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langoulangou
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Merge pull request #941 from Reference-LAPACK/lapack-new-feature
Update of the documentation to the pull request "Truncated QR with Pivoting #891"
2 parents d811d85 + bd4455f commit b231dd5

12 files changed

+36
-36
lines changed

‎SRC/cgeqp3rk.f

+6-6
Original file line numberDiff line numberDiff line change
@@ -55,7 +55,7 @@
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*> where:
5656
*>
5757
*> P(K) is an N-by-N permutation matrix;
58-
*> Q(K) is an M-by-M orthogonal matrix;
58+
*> Q(K) is an M-by-M unitary matrix;
5959
*> R(K)_approx = ( R11(K), R12(K) ) is a rank K approximation of the
6060
*> full rank factor R with K-by-K upper-triangular
6161
*> R11(K) and K-by-N rectangular R12(K). The diagonal
@@ -124,14 +124,14 @@
124124
*> d) RELMAXC2NRMK equals MAXC2NRMK divided by MAXC2NRM, the maximum
125125
*> column 2-norm of the original matrix A, which is equal
126126
*> to abs(R(1,1)), ( if K = min(M,N), RELMAXC2NRMK = 0.0 );
127-
*> e) Q(K)**H * B, the matrix B with the orthogonal
127+
*> e) Q(K)**H * B, the matrix B with the unitary
128128
*> transformation Q(K)**H applied on the left.
129129
*>
130130
*> The N-by-N permutation matrix P(K) is stored in a compact form in
131131
*> the integer array JPIV. For 1 <= j <= N, column j
132132
*> of the matrix A was interchanged with column JPIV(j).
133133
*>
134-
*> The M-by-M orthogonal matrix Q is represented as a product
134+
*> The M-by-M unitary matrix Q is represented as a product
135135
*> of elementary Householder reflectors
136136
*>
137137
*> Q(K) = H(1) * H(2) * . . . * H(K),
@@ -300,7 +300,7 @@
300300
*>
301301
*> 1. The elements below the diagonal of the subarray
302302
*> A(1:M,1:K) together with TAU(1:K) represent the
303-
*> orthogonal matrix Q(K) as a product of K Householder
303+
*> unitary matrix Q(K) as a product of K Householder
304304
*> elementary reflectors.
305305
*>
306306
*> 2. The elements on and above the diagonal of
@@ -579,8 +579,8 @@
579579
*> \verbatim
580580
*>
581581
*> November 2023, Igor Kozachenko, James Demmel,
582-
*> Computer Science Division,
583-
*> University of California, Berkeley
582+
*> EECS Department,
583+
*> University of California, Berkeley, USA.
584584
*>
585585
*> \endverbatim
586586
*

‎SRC/claqp2rk.f

+3-3
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@@ -178,7 +178,7 @@
178178
*> On exit:
179179
*> 1. The elements in block A(IOFFSET+1:M,1:K) below
180180
*> the diagonal together with the array TAU represent
181-
*> the orthogonal matrix Q(K) as a product of elementary
181+
*> the unitary matrix Q(K) as a product of elementary
182182
*> reflectors.
183183
*> 2. The upper triangular block of the matrix A stored
184184
*> in A(IOFFSET+1:M,1:K) is the triangular factor obtained.
@@ -332,8 +332,8 @@
332332
*> \verbatim
333333
*>
334334
*> November 2023, Igor Kozachenko, James Demmel,
335-
*> Computer Science Division,
336-
*> University of California, Berkeley
335+
*> EECS Department,
336+
*> University of California, Berkeley, USA.
337337
*>
338338
*> \endverbatim
339339
*

‎SRC/claqp3rk.f

+3-3
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@@ -196,7 +196,7 @@
196196
*> On exit:
197197
*> 1. The elements in block A(IOFFSET+1:M,1:KB) below
198198
*> the diagonal together with the array TAU represent
199-
*> the orthogonal matrix Q(KB) as a product of elementary
199+
*> the unitary matrix Q(KB) as a product of elementary
200200
*> reflectors.
201201
*> 2. The upper triangular block of the matrix A stored
202202
*> in A(IOFFSET+1:M,1:KB) is the triangular factor obtained.
@@ -383,8 +383,8 @@
383383
*> \verbatim
384384
*>
385385
*> November 2023, Igor Kozachenko, James Demmel,
386-
*> Computer Science Division,
387-
*> University of California, Berkeley
386+
*> EECS Department,
387+
*> University of California, Berkeley, USA.
388388
*>
389389
*> \endverbatim
390390
*

‎SRC/dgeqp3rk.f

+2-2
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@@ -573,8 +573,8 @@
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*> \verbatim
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*>
575575
*> November 2023, Igor Kozachenko, James Demmel,
576-
*> Computer Science Division,
577-
*> University of California, Berkeley
576+
*> EECS Department,
577+
*> University of California, Berkeley, USA.
578578
*>
579579
*> \endverbatim
580580
*

‎SRC/dlaqp2rk.f

+2-2
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@@ -331,8 +331,8 @@
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*> \verbatim
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*>
333333
*> November 2023, Igor Kozachenko, James Demmel,
334-
*> Computer Science Division,
335-
*> University of California, Berkeley
334+
*> EECS Department,
335+
*> University of California, Berkeley, USA.
336336
*>
337337
*> \endverbatim
338338
*

‎SRC/dlaqp3rk.f

+2-2
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@@ -389,8 +389,8 @@
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*> \verbatim
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*>
391391
*> November 2023, Igor Kozachenko, James Demmel,
392-
*> Computer Science Division,
393-
*> University of California, Berkeley
392+
*> EECS Department,
393+
*> University of California, Berkeley, USA.
394394
*>
395395
*> \endverbatim
396396
*

‎SRC/sgeqp3rk.f

+2-2
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@@ -573,8 +573,8 @@
573573
*> \verbatim
574574
*>
575575
*> November 2023, Igor Kozachenko, James Demmel,
576-
*> Computer Science Division,
577-
*> University of California, Berkeley
576+
*> EECS Department,
577+
*> University of California, Berkeley, USA.
578578
*>
579579
*> \endverbatim
580580
*

‎SRC/slaqp2rk.f

+2-2
Original file line numberDiff line numberDiff line change
@@ -331,8 +331,8 @@
331331
*> \verbatim
332332
*>
333333
*> November 2023, Igor Kozachenko, James Demmel,
334-
*> Computer Science Division,
335-
*> University of California, Berkeley
334+
*> EECS Department,
335+
*> University of California, Berkeley, USA.
336336
*>
337337
*> \endverbatim
338338
*

‎SRC/slaqp3rk.f

+2-2
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@@ -389,8 +389,8 @@
389389
*> \verbatim
390390
*>
391391
*> November 2023, Igor Kozachenko, James Demmel,
392-
*> Computer Science Division,
393-
*> University of California, Berkeley
392+
*> EECS Department,
393+
*> University of California, Berkeley, USA.
394394
*>
395395
*> \endverbatim
396396
*

‎SRC/zgeqp3rk.f

+6-6
Original file line numberDiff line numberDiff line change
@@ -55,7 +55,7 @@
5555
*> where:
5656
*>
5757
*> P(K) is an N-by-N permutation matrix;
58-
*> Q(K) is an M-by-M orthogonal matrix;
58+
*> Q(K) is an M-by-M unitary matrix;
5959
*> R(K)_approx = ( R11(K), R12(K) ) is a rank K approximation of the
6060
*> full rank factor R with K-by-K upper-triangular
6161
*> R11(K) and K-by-N rectangular R12(K). The diagonal
@@ -124,14 +124,14 @@
124124
*> d) RELMAXC2NRMK equals MAXC2NRMK divided by MAXC2NRM, the maximum
125125
*> column 2-norm of the original matrix A, which is equal
126126
*> to abs(R(1,1)), ( if K = min(M,N), RELMAXC2NRMK = 0.0 );
127-
*> e) Q(K)**H * B, the matrix B with the orthogonal
127+
*> e) Q(K)**H * B, the matrix B with the unitary
128128
*> transformation Q(K)**H applied on the left.
129129
*>
130130
*> The N-by-N permutation matrix P(K) is stored in a compact form in
131131
*> the integer array JPIV. For 1 <= j <= N, column j
132132
*> of the matrix A was interchanged with column JPIV(j).
133133
*>
134-
*> The M-by-M orthogonal matrix Q is represented as a product
134+
*> The M-by-M unitary matrix Q is represented as a product
135135
*> of elementary Householder reflectors
136136
*>
137137
*> Q(K) = H(1) * H(2) * . . . * H(K),
@@ -300,7 +300,7 @@
300300
*>
301301
*> 1. The elements below the diagonal of the subarray
302302
*> A(1:M,1:K) together with TAU(1:K) represent the
303-
*> orthogonal matrix Q(K) as a product of K Householder
303+
*> unitary matrix Q(K) as a product of K Householder
304304
*> elementary reflectors.
305305
*>
306306
*> 2. The elements on and above the diagonal of
@@ -579,8 +579,8 @@
579579
*> \verbatim
580580
*>
581581
*> November 2023, Igor Kozachenko, James Demmel,
582-
*> Computer Science Division,
583-
*> University of California, Berkeley
582+
*> EECS Department,
583+
*> University of California, Berkeley, USA.
584584
*>
585585
*> \endverbatim
586586
*

‎SRC/zlaqp2rk.f

+3-3
Original file line numberDiff line numberDiff line change
@@ -178,7 +178,7 @@
178178
*> On exit:
179179
*> 1. The elements in block A(IOFFSET+1:M,1:K) below
180180
*> the diagonal together with the array TAU represent
181-
*> the orthogonal matrix Q(K) as a product of elementary
181+
*> the unitary matrix Q(K) as a product of elementary
182182
*> reflectors.
183183
*> 2. The upper triangular block of the matrix A stored
184184
*> in A(IOFFSET+1:M,1:K) is the triangular factor obtained.
@@ -332,8 +332,8 @@
332332
*> \verbatim
333333
*>
334334
*> November 2023, Igor Kozachenko, James Demmel,
335-
*> Computer Science Division,
336-
*> University of California, Berkeley
335+
*> EECS Department,
336+
*> University of California, Berkeley, USA.
337337
*>
338338
*> \endverbatim
339339
*

‎SRC/zlaqp3rk.f

+3-3
Original file line numberDiff line numberDiff line change
@@ -196,7 +196,7 @@
196196
*> On exit:
197197
*> 1. The elements in block A(IOFFSET+1:M,1:KB) below
198198
*> the diagonal together with the array TAU represent
199-
*> the orthogonal matrix Q(KB) as a product of elementary
199+
*> the unitary matrix Q(KB) as a product of elementary
200200
*> reflectors.
201201
*> 2. The upper triangular block of the matrix A stored
202202
*> in A(IOFFSET+1:M,1:KB) is the triangular factor obtained.
@@ -383,8 +383,8 @@
383383
*> \verbatim
384384
*>
385385
*> November 2023, Igor Kozachenko, James Demmel,
386-
*> Computer Science Division,
387-
*> University of California, Berkeley
386+
*> EECS Department,
387+
*> University of California, Berkeley, USA.
388388
*>
389389
*> \endverbatim
390390
*

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