001: SUBROUTINE CLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) 002: * 003: * -- LAPACK auxiliary routine (version 3.2) -- 004: * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 005: * November 2006 006: * 007: * .. Scalar Arguments .. 008: CHARACTER DIRECT, PIVOT, SIDE 009: INTEGER LDA, M, N 010: * .. 011: * .. Array Arguments .. 012: REAL C( * ), S( * ) 013: COMPLEX A( LDA, * ) 014: * .. 015: * 016: * Purpose 017: * ======= 018: * 019: * CLASR applies a sequence of real plane rotations to a complex matrix 020: * A, from either the left or the right. 021: * 022: * When SIDE = 'L', the transformation takes the form 023: * 024: * A := P*A 025: * 026: * and when SIDE = 'R', the transformation takes the form 027: * 028: * A := A*P**T 029: * 030: * where P is an orthogonal matrix consisting of a sequence of z plane 031: * rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', 032: * and P**T is the transpose of P. 033: * 034: * When DIRECT = 'F' (Forward sequence), then 035: * 036: * P = P(z-1) * ... * P(2) * P(1) 037: * 038: * and when DIRECT = 'B' (Backward sequence), then 039: * 040: * P = P(1) * P(2) * ... * P(z-1) 041: * 042: * where P(k) is a plane rotation matrix defined by the 2-by-2 rotation 043: * 044: * R(k) = ( c(k) s(k) ) 045: * = ( -s(k) c(k) ). 046: * 047: * When PIVOT = 'V' (Variable pivot), the rotation is performed 048: * for the plane (k,k+1), i.e., P(k) has the form 049: * 050: * P(k) = ( 1 ) 051: * ( ... ) 052: * ( 1 ) 053: * ( c(k) s(k) ) 054: * ( -s(k) c(k) ) 055: * ( 1 ) 056: * ( ... ) 057: * ( 1 ) 058: * 059: * where R(k) appears as a rank-2 modification to the identity matrix in 060: * rows and columns k and k+1. 061: * 062: * When PIVOT = 'T' (Top pivot), the rotation is performed for the 063: * plane (1,k+1), so P(k) has the form 064: * 065: * P(k) = ( c(k) s(k) ) 066: * ( 1 ) 067: * ( ... ) 068: * ( 1 ) 069: * ( -s(k) c(k) ) 070: * ( 1 ) 071: * ( ... ) 072: * ( 1 ) 073: * 074: * where R(k) appears in rows and columns 1 and k+1. 075: * 076: * Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is 077: * performed for the plane (k,z), giving P(k) the form 078: * 079: * P(k) = ( 1 ) 080: * ( ... ) 081: * ( 1 ) 082: * ( c(k) s(k) ) 083: * ( 1 ) 084: * ( ... ) 085: * ( 1 ) 086: * ( -s(k) c(k) ) 087: * 088: * where R(k) appears in rows and columns k and z. The rotations are 089: * performed without ever forming P(k) explicitly. 090: * 091: * Arguments 092: * ========= 093: * 094: * SIDE (input) CHARACTER*1 095: * Specifies whether the plane rotation matrix P is applied to 096: * A on the left or the right. 097: * = 'L': Left, compute A := P*A 098: * = 'R': Right, compute A:= A*P**T 099: * 100: * PIVOT (input) CHARACTER*1 101: * Specifies the plane for which P(k) is a plane rotation 102: * matrix. 103: * = 'V': Variable pivot, the plane (k,k+1) 104: * = 'T': Top pivot, the plane (1,k+1) 105: * = 'B': Bottom pivot, the plane (k,z) 106: * 107: * DIRECT (input) CHARACTER*1 108: * Specifies whether P is a forward or backward sequence of 109: * plane rotations. 110: * = 'F': Forward, P = P(z-1)*...*P(2)*P(1) 111: * = 'B': Backward, P = P(1)*P(2)*...*P(z-1) 112: * 113: * M (input) INTEGER 114: * The number of rows of the matrix A. If m <= 1, an immediate 115: * return is effected. 116: * 117: * N (input) INTEGER 118: * The number of columns of the matrix A. If n <= 1, an 119: * immediate return is effected. 120: * 121: * C (input) REAL array, dimension 122: * (M-1) if SIDE = 'L' 123: * (N-1) if SIDE = 'R' 124: * The cosines c(k) of the plane rotations. 125: * 126: * S (input) REAL array, dimension 127: * (M-1) if SIDE = 'L' 128: * (N-1) if SIDE = 'R' 129: * The sines s(k) of the plane rotations. The 2-by-2 plane 130: * rotation part of the matrix P(k), R(k), has the form 131: * R(k) = ( c(k) s(k) ) 132: * ( -s(k) c(k) ). 133: * 134: * A (input/output) COMPLEX array, dimension (LDA,N) 135: * The M-by-N matrix A. On exit, A is overwritten by P*A if 136: * SIDE = 'R' or by A*P**T if SIDE = 'L'. 137: * 138: * LDA (input) INTEGER 139: * The leading dimension of the array A. LDA >= max(1,M). 140: * 141: * ===================================================================== 142: * 143: * .. Parameters .. 144: REAL ONE, ZERO 145: PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 146: * .. 147: * .. Local Scalars .. 148: INTEGER I, INFO, J 149: REAL CTEMP, STEMP 150: COMPLEX TEMP 151: * .. 152: * .. Intrinsic Functions .. 153: INTRINSIC MAX 154: * .. 155: * .. External Functions .. 156: LOGICAL LSAME 157: EXTERNAL LSAME 158: * .. 159: * .. External Subroutines .. 160: EXTERNAL XERBLA 161: * .. 162: * .. Executable Statements .. 163: * 164: * Test the input parameters 165: * 166: INFO = 0 167: IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN 168: INFO = 1 169: ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT, 170: $ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN 171: INFO = 2 172: ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) ) 173: $ THEN 174: INFO = 3 175: ELSE IF( M.LT.0 ) THEN 176: INFO = 4 177: ELSE IF( N.LT.0 ) THEN 178: INFO = 5 179: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 180: INFO = 9 181: END IF 182: IF( INFO.NE.0 ) THEN 183: CALL XERBLA( 'CLASR ', INFO ) 184: RETURN 185: END IF 186: * 187: * Quick return if possible 188: * 189: IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) ) 190: $ RETURN 191: IF( LSAME( SIDE, 'L' ) ) THEN 192: * 193: * Form P * A 194: * 195: IF( LSAME( PIVOT, 'V' ) ) THEN 196: IF( LSAME( DIRECT, 'F' ) ) THEN 197: DO 20 J = 1, M - 1 198: CTEMP = C( J ) 199: STEMP = S( J ) 200: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 201: DO 10 I = 1, N 202: TEMP = A( J+1, I ) 203: A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) 204: A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) 205: 10 CONTINUE 206: END IF 207: 20 CONTINUE 208: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 209: DO 40 J = M - 1, 1, -1 210: CTEMP = C( J ) 211: STEMP = S( J ) 212: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 213: DO 30 I = 1, N 214: TEMP = A( J+1, I ) 215: A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) 216: A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) 217: 30 CONTINUE 218: END IF 219: 40 CONTINUE 220: END IF 221: ELSE IF( LSAME( PIVOT, 'T' ) ) THEN 222: IF( LSAME( DIRECT, 'F' ) ) THEN 223: DO 60 J = 2, M 224: CTEMP = C( J-1 ) 225: STEMP = S( J-1 ) 226: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 227: DO 50 I = 1, N 228: TEMP = A( J, I ) 229: A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) 230: A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) 231: 50 CONTINUE 232: END IF 233: 60 CONTINUE 234: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 235: DO 80 J = M, 2, -1 236: CTEMP = C( J-1 ) 237: STEMP = S( J-1 ) 238: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 239: DO 70 I = 1, N 240: TEMP = A( J, I ) 241: A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) 242: A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) 243: 70 CONTINUE 244: END IF 245: 80 CONTINUE 246: END IF 247: ELSE IF( LSAME( PIVOT, 'B' ) ) THEN 248: IF( LSAME( DIRECT, 'F' ) ) THEN 249: DO 100 J = 1, M - 1 250: CTEMP = C( J ) 251: STEMP = S( J ) 252: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 253: DO 90 I = 1, N 254: TEMP = A( J, I ) 255: A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP 256: A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP 257: 90 CONTINUE 258: END IF 259: 100 CONTINUE 260: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 261: DO 120 J = M - 1, 1, -1 262: CTEMP = C( J ) 263: STEMP = S( J ) 264: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 265: DO 110 I = 1, N 266: TEMP = A( J, I ) 267: A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP 268: A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP 269: 110 CONTINUE 270: END IF 271: 120 CONTINUE 272: END IF 273: END IF 274: ELSE IF( LSAME( SIDE, 'R' ) ) THEN 275: * 276: * Form A * P' 277: * 278: IF( LSAME( PIVOT, 'V' ) ) THEN 279: IF( LSAME( DIRECT, 'F' ) ) THEN 280: DO 140 J = 1, N - 1 281: CTEMP = C( J ) 282: STEMP = S( J ) 283: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 284: DO 130 I = 1, M 285: TEMP = A( I, J+1 ) 286: A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) 287: A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) 288: 130 CONTINUE 289: END IF 290: 140 CONTINUE 291: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 292: DO 160 J = N - 1, 1, -1 293: CTEMP = C( J ) 294: STEMP = S( J ) 295: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 296: DO 150 I = 1, M 297: TEMP = A( I, J+1 ) 298: A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) 299: A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) 300: 150 CONTINUE 301: END IF 302: 160 CONTINUE 303: END IF 304: ELSE IF( LSAME( PIVOT, 'T' ) ) THEN 305: IF( LSAME( DIRECT, 'F' ) ) THEN 306: DO 180 J = 2, N 307: CTEMP = C( J-1 ) 308: STEMP = S( J-1 ) 309: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 310: DO 170 I = 1, M 311: TEMP = A( I, J ) 312: A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) 313: A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) 314: 170 CONTINUE 315: END IF 316: 180 CONTINUE 317: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 318: DO 200 J = N, 2, -1 319: CTEMP = C( J-1 ) 320: STEMP = S( J-1 ) 321: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 322: DO 190 I = 1, M 323: TEMP = A( I, J ) 324: A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) 325: A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) 326: 190 CONTINUE 327: END IF 328: 200 CONTINUE 329: END IF 330: ELSE IF( LSAME( PIVOT, 'B' ) ) THEN 331: IF( LSAME( DIRECT, 'F' ) ) THEN 332: DO 220 J = 1, N - 1 333: CTEMP = C( J ) 334: STEMP = S( J ) 335: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 336: DO 210 I = 1, M 337: TEMP = A( I, J ) 338: A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP 339: A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP 340: 210 CONTINUE 341: END IF 342: 220 CONTINUE 343: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 344: DO 240 J = N - 1, 1, -1 345: CTEMP = C( J ) 346: STEMP = S( J ) 347: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 348: DO 230 I = 1, M 349: TEMP = A( I, J ) 350: A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP 351: A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP 352: 230 CONTINUE 353: END IF 354: 240 CONTINUE 355: END IF 356: END IF 357: END IF 358: * 359: RETURN 360: * 361: * End of CLASR 362: * 363: END 364: