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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| subroutine sgemqr | ( | character | side, |
| character | trans, | ||
| integer | m, | ||
| integer | n, | ||
| integer | k, | ||
| real, dimension( lda, * ) | a, | ||
| integer | lda, | ||
| real, dimension( * ) | t, | ||
| integer | tsize, | ||
| real, dimension( ldc, * ) | c, | ||
| integer | ldc, | ||
| real, dimension( * ) | work, | ||
| integer | lwork, | ||
| integer | info | ||
| ) |
SGEMQR
SGEMQR overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**T * C C * Q**T
where Q is a real orthogonal matrix defined as the product
of blocked elementary reflectors computed by tall skinny
QR factorization (SGEQR) | [in] | SIDE | SIDE is CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right. |
| [in] | TRANS | TRANS is CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T. |
| [in] | M | M is INTEGER
The number of rows of the matrix A. M >=0. |
| [in] | N | N is INTEGER
The number of columns of the matrix C. N >= 0. |
| [in] | K | K is INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0. |
| [in] | A | A is REAL array, dimension (LDA,K)
Part of the data structure to represent Q as returned by SGEQR. |
| [in] | LDA | LDA is INTEGER
The leading dimension of the array A.
If SIDE = 'L', LDA >= max(1,M);
if SIDE = 'R', LDA >= max(1,N). |
| [in] | T | T is REAL array, dimension (MAX(5,TSIZE)).
Part of the data structure to represent Q as returned by SGEQR. |
| [in] | TSIZE | TSIZE is INTEGER
The dimension of the array T. TSIZE >= 5. |
| [in,out] | C | C is REAL array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. |
| [in] | LDC | LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M). |
| [out] | WORK | (workspace) REAL array, dimension (MAX(1,LWORK)) |
| [in] | LWORK | LWORK is INTEGER
The dimension of the array WORK.
If LWORK = -1, then a workspace query is assumed. The routine
only calculates the size of the WORK array, returns this
value as WORK(1), and no error message related to WORK
is issued by XERBLA. |
| [out] | INFO | INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value |
These details are particular for this LAPACK implementation. Users should not
take them for granted. These details may change in the future, and are not likely
true for another LAPACK implementation. These details are relevant if one wants
to try to understand the code. They are not part of the interface.
In this version,
T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
SLATSQR or SGEQRT
Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, SGEQR will use either
SLATSQR (if the matrix is tall-and-skinny) or SGEQRT to compute
the QR factorization.
This version of SGEMQR will use either SLAMTSQR or SGEMQRT to
multiply matrix Q by another matrix.
Further Details in SLAMTSQR or SGEMQRT. Definition at line 172 of file sgemqr.f.
1.9.7