# slamtsqr.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **slamtsqr** (SIDE, TRANS, M, **N**, K, MB, NB, A, **LDA**, T, LDT, C, LDC, WORK, LWORK, INFO)

## Function/Subroutine Documentation

### subroutine slamtsqr (character SIDE, character TRANS, integer M, integer N, integer K, integer MB, integer NB, real, dimension( lda, * ) A, integer LDA, real, dimension( ldt, * ) T, integer LDT, real, dimension(ldc, * ) C, integer LDC, real, dimension( * ) WORK, integer LWORK, integer INFO)

**Purpose:**

SLAMTSQR 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 (DLATSQR)

**Parameters:***SIDE*SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right.

*TRANS*TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T.

*M*M is INTEGER The number of rows of the matrix A. M >=0.

*N*N is INTEGER The number of columns of the matrix C. M >= N >= 0.

*K*K is INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0;

*MB*MB is INTEGER The block size to be used in the blocked QR. MB > N. (must be the same as DLATSQR)

*NB*NB is INTEGER The column block size to be used in the blocked QR. N >= NB >= 1.

*A*A is REAL array, dimension (LDA,K) The i-th column must contain the vector which defines the blockedelementary reflector H(i), for i = 1,2,...,k, as returned by DLATSQR in the first k columns of its array argument A.

*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).

*T*T is REAL array, dimension ( N * Number of blocks(CEIL(M-K/MB-K)), The blocked upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details.

*LDT*LDT is INTEGER The leading dimension of the array T. LDT >= NB.

*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.

*LDC*LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).

*WORK*(workspace) REAL array, dimension (MAX(1,LWORK))

*LWORK*LWORK is INTEGER The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N)*NB; if SIDE = 'R', LWORK >= max(1,MB)*NB. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**Tall-Skinny QR (TSQR) performs QR by a sequence of orthogonal transformations, representing Q as a product of other orthogonal matrices Q = Q(1) * Q(2) * . . . * Q(k) where each Q(i) zeros out subdiagonal entries of a block of MB rows of A: Q(1) zeros out the subdiagonal entries of rows 1:MB of A Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A . . .

Q(1) is computed by GEQRT, which represents Q(1) by Householder vectors stored under the diagonal of rows 1:MB of A, and by upper triangular block reflectors, stored in array T(1:LDT,1:N). For more information see Further Details in GEQRT.

Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N). The last Q(k) may use fewer rows. For more information see Further Details in TPQRT.

For more details of the overall algorithm, see the description of Sequential TSQR in Section 2.2 of [1].

[1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,” J. Demmel, L. Grigori, M. Hoemmen, J. Langou, SIAM J. Sci. Comput, vol. 34, no. 1, 2012

Definition at line 197 of file slamtsqr.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slamtsqr(3) is an alias of slamtsqr.f(3).