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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 DGELQS( 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 DOUBLE PRECISION 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 LQ factorization 00022 * A = L*Q 00023 * computed by DGELQF. 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) DOUBLE PRECISION array, dimension (LDA,N) 00038 * Details of the LQ factorization of the original matrix A as 00039 * returned by DGELQF. 00040 * 00041 * LDA (input) INTEGER 00042 * The leading dimension of the array A. LDA >= M. 00043 * 00044 * TAU (input) DOUBLE PRECISION array, dimension (M) 00045 * Details of the orthogonal matrix Q. 00046 * 00047 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) 00048 * On entry, the m-by-nrhs right hand side matrix B. 00049 * On exit, the n-by-nrhs solution matrix X. 00050 * 00051 * LDB (input) INTEGER 00052 * The leading dimension of the array B. LDB >= N. 00053 * 00054 * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) 00055 * 00056 * LWORK (input) INTEGER 00057 * The length of the array WORK. LWORK must be at least NRHS, 00058 * and should be at least NRHS*NB, where NB is the block size 00059 * for this environment. 00060 * 00061 * INFO (output) INTEGER 00062 * = 0: successful exit 00063 * < 0: if INFO = -i, the i-th argument had an illegal value 00064 * 00065 * ===================================================================== 00066 * 00067 * .. Parameters .. 00068 DOUBLE PRECISION ZERO, ONE 00069 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00070 * .. 00071 * .. External Subroutines .. 00072 EXTERNAL DLASET, DORMLQ, DTRSM, XERBLA 00073 * .. 00074 * .. Intrinsic Functions .. 00075 INTRINSIC MAX 00076 * .. 00077 * .. Executable Statements .. 00078 * 00079 * Test the input parameters. 00080 * 00081 INFO = 0 00082 IF( M.LT.0 ) THEN 00083 INFO = -1 00084 ELSE IF( N.LT.0 .OR. M.GT.N ) THEN 00085 INFO = -2 00086 ELSE IF( NRHS.LT.0 ) THEN 00087 INFO = -3 00088 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00089 INFO = -5 00090 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00091 INFO = -8 00092 ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 ) 00093 $ THEN 00094 INFO = -10 00095 END IF 00096 IF( INFO.NE.0 ) THEN 00097 CALL XERBLA( 'DGELQS', -INFO ) 00098 RETURN 00099 END IF 00100 * 00101 * Quick return if possible 00102 * 00103 IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 ) 00104 $ RETURN 00105 * 00106 * Solve L*X = B(1:m,:) 00107 * 00108 CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', M, NRHS, 00109 $ ONE, A, LDA, B, LDB ) 00110 * 00111 * Set B(m+1:n,:) to zero 00112 * 00113 IF( M.LT.N ) 00114 $ CALL DLASET( 'Full', N-M, NRHS, ZERO, ZERO, B( M+1, 1 ), LDB ) 00115 * 00116 * B := Q' * B 00117 * 00118 CALL DORMLQ( 'Left', 'Transpose', N, NRHS, M, A, LDA, TAU, B, LDB, 00119 $ WORK, LWORK, INFO ) 00120 * 00121 RETURN 00122 * 00123 * End of DGELQS 00124 * 00125 END
1.7.3 
