Annotation of rpl/lapack/lapack/zlasr.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZLASR( 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 C( * ), S( * )
! 14: COMPLEX*16 A( LDA, * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZLASR applies a sequence of real plane rotations to a complex matrix
! 21: * A, from either the left or the right.
! 22: *
! 23: * When SIDE = 'L', the transformation takes the form
! 24: *
! 25: * A := P*A
! 26: *
! 27: * and when SIDE = 'R', the transformation takes the form
! 28: *
! 29: * A := A*P**T
! 30: *
! 31: * where P is an orthogonal matrix consisting of a sequence of z plane
! 32: * rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
! 33: * and P**T is the transpose of P.
! 34: *
! 35: * When DIRECT = 'F' (Forward sequence), then
! 36: *
! 37: * P = P(z-1) * ... * P(2) * P(1)
! 38: *
! 39: * and when DIRECT = 'B' (Backward sequence), then
! 40: *
! 41: * P = P(1) * P(2) * ... * P(z-1)
! 42: *
! 43: * where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
! 44: *
! 45: * R(k) = ( c(k) s(k) )
! 46: * = ( -s(k) c(k) ).
! 47: *
! 48: * When PIVOT = 'V' (Variable pivot), the rotation is performed
! 49: * for the plane (k,k+1), i.e., P(k) has the form
! 50: *
! 51: * P(k) = ( 1 )
! 52: * ( ... )
! 53: * ( 1 )
! 54: * ( c(k) s(k) )
! 55: * ( -s(k) c(k) )
! 56: * ( 1 )
! 57: * ( ... )
! 58: * ( 1 )
! 59: *
! 60: * where R(k) appears as a rank-2 modification to the identity matrix in
! 61: * rows and columns k and k+1.
! 62: *
! 63: * When PIVOT = 'T' (Top pivot), the rotation is performed for the
! 64: * plane (1,k+1), so P(k) has the form
! 65: *
! 66: * P(k) = ( c(k) s(k) )
! 67: * ( 1 )
! 68: * ( ... )
! 69: * ( 1 )
! 70: * ( -s(k) c(k) )
! 71: * ( 1 )
! 72: * ( ... )
! 73: * ( 1 )
! 74: *
! 75: * where R(k) appears in rows and columns 1 and k+1.
! 76: *
! 77: * Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
! 78: * performed for the plane (k,z), giving P(k) the form
! 79: *
! 80: * P(k) = ( 1 )
! 81: * ( ... )
! 82: * ( 1 )
! 83: * ( c(k) s(k) )
! 84: * ( 1 )
! 85: * ( ... )
! 86: * ( 1 )
! 87: * ( -s(k) c(k) )
! 88: *
! 89: * where R(k) appears in rows and columns k and z. The rotations are
! 90: * performed without ever forming P(k) explicitly.
! 91: *
! 92: * Arguments
! 93: * =========
! 94: *
! 95: * SIDE (input) CHARACTER*1
! 96: * Specifies whether the plane rotation matrix P is applied to
! 97: * A on the left or the right.
! 98: * = 'L': Left, compute A := P*A
! 99: * = 'R': Right, compute A:= A*P**T
! 100: *
! 101: * PIVOT (input) CHARACTER*1
! 102: * Specifies the plane for which P(k) is a plane rotation
! 103: * matrix.
! 104: * = 'V': Variable pivot, the plane (k,k+1)
! 105: * = 'T': Top pivot, the plane (1,k+1)
! 106: * = 'B': Bottom pivot, the plane (k,z)
! 107: *
! 108: * DIRECT (input) CHARACTER*1
! 109: * Specifies whether P is a forward or backward sequence of
! 110: * plane rotations.
! 111: * = 'F': Forward, P = P(z-1)*...*P(2)*P(1)
! 112: * = 'B': Backward, P = P(1)*P(2)*...*P(z-1)
! 113: *
! 114: * M (input) INTEGER
! 115: * The number of rows of the matrix A. If m <= 1, an immediate
! 116: * return is effected.
! 117: *
! 118: * N (input) INTEGER
! 119: * The number of columns of the matrix A. If n <= 1, an
! 120: * immediate return is effected.
! 121: *
! 122: * C (input) DOUBLE PRECISION array, dimension
! 123: * (M-1) if SIDE = 'L'
! 124: * (N-1) if SIDE = 'R'
! 125: * The cosines c(k) of the plane rotations.
! 126: *
! 127: * S (input) DOUBLE PRECISION array, dimension
! 128: * (M-1) if SIDE = 'L'
! 129: * (N-1) if SIDE = 'R'
! 130: * The sines s(k) of the plane rotations. The 2-by-2 plane
! 131: * rotation part of the matrix P(k), R(k), has the form
! 132: * R(k) = ( c(k) s(k) )
! 133: * ( -s(k) c(k) ).
! 134: *
! 135: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 136: * The M-by-N matrix A. On exit, A is overwritten by P*A if
! 137: * SIDE = 'R' or by A*P**T if SIDE = 'L'.
! 138: *
! 139: * LDA (input) INTEGER
! 140: * The leading dimension of the array A. LDA >= max(1,M).
! 141: *
! 142: * =====================================================================
! 143: *
! 144: * .. Parameters ..
! 145: DOUBLE PRECISION ONE, ZERO
! 146: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 147: * ..
! 148: * .. Local Scalars ..
! 149: INTEGER I, INFO, J
! 150: DOUBLE PRECISION CTEMP, STEMP
! 151: COMPLEX*16 TEMP
! 152: * ..
! 153: * .. Intrinsic Functions ..
! 154: INTRINSIC MAX
! 155: * ..
! 156: * .. External Functions ..
! 157: LOGICAL LSAME
! 158: EXTERNAL LSAME
! 159: * ..
! 160: * .. External Subroutines ..
! 161: EXTERNAL XERBLA
! 162: * ..
! 163: * .. Executable Statements ..
! 164: *
! 165: * Test the input parameters
! 166: *
! 167: INFO = 0
! 168: IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN
! 169: INFO = 1
! 170: ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT,
! 171: $ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN
! 172: INFO = 2
! 173: ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) )
! 174: $ THEN
! 175: INFO = 3
! 176: ELSE IF( M.LT.0 ) THEN
! 177: INFO = 4
! 178: ELSE IF( N.LT.0 ) THEN
! 179: INFO = 5
! 180: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 181: INFO = 9
! 182: END IF
! 183: IF( INFO.NE.0 ) THEN
! 184: CALL XERBLA( 'ZLASR ', INFO )
! 185: RETURN
! 186: END IF
! 187: *
! 188: * Quick return if possible
! 189: *
! 190: IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) )
! 191: $ RETURN
! 192: IF( LSAME( SIDE, 'L' ) ) THEN
! 193: *
! 194: * Form P * A
! 195: *
! 196: IF( LSAME( PIVOT, 'V' ) ) THEN
! 197: IF( LSAME( DIRECT, 'F' ) ) THEN
! 198: DO 20 J = 1, M - 1
! 199: CTEMP = C( J )
! 200: STEMP = S( J )
! 201: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
! 202: DO 10 I = 1, N
! 203: TEMP = A( J+1, I )
! 204: A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
! 205: A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
! 206: 10 CONTINUE
! 207: END IF
! 208: 20 CONTINUE
! 209: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
! 210: DO 40 J = M - 1, 1, -1
! 211: CTEMP = C( J )
! 212: STEMP = S( J )
! 213: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
! 214: DO 30 I = 1, N
! 215: TEMP = A( J+1, I )
! 216: A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
! 217: A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
! 218: 30 CONTINUE
! 219: END IF
! 220: 40 CONTINUE
! 221: END IF
! 222: ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
! 223: IF( LSAME( DIRECT, 'F' ) ) THEN
! 224: DO 60 J = 2, M
! 225: CTEMP = C( J-1 )
! 226: STEMP = S( J-1 )
! 227: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
! 228: DO 50 I = 1, N
! 229: TEMP = A( J, I )
! 230: A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
! 231: A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
! 232: 50 CONTINUE
! 233: END IF
! 234: 60 CONTINUE
! 235: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
! 236: DO 80 J = M, 2, -1
! 237: CTEMP = C( J-1 )
! 238: STEMP = S( J-1 )
! 239: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
! 240: DO 70 I = 1, N
! 241: TEMP = A( J, I )
! 242: A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
! 243: A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
! 244: 70 CONTINUE
! 245: END IF
! 246: 80 CONTINUE
! 247: END IF
! 248: ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
! 249: IF( LSAME( DIRECT, 'F' ) ) THEN
! 250: DO 100 J = 1, M - 1
! 251: CTEMP = C( J )
! 252: STEMP = S( J )
! 253: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
! 254: DO 90 I = 1, N
! 255: TEMP = A( J, I )
! 256: A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
! 257: A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
! 258: 90 CONTINUE
! 259: END IF
! 260: 100 CONTINUE
! 261: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
! 262: DO 120 J = M - 1, 1, -1
! 263: CTEMP = C( J )
! 264: STEMP = S( J )
! 265: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
! 266: DO 110 I = 1, N
! 267: TEMP = A( J, I )
! 268: A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
! 269: A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
! 270: 110 CONTINUE
! 271: END IF
! 272: 120 CONTINUE
! 273: END IF
! 274: END IF
! 275: ELSE IF( LSAME( SIDE, 'R' ) ) THEN
! 276: *
! 277: * Form A * P'
! 278: *
! 279: IF( LSAME( PIVOT, 'V' ) ) THEN
! 280: IF( LSAME( DIRECT, 'F' ) ) THEN
! 281: DO 140 J = 1, N - 1
! 282: CTEMP = C( J )
! 283: STEMP = S( J )
! 284: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
! 285: DO 130 I = 1, M
! 286: TEMP = A( I, J+1 )
! 287: A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
! 288: A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
! 289: 130 CONTINUE
! 290: END IF
! 291: 140 CONTINUE
! 292: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
! 293: DO 160 J = N - 1, 1, -1
! 294: CTEMP = C( J )
! 295: STEMP = S( J )
! 296: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
! 297: DO 150 I = 1, M
! 298: TEMP = A( I, J+1 )
! 299: A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
! 300: A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
! 301: 150 CONTINUE
! 302: END IF
! 303: 160 CONTINUE
! 304: END IF
! 305: ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
! 306: IF( LSAME( DIRECT, 'F' ) ) THEN
! 307: DO 180 J = 2, N
! 308: CTEMP = C( J-1 )
! 309: STEMP = S( J-1 )
! 310: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
! 311: DO 170 I = 1, M
! 312: TEMP = A( I, J )
! 313: A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
! 314: A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
! 315: 170 CONTINUE
! 316: END IF
! 317: 180 CONTINUE
! 318: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
! 319: DO 200 J = N, 2, -1
! 320: CTEMP = C( J-1 )
! 321: STEMP = S( J-1 )
! 322: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
! 323: DO 190 I = 1, M
! 324: TEMP = A( I, J )
! 325: A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
! 326: A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
! 327: 190 CONTINUE
! 328: END IF
! 329: 200 CONTINUE
! 330: END IF
! 331: ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
! 332: IF( LSAME( DIRECT, 'F' ) ) THEN
! 333: DO 220 J = 1, N - 1
! 334: CTEMP = C( J )
! 335: STEMP = S( J )
! 336: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
! 337: DO 210 I = 1, M
! 338: TEMP = A( I, J )
! 339: A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
! 340: A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
! 341: 210 CONTINUE
! 342: END IF
! 343: 220 CONTINUE
! 344: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
! 345: DO 240 J = N - 1, 1, -1
! 346: CTEMP = C( J )
! 347: STEMP = S( J )
! 348: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
! 349: DO 230 I = 1, M
! 350: TEMP = A( I, J )
! 351: A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
! 352: A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
! 353: 230 CONTINUE
! 354: END IF
! 355: 240 CONTINUE
! 356: END IF
! 357: END IF
! 358: END IF
! 359: *
! 360: RETURN
! 361: *
! 362: * End of ZLASR
! 363: *
! 364: END
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