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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 SGERQS( 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 REAL 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 SGERQF. 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) REAL array, dimension (LDA,N) 00038 * Details of the RQ factorization of the original matrix A as 00039 * returned by SGERQF. 00040 * 00041 * LDA (input) INTEGER 00042 * The leading dimension of the array A. LDA >= M. 00043 * 00044 * TAU (input) REAL array, dimension (M) 00045 * Details of the orthogonal matrix Q. 00046 * 00047 * B (input/output) REAL 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) REAL 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 REAL ZERO, ONE 00070 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00071 * .. 00072 * .. External Subroutines .. 00073 EXTERNAL SLASET, SORMRQ, STRSM, XERBLA 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( 'SGERQS', -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 R*X = B(n-m+1:n,:) 00108 * 00109 CALL STRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', M, NRHS, 00110 $ ONE, A( 1, N-M+1 ), LDA, B( N-M+1, 1 ), LDB ) 00111 * 00112 * Set B(1:n-m,:) to zero 00113 * 00114 CALL SLASET( 'Full', N-M, NRHS, ZERO, ZERO, B, LDB ) 00115 * 00116 * B := Q' * B 00117 * 00118 CALL SORMRQ( 'Left', 'Transpose', N, NRHS, M, A, LDA, TAU, B, LDB, 00119 $ WORK, LWORK, INFO ) 00120 * 00121 RETURN 00122 * 00123 * End of SGERQS 00124 * 00125 END
1.7.3 
