 |
LAPACK 3.3.1
Linear Algebra PACKage
|
|
LAPACK 3.3.1
Linear Algebra PACKage
|
00001 SUBROUTINE SORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, 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 VECT 00010 INTEGER INFO, K, LDA, LWORK, M, N 00011 * .. 00012 * .. Array Arguments .. 00013 REAL A( LDA, * ), TAU( * ), WORK( * ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * SORGBR generates one of the real orthogonal matrices Q or P**T 00020 * determined by SGEBRD when reducing a real matrix A to bidiagonal 00021 * form: A = Q * B * P**T. Q and P**T are defined as products of 00022 * elementary reflectors H(i) or G(i) respectively. 00023 * 00024 * If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q 00025 * is of order M: 00026 * if m >= k, Q = H(1) H(2) . . . H(k) and SORGBR returns the first n 00027 * columns of Q, where m >= n >= k; 00028 * if m < k, Q = H(1) H(2) . . . H(m-1) and SORGBR returns Q as an 00029 * M-by-M matrix. 00030 * 00031 * If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T 00032 * is of order N: 00033 * if k < n, P**T = G(k) . . . G(2) G(1) and SORGBR returns the first m 00034 * rows of P**T, where n >= m >= k; 00035 * if k >= n, P**T = G(n-1) . . . G(2) G(1) and SORGBR returns P**T as 00036 * an N-by-N matrix. 00037 * 00038 * Arguments 00039 * ========= 00040 * 00041 * VECT (input) CHARACTER*1 00042 * Specifies whether the matrix Q or the matrix P**T is 00043 * required, as defined in the transformation applied by SGEBRD: 00044 * = 'Q': generate Q; 00045 * = 'P': generate P**T. 00046 * 00047 * M (input) INTEGER 00048 * The number of rows of the matrix Q or P**T to be returned. 00049 * M >= 0. 00050 * 00051 * N (input) INTEGER 00052 * The number of columns of the matrix Q or P**T to be returned. 00053 * N >= 0. 00054 * If VECT = 'Q', M >= N >= min(M,K); 00055 * if VECT = 'P', N >= M >= min(N,K). 00056 * 00057 * K (input) INTEGER 00058 * If VECT = 'Q', the number of columns in the original M-by-K 00059 * matrix reduced by SGEBRD. 00060 * If VECT = 'P', the number of rows in the original K-by-N 00061 * matrix reduced by SGEBRD. 00062 * K >= 0. 00063 * 00064 * A (input/output) REAL array, dimension (LDA,N) 00065 * On entry, the vectors which define the elementary reflectors, 00066 * as returned by SGEBRD. 00067 * On exit, the M-by-N matrix Q or P**T. 00068 * 00069 * LDA (input) INTEGER 00070 * The leading dimension of the array A. LDA >= max(1,M). 00071 * 00072 * TAU (input) REAL array, dimension 00073 * (min(M,K)) if VECT = 'Q' 00074 * (min(N,K)) if VECT = 'P' 00075 * TAU(i) must contain the scalar factor of the elementary 00076 * reflector H(i) or G(i), which determines Q or P**T, as 00077 * returned by SGEBRD in its array argument TAUQ or TAUP. 00078 * 00079 * WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) 00080 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00081 * 00082 * LWORK (input) INTEGER 00083 * The dimension of the array WORK. LWORK >= max(1,min(M,N)). 00084 * For optimum performance LWORK >= min(M,N)*NB, where NB 00085 * is the optimal blocksize. 00086 * 00087 * If LWORK = -1, then a workspace query is assumed; the routine 00088 * only calculates the optimal size of the WORK array, returns 00089 * this value as the first entry of the WORK array, and no error 00090 * message related to LWORK is issued by XERBLA. 00091 * 00092 * INFO (output) INTEGER 00093 * = 0: successful exit 00094 * < 0: if INFO = -i, the i-th argument had an illegal value 00095 * 00096 * ===================================================================== 00097 * 00098 * .. Parameters .. 00099 REAL ZERO, ONE 00100 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00101 * .. 00102 * .. Local Scalars .. 00103 LOGICAL LQUERY, WANTQ 00104 INTEGER I, IINFO, J, LWKOPT, MN, NB 00105 * .. 00106 * .. External Functions .. 00107 LOGICAL LSAME 00108 INTEGER ILAENV 00109 EXTERNAL ILAENV, LSAME 00110 * .. 00111 * .. External Subroutines .. 00112 EXTERNAL SORGLQ, SORGQR, XERBLA 00113 * .. 00114 * .. Intrinsic Functions .. 00115 INTRINSIC MAX, MIN 00116 * .. 00117 * .. Executable Statements .. 00118 * 00119 * Test the input arguments 00120 * 00121 INFO = 0 00122 WANTQ = LSAME( VECT, 'Q' ) 00123 MN = MIN( M, N ) 00124 LQUERY = ( LWORK.EQ.-1 ) 00125 IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN 00126 INFO = -1 00127 ELSE IF( M.LT.0 ) THEN 00128 INFO = -2 00129 ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M, 00130 $ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT. 00131 $ MIN( N, K ) ) ) ) THEN 00132 INFO = -3 00133 ELSE IF( K.LT.0 ) THEN 00134 INFO = -4 00135 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00136 INFO = -6 00137 ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN 00138 INFO = -9 00139 END IF 00140 * 00141 IF( INFO.EQ.0 ) THEN 00142 IF( WANTQ ) THEN 00143 NB = ILAENV( 1, 'SORGQR', ' ', M, N, K, -1 ) 00144 ELSE 00145 NB = ILAENV( 1, 'SORGLQ', ' ', M, N, K, -1 ) 00146 END IF 00147 LWKOPT = MAX( 1, MN )*NB 00148 WORK( 1 ) = LWKOPT 00149 END IF 00150 * 00151 IF( INFO.NE.0 ) THEN 00152 CALL XERBLA( 'SORGBR', -INFO ) 00153 RETURN 00154 ELSE IF( LQUERY ) THEN 00155 RETURN 00156 END IF 00157 * 00158 * Quick return if possible 00159 * 00160 IF( M.EQ.0 .OR. N.EQ.0 ) THEN 00161 WORK( 1 ) = 1 00162 RETURN 00163 END IF 00164 * 00165 IF( WANTQ ) THEN 00166 * 00167 * Form Q, determined by a call to SGEBRD to reduce an m-by-k 00168 * matrix 00169 * 00170 IF( M.GE.K ) THEN 00171 * 00172 * If m >= k, assume m >= n >= k 00173 * 00174 CALL SORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO ) 00175 * 00176 ELSE 00177 * 00178 * If m < k, assume m = n 00179 * 00180 * Shift the vectors which define the elementary reflectors one 00181 * column to the right, and set the first row and column of Q 00182 * to those of the unit matrix 00183 * 00184 DO 20 J = M, 2, -1 00185 A( 1, J ) = ZERO 00186 DO 10 I = J + 1, M 00187 A( I, J ) = A( I, J-1 ) 00188 10 CONTINUE 00189 20 CONTINUE 00190 A( 1, 1 ) = ONE 00191 DO 30 I = 2, M 00192 A( I, 1 ) = ZERO 00193 30 CONTINUE 00194 IF( M.GT.1 ) THEN 00195 * 00196 * Form Q(2:m,2:m) 00197 * 00198 CALL SORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK, 00199 $ LWORK, IINFO ) 00200 END IF 00201 END IF 00202 ELSE 00203 * 00204 * Form P**T, determined by a call to SGEBRD to reduce a k-by-n 00205 * matrix 00206 * 00207 IF( K.LT.N ) THEN 00208 * 00209 * If k < n, assume k <= m <= n 00210 * 00211 CALL SORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO ) 00212 * 00213 ELSE 00214 * 00215 * If k >= n, assume m = n 00216 * 00217 * Shift the vectors which define the elementary reflectors one 00218 * row downward, and set the first row and column of P**T to 00219 * those of the unit matrix 00220 * 00221 A( 1, 1 ) = ONE 00222 DO 40 I = 2, N 00223 A( I, 1 ) = ZERO 00224 40 CONTINUE 00225 DO 60 J = 2, N 00226 DO 50 I = J - 1, 2, -1 00227 A( I, J ) = A( I-1, J ) 00228 50 CONTINUE 00229 A( 1, J ) = ZERO 00230 60 CONTINUE 00231 IF( N.GT.1 ) THEN 00232 * 00233 * Form P**T(2:n,2:n) 00234 * 00235 CALL SORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK, 00236 $ LWORK, IINFO ) 00237 END IF 00238 END IF 00239 END IF 00240 WORK( 1 ) = LWKOPT 00241 RETURN 00242 * 00243 * End of SORGBR 00244 * 00245 END
1.7.3 
