1 SUBROUTINE CGERQ2( M, N, A, LDA, TAU, WORK, INFO ) 2* 3* -- LAPACK routine (version 3.0) -- 4* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., 5* Courant Institute, Argonne National Lab, and Rice University 6* September 30, 1994 7* 8* .. Scalar Arguments .. 9 INTEGER INFO, LDA, M, N 10* .. 11* .. Array Arguments .. 12 COMPLEX A( LDA, * ), TAU( * ), WORK( * ) 13* .. 14* 15* Purpose 16* ======= 17* 18* CGERQ2 computes an RQ factorization of a complex m by n matrix A: 19* A = R * Q. 20* 21* Arguments 22* ========= 23* 24* M (input) INTEGER 25* The number of rows of the matrix A. M >= 0. 26* 27* N (input) INTEGER 28* The number of columns of the matrix A. N >= 0. 29* 30* A (input/output) COMPLEX array, dimension (LDA,N) 31* On entry, the m by n matrix A. 32* On exit, if m <= n, the upper triangle of the subarray 33* A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; 34* if m >= n, the elements on and above the (m-n)-th subdiagonal 35* contain the m by n upper trapezoidal matrix R; the remaining 36* elements, with the array TAU, represent the unitary matrix 37* Q as a product of elementary reflectors (see Further 38* Details). 39* 40* LDA (input) INTEGER 41* The leading dimension of the array A. LDA >= max(1,M). 42* 43* TAU (output) COMPLEX array, dimension (min(M,N)) 44* The scalar factors of the elementary reflectors (see Further 45* Details). 46* 47* WORK (workspace) COMPLEX array, dimension (M) 48* 49* INFO (output) INTEGER 50* = 0: successful exit 51* < 0: if INFO = -i, the i-th argument had an illegal value 52* 53* Further Details 54* =============== 55* 56* The matrix Q is represented as a product of elementary reflectors 57* 58* Q = H(1)' H(2)' . . . H(k)', where k = min(m,n). 59* 60* Each H(i) has the form 61* 62* H(i) = I - tau * v * v' 63* 64* where tau is a complex scalar, and v is a complex vector with 65* v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on 66* exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). 67* 68* ===================================================================== 69* 70* .. Parameters .. 71 COMPLEX ONE 72 PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) 73* .. 74* .. Local Scalars .. 75 INTEGER I, K 76 COMPLEX ALPHA 77* .. 78* .. External Subroutines .. 79 EXTERNAL CLACGV, CLARF, CLARFG, XERBLA 80* .. 81* .. Intrinsic Functions .. 82 INTRINSIC MAX, MIN 83* .. 84* .. Executable Statements .. 85* 86* Test the input arguments 87* 88 INFO = 0 89 IF( M.LT.0 ) THEN 90 INFO = -1 91 ELSE IF( N.LT.0 ) THEN 92 INFO = -2 93 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 94 INFO = -4 95 END IF 96 IF( INFO.NE.0 ) THEN 97 CALL XERBLA( 'CGERQ2', -INFO ) 98 RETURN 99 END IF 100* 101 K = MIN( M, N ) 102* 103 DO 10 I = K, 1, -1 104* 105* Generate elementary reflector H(i) to annihilate 106* A(m-k+i,1:n-k+i-1) 107* 108 CALL CLACGV( N-K+I, A( M-K+I, 1 ), LDA ) 109 ALPHA = A( M-K+I, N-K+I ) 110 CALL CLARFG( N-K+I, ALPHA, A( M-K+I, 1 ), LDA, 111 $ TAU( I ) ) 112* 113* Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right 114* 115 A( M-K+I, N-K+I ) = ONE 116 CALL CLARF( 'Right', M-K+I-1, N-K+I, A( M-K+I, 1 ), LDA, 117 $ TAU( I ), A, LDA, WORK ) 118 A( M-K+I, N-K+I ) = ALPHA 119 CALL CLACGV( N-K+I-1, A( M-K+I, 1 ), LDA ) 120 10 CONTINUE 121 RETURN 122* 123* End of CGERQ2 124* 125 END 126