Annotation of rpl/lapack/lapack/dlasr.f, revision 1.1
1.1 ! bertrand 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
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