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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 CLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) 00002 * 00003 * -- LAPACK auxiliary 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 DIRECT, PIVOT, SIDE 00010 INTEGER LDA, M, N 00011 * .. 00012 * .. Array Arguments .. 00013 REAL C( * ), S( * ) 00014 COMPLEX A( LDA, * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * CLASR applies a sequence of real plane rotations to a complex matrix 00021 * A, from either the left or the right. 00022 * 00023 * When SIDE = 'L', the transformation takes the form 00024 * 00025 * A := P*A 00026 * 00027 * and when SIDE = 'R', the transformation takes the form 00028 * 00029 * A := A*P**T 00030 * 00031 * where P is an orthogonal matrix consisting of a sequence of z plane 00032 * rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', 00033 * and P**T is the transpose of P. 00034 * 00035 * When DIRECT = 'F' (Forward sequence), then 00036 * 00037 * P = P(z-1) * ... * P(2) * P(1) 00038 * 00039 * and when DIRECT = 'B' (Backward sequence), then 00040 * 00041 * P = P(1) * P(2) * ... * P(z-1) 00042 * 00043 * where P(k) is a plane rotation matrix defined by the 2-by-2 rotation 00044 * 00045 * R(k) = ( c(k) s(k) ) 00046 * = ( -s(k) c(k) ). 00047 * 00048 * When PIVOT = 'V' (Variable pivot), the rotation is performed 00049 * for the plane (k,k+1), i.e., P(k) has the form 00050 * 00051 * P(k) = ( 1 ) 00052 * ( ... ) 00053 * ( 1 ) 00054 * ( c(k) s(k) ) 00055 * ( -s(k) c(k) ) 00056 * ( 1 ) 00057 * ( ... ) 00058 * ( 1 ) 00059 * 00060 * where R(k) appears as a rank-2 modification to the identity matrix in 00061 * rows and columns k and k+1. 00062 * 00063 * When PIVOT = 'T' (Top pivot), the rotation is performed for the 00064 * plane (1,k+1), so P(k) has the form 00065 * 00066 * P(k) = ( c(k) s(k) ) 00067 * ( 1 ) 00068 * ( ... ) 00069 * ( 1 ) 00070 * ( -s(k) c(k) ) 00071 * ( 1 ) 00072 * ( ... ) 00073 * ( 1 ) 00074 * 00075 * where R(k) appears in rows and columns 1 and k+1. 00076 * 00077 * Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is 00078 * performed for the plane (k,z), giving P(k) the form 00079 * 00080 * P(k) = ( 1 ) 00081 * ( ... ) 00082 * ( 1 ) 00083 * ( c(k) s(k) ) 00084 * ( 1 ) 00085 * ( ... ) 00086 * ( 1 ) 00087 * ( -s(k) c(k) ) 00088 * 00089 * where R(k) appears in rows and columns k and z. The rotations are 00090 * performed without ever forming P(k) explicitly. 00091 * 00092 * Arguments 00093 * ========= 00094 * 00095 * SIDE (input) CHARACTER*1 00096 * Specifies whether the plane rotation matrix P is applied to 00097 * A on the left or the right. 00098 * = 'L': Left, compute A := P*A 00099 * = 'R': Right, compute A:= A*P**T 00100 * 00101 * PIVOT (input) CHARACTER*1 00102 * Specifies the plane for which P(k) is a plane rotation 00103 * matrix. 00104 * = 'V': Variable pivot, the plane (k,k+1) 00105 * = 'T': Top pivot, the plane (1,k+1) 00106 * = 'B': Bottom pivot, the plane (k,z) 00107 * 00108 * DIRECT (input) CHARACTER*1 00109 * Specifies whether P is a forward or backward sequence of 00110 * plane rotations. 00111 * = 'F': Forward, P = P(z-1)*...*P(2)*P(1) 00112 * = 'B': Backward, P = P(1)*P(2)*...*P(z-1) 00113 * 00114 * M (input) INTEGER 00115 * The number of rows of the matrix A. If m <= 1, an immediate 00116 * return is effected. 00117 * 00118 * N (input) INTEGER 00119 * The number of columns of the matrix A. If n <= 1, an 00120 * immediate return is effected. 00121 * 00122 * C (input) REAL array, dimension 00123 * (M-1) if SIDE = 'L' 00124 * (N-1) if SIDE = 'R' 00125 * The cosines c(k) of the plane rotations. 00126 * 00127 * S (input) REAL array, dimension 00128 * (M-1) if SIDE = 'L' 00129 * (N-1) if SIDE = 'R' 00130 * The sines s(k) of the plane rotations. The 2-by-2 plane 00131 * rotation part of the matrix P(k), R(k), has the form 00132 * R(k) = ( c(k) s(k) ) 00133 * ( -s(k) c(k) ). 00134 * 00135 * A (input/output) COMPLEX array, dimension (LDA,N) 00136 * The M-by-N matrix A. On exit, A is overwritten by P*A if 00137 * SIDE = 'R' or by A*P**T if SIDE = 'L'. 00138 * 00139 * LDA (input) INTEGER 00140 * The leading dimension of the array A. LDA >= max(1,M). 00141 * 00142 * ===================================================================== 00143 * 00144 * .. Parameters .. 00145 REAL ONE, ZERO 00146 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 00147 * .. 00148 * .. Local Scalars .. 00149 INTEGER I, INFO, J 00150 REAL CTEMP, STEMP 00151 COMPLEX TEMP 00152 * .. 00153 * .. Intrinsic Functions .. 00154 INTRINSIC MAX 00155 * .. 00156 * .. External Functions .. 00157 LOGICAL LSAME 00158 EXTERNAL LSAME 00159 * .. 00160 * .. External Subroutines .. 00161 EXTERNAL XERBLA 00162 * .. 00163 * .. Executable Statements .. 00164 * 00165 * Test the input parameters 00166 * 00167 INFO = 0 00168 IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN 00169 INFO = 1 00170 ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT, 00171 $ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN 00172 INFO = 2 00173 ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) ) 00174 $ THEN 00175 INFO = 3 00176 ELSE IF( M.LT.0 ) THEN 00177 INFO = 4 00178 ELSE IF( N.LT.0 ) THEN 00179 INFO = 5 00180 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00181 INFO = 9 00182 END IF 00183 IF( INFO.NE.0 ) THEN 00184 CALL XERBLA( 'CLASR ', INFO ) 00185 RETURN 00186 END IF 00187 * 00188 * Quick return if possible 00189 * 00190 IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) ) 00191 $ RETURN 00192 IF( LSAME( SIDE, 'L' ) ) THEN 00193 * 00194 * Form P * A 00195 * 00196 IF( LSAME( PIVOT, 'V' ) ) THEN 00197 IF( LSAME( DIRECT, 'F' ) ) THEN 00198 DO 20 J = 1, M - 1 00199 CTEMP = C( J ) 00200 STEMP = S( J ) 00201 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00202 DO 10 I = 1, N 00203 TEMP = A( J+1, I ) 00204 A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) 00205 A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) 00206 10 CONTINUE 00207 END IF 00208 20 CONTINUE 00209 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 00210 DO 40 J = M - 1, 1, -1 00211 CTEMP = C( J ) 00212 STEMP = S( J ) 00213 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00214 DO 30 I = 1, N 00215 TEMP = A( J+1, I ) 00216 A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) 00217 A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) 00218 30 CONTINUE 00219 END IF 00220 40 CONTINUE 00221 END IF 00222 ELSE IF( LSAME( PIVOT, 'T' ) ) THEN 00223 IF( LSAME( DIRECT, 'F' ) ) THEN 00224 DO 60 J = 2, M 00225 CTEMP = C( J-1 ) 00226 STEMP = S( J-1 ) 00227 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00228 DO 50 I = 1, N 00229 TEMP = A( J, I ) 00230 A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) 00231 A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) 00232 50 CONTINUE 00233 END IF 00234 60 CONTINUE 00235 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 00236 DO 80 J = M, 2, -1 00237 CTEMP = C( J-1 ) 00238 STEMP = S( J-1 ) 00239 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00240 DO 70 I = 1, N 00241 TEMP = A( J, I ) 00242 A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) 00243 A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) 00244 70 CONTINUE 00245 END IF 00246 80 CONTINUE 00247 END IF 00248 ELSE IF( LSAME( PIVOT, 'B' ) ) THEN 00249 IF( LSAME( DIRECT, 'F' ) ) THEN 00250 DO 100 J = 1, M - 1 00251 CTEMP = C( J ) 00252 STEMP = S( J ) 00253 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00254 DO 90 I = 1, N 00255 TEMP = A( J, I ) 00256 A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP 00257 A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP 00258 90 CONTINUE 00259 END IF 00260 100 CONTINUE 00261 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 00262 DO 120 J = M - 1, 1, -1 00263 CTEMP = C( J ) 00264 STEMP = S( J ) 00265 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00266 DO 110 I = 1, N 00267 TEMP = A( J, I ) 00268 A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP 00269 A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP 00270 110 CONTINUE 00271 END IF 00272 120 CONTINUE 00273 END IF 00274 END IF 00275 ELSE IF( LSAME( SIDE, 'R' ) ) THEN 00276 * 00277 * Form A * P**T 00278 * 00279 IF( LSAME( PIVOT, 'V' ) ) THEN 00280 IF( LSAME( DIRECT, 'F' ) ) THEN 00281 DO 140 J = 1, N - 1 00282 CTEMP = C( J ) 00283 STEMP = S( J ) 00284 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00285 DO 130 I = 1, M 00286 TEMP = A( I, J+1 ) 00287 A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) 00288 A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) 00289 130 CONTINUE 00290 END IF 00291 140 CONTINUE 00292 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 00293 DO 160 J = N - 1, 1, -1 00294 CTEMP = C( J ) 00295 STEMP = S( J ) 00296 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00297 DO 150 I = 1, M 00298 TEMP = A( I, J+1 ) 00299 A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) 00300 A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) 00301 150 CONTINUE 00302 END IF 00303 160 CONTINUE 00304 END IF 00305 ELSE IF( LSAME( PIVOT, 'T' ) ) THEN 00306 IF( LSAME( DIRECT, 'F' ) ) THEN 00307 DO 180 J = 2, N 00308 CTEMP = C( J-1 ) 00309 STEMP = S( J-1 ) 00310 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00311 DO 170 I = 1, M 00312 TEMP = A( I, J ) 00313 A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) 00314 A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) 00315 170 CONTINUE 00316 END IF 00317 180 CONTINUE 00318 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 00319 DO 200 J = N, 2, -1 00320 CTEMP = C( J-1 ) 00321 STEMP = S( J-1 ) 00322 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00323 DO 190 I = 1, M 00324 TEMP = A( I, J ) 00325 A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) 00326 A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) 00327 190 CONTINUE 00328 END IF 00329 200 CONTINUE 00330 END IF 00331 ELSE IF( LSAME( PIVOT, 'B' ) ) THEN 00332 IF( LSAME( DIRECT, 'F' ) ) THEN 00333 DO 220 J = 1, N - 1 00334 CTEMP = C( J ) 00335 STEMP = S( J ) 00336 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00337 DO 210 I = 1, M 00338 TEMP = A( I, J ) 00339 A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP 00340 A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP 00341 210 CONTINUE 00342 END IF 00343 220 CONTINUE 00344 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 00345 DO 240 J = N - 1, 1, -1 00346 CTEMP = C( J ) 00347 STEMP = S( J ) 00348 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00349 DO 230 I = 1, M 00350 TEMP = A( I, J ) 00351 A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP 00352 A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP 00353 230 CONTINUE 00354 END IF 00355 240 CONTINUE 00356 END IF 00357 END IF 00358 END IF 00359 * 00360 RETURN 00361 * 00362 * End of CLASR 00363 * 00364 END
1.7.3 
