 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ sgelqt()

 subroutine sgelqt ( integer M, integer N, integer MB, real, dimension( lda, * ) A, integer LDA, real, dimension( ldt, * ) T, integer LDT, real, dimension( * ) WORK, integer INFO )
Purpose:

DGELQT computes a blocked LQ factorization of a real M-by-N matrix A using the compact WY representation of Q.

Parameters
 [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 A. N >= 0.``` [in] MB ``` MB is INTEGER The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1.``` [in,out] A ``` A is REAL array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is lower triangular if M <= N); the elements above the diagonal are the rows of V.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).``` [out] T ``` T is REAL array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details.``` [in] LDT ``` LDT is INTEGER The leading dimension of the array T. LDT >= MB.``` [out] WORK ` WORK is REAL array, dimension (MB*N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```
Date
November 2017
Further Details:

The matrix V stores the elementary reflectors H(i) in the i-th row above the diagonal. For example, if M=5 and N=3, the matrix V is

V = ( 1 v1 v1 v1 v1 ) ( 1 v2 v2 v2 ) ( 1 v3 v3 )

where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each block is of order MB except for the last block, which is of order IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-K matrix T as

T = (T1 T2 ... TB).

Definition at line 124 of file sgelqt.f.

124 *
125 * -- LAPACK computational routine (version 3.8.0) --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 * November 2017
129 *
130 * .. Scalar Arguments ..
131  INTEGER info, lda, ldt, m, n, mb
132 * ..
133 * .. Array Arguments ..
134  REAL a( lda, * ), t( ldt, * ), work( * )
135 * ..
136 *
137 * =====================================================================
138 *
139 * ..
140 * .. Local Scalars ..
141  INTEGER i, ib, iinfo, k
142 * ..
143 * .. External Subroutines ..
144  EXTERNAL sgeqrt2, sgeqrt3, sgelqt3, slarfb, xerbla
145 * ..
146 * .. Executable Statements ..
147 *
148 * Test the input arguments
149 *
150  info = 0
151  IF( m.LT.0 ) THEN
152  info = -1
153  ELSE IF( n.LT.0 ) THEN
154  info = -2
155  ELSE IF( mb.LT.1 .OR. ( mb.GT.min(m,n) .AND. min(m,n).GT.0 ) )THEN
156  info = -3
157  ELSE IF( lda.LT.max( 1, m ) ) THEN
158  info = -5
159  ELSE IF( ldt.LT.mb ) THEN
160  info = -7
161  END IF
162  IF( info.NE.0 ) THEN
163  CALL xerbla( 'SGELQT', -info )
164  RETURN
165  END IF
166 *
167 * Quick return if possible
168 *
169  k = min( m, n )
170  IF( k.EQ.0 ) RETURN
171 *
172 * Blocked loop of length K
173 *
174  DO i = 1, k, mb
175  ib = min( k-i+1, mb )
176 *
177 * Compute the LQ factorization of the current block A(I:M,I:I+IB-1)
178 *
179  CALL sgelqt3( ib, n-i+1, a(i,i), lda, t(1,i), ldt, iinfo )
180  IF( i+ib.LE.m ) THEN
181 *
182 * Update by applying H**T to A(I:M,I+IB:N) from the right
183 *
184  CALL slarfb( 'R', 'N', 'F', 'R', m-i-ib+1, n-i+1, ib,
185  \$ a( i, i ), lda, t( 1, i ), ldt,
186  \$ a( i+ib, i ), lda, work , m-i-ib+1 )
187  END IF
188  END DO
189  RETURN
190 *
191 * End of SGELQT
192 *
subroutine sgeqrt2(M, N, A, LDA, T, LDT, INFO)
SGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY represen...
Definition: sgeqrt2.f:129
subroutine slarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
SLARFB applies a block reflector or its transpose to a general rectangular matrix.
Definition: slarfb.f:197
recursive subroutine sgelqt3(M, N, A, LDA, T, LDT, INFO)
Definition: sgelqt3.f:116
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
recursive subroutine sgeqrt3(M, N, A, LDA, T, LDT, INFO)
SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact...
Definition: sgeqrt3.f:134
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