00001 SUBROUTINE SOPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO ) 00002 * 00003 * -- LAPACK routine (version 3.2) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 CHARACTER UPLO 00010 INTEGER INFO, LDQ, N 00011 * .. 00012 * .. Array Arguments .. 00013 REAL AP( * ), Q( LDQ, * ), TAU( * ), WORK( * ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * SOPGTR generates a real orthogonal matrix Q which is defined as the 00020 * product of n-1 elementary reflectors H(i) of order n, as returned by 00021 * SSPTRD using packed storage: 00022 * 00023 * if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), 00024 * 00025 * if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). 00026 * 00027 * Arguments 00028 * ========= 00029 * 00030 * UPLO (input) CHARACTER*1 00031 * = 'U': Upper triangular packed storage used in previous 00032 * call to SSPTRD; 00033 * = 'L': Lower triangular packed storage used in previous 00034 * call to SSPTRD. 00035 * 00036 * N (input) INTEGER 00037 * The order of the matrix Q. N >= 0. 00038 * 00039 * AP (input) REAL array, dimension (N*(N+1)/2) 00040 * The vectors which define the elementary reflectors, as 00041 * returned by SSPTRD. 00042 * 00043 * TAU (input) REAL array, dimension (N-1) 00044 * TAU(i) must contain the scalar factor of the elementary 00045 * reflector H(i), as returned by SSPTRD. 00046 * 00047 * Q (output) REAL array, dimension (LDQ,N) 00048 * The N-by-N orthogonal matrix Q. 00049 * 00050 * LDQ (input) INTEGER 00051 * The leading dimension of the array Q. LDQ >= max(1,N). 00052 * 00053 * WORK (workspace) REAL array, dimension (N-1) 00054 * 00055 * INFO (output) INTEGER 00056 * = 0: successful exit 00057 * < 0: if INFO = -i, the i-th argument had an illegal value 00058 * 00059 * ===================================================================== 00060 * 00061 * .. Parameters .. 00062 REAL ZERO, ONE 00063 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00064 * .. 00065 * .. Local Scalars .. 00066 LOGICAL UPPER 00067 INTEGER I, IINFO, IJ, J 00068 * .. 00069 * .. External Functions .. 00070 LOGICAL LSAME 00071 EXTERNAL LSAME 00072 * .. 00073 * .. External Subroutines .. 00074 EXTERNAL SORG2L, SORG2R, XERBLA 00075 * .. 00076 * .. Intrinsic Functions .. 00077 INTRINSIC MAX 00078 * .. 00079 * .. Executable Statements .. 00080 * 00081 * Test the input arguments 00082 * 00083 INFO = 0 00084 UPPER = LSAME( UPLO, 'U' ) 00085 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00086 INFO = -1 00087 ELSE IF( N.LT.0 ) THEN 00088 INFO = -2 00089 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN 00090 INFO = -6 00091 END IF 00092 IF( INFO.NE.0 ) THEN 00093 CALL XERBLA( 'SOPGTR', -INFO ) 00094 RETURN 00095 END IF 00096 * 00097 * Quick return if possible 00098 * 00099 IF( N.EQ.0 ) 00100 $ RETURN 00101 * 00102 IF( UPPER ) THEN 00103 * 00104 * Q was determined by a call to SSPTRD with UPLO = 'U' 00105 * 00106 * Unpack the vectors which define the elementary reflectors and 00107 * set the last row and column of Q equal to those of the unit 00108 * matrix 00109 * 00110 IJ = 2 00111 DO 20 J = 1, N - 1 00112 DO 10 I = 1, J - 1 00113 Q( I, J ) = AP( IJ ) 00114 IJ = IJ + 1 00115 10 CONTINUE 00116 IJ = IJ + 2 00117 Q( N, J ) = ZERO 00118 20 CONTINUE 00119 DO 30 I = 1, N - 1 00120 Q( I, N ) = ZERO 00121 30 CONTINUE 00122 Q( N, N ) = ONE 00123 * 00124 * Generate Q(1:n-1,1:n-1) 00125 * 00126 CALL SORG2L( N-1, N-1, N-1, Q, LDQ, TAU, WORK, IINFO ) 00127 * 00128 ELSE 00129 * 00130 * Q was determined by a call to SSPTRD with UPLO = 'L'. 00131 * 00132 * Unpack the vectors which define the elementary reflectors and 00133 * set the first row and column of Q equal to those of the unit 00134 * matrix 00135 * 00136 Q( 1, 1 ) = ONE 00137 DO 40 I = 2, N 00138 Q( I, 1 ) = ZERO 00139 40 CONTINUE 00140 IJ = 3 00141 DO 60 J = 2, N 00142 Q( 1, J ) = ZERO 00143 DO 50 I = J + 1, N 00144 Q( I, J ) = AP( IJ ) 00145 IJ = IJ + 1 00146 50 CONTINUE 00147 IJ = IJ + 2 00148 60 CONTINUE 00149 IF( N.GT.1 ) THEN 00150 * 00151 * Generate Q(2:n,2:n) 00152 * 00153 CALL SORG2R( N-1, N-1, N-1, Q( 2, 2 ), LDQ, TAU, WORK, 00154 $ IINFO ) 00155 END IF 00156 END IF 00157 RETURN 00158 * 00159 * End of SOPGTR 00160 * 00161 END
1.7.2