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Small documentation fix for Truncated QR With Pivoting (Reference-LAPACK PR 941)

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Martin Kroeker 2023-11-25 15:31:18 +01:00 committed by GitHub
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commit ca5a87ff1d
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12 changed files with 36 additions and 36 deletions
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12
lapack-netlib/SRC/cgeqp3rk.f
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@ -55,7 +55,7 @@
*> where: *> where:
*> *>
*> P(K) is an N-by-N permutation matrix; *> P(K) is an N-by-N permutation matrix;
*> Q(K) is an M-by-M orthogonal matrix; *> Q(K) is an M-by-M unitary matrix;
*> R(K)_approx = ( R11(K), R12(K) ) is a rank K approximation of the *> R(K)_approx = ( R11(K), R12(K) ) is a rank K approximation of the
*> full rank factor R with K-by-K upper-triangular *> full rank factor R with K-by-K upper-triangular
*> R11(K) and K-by-N rectangular R12(K). The diagonal *> R11(K) and K-by-N rectangular R12(K). The diagonal
@ -124,14 +124,14 @@
*> d) RELMAXC2NRMK equals MAXC2NRMK divided by MAXC2NRM, the maximum *> d) RELMAXC2NRMK equals MAXC2NRMK divided by MAXC2NRM, the maximum
*> column 2-norm of the original matrix A, which is equal *> column 2-norm of the original matrix A, which is equal
*> to abs(R(1,1)), ( if K = min(M,N), RELMAXC2NRMK = 0.0 ); *> to abs(R(1,1)), ( if K = min(M,N), RELMAXC2NRMK = 0.0 );
*> e) Q(K)**H * B, the matrix B with the orthogonal *> e) Q(K)**H * B, the matrix B with the unitary
*> transformation Q(K)**H applied on the left. *> transformation Q(K)**H applied on the left.
*> *>
*> The N-by-N permutation matrix P(K) is stored in a compact form in *> The N-by-N permutation matrix P(K) is stored in a compact form in
*> the integer array JPIV. For 1 <= j <= N, column j *> the integer array JPIV. For 1 <= j <= N, column j
*> of the matrix A was interchanged with column JPIV(j). *> of the matrix A was interchanged with column JPIV(j).
*> *>
*> The M-by-M orthogonal matrix Q is represented as a product *> The M-by-M unitary matrix Q is represented as a product
*> of elementary Householder reflectors *> of elementary Householder reflectors
*> *>
*> Q(K) = H(1) * H(2) * . . . * H(K), *> Q(K) = H(1) * H(2) * . . . * H(K),
@ -300,7 +300,7 @@
*> *>
*> 1. The elements below the diagonal of the subarray *> 1. The elements below the diagonal of the subarray
*> A(1:M,1:K) together with TAU(1:K) represent the *> A(1:M,1:K) together with TAU(1:K) represent the
*> orthogonal matrix Q(K) as a product of K Householder *> unitary matrix Q(K) as a product of K Householder
*> elementary reflectors. *> elementary reflectors.
*> *>
*> 2. The elements on and above the diagonal of *> 2. The elements on and above the diagonal of
@ -579,8 +579,8 @@
*> \verbatim *> \verbatim
*> *>
*> November 2023, Igor Kozachenko, James Demmel, *> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division, *> EECS Department,
*> University of California, Berkeley *> University of California, Berkeley, USA.
*> *>
*> \endverbatim *> \endverbatim
* *

6
lapack-netlib/SRC/claqp2rk.f
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@ -178,7 +178,7 @@
*> On exit: *> On exit:
*> 1. The elements in block A(IOFFSET+1:M,1:K) below *> 1. The elements in block A(IOFFSET+1:M,1:K) below
*> the diagonal together with the array TAU represent *> the diagonal together with the array TAU represent
*> the orthogonal matrix Q(K) as a product of elementary *> the unitary matrix Q(K) as a product of elementary
*> reflectors. *> reflectors.
*> 2. The upper triangular block of the matrix A stored *> 2. The upper triangular block of the matrix A stored
*> in A(IOFFSET+1:M,1:K) is the triangular factor obtained. *> in A(IOFFSET+1:M,1:K) is the triangular factor obtained.
@ -332,8 +332,8 @@
*> \verbatim *> \verbatim
*> *>
*> November 2023, Igor Kozachenko, James Demmel, *> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division, *> EECS Department,
*> University of California, Berkeley *> University of California, Berkeley, USA.
*> *>
*> \endverbatim *> \endverbatim
* *

6
lapack-netlib/SRC/claqp3rk.f
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@ -196,7 +196,7 @@
*> On exit: *> On exit:
*> 1. The elements in block A(IOFFSET+1:M,1:KB) below *> 1. The elements in block A(IOFFSET+1:M,1:KB) below
*> the diagonal together with the array TAU represent *> the diagonal together with the array TAU represent
*> the orthogonal matrix Q(KB) as a product of elementary *> the unitary matrix Q(KB) as a product of elementary
*> reflectors. *> reflectors.
*> 2. The upper triangular block of the matrix A stored *> 2. The upper triangular block of the matrix A stored
*> in A(IOFFSET+1:M,1:KB) is the triangular factor obtained. *> in A(IOFFSET+1:M,1:KB) is the triangular factor obtained.
@ -383,8 +383,8 @@
*> \verbatim *> \verbatim
*> *>
*> November 2023, Igor Kozachenko, James Demmel, *> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division, *> EECS Department,
*> University of California, Berkeley *> University of California, Berkeley, USA.
*> *>
*> \endverbatim *> \endverbatim
* *

4
lapack-netlib/SRC/dgeqp3rk.f
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@ -573,8 +573,8 @@
*> \verbatim *> \verbatim
*> *>
*> November 2023, Igor Kozachenko, James Demmel, *> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division, *> EECS Department,
*> University of California, Berkeley *> University of California, Berkeley, USA.
*> *>
*> \endverbatim *> \endverbatim
* *

4
lapack-netlib/SRC/dlaqp2rk.f
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@ -331,8 +331,8 @@
*> \verbatim *> \verbatim
*> *>
*> November 2023, Igor Kozachenko, James Demmel, *> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division, *> EECS Department,
*> University of California, Berkeley *> University of California, Berkeley, USA.
*> *>
*> \endverbatim *> \endverbatim
* *

4
lapack-netlib/SRC/dlaqp3rk.f
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@ -389,8 +389,8 @@
*> \verbatim *> \verbatim
*> *>
*> November 2023, Igor Kozachenko, James Demmel, *> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division, *> EECS Department,
*> University of California, Berkeley *> University of California, Berkeley, USA.
*> *>
*> \endverbatim *> \endverbatim
* *

4
lapack-netlib/SRC/sgeqp3rk.f
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@ -573,8 +573,8 @@
*> \verbatim *> \verbatim
*> *>
*> November 2023, Igor Kozachenko, James Demmel, *> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division, *> EECS Department,
*> University of California, Berkeley *> University of California, Berkeley, USA.
*> *>
*> \endverbatim *> \endverbatim
* *

4
lapack-netlib/SRC/slaqp2rk.f
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@ -331,8 +331,8 @@
*> \verbatim *> \verbatim
*> *>
*> November 2023, Igor Kozachenko, James Demmel, *> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division, *> EECS Department,
*> University of California, Berkeley *> University of California, Berkeley, USA.
*> *>
*> \endverbatim *> \endverbatim
* *

4
lapack-netlib/SRC/slaqp3rk.f
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@ -389,8 +389,8 @@
*> \verbatim *> \verbatim
*> *>
*> November 2023, Igor Kozachenko, James Demmel, *> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division, *> EECS Department,
*> University of California, Berkeley *> University of California, Berkeley, USA.
*> *>
*> \endverbatim *> \endverbatim
* *

12
lapack-netlib/SRC/zgeqp3rk.f
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@ -55,7 +55,7 @@
*> where: *> where:
*> *>
*> P(K) is an N-by-N permutation matrix; *> P(K) is an N-by-N permutation matrix;
*> Q(K) is an M-by-M orthogonal matrix; *> Q(K) is an M-by-M unitary matrix;
*> R(K)_approx = ( R11(K), R12(K) ) is a rank K approximation of the *> R(K)_approx = ( R11(K), R12(K) ) is a rank K approximation of the
*> full rank factor R with K-by-K upper-triangular *> full rank factor R with K-by-K upper-triangular
*> R11(K) and K-by-N rectangular R12(K). The diagonal *> R11(K) and K-by-N rectangular R12(K). The diagonal
@ -124,14 +124,14 @@
*> d) RELMAXC2NRMK equals MAXC2NRMK divided by MAXC2NRM, the maximum *> d) RELMAXC2NRMK equals MAXC2NRMK divided by MAXC2NRM, the maximum
*> column 2-norm of the original matrix A, which is equal *> column 2-norm of the original matrix A, which is equal
*> to abs(R(1,1)), ( if K = min(M,N), RELMAXC2NRMK = 0.0 ); *> to abs(R(1,1)), ( if K = min(M,N), RELMAXC2NRMK = 0.0 );
*> e) Q(K)**H * B, the matrix B with the orthogonal *> e) Q(K)**H * B, the matrix B with the unitary
*> transformation Q(K)**H applied on the left. *> transformation Q(K)**H applied on the left.
*> *>
*> The N-by-N permutation matrix P(K) is stored in a compact form in *> The N-by-N permutation matrix P(K) is stored in a compact form in
*> the integer array JPIV. For 1 <= j <= N, column j *> the integer array JPIV. For 1 <= j <= N, column j
*> of the matrix A was interchanged with column JPIV(j). *> of the matrix A was interchanged with column JPIV(j).
*> *>
*> The M-by-M orthogonal matrix Q is represented as a product *> The M-by-M unitary matrix Q is represented as a product
*> of elementary Householder reflectors *> of elementary Householder reflectors
*> *>
*> Q(K) = H(1) * H(2) * . . . * H(K), *> Q(K) = H(1) * H(2) * . . . * H(K),
@ -300,7 +300,7 @@
*> *>
*> 1. The elements below the diagonal of the subarray *> 1. The elements below the diagonal of the subarray
*> A(1:M,1:K) together with TAU(1:K) represent the *> A(1:M,1:K) together with TAU(1:K) represent the
*> orthogonal matrix Q(K) as a product of K Householder *> unitary matrix Q(K) as a product of K Householder
*> elementary reflectors. *> elementary reflectors.
*> *>
*> 2. The elements on and above the diagonal of *> 2. The elements on and above the diagonal of
@ -579,8 +579,8 @@
*> \verbatim *> \verbatim
*> *>
*> November 2023, Igor Kozachenko, James Demmel, *> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division, *> EECS Department,
*> University of California, Berkeley *> University of California, Berkeley, USA.
*> *>
*> \endverbatim *> \endverbatim
* *

6
lapack-netlib/SRC/zlaqp2rk.f
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@ -178,7 +178,7 @@
*> On exit: *> On exit:
*> 1. The elements in block A(IOFFSET+1:M,1:K) below *> 1. The elements in block A(IOFFSET+1:M,1:K) below
*> the diagonal together with the array TAU represent *> the diagonal together with the array TAU represent
*> the orthogonal matrix Q(K) as a product of elementary *> the unitary matrix Q(K) as a product of elementary
*> reflectors. *> reflectors.
*> 2. The upper triangular block of the matrix A stored *> 2. The upper triangular block of the matrix A stored
*> in A(IOFFSET+1:M,1:K) is the triangular factor obtained. *> in A(IOFFSET+1:M,1:K) is the triangular factor obtained.
@ -332,8 +332,8 @@
*> \verbatim *> \verbatim
*> *>
*> November 2023, Igor Kozachenko, James Demmel, *> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division, *> EECS Department,
*> University of California, Berkeley *> University of California, Berkeley, USA.
*> *>
*> \endverbatim *> \endverbatim
* *

6
lapack-netlib/SRC/zlaqp3rk.f
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@ -196,7 +196,7 @@
*> On exit: *> On exit:
*> 1. The elements in block A(IOFFSET+1:M,1:KB) below *> 1. The elements in block A(IOFFSET+1:M,1:KB) below
*> the diagonal together with the array TAU represent *> the diagonal together with the array TAU represent
*> the orthogonal matrix Q(KB) as a product of elementary *> the unitary matrix Q(KB) as a product of elementary
*> reflectors. *> reflectors.
*> 2. The upper triangular block of the matrix A stored *> 2. The upper triangular block of the matrix A stored
*> in A(IOFFSET+1:M,1:KB) is the triangular factor obtained. *> in A(IOFFSET+1:M,1:KB) is the triangular factor obtained.
@ -383,8 +383,8 @@
*> \verbatim *> \verbatim
*> *>
*> November 2023, Igor Kozachenko, James Demmel, *> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division, *> EECS Department,
*> University of California, Berkeley *> University of California, Berkeley, USA.
*> *>
*> \endverbatim *> \endverbatim
* *