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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) 2: * 3: * -- LAPACK auxiliary routine (version 3.2) -- 4: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 6: * November 2006 7: * 8: * .. Scalar Arguments .. 9: CHARACTER DIRECT, PIVOT, SIDE 10: INTEGER LDA, M, N 11: * .. 12: * .. Array Arguments .. 13: DOUBLE PRECISION A( LDA, * ), C( * ), S( * ) 14: * .. 15: * 16: * Purpose 17: * ======= 18: * 19: * DLASR applies a sequence of plane rotations to a real matrix A, 20: * from either the left or the right. 21: * 22: * When SIDE = 'L', the transformation takes the form 23: * 24: * A := P*A 25: * 26: * and when SIDE = 'R', the transformation takes the form 27: * 28: * A := A*P**T 29: * 30: * where P is an orthogonal matrix consisting of a sequence of z plane 31: * rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', 32: * and P**T is the transpose of P. 33: * 34: * When DIRECT = 'F' (Forward sequence), then 35: * 36: * P = P(z-1) * ... * P(2) * P(1) 37: * 38: * and when DIRECT = 'B' (Backward sequence), then 39: * 40: * P = P(1) * P(2) * ... * P(z-1) 41: * 42: * where P(k) is a plane rotation matrix defined by the 2-by-2 rotation 43: * 44: * R(k) = ( c(k) s(k) ) 45: * = ( -s(k) c(k) ). 46: * 47: * When PIVOT = 'V' (Variable pivot), the rotation is performed 48: * for the plane (k,k+1), i.e., P(k) has the form 49: * 50: * P(k) = ( 1 ) 51: * ( ... ) 52: * ( 1 ) 53: * ( c(k) s(k) ) 54: * ( -s(k) c(k) ) 55: * ( 1 ) 56: * ( ... ) 57: * ( 1 ) 58: * 59: * where R(k) appears as a rank-2 modification to the identity matrix in 60: * rows and columns k and k+1. 61: * 62: * When PIVOT = 'T' (Top pivot), the rotation is performed for the 63: * plane (1,k+1), so P(k) has the form 64: * 65: * P(k) = ( c(k) s(k) ) 66: * ( 1 ) 67: * ( ... ) 68: * ( 1 ) 69: * ( -s(k) c(k) ) 70: * ( 1 ) 71: * ( ... ) 72: * ( 1 ) 73: * 74: * where R(k) appears in rows and columns 1 and k+1. 75: * 76: * Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is 77: * performed for the plane (k,z), giving P(k) the form 78: * 79: * P(k) = ( 1 ) 80: * ( ... ) 81: * ( 1 ) 82: * ( c(k) s(k) ) 83: * ( 1 ) 84: * ( ... ) 85: * ( 1 ) 86: * ( -s(k) c(k) ) 87: * 88: * where R(k) appears in rows and columns k and z. The rotations are 89: * performed without ever forming P(k) explicitly. 90: * 91: * Arguments 92: * ========= 93: * 94: * SIDE (input) CHARACTER*1 95: * Specifies whether the plane rotation matrix P is applied to 96: * A on the left or the right. 97: * = 'L': Left, compute A := P*A 98: * = 'R': Right, compute A:= A*P**T 99: * 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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: DOUBLE PRECISION ONE, ZERO 145: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 146: * .. 147: * .. Local Scalars .. 148: INTEGER I, INFO, J 149: DOUBLE PRECISION CTEMP, STEMP, TEMP 150: * .. 151: * .. External Functions .. 152: LOGICAL LSAME 153: EXTERNAL LSAME 154: * .. 155: * .. External Subroutines .. 156: EXTERNAL XERBLA 157: * .. 158: * .. Intrinsic Functions .. 159: INTRINSIC MAX 160: * .. 161: * .. Executable Statements .. 162: * 163: * Test the input parameters 164: * 165: INFO = 0 166: IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN 167: INFO = 1 168: ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT, 169: $ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN 170: INFO = 2 171: ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) ) 172: $ THEN 173: INFO = 3 174: ELSE IF( M.LT.0 ) THEN 175: INFO = 4 176: ELSE IF( N.LT.0 ) THEN 177: INFO = 5 178: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 179: INFO = 9 180: END IF 181: IF( INFO.NE.0 ) THEN 182: CALL XERBLA( 'DLASR ', INFO ) 183: RETURN 184: END IF 185: * 186: * Quick return if possible 187: * 188: IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) ) 189: $ RETURN 190: IF( LSAME( SIDE, 'L' ) ) THEN 191: * 192: * Form P * A 193: * 194: IF( LSAME( PIVOT, 'V' ) ) THEN 195: IF( LSAME( DIRECT, 'F' ) ) THEN 196: DO 20 J = 1, M - 1 197: CTEMP = C( J ) 198: STEMP = S( J ) 199: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 200: DO 10 I = 1, N 201: TEMP = A( J+1, I ) 202: A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) 203: A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) 204: 10 CONTINUE 205: END IF 206: 20 CONTINUE 207: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 208: DO 40 J = M - 1, 1, -1 209: CTEMP = C( J ) 210: STEMP = S( J ) 211: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 212: DO 30 I = 1, N 213: TEMP = A( J+1, I ) 214: A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) 215: A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) 216: 30 CONTINUE 217: END IF 218: 40 CONTINUE 219: END IF 220: ELSE IF( LSAME( PIVOT, 'T' ) ) THEN 221: IF( LSAME( DIRECT, 'F' ) ) THEN 222: DO 60 J = 2, M 223: CTEMP = C( J-1 ) 224: STEMP = S( J-1 ) 225: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 226: DO 50 I = 1, N 227: TEMP = A( J, I ) 228: A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) 229: A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) 230: 50 CONTINUE 231: END IF 232: 60 CONTINUE 233: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 234: DO 80 J = M, 2, -1 235: CTEMP = C( J-1 ) 236: STEMP = S( J-1 ) 237: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 238: DO 70 I = 1, N 239: TEMP = A( J, I ) 240: A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) 241: A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) 242: 70 CONTINUE 243: END IF 244: 80 CONTINUE 245: END IF 246: ELSE IF( LSAME( PIVOT, 'B' ) ) THEN 247: IF( LSAME( DIRECT, 'F' ) ) THEN 248: DO 100 J = 1, M - 1 249: CTEMP = C( J ) 250: STEMP = S( J ) 251: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 252: DO 90 I = 1, N 253: TEMP = A( J, I ) 254: A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP 255: A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP 256: 90 CONTINUE 257: END IF 258: 100 CONTINUE 259: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 260: DO 120 J = M - 1, 1, -1 261: CTEMP = C( J ) 262: STEMP = S( J ) 263: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 264: DO 110 I = 1, N 265: TEMP = A( J, I ) 266: A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP 267: A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP 268: 110 CONTINUE 269: END IF 270: 120 CONTINUE 271: END IF 272: END IF 273: ELSE IF( LSAME( SIDE, 'R' ) ) THEN 274: * 275: * Form A * P' 276: * 277: IF( LSAME( PIVOT, 'V' ) ) THEN 278: IF( LSAME( DIRECT, 'F' ) ) THEN 279: DO 140 J = 1, N - 1 280: CTEMP = C( J ) 281: STEMP = S( J ) 282: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 283: DO 130 I = 1, M 284: TEMP = A( I, J+1 ) 285: A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) 286: A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) 287: 130 CONTINUE 288: END IF 289: 140 CONTINUE 290: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 291: DO 160 J = N - 1, 1, -1 292: CTEMP = C( J ) 293: STEMP = S( J ) 294: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 295: DO 150 I = 1, M 296: TEMP = A( I, J+1 ) 297: A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) 298: A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) 299: 150 CONTINUE 300: END IF 301: 160 CONTINUE 302: END IF 303: ELSE IF( LSAME( PIVOT, 'T' ) ) THEN 304: IF( LSAME( DIRECT, 'F' ) ) THEN 305: DO 180 J = 2, N 306: CTEMP = C( J-1 ) 307: STEMP = S( J-1 ) 308: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 309: DO 170 I = 1, M 310: TEMP = A( I, J ) 311: A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) 312: A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) 313: 170 CONTINUE 314: END IF 315: 180 CONTINUE 316: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 317: DO 200 J = N, 2, -1 318: CTEMP = C( J-1 ) 319: STEMP = S( J-1 ) 320: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 321: DO 190 I = 1, M 322: TEMP = A( I, J ) 323: A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) 324: A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) 325: 190 CONTINUE 326: END IF 327: 200 CONTINUE 328: END IF 329: ELSE IF( LSAME( PIVOT, 'B' ) ) THEN 330: IF( LSAME( DIRECT, 'F' ) ) THEN 331: DO 220 J = 1, N - 1 332: CTEMP = C( J ) 333: STEMP = S( J ) 334: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 335: DO 210 I = 1, M 336: TEMP = A( I, J ) 337: A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP 338: A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP 339: 210 CONTINUE 340: END IF 341: 220 CONTINUE 342: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 343: DO 240 J = N - 1, 1, -1 344: CTEMP = C( J ) 345: STEMP = S( J ) 346: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 347: DO 230 I = 1, M 348: TEMP = A( I, J ) 349: A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP 350: A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP 351: 230 CONTINUE 352: END IF 353: 240 CONTINUE 354: END IF 355: END IF 356: END IF 357: * 358: RETURN 359: * 360: * End of DLASR 361: * 362: END