LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cgeqr2p()

 subroutine cgeqr2p ( integer M, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( * ) WORK, integer INFO )

CGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

Purpose:
``` CGEQR2P computes a QR factorization of a complex m-by-n matrix A:

A = Q * ( R ),
( 0 )

where:

Q is a m-by-m orthogonal matrix;
R is an upper-triangular n-by-n matrix with nonnegative diagonal
entries;
0 is a (m-n)-by-n zero matrix, if m > n.```
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 COMPLEX 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 real and nonnegative; the elements below the diagonal, with the array TAU, represent the unitary 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 COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).``` [out] WORK ` WORK is COMPLEX array, dimension (N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```
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**H

where tau is a complex scalar, and v is a complex 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 133 of file cgeqr2p.f.

134*
135* -- LAPACK computational routine --
136* -- LAPACK is a software package provided by Univ. of Tennessee, --
137* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138*
139* .. Scalar Arguments ..
140 INTEGER INFO, LDA, M, N
141* ..
142* .. Array Arguments ..
143 COMPLEX A( LDA, * ), TAU( * ), WORK( * )
144* ..
145*
146* =====================================================================
147*
148* .. Parameters ..
149 COMPLEX ONE
150 parameter( one = ( 1.0e+0, 0.0e+0 ) )
151* ..
152* .. Local Scalars ..
153 INTEGER I, K
154 COMPLEX ALPHA
155* ..
156* .. External Subroutines ..
157 EXTERNAL clarf, clarfgp, xerbla
158* ..
159* .. Intrinsic Functions ..
160 INTRINSIC conjg, max, min
161* ..
162* .. Executable Statements ..
163*
164* Test the input arguments
165*
166 info = 0
167 IF( m.LT.0 ) THEN
168 info = -1
169 ELSE IF( n.LT.0 ) THEN
170 info = -2
171 ELSE IF( lda.LT.max( 1, m ) ) THEN
172 info = -4
173 END IF
174 IF( info.NE.0 ) THEN
175 CALL xerbla( 'CGEQR2P', -info )
176 RETURN
177 END IF
178*
179 k = min( m, n )
180*
181 DO 10 i = 1, k
182*
183* Generate elementary reflector H(i) to annihilate A(i+1:m,i)
184*
185 CALL clarfgp( m-i+1, a( i, i ), a( min( i+1, m ), i ), 1,
186 \$ tau( i ) )
187 IF( i.LT.n ) THEN
188*
189* Apply H(i)**H to A(i:m,i+1:n) from the left
190*
191 alpha = a( i, i )
192 a( i, i ) = one
193 CALL clarf( 'Left', m-i+1, n-i, a( i, i ), 1,
194 \$ conjg( tau( i ) ), a( i, i+1 ), lda, work )
195 a( i, i ) = alpha
196 END IF
197 10 CONTINUE
198 RETURN
199*
200* End of CGEQR2P
201*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine clarfgp(N, ALPHA, X, INCX, TAU)
CLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.
Definition: clarfgp.f:104
subroutine clarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
CLARF applies an elementary reflector to a general rectangular matrix.
Definition: clarf.f:128
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