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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE SGELQ2( M, N, A, LDA, TAU, WORK, INFO ) 00002 * 00003 * -- LAPACK routine (version 3.3.1) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * -- April 2011 -- 00007 * 00008 * .. Scalar Arguments .. 00009 INTEGER INFO, LDA, M, N 00010 * .. 00011 * .. Array Arguments .. 00012 REAL A( LDA, * ), TAU( * ), WORK( * ) 00013 * .. 00014 * 00015 * Purpose 00016 * ======= 00017 * 00018 * SGELQ2 computes an LQ factorization of a real m by n matrix A: 00019 * A = L * Q. 00020 * 00021 * Arguments 00022 * ========= 00023 * 00024 * M (input) INTEGER 00025 * The number of rows of the matrix A. M >= 0. 00026 * 00027 * N (input) INTEGER 00028 * The number of columns of the matrix A. N >= 0. 00029 * 00030 * A (input/output) REAL array, dimension (LDA,N) 00031 * On entry, the m by n matrix A. 00032 * On exit, the elements on and below the diagonal of the array 00033 * contain the m by min(m,n) lower trapezoidal matrix L (L is 00034 * lower triangular if m <= n); the elements above the diagonal, 00035 * with the array TAU, represent the orthogonal matrix Q as a 00036 * product of elementary reflectors (see Further Details). 00037 * 00038 * LDA (input) INTEGER 00039 * The leading dimension of the array A. LDA >= max(1,M). 00040 * 00041 * TAU (output) REAL array, dimension (min(M,N)) 00042 * The scalar factors of the elementary reflectors (see Further 00043 * Details). 00044 * 00045 * WORK (workspace) REAL array, dimension (M) 00046 * 00047 * INFO (output) INTEGER 00048 * = 0: successful exit 00049 * < 0: if INFO = -i, the i-th argument had an illegal value 00050 * 00051 * Further Details 00052 * =============== 00053 * 00054 * The matrix Q is represented as a product of elementary reflectors 00055 * 00056 * Q = H(k) . . . H(2) H(1), where k = min(m,n). 00057 * 00058 * Each H(i) has the form 00059 * 00060 * H(i) = I - tau * v * v**T 00061 * 00062 * where tau is a real scalar, and v is a real vector with 00063 * v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), 00064 * and tau in TAU(i). 00065 * 00066 * ===================================================================== 00067 * 00068 * .. Parameters .. 00069 REAL ONE 00070 PARAMETER ( ONE = 1.0E+0 ) 00071 * .. 00072 * .. Local Scalars .. 00073 INTEGER I, K 00074 REAL AII 00075 * .. 00076 * .. External Subroutines .. 00077 EXTERNAL SLARF, SLARFG, XERBLA 00078 * .. 00079 * .. Intrinsic Functions .. 00080 INTRINSIC MAX, MIN 00081 * .. 00082 * .. Executable Statements .. 00083 * 00084 * Test the input arguments 00085 * 00086 INFO = 0 00087 IF( M.LT.0 ) THEN 00088 INFO = -1 00089 ELSE IF( N.LT.0 ) THEN 00090 INFO = -2 00091 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00092 INFO = -4 00093 END IF 00094 IF( INFO.NE.0 ) THEN 00095 CALL XERBLA( 'SGELQ2', -INFO ) 00096 RETURN 00097 END IF 00098 * 00099 K = MIN( M, N ) 00100 * 00101 DO 10 I = 1, K 00102 * 00103 * Generate elementary reflector H(i) to annihilate A(i,i+1:n) 00104 * 00105 CALL SLARFG( N-I+1, A( I, I ), A( I, MIN( I+1, N ) ), LDA, 00106 $ TAU( I ) ) 00107 IF( I.LT.M ) THEN 00108 * 00109 * Apply H(i) to A(i+1:m,i:n) from the right 00110 * 00111 AII = A( I, I ) 00112 A( I, I ) = ONE 00113 CALL SLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, TAU( I ), 00114 $ A( I+1, I ), LDA, WORK ) 00115 A( I, I ) = AII 00116 END IF 00117 10 CONTINUE 00118 RETURN 00119 * 00120 * End of SGELQ2 00121 * 00122 END
1.7.3 
