = S0-1; i0 &gt; k; i0-- ) { // note: `k` serves as a lower row index bound, thus shrinking the number of rows we need to check when scanning columns
483+
if ( A[ ia ] !== 0.0 ) {
484+
// We found a non-zero element, which means we no longer have to search this row...
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k = i0;
486+
break; // note: in principle, if `k == M-1`, we could early return; however, this is a hot loop and adding an additional conditional is likely to degrade average performance in order to cater to what is effectively an edge case
487+
}
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ia -= da0;
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}
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iladlr = max( i, iladlr );
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ia2 += strideA2;
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}
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&nbsp;
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return iladlr;
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return k;
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}
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&nbsp;
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<div class='footer quiet pad2 space-top1 center small'>
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Code coverage generated by
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at 2025-06-04T20:05:39.645Z
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‎lapack/base/iladlr/coverage.ndjson‎

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[326,328,99.3902,33,34,97.0588,3,3,100,326,328,99.3902,"3d91f56a6d679613fafaefe96c7b34a1e03d4f7a","2025-06-04 20:03:34 +0000"]
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[364,366,99.4536,34,35,97.1429,3,3,100,364,366,99.4536,"c0941f24d9d4390c0490fa32ad2b0cb5c6c1805e","2025-06-05 00:47:35 -0700"]

‎lapack/base/iladlr/iladlr.js.html‎

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<div class='footer quiet pad2 space-top1 center small'>
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Code coverage generated by
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at 2025-06-04T20:05:39.645Z
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