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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE ZGELQS( 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*16 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 ZGELQF. 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*16 array, dimension (LDA,N) 00038 * Details of the LQ factorization of the original matrix A as 00039 * returned by ZGELQF. 00040 * 00041 * LDA (input) INTEGER 00042 * The leading dimension of the array A. LDA >= M. 00043 * 00044 * TAU (input) COMPLEX*16 array, dimension (M) 00045 * Details of the orthogonal matrix Q. 00046 * 00047 * B (input/output) COMPLEX*16 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) COMPLEX*16 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 COMPLEX*16 CZERO, CONE 00069 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), 00070 $ CONE = ( 1.0D+0, 0.0D+0 ) ) 00071 * .. 00072 * .. External Subroutines .. 00073 EXTERNAL XERBLA, ZLASET, ZTRSM, ZUNMLQ 00074 * .. 00075 * .. Intrinsic Functions .. 00076 INTRINSIC MAX 00077 * .. 00078 * .. Executable Statements .. 00079 * 00080 * Test the input parameters. 00081 * 00082 INFO = 0 00083 IF( M.LT.0 ) THEN 00084 INFO = -1 00085 ELSE IF( N.LT.0 .OR. M.GT.N ) THEN 00086 INFO = -2 00087 ELSE IF( NRHS.LT.0 ) THEN 00088 INFO = -3 00089 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00090 INFO = -5 00091 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00092 INFO = -8 00093 ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 ) 00094 $ THEN 00095 INFO = -10 00096 END IF 00097 IF( INFO.NE.0 ) THEN 00098 CALL XERBLA( 'ZGELQS', -INFO ) 00099 RETURN 00100 END IF 00101 * 00102 * Quick return if possible 00103 * 00104 IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 ) 00105 $ RETURN 00106 * 00107 * Solve L*X = B(1:m,:) 00108 * 00109 CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', M, NRHS, 00110 $ CONE, A, LDA, B, LDB ) 00111 * 00112 * Set B(m+1:n,:) to zero 00113 * 00114 IF( M.LT.N ) 00115 $ CALL ZLASET( 'Full', N-M, NRHS, CZERO, CZERO, B( M+1, 1 ), 00116 $ LDB ) 00117 * 00118 * B := Q' * B 00119 * 00120 CALL ZUNMLQ( 'Left', 'Conjugate transpose', N, NRHS, M, A, LDA, 00121 $ TAU, B, LDB, WORK, LWORK, INFO ) 00122 * 00123 RETURN 00124 * 00125 * End of ZGELQS 00126 * 00127 END
1.7.3 
