00001 SUBROUTINE CGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, 00002 $ INFO ) 00003 * 00004 * -- LAPACK routine (version 3.1) -- 00005 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS 00010 * .. 00011 * .. Array Arguments .. 00012 COMPLEX A( LDA, * ), B( LDB, * ), TAU( * ), 00013 $ WORK( LWORK ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * Compute a minimum-norm solution 00020 * min || A*X - B || 00021 * using the RQ factorization 00022 * A = R*Q 00023 * computed by CGERQF. 00024 * 00025 * Arguments 00026 * ========= 00027 * 00028 * M (input) INTEGER 00029 * The number of rows of the matrix A. M >= 0. 00030 * 00031 * N (input) INTEGER 00032 * The number of columns of the matrix A. N >= M >= 0. 00033 * 00034 * NRHS (input) INTEGER 00035 * The number of columns of B. NRHS >= 0. 00036 * 00037 * A (input) COMPLEX array, dimension (LDA,N) 00038 * Details of the RQ factorization of the original matrix A as 00039 * returned by CGERQF. 00040 * 00041 * LDA (input) INTEGER 00042 * The leading dimension of the array A. LDA >= M. 00043 * 00044 * TAU (input) COMPLEX array, dimension (M) 00045 * Details of the orthogonal matrix Q. 00046 * 00047 * B (input/output) COMPLEX array, dimension (LDB,NRHS) 00048 * On entry, the right hand side vectors for the linear system. 00049 * On exit, the solution vectors X. Each solution vector 00050 * is contained in rows 1:N of a column of B. 00051 * 00052 * LDB (input) INTEGER 00053 * The leading dimension of the array B. LDB >= max(1,N). 00054 * 00055 * WORK (workspace) COMPLEX array, dimension (LWORK) 00056 * 00057 * LWORK (input) INTEGER 00058 * The length of the array WORK. LWORK must be at least NRHS, 00059 * and should be at least NRHS*NB, where NB is the block size 00060 * for this environment. 00061 * 00062 * INFO (output) INTEGER 00063 * = 0: successful exit 00064 * < 0: if INFO = -i, the i-th argument had an illegal value 00065 * 00066 * ===================================================================== 00067 * 00068 * .. Parameters .. 00069 COMPLEX CZERO, CONE 00070 PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ), 00071 $ CONE = ( 1.0E+0, 0.0E+0 ) ) 00072 * .. 00073 * .. External Subroutines .. 00074 EXTERNAL CLASET, CTRSM, CUNMRQ, XERBLA 00075 * .. 00076 * .. Intrinsic Functions .. 00077 INTRINSIC MAX 00078 * .. 00079 * .. Executable Statements .. 00080 * 00081 * Test the input parameters. 00082 * 00083 INFO = 0 00084 IF( M.LT.0 ) THEN 00085 INFO = -1 00086 ELSE IF( N.LT.0 .OR. M.GT.N ) THEN 00087 INFO = -2 00088 ELSE IF( NRHS.LT.0 ) THEN 00089 INFO = -3 00090 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00091 INFO = -5 00092 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00093 INFO = -8 00094 ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 ) 00095 $ THEN 00096 INFO = -10 00097 END IF 00098 IF( INFO.NE.0 ) THEN 00099 CALL XERBLA( 'CGERQS', -INFO ) 00100 RETURN 00101 END IF 00102 * 00103 * Quick return if possible 00104 * 00105 IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 ) 00106 $ RETURN 00107 * 00108 * Solve R*X = B(n-m+1:n,:) 00109 * 00110 CALL CTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', M, NRHS, 00111 $ CONE, A( 1, N-M+1 ), LDA, B( N-M+1, 1 ), LDB ) 00112 * 00113 * Set B(1:n-m,:) to zero 00114 * 00115 CALL CLASET( 'Full', N-M, NRHS, CZERO, CZERO, B, LDB ) 00116 * 00117 * B := Q' * B 00118 * 00119 CALL CUNMRQ( 'Left', 'Conjugate transpose', N, NRHS, M, A, LDA, 00120 $ TAU, B, LDB, WORK, LWORK, INFO ) 00121 * 00122 RETURN 00123 * 00124 * End of CGERQS 00125 * 00126 END
1.7.2