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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 ZGERQF( M, N, 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, LDA, LWORK, M, N 00010 * .. 00011 * .. Array Arguments .. 00012 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) 00013 * .. 00014 * 00015 * Purpose 00016 * ======= 00017 * 00018 * ZGERQF computes an RQ factorization of a complex M-by-N matrix A: 00019 * A = R * Q. 00020 * 00021 * Arguments 00022 * ========= 00023 * 00024 * M (input) INTEGER 00025 * The number of rows of the matrix A. M >= 0. 00026 * 00027 * N (input) INTEGER 00028 * The number of columns of the matrix A. N >= 0. 00029 * 00030 * A (input/output) COMPLEX*16 array, dimension (LDA,N) 00031 * On entry, the M-by-N matrix A. 00032 * On exit, 00033 * if m <= n, the upper triangle of the subarray 00034 * A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; 00035 * if m >= n, the elements on and above the (m-n)-th subdiagonal 00036 * contain the M-by-N upper trapezoidal matrix R; 00037 * the remaining elements, with the array TAU, represent the 00038 * unitary matrix Q as a product of min(m,n) elementary 00039 * reflectors (see Further Details). 00040 * 00041 * LDA (input) INTEGER 00042 * The leading dimension of the array A. LDA >= max(1,M). 00043 * 00044 * TAU (output) COMPLEX*16 array, dimension (min(M,N)) 00045 * The scalar factors of the elementary reflectors (see Further 00046 * Details). 00047 * 00048 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) 00049 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00050 * 00051 * LWORK (input) INTEGER 00052 * The dimension of the array WORK. LWORK >= max(1,M). 00053 * For optimum performance LWORK >= M*NB, where NB is 00054 * the optimal blocksize. 00055 * 00056 * If LWORK = -1, then a workspace query is assumed; the routine 00057 * only calculates the optimal size of the WORK array, returns 00058 * this value as the first entry of the WORK array, and no error 00059 * message related to LWORK is issued by XERBLA. 00060 * 00061 * INFO (output) INTEGER 00062 * = 0: successful exit 00063 * < 0: if INFO = -i, the i-th argument had an illegal value 00064 * 00065 * Further Details 00066 * =============== 00067 * 00068 * The matrix Q is represented as a product of elementary reflectors 00069 * 00070 * Q = H(1)**H H(2)**H . . . H(k)**H, where k = min(m,n). 00071 * 00072 * Each H(i) has the form 00073 * 00074 * H(i) = I - tau * v * v**H 00075 * 00076 * where tau is a complex scalar, and v is a complex vector with 00077 * v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on 00078 * exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). 00079 * 00080 * ===================================================================== 00081 * 00082 * .. Local Scalars .. 00083 LOGICAL LQUERY 00084 INTEGER I, IB, IINFO, IWS, K, KI, KK, LDWORK, LWKOPT, 00085 $ MU, NB, NBMIN, NU, NX 00086 * .. 00087 * .. External Subroutines .. 00088 EXTERNAL XERBLA, ZGERQ2, ZLARFB, ZLARFT 00089 * .. 00090 * .. Intrinsic Functions .. 00091 INTRINSIC MAX, MIN 00092 * .. 00093 * .. External Functions .. 00094 INTEGER ILAENV 00095 EXTERNAL ILAENV 00096 * .. 00097 * .. Executable Statements .. 00098 * 00099 * Test the input arguments 00100 * 00101 INFO = 0 00102 LQUERY = ( LWORK.EQ.-1 ) 00103 IF( M.LT.0 ) THEN 00104 INFO = -1 00105 ELSE IF( N.LT.0 ) THEN 00106 INFO = -2 00107 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00108 INFO = -4 00109 END IF 00110 * 00111 IF( INFO.EQ.0 ) THEN 00112 K = MIN( M, N ) 00113 IF( K.EQ.0 ) THEN 00114 LWKOPT = 1 00115 ELSE 00116 NB = ILAENV( 1, 'ZGERQF', ' ', M, N, -1, -1 ) 00117 LWKOPT = M*NB 00118 END IF 00119 WORK( 1 ) = LWKOPT 00120 * 00121 IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN 00122 INFO = -7 00123 END IF 00124 END IF 00125 * 00126 IF( INFO.NE.0 ) THEN 00127 CALL XERBLA( 'ZGERQF', -INFO ) 00128 RETURN 00129 ELSE IF( LQUERY ) THEN 00130 RETURN 00131 END IF 00132 * 00133 * Quick return if possible 00134 * 00135 IF( K.EQ.0 ) THEN 00136 RETURN 00137 END IF 00138 * 00139 NBMIN = 2 00140 NX = 1 00141 IWS = M 00142 IF( NB.GT.1 .AND. NB.LT.K ) THEN 00143 * 00144 * Determine when to cross over from blocked to unblocked code. 00145 * 00146 NX = MAX( 0, ILAENV( 3, 'ZGERQF', ' ', M, N, -1, -1 ) ) 00147 IF( NX.LT.K ) THEN 00148 * 00149 * Determine if workspace is large enough for blocked code. 00150 * 00151 LDWORK = M 00152 IWS = LDWORK*NB 00153 IF( LWORK.LT.IWS ) THEN 00154 * 00155 * Not enough workspace to use optimal NB: reduce NB and 00156 * determine the minimum value of NB. 00157 * 00158 NB = LWORK / LDWORK 00159 NBMIN = MAX( 2, ILAENV( 2, 'ZGERQF', ' ', M, N, -1, 00160 $ -1 ) ) 00161 END IF 00162 END IF 00163 END IF 00164 * 00165 IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN 00166 * 00167 * Use blocked code initially. 00168 * The last kk rows are handled by the block method. 00169 * 00170 KI = ( ( K-NX-1 ) / NB )*NB 00171 KK = MIN( K, KI+NB ) 00172 * 00173 DO 10 I = K - KK + KI + 1, K - KK + 1, -NB 00174 IB = MIN( K-I+1, NB ) 00175 * 00176 * Compute the RQ factorization of the current block 00177 * A(m-k+i:m-k+i+ib-1,1:n-k+i+ib-1) 00178 * 00179 CALL ZGERQ2( IB, N-K+I+IB-1, A( M-K+I, 1 ), LDA, TAU( I ), 00180 $ WORK, IINFO ) 00181 IF( M-K+I.GT.1 ) THEN 00182 * 00183 * Form the triangular factor of the block reflector 00184 * H = H(i+ib-1) . . . H(i+1) H(i) 00185 * 00186 CALL ZLARFT( 'Backward', 'Rowwise', N-K+I+IB-1, IB, 00187 $ A( M-K+I, 1 ), LDA, TAU( I ), WORK, LDWORK ) 00188 * 00189 * Apply H to A(1:m-k+i-1,1:n-k+i+ib-1) from the right 00190 * 00191 CALL ZLARFB( 'Right', 'No transpose', 'Backward', 00192 $ 'Rowwise', M-K+I-1, N-K+I+IB-1, IB, 00193 $ A( M-K+I, 1 ), LDA, WORK, LDWORK, A, LDA, 00194 $ WORK( IB+1 ), LDWORK ) 00195 END IF 00196 10 CONTINUE 00197 MU = M - K + I + NB - 1 00198 NU = N - K + I + NB - 1 00199 ELSE 00200 MU = M 00201 NU = N 00202 END IF 00203 * 00204 * Use unblocked code to factor the last or only block 00205 * 00206 IF( MU.GT.0 .AND. NU.GT.0 ) 00207 $ CALL ZGERQ2( MU, NU, A, LDA, TAU, WORK, IINFO ) 00208 * 00209 WORK( 1 ) = IWS 00210 RETURN 00211 * 00212 * End of ZGERQF 00213 * 00214 END
1.7.3 
