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Update of the documentation to the pull request "Truncated QR with Pivoting #891" #941

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Merged
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Nov 21, 2023
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Update of the documentation to the pull request "Truncated QR with Pivoting #891" #941

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aec6cb3
Fixed an error in the description of complex routines, changed othogo…
scr2016 Nov 21, 2023
dcbd803
updated descriptions for the truncated QR routines
scr2016 Nov 21, 2023
bd4455f
updated descriptions for the truncated QR routines second time
scr2016 Nov 21, 2023
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Fixed an error in the description of complex routines, changed othogo… 
…nal into unitary
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@scr2016
scr2016 committed Nov 21, 2023
commit aec6cb32817bd2acc71b66d67d036b454278dff7
8 changes: 4 additions & 4 deletions SRC/cgeqp3rk.f
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*> where:
*>
*> 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
*> full rank factor R with K-by-K upper-triangular
*> R11(K) and K-by-N rectangular R12(K). The diagonal
Expand Down Expand Up @@ -124,14 +124,14 @@
*> d) RELMAXC2NRMK equals MAXC2NRMK divided by MAXC2NRM, the maximum
*> column 2-norm of the original matrix A, which is equal
*> 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.
*>
*> 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
*> 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
*>
*> Q(K) = H(1) * H(2) * . . . * H(K),
Expand Down Expand Up @@ -300,7 +300,7 @@
*>
*> 1. The elements below the diagonal of the subarray
*> 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.
*>
*> 2. The elements on and above the diagonal of
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2 changes: 1 addition & 1 deletion SRC/claqp2rk.f
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*> On exit:
*> 1. The elements in block A(IOFFSET+1:M,1:K) below
*> 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.
*> 2. The upper triangular block of the matrix A stored
*> in A(IOFFSET+1:M,1:K) is the triangular factor obtained.
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2 changes: 1 addition & 1 deletion SRC/claqp3rk.f
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Expand Up @@ -196,7 +196,7 @@
*> On exit:
*> 1. The elements in block A(IOFFSET+1:M,1:KB) below
*> 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.
*> 2. The upper triangular block of the matrix A stored
*> in A(IOFFSET+1:M,1:KB) is the triangular factor obtained.
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8 changes: 4 additions & 4 deletions SRC/zgeqp3rk.f
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Expand Up @@ -55,7 +55,7 @@
*> where:
*>
*> 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
*> full rank factor R with K-by-K upper-triangular
*> R11(K) and K-by-N rectangular R12(K). The diagonal
Expand Down Expand Up @@ -124,14 +124,14 @@
*> d) RELMAXC2NRMK equals MAXC2NRMK divided by MAXC2NRM, the maximum
*> column 2-norm of the original matrix A, which is equal
*> 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.
*>
*> 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
*> 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
*>
*> Q(K) = H(1) * H(2) * . . . * H(K),
Expand Down Expand Up @@ -300,7 +300,7 @@
*>
*> 1. The elements below the diagonal of the subarray
*> 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.
*>
*> 2. The elements on and above the diagonal of
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2 changes: 1 addition & 1 deletion SRC/zlaqp2rk.f
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Expand Up @@ -178,7 +178,7 @@
*> On exit:
*> 1. The elements in block A(IOFFSET+1:M,1:K) below
*> 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.
*> 2. The upper triangular block of the matrix A stored
*> in A(IOFFSET+1:M,1:K) is the triangular factor obtained.
Expand Down
2 changes: 1 addition & 1 deletion SRC/zlaqp3rk.f
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Original file line number Diff line number Diff line change
Expand Up @@ -196,7 +196,7 @@
*> On exit:
*> 1. The elements in block A(IOFFSET+1:M,1:KB) below
*> 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.
*> 2. The upper triangular block of the matrix A stored
*> in A(IOFFSET+1:M,1:KB) is the triangular factor obtained.
Expand Down