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Diffstat (limited to 'SRC/zgelq2.f')
-rw-r--r-- | SRC/zgelq2.f | 123 |
1 files changed, 123 insertions, 0 deletions
diff --git a/SRC/zgelq2.f b/SRC/zgelq2.f new file mode 100644 index 00000000..4c2368aa --- /dev/null +++ b/SRC/zgelq2.f @@ -0,0 +1,123 @@ + SUBROUTINE ZGELQ2( M, N, A, LDA, TAU, WORK, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + INTEGER INFO, LDA, M, N +* .. +* .. Array Arguments .. + COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* ZGELQ2 computes an LQ factorization of a complex m by n matrix A: +* A = L * Q. +* +* Arguments +* ========= +* +* M (input) INTEGER +* The number of rows of the matrix A. M >= 0. +* +* N (input) INTEGER +* The number of columns of the matrix A. N >= 0. +* +* A (input/output) COMPLEX*16 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, +* with the array TAU, represent the unitary matrix Q as a +* product of elementary reflectors (see Further Details). +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,M). +* +* TAU (output) COMPLEX*16 array, dimension (min(M,N)) +* The scalar factors of the elementary reflectors (see Further +* Details). +* +* WORK (workspace) COMPLEX*16 array, dimension (M) +* +* INFO (output) 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(k)' . . . H(2)' H(1)', where k = min(m,n). +* +* Each H(i) has the form +* +* H(i) = I - tau * v * v' +* +* where tau is a complex scalar, and v is a complex vector with +* v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in +* A(i,i+1:n), and tau in TAU(i). +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 ONE + PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) +* .. +* .. Local Scalars .. + INTEGER I, K + COMPLEX*16 ALPHA +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, ZLACGV, ZLARF, ZLARFP +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. Executable Statements .. +* +* Test the input arguments +* + INFO = 0 + IF( M.LT.0 ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( LDA.LT.MAX( 1, M ) ) THEN + INFO = -4 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'ZGELQ2', -INFO ) + RETURN + END IF +* + K = MIN( M, N ) +* + DO 10 I = 1, K +* +* Generate elementary reflector H(i) to annihilate A(i,i+1:n) +* + CALL ZLACGV( N-I+1, A( I, I ), LDA ) + ALPHA = A( I, I ) + CALL ZLARFP( N-I+1, ALPHA, A( I, MIN( I+1, N ) ), LDA, + $ TAU( I ) ) + IF( I.LT.M ) THEN +* +* Apply H(i) to A(i+1:m,i:n) from the right +* + A( I, I ) = ONE + CALL ZLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, TAU( I ), + $ A( I+1, I ), LDA, WORK ) + END IF + A( I, I ) = ALPHA + CALL ZLACGV( N-I+1, A( I, I ), LDA ) + 10 CONTINUE + RETURN +* +* End of ZGELQ2 +* + END |