 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine sgeqr2p ( integer M, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) TAU, real, dimension( * ) WORK, integer INFO )

SGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

Purpose:
``` SGEQR2P computes a QR factorization of a real m by n matrix A:
A = Q * R. The diagonal entries of R are nonnegative.```
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,out] A ``` A is REAL array, dimension (LDA,N) On entry, the m by n matrix A. On exit, the elements on and above the diagonal of the array contain the min(m,n) by n upper trapezoidal matrix R (R is upper triangular if m >= n). The diagonal entries of R are nonnegative; the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details).``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).``` [out] TAU ``` TAU is REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).``` [out] WORK ` WORK is REAL array, dimension (N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```
Date
November 2015
Further Details:
```  The matrix Q is represented as a product of elementary reflectors

Q = H(1) H(2) . . . H(k), where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v**T

where tau is a real scalar, and v is a real vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).

See Lapack Working Note 203 for details```

Definition at line 126 of file sgeqr2p.f.

126 *
127 * -- LAPACK computational routine (version 3.6.0) --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 * November 2015
131 *
132 * .. Scalar Arguments ..
133  INTEGER info, lda, m, n
134 * ..
135 * .. Array Arguments ..
136  REAL a( lda, * ), tau( * ), work( * )
137 * ..
138 *
139 * =====================================================================
140 *
141 * .. Parameters ..
142  REAL one
143  parameter ( one = 1.0e+0 )
144 * ..
145 * .. Local Scalars ..
146  INTEGER i, k
147  REAL aii
148 * ..
149 * .. External Subroutines ..
150  EXTERNAL slarf, slarfgp, xerbla
151 * ..
152 * .. Intrinsic Functions ..
153  INTRINSIC max, min
154 * ..
155 * .. Executable Statements ..
156 *
157 * Test the input arguments
158 *
159  info = 0
160  IF( m.LT.0 ) THEN
161  info = -1
162  ELSE IF( n.LT.0 ) THEN
163  info = -2
164  ELSE IF( lda.LT.max( 1, m ) ) THEN
165  info = -4
166  END IF
167  IF( info.NE.0 ) THEN
168  CALL xerbla( 'SGEQR2P', -info )
169  RETURN
170  END IF
171 *
172  k = min( m, n )
173 *
174  DO 10 i = 1, k
175 *
176 * Generate elementary reflector H(i) to annihilate A(i+1:m,i)
177 *
178  CALL slarfgp( m-i+1, a( i, i ), a( min( i+1, m ), i ), 1,
179  \$ tau( i ) )
180  IF( i.LT.n ) THEN
181 *
182 * Apply H(i) to A(i:m,i+1:n) from the left
183 *
184  aii = a( i, i )
185  a( i, i ) = one
186  CALL slarf( 'Left', m-i+1, n-i, a( i, i ), 1, tau( i ),
187  \$ a( i, i+1 ), lda, work )
188  a( i, i ) = aii
189  END IF
190  10 CONTINUE
191  RETURN
192 *
193 * End of SGEQR2P
194 *
subroutine slarfgp(N, ALPHA, X, INCX, TAU)
SLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.
Definition: slarfgp.f:106
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine slarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
SLARF applies an elementary reflector to a general rectangular matrix.
Definition: slarf.f:126

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