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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 ZUNGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) 00002 * 00003 * -- LAPACK routine (version 3.3.1) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * -- April 2011 -- 00007 * 00008 * .. Scalar Arguments .. 00009 INTEGER INFO, K, LDA, LWORK, M, N 00010 * .. 00011 * .. Array Arguments .. 00012 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) 00013 * .. 00014 * 00015 * Purpose 00016 * ======= 00017 * 00018 * ZUNGLQ generates an M-by-N complex matrix Q with orthonormal rows, 00019 * which is defined as the first M rows of a product of K elementary 00020 * reflectors of order N 00021 * 00022 * Q = H(k)**H . . . H(2)**H H(1)**H 00023 * 00024 * as returned by ZGELQF. 00025 * 00026 * Arguments 00027 * ========= 00028 * 00029 * M (input) INTEGER 00030 * The number of rows of the matrix Q. M >= 0. 00031 * 00032 * N (input) INTEGER 00033 * The number of columns of the matrix Q. N >= M. 00034 * 00035 * K (input) INTEGER 00036 * The number of elementary reflectors whose product defines the 00037 * matrix Q. M >= K >= 0. 00038 * 00039 * A (input/output) COMPLEX*16 array, dimension (LDA,N) 00040 * On entry, the i-th row must contain the vector which defines 00041 * the elementary reflector H(i), for i = 1,2,...,k, as returned 00042 * by ZGELQF in the first k rows of its array argument A. 00043 * On exit, the M-by-N matrix Q. 00044 * 00045 * LDA (input) INTEGER 00046 * The first dimension of the array A. LDA >= max(1,M). 00047 * 00048 * TAU (input) COMPLEX*16 array, dimension (K) 00049 * TAU(i) must contain the scalar factor of the elementary 00050 * reflector H(i), as returned by ZGELQF. 00051 * 00052 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) 00053 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00054 * 00055 * LWORK (input) INTEGER 00056 * The dimension of the array WORK. LWORK >= max(1,M). 00057 * For optimum performance LWORK >= M*NB, where NB is 00058 * the optimal blocksize. 00059 * 00060 * If LWORK = -1, then a workspace query is assumed; the routine 00061 * only calculates the optimal size of the WORK array, returns 00062 * this value as the first entry of the WORK array, and no error 00063 * message related to LWORK is issued by XERBLA. 00064 * 00065 * INFO (output) INTEGER 00066 * = 0: successful exit; 00067 * < 0: if INFO = -i, the i-th argument has an illegal value 00068 * 00069 * ===================================================================== 00070 * 00071 * .. Parameters .. 00072 COMPLEX*16 ZERO 00073 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) 00074 * .. 00075 * .. Local Scalars .. 00076 LOGICAL LQUERY 00077 INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK, 00078 $ LWKOPT, NB, NBMIN, NX 00079 * .. 00080 * .. External Subroutines .. 00081 EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNGL2 00082 * .. 00083 * .. Intrinsic Functions .. 00084 INTRINSIC MAX, MIN 00085 * .. 00086 * .. External Functions .. 00087 INTEGER ILAENV 00088 EXTERNAL ILAENV 00089 * .. 00090 * .. Executable Statements .. 00091 * 00092 * Test the input arguments 00093 * 00094 INFO = 0 00095 NB = ILAENV( 1, 'ZUNGLQ', ' ', M, N, K, -1 ) 00096 LWKOPT = MAX( 1, M )*NB 00097 WORK( 1 ) = LWKOPT 00098 LQUERY = ( LWORK.EQ.-1 ) 00099 IF( M.LT.0 ) THEN 00100 INFO = -1 00101 ELSE IF( N.LT.M ) THEN 00102 INFO = -2 00103 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN 00104 INFO = -3 00105 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00106 INFO = -5 00107 ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN 00108 INFO = -8 00109 END IF 00110 IF( INFO.NE.0 ) THEN 00111 CALL XERBLA( 'ZUNGLQ', -INFO ) 00112 RETURN 00113 ELSE IF( LQUERY ) THEN 00114 RETURN 00115 END IF 00116 * 00117 * Quick return if possible 00118 * 00119 IF( M.LE.0 ) THEN 00120 WORK( 1 ) = 1 00121 RETURN 00122 END IF 00123 * 00124 NBMIN = 2 00125 NX = 0 00126 IWS = M 00127 IF( NB.GT.1 .AND. NB.LT.K ) THEN 00128 * 00129 * Determine when to cross over from blocked to unblocked code. 00130 * 00131 NX = MAX( 0, ILAENV( 3, 'ZUNGLQ', ' ', M, N, K, -1 ) ) 00132 IF( NX.LT.K ) THEN 00133 * 00134 * Determine if workspace is large enough for blocked code. 00135 * 00136 LDWORK = M 00137 IWS = LDWORK*NB 00138 IF( LWORK.LT.IWS ) THEN 00139 * 00140 * Not enough workspace to use optimal NB: reduce NB and 00141 * determine the minimum value of NB. 00142 * 00143 NB = LWORK / LDWORK 00144 NBMIN = MAX( 2, ILAENV( 2, 'ZUNGLQ', ' ', M, N, K, -1 ) ) 00145 END IF 00146 END IF 00147 END IF 00148 * 00149 IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN 00150 * 00151 * Use blocked code after the last block. 00152 * The first kk rows are handled by the block method. 00153 * 00154 KI = ( ( K-NX-1 ) / NB )*NB 00155 KK = MIN( K, KI+NB ) 00156 * 00157 * Set A(kk+1:m,1:kk) to zero. 00158 * 00159 DO 20 J = 1, KK 00160 DO 10 I = KK + 1, M 00161 A( I, J ) = ZERO 00162 10 CONTINUE 00163 20 CONTINUE 00164 ELSE 00165 KK = 0 00166 END IF 00167 * 00168 * Use unblocked code for the last or only block. 00169 * 00170 IF( KK.LT.M ) 00171 $ CALL ZUNGL2( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA, 00172 $ TAU( KK+1 ), WORK, IINFO ) 00173 * 00174 IF( KK.GT.0 ) THEN 00175 * 00176 * Use blocked code 00177 * 00178 DO 50 I = KI + 1, 1, -NB 00179 IB = MIN( NB, K-I+1 ) 00180 IF( I+IB.LE.M ) THEN 00181 * 00182 * Form the triangular factor of the block reflector 00183 * H = H(i) H(i+1) . . . H(i+ib-1) 00184 * 00185 CALL ZLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ), 00186 $ LDA, TAU( I ), WORK, LDWORK ) 00187 * 00188 * Apply H**H to A(i+ib:m,i:n) from the right 00189 * 00190 CALL ZLARFB( 'Right', 'Conjugate transpose', 'Forward', 00191 $ 'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ), 00192 $ LDA, WORK, LDWORK, A( I+IB, I ), LDA, 00193 $ WORK( IB+1 ), LDWORK ) 00194 END IF 00195 * 00196 * Apply H**H to columns i:n of current block 00197 * 00198 CALL ZUNGL2( IB, N-I+1, IB, A( I, I ), LDA, TAU( I ), WORK, 00199 $ IINFO ) 00200 * 00201 * Set columns 1:i-1 of current block to zero 00202 * 00203 DO 40 J = 1, I - 1 00204 DO 30 L = I, I + IB - 1 00205 A( L, J ) = ZERO 00206 30 CONTINUE 00207 40 CONTINUE 00208 50 CONTINUE 00209 END IF 00210 * 00211 WORK( 1 ) = IWS 00212 RETURN 00213 * 00214 * End of ZUNGLQ 00215 * 00216 END
1.7.3 
