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refactor: move branches to separate functions
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‎lib/node_modules/@stdlib/lapack/base/dlange/lib/base.js‎

Lines changed: 219 additions & 98 deletions
Original file line numberDiff line numberDiff line change
@@ -23,27 +23,117 @@
2323
var isnan = require( '@stdlib/math/base/assert/is-nan' );
2424
var dlassq = require( '@stdlib/lapack/base/dlassq' ).ndarray;
2525
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
26-
var dasumpw = require( '@stdlib/blas/ext/base/dasumpw' ).ndarray;
26+
var loopOrder = require( '@stdlib/ndarray/base/nullary-loop-interchange-order' );
27+
var dasum = require( '@stdlib/blas/base/dasum' ).ndarray;
2728
var Float64Array = require( '@stdlib/array/float64' );
2829
var min = require( '@stdlib/math/base/special/min' );
29-
var abs = require( '@stdlib/math/base/special/abs' );
3030
var sqrt = require( '@stdlib/math/base/special/sqrt' );
31+
var abs = require( '@stdlib/math/base/special/abs' );
3132

3233

33-
// MAIN //
34+
// FUNCTIONS //
3435

3536
/**
36-
* Returns the value of the one norm, or the frobenius norm, or the infinity norm, or the element with the largest absolute value of a real matrix `A`.
37+
* Returns the value of the one norm of a real matrix `A`.
3738
*
38-
* ## Notes
39+
* @private
40+
* @param {NonNegativeInteger} M - number of rows in `A`
41+
* @param {NonNegativeInteger} N - number of columns in `A`
42+
* @param {Float64Array} A - input array
43+
* @param {integer} strideA1 - stride of the first dimension of `A`
44+
* @param {integer} strideA2 - stride of the second dimension of `A`
45+
* @param {NonNegativeInteger} offsetA - starting index of `A`
46+
* @returns {number} required norm value
3947
*
40-
* - use `norm` = `max`, to calculate the element with the largest absolute value
41-
* - use `norm` = `one`, to calculate the one norm
42-
* - use `norm` = `infinity`, to calculate the infinity norm
43-
* - use `norm` = `frobenius`, to calculate the frobenius norm
48+
* @example
49+
* var Float64Array = require( '@stdlib/array/float64' );
50+
*
51+
* var A = new Float64Array( [ 1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0 ] );
52+
*
53+
* var out = oneNorm( 3, 4, A, 4, 1, 0 );
54+
* // returns 33.0
55+
*/
56+
function oneNorm( M, N, A, strideA1, strideA2, offsetA ) {
57+
var value;
58+
var ia1;
59+
var sum;
60+
var j;
61+
62+
value = 0.0;
63+
ia1 = offsetA;
64+
for ( j = 0; j < N; j++ ) {
65+
sum = dasum( M, A, strideA1, ia1 );
66+
if ( value < sum || isnan( sum ) ) {
67+
value = sum;
68+
}
69+
ia1 += strideA2;
70+
}
71+
return value;
72+
}
73+
74+
/**
75+
* Returns the absolute value of the maximum element of a real matrix `A`.
76+
*
77+
* @private
78+
* @param {NonNegativeInteger} M - number of rows in `A`
79+
* @param {NonNegativeInteger} N - number of columns in `A`
80+
* @param {Float64Array} A - input array
81+
* @param {integer} strideA1 - stride of the first dimension of `A`
82+
* @param {integer} strideA2 - stride of the second dimension of `A`
83+
* @param {NonNegativeInteger} offsetA - starting index of `A`
84+
* @returns {number} required norm value
85+
*
86+
* @example
87+
* var Float64Array = require( '@stdlib/array/float64' );
88+
*
89+
* var A = new Float64Array( [ 1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0 ] );
90+
*
91+
* var out = maxAbs( 3, 4, A, 4, 1, 0 );
92+
* // returns 12.0
93+
*/
94+
function maxAbs( M, N, A, strideA1, strideA2, offsetA ) {
95+
var value;
96+
var temp;
97+
var da0;
98+
var da1;
99+
var ia;
100+
var sa;
101+
var sh;
102+
var S0;
103+
var S1;
104+
var o;
105+
var i;
106+
var j;
107+
108+
value = 0.0;
109+
110+
// Resolve the loop interchange order:
111+
o = loopOrder( [ M, N ], [ strideA1, strideA2 ] );
112+
sh = o.sh;
113+
sa = o.sx;
114+
S0 = sh[ 0 ];
115+
S1 = sh[ 1 ];
116+
da0 = sa[ 0 ];
117+
da1 = sa[ 1 ] - ( S0*sa[0] );
118+
ia = offsetA;
119+
120+
for ( i = 0; i < S1; i++ ) {
121+
for ( j = 0; j < S0; j++ ) {
122+
temp = A[ ia ];
123+
if ( value < temp || isnan( temp ) ) {
124+
value = temp;
125+
}
126+
ia += da0;
127+
}
128+
ia += da1;
129+
}
130+
return value;
131+
}
132+
133+
/**
134+
* Returns the value of the infinity norm of a real matrix `A`.
44135
*
45136
* @private
46-
* @param {string} norm - specifies the type of norm to be calculated
47137
* @param {NonNegativeInteger} M - number of rows in `A`
48138
* @param {NonNegativeInteger} N - number of columns in `A`
49139
* @param {Float64Array} A - input array
@@ -61,123 +151,154 @@ var sqrt = require( '@stdlib/math/base/special/sqrt' );
61151
* var A = new Float64Array( [ 1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0 ] );
62152
* var work = new Float64Array( 3 );
63153
*
64-
* var out = dlange( 'frobenius', 3, 4, A, 4, 1, 0, work, 1, 0 );
65-
* // returns ~25.5
154+
* var out = infinityNorm( 3, 4, A, 4, 1, 0, work, 1, 0 );
155+
* // returns 30.0
66156
*/
67-
function dlange( norm, M, N, A, strideA1, strideA2, offsetA, work, strideWork, offsetWork ) { // eslint-disable-line max-len
157+
function infinityNorm( M, N, A, strideA1, strideA2, offsetA, work, strideWork, offsetWork ) { // eslint-disable-line max-len
68158
var value;
69159
var temp;
70-
var sum;
71-
var out;
72160
var ia1;
73161
var ia2;
74162
var iw;
75163
var i;
76164
var j;
77165

78-
if ( min( M, N ) === 0 ) {
79-
value = 0.0;
166+
iw = offsetWork;
167+
for ( i = 0; i < M; i++ ) {
168+
work[ iw ] = 0.0;
169+
iw += strideWork;
80170
}
81171

82-
else if ( norm === 'max' ) {
83-
value = 0.0;
84-
if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
85-
ia1 = offsetA;
86-
for ( i = 0; i < M; i++ ) {
87-
ia2 = 0;
88-
for ( j = 0; j < N; j++ ) {
89-
temp = A[ ia1 + ia2 ];
90-
if ( value < temp || isnan( temp ) ) {
91-
value = temp;
92-
}
93-
ia2 += strideA2;
94-
}
95-
ia1 += strideA1;
96-
}
97-
} else {
98-
ia1 = offsetA;
172+
if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
173+
ia1 = offsetA;
174+
iw = offsetWork;
175+
for ( i = 0; i < M; i++ ) {
176+
ia2 = 0;
99177
for ( j = 0; j < N; j++ ) {
100-
ia2 = 0;
101-
for ( i = 0; i < M; i++ ) {
102-
temp = A[ ia1 + ia2 ];
103-
if ( value < temp || isnan( temp ) ) {
104-
value = temp;
105-
}
106-
ia2 += strideA1;
107-
}
108-
ia1 += strideA2;
178+
work[ iw ] += abs( A[ ia1 + ia2 ] );
179+
ia2 += strideA2;
109180
}
181+
ia1 += strideA1;
182+
iw += strideWork;
110183
}
111-
}
112-
113-
else if ( norm === 'one' ) {
114-
value = 0.0;
184+
} else {
115185
ia1 = offsetA;
116186
for ( j = 0; j < N; j++ ) {
117-
sum = dasumpw( M, A, strideA1, ia1 );
118-
if ( value < sum || isnan( sum ) ) {
119-
value = sum;
187+
ia2 = 0;
188+
iw = offsetWork;
189+
for ( i = 0; i < M; i++ ) {
190+
work[ iw ] += abs( A[ ia1 + ia2 ] );
191+
iw += strideWork;
192+
ia2 += strideA1;
120193
}
121194
ia1 += strideA2;
122195
}
123196
}
124197

125-
else if ( norm === 'infinity' ) {
126-
iw = offsetWork;
127-
for ( i = 0; i < M; i++ ) {
128-
work[ iw ] = 0.0;
129-
iw += strideWork;
130-
}
198+
value = 0.0;
131199

132-
if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
133-
ia1 = offsetA;
134-
iw = offsetWork;
135-
for ( i = 0; i < M; i++ ) {
136-
ia2 = 0;
137-
for ( j = 0; j < N; j++ ) {
138-
work[ iw ] += abs( A[ ia1 + ia2 ] );
139-
ia2 += strideA2;
140-
}
141-
ia1 += strideA1;
142-
iw += strideWork;
143-
}
144-
} else {
145-
ia1 = offsetA;
146-
for ( j = 0; j < N; j++ ) {
147-
ia2 = 0;
148-
iw = offsetWork;
149-
for ( i = 0; i < M; i++ ) {
150-
work[ iw ] += abs( A[ ia1 + ia2 ] );
151-
iw += strideWork;
152-
ia2 += strideA1;
153-
}
154-
ia1 += strideA2;
155-
}
200+
iw = offsetWork;
201+
for ( i = 0; i < M; i++ ) {
202+
temp = work[ iw ];
203+
if ( value < temp || isnan( temp ) ) {
204+
value = temp;
156205
}
206+
iw += strideWork;
207+
}
157208

158-
value = 0.0;
209+
return value;
210+
}
159211

160-
iw = offsetWork;
161-
for ( i = 0; i < M; i++ ) {
162-
temp = work[ iw ];
163-
if ( value < temp || isnan( temp ) ) {
164-
value = temp;
165-
}
166-
iw += strideWork;
167-
}
212+
/**
213+
* Returns the absolute value of the frobenius norm of a real matrix `A`.
214+
*
215+
* @private
216+
* @param {NonNegativeInteger} M - number of rows in `A`
217+
* @param {NonNegativeInteger} N - number of columns in `A`
218+
* @param {Float64Array} A - input array
219+
* @param {integer} strideA1 - stride of the first dimension of `A`
220+
* @param {integer} strideA2 - stride of the second dimension of `A`
221+
* @param {NonNegativeInteger} offsetA - starting index of `A`
222+
* @returns {number} required norm value
223+
*
224+
* @example
225+
* var Float64Array = require( '@stdlib/array/float64' );
226+
*
227+
* var A = new Float64Array( [ 1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0 ] );
228+
*
229+
* var out = frobeniusNorm( 3, 4, A, 4, 1, 0 );
230+
* // returns ~25.5
231+
*/
232+
function frobeniusNorm( M, N, A, strideA1, strideA2, offsetA ) {
233+
var ia1;
234+
var out;
235+
var i;
236+
237+
ia1 = offsetA;
238+
out = new Float64Array( [ 0.0, 1.0 ] );
239+
for ( i = 0; i < N; i++ ) {
240+
dlassq( M, A, strideA1, ia1, out[ 0 ], out[ 1 ], out, 1, 0 );
241+
ia1 += strideA2;
168242
}
169243

170-
else if ( norm === 'frobenius' ) {
171-
out = new Float64Array( [ 0.0, 1.0 ] );
172-
ia1 = offsetA;
173-
for ( i = 0; i < N; i++ ) {
174-
dlassq( M, A, strideA1, ia1, out[ 0 ], out[ 1 ], out, 1, 0 );
175-
ia1 += strideA2;
176-
}
177-
value = out[ 0 ] * sqrt( out[ 1 ] );
244+
return out[ 0 ] * sqrt( out[ 1 ] );
245+
}
246+
247+
248+
// MAIN //
249+
250+
/**
251+
* Returns the value of the one norm, or the frobenius norm, or the infinity norm, or the element with the largest absolute value of a real matrix `A`.
252+
*
253+
* ## Notes
254+
*
255+
* - use `norm` = `max`, to calculate the element with the largest absolute value
256+
* - use `norm` = `one`, to calculate the one norm
257+
* - use `norm` = `infinity`, to calculate the infinity norm
258+
* - use `norm` = `frobenius`, to calculate the frobenius norm
259+
*
260+
* @private
261+
* @param {string} norm - specifies the type of norm to be calculated
262+
* @param {NonNegativeInteger} M - number of rows in `A`
263+
* @param {NonNegativeInteger} N - number of columns in `A`
264+
* @param {Float64Array} A - input array
265+
* @param {integer} strideA1 - stride of the first dimension of `A`
266+
* @param {integer} strideA2 - stride of the second dimension of `A`
267+
* @param {NonNegativeInteger} offsetA - starting index of `A`
268+
* @param {Float64Array} work - only used to compute the infinity norm, expects `M` indexed elements if computing the infinity norm otherwise it's fine to pass a dummy array
269+
* @param {integer} strideWork - stride length of `work`
270+
* @param {NonNegativeInteger} offsetWork - starting index of `work`
271+
* @returns {number} required norm value
272+
*
273+
* @example
274+
* var Float64Array = require( '@stdlib/array/float64' );
275+
*
276+
* var A = new Float64Array( [ 1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0 ] );
277+
* var work = new Float64Array( 3 );
278+
*
279+
* var out = dlange( 'frobenius', 3, 4, A, 4, 1, 0, work, 1, 0 );
280+
* // returns ~25.5
281+
*/
282+
function dlange( norm, M, N, A, strideA1, strideA2, offsetA, work, strideWork, offsetWork ) { // eslint-disable-line max-len
283+
if ( min( M, N ) === 0 ) {
284+
return 0.0;
178285
}
179286

180-
return value;
287+
if ( norm === 'max' ) {
288+
return maxAbs( M, N, A, strideA1, strideA2, offsetA );
289+
}
290+
291+
if ( norm === 'one' ) {
292+
return oneNorm( M, N, A, strideA1, strideA2, offsetA );
293+
}
294+
295+
if ( norm === 'infinity' ) {
296+
return infinityNorm( M, N, A, strideA1, strideA2, offsetA, work, strideWork, offsetWork ); // eslint-disable-line max-len
297+
}
298+
299+
if ( norm === 'frobenius' ) {
300+
return frobeniusNorm( M, N, A, strideA1, strideA2, offsetA );
301+
}
181302
}
182303

183304

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