Annotation of rpl/lapack/lapack/dopmtr.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
! 2: $ INFO )
! 3: *
! 4: * -- LAPACK routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: CHARACTER SIDE, TRANS, UPLO
! 11: INTEGER INFO, LDC, M, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION AP( * ), C( LDC, * ), TAU( * ), WORK( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * DOPMTR overwrites the general real M-by-N matrix C with
! 21: *
! 22: * SIDE = 'L' SIDE = 'R'
! 23: * TRANS = 'N': Q * C C * Q
! 24: * TRANS = 'T': Q**T * C C * Q**T
! 25: *
! 26: * where Q is a real orthogonal matrix of order nq, with nq = m if
! 27: * SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
! 28: * nq-1 elementary reflectors, as returned by DSPTRD using packed
! 29: * storage:
! 30: *
! 31: * if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
! 32: *
! 33: * if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
! 34: *
! 35: * Arguments
! 36: * =========
! 37: *
! 38: * SIDE (input) CHARACTER*1
! 39: * = 'L': apply Q or Q**T from the Left;
! 40: * = 'R': apply Q or Q**T from the Right.
! 41: *
! 42: * UPLO (input) CHARACTER*1
! 43: * = 'U': Upper triangular packed storage used in previous
! 44: * call to DSPTRD;
! 45: * = 'L': Lower triangular packed storage used in previous
! 46: * call to DSPTRD.
! 47: *
! 48: * TRANS (input) CHARACTER*1
! 49: * = 'N': No transpose, apply Q;
! 50: * = 'T': Transpose, apply Q**T.
! 51: *
! 52: * M (input) INTEGER
! 53: * The number of rows of the matrix C. M >= 0.
! 54: *
! 55: * N (input) INTEGER
! 56: * The number of columns of the matrix C. N >= 0.
! 57: *
! 58: * AP (input) DOUBLE PRECISION array, dimension
! 59: * (M*(M+1)/2) if SIDE = 'L'
! 60: * (N*(N+1)/2) if SIDE = 'R'
! 61: * The vectors which define the elementary reflectors, as
! 62: * returned by DSPTRD. AP is modified by the routine but
! 63: * restored on exit.
! 64: *
! 65: * TAU (input) DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L'
! 66: * or (N-1) if SIDE = 'R'
! 67: * TAU(i) must contain the scalar factor of the elementary
! 68: * reflector H(i), as returned by DSPTRD.
! 69: *
! 70: * C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
! 71: * On entry, the M-by-N matrix C.
! 72: * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
! 73: *
! 74: * LDC (input) INTEGER
! 75: * The leading dimension of the array C. LDC >= max(1,M).
! 76: *
! 77: * WORK (workspace) DOUBLE PRECISION array, dimension
! 78: * (N) if SIDE = 'L'
! 79: * (M) if SIDE = 'R'
! 80: *
! 81: * INFO (output) INTEGER
! 82: * = 0: successful exit
! 83: * < 0: if INFO = -i, the i-th argument had an illegal value
! 84: *
! 85: * =====================================================================
! 86: *
! 87: * .. Parameters ..
! 88: DOUBLE PRECISION ONE
! 89: PARAMETER ( ONE = 1.0D+0 )
! 90: * ..
! 91: * .. Local Scalars ..
! 92: LOGICAL FORWRD, LEFT, NOTRAN, UPPER
! 93: INTEGER I, I1, I2, I3, IC, II, JC, MI, NI, NQ
! 94: DOUBLE PRECISION AII
! 95: * ..
! 96: * .. External Functions ..
! 97: LOGICAL LSAME
! 98: EXTERNAL LSAME
! 99: * ..
! 100: * .. External Subroutines ..
! 101: EXTERNAL DLARF, XERBLA
! 102: * ..
! 103: * .. Intrinsic Functions ..
! 104: INTRINSIC MAX
! 105: * ..
! 106: * .. Executable Statements ..
! 107: *
! 108: * Test the input arguments
! 109: *
! 110: INFO = 0
! 111: LEFT = LSAME( SIDE, 'L' )
! 112: NOTRAN = LSAME( TRANS, 'N' )
! 113: UPPER = LSAME( UPLO, 'U' )
! 114: *
! 115: * NQ is the order of Q
! 116: *
! 117: IF( LEFT ) THEN
! 118: NQ = M
! 119: ELSE
! 120: NQ = N
! 121: END IF
! 122: IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
! 123: INFO = -1
! 124: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 125: INFO = -2
! 126: ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
! 127: INFO = -3
! 128: ELSE IF( M.LT.0 ) THEN
! 129: INFO = -4
! 130: ELSE IF( N.LT.0 ) THEN
! 131: INFO = -5
! 132: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
! 133: INFO = -9
! 134: END IF
! 135: IF( INFO.NE.0 ) THEN
! 136: CALL XERBLA( 'DOPMTR', -INFO )
! 137: RETURN
! 138: END IF
! 139: *
! 140: * Quick return if possible
! 141: *
! 142: IF( M.EQ.0 .OR. N.EQ.0 )
! 143: $ RETURN
! 144: *
! 145: IF( UPPER ) THEN
! 146: *
! 147: * Q was determined by a call to DSPTRD with UPLO = 'U'
! 148: *
! 149: FORWRD = ( LEFT .AND. NOTRAN ) .OR.
! 150: $ ( .NOT.LEFT .AND. .NOT.NOTRAN )
! 151: *
! 152: IF( FORWRD ) THEN
! 153: I1 = 1
! 154: I2 = NQ - 1
! 155: I3 = 1
! 156: II = 2
! 157: ELSE
! 158: I1 = NQ - 1
! 159: I2 = 1
! 160: I3 = -1
! 161: II = NQ*( NQ+1 ) / 2 - 1
! 162: END IF
! 163: *
! 164: IF( LEFT ) THEN
! 165: NI = N
! 166: ELSE
! 167: MI = M
! 168: END IF
! 169: *
! 170: DO 10 I = I1, I2, I3
! 171: IF( LEFT ) THEN
! 172: *
! 173: * H(i) is applied to C(1:i,1:n)
! 174: *
! 175: MI = I
! 176: ELSE
! 177: *
! 178: * H(i) is applied to C(1:m,1:i)
! 179: *
! 180: NI = I
! 181: END IF
! 182: *
! 183: * Apply H(i)
! 184: *
! 185: AII = AP( II )
! 186: AP( II ) = ONE
! 187: CALL DLARF( SIDE, MI, NI, AP( II-I+1 ), 1, TAU( I ), C, LDC,
! 188: $ WORK )
! 189: AP( II ) = AII
! 190: *
! 191: IF( FORWRD ) THEN
! 192: II = II + I + 2
! 193: ELSE
! 194: II = II - I - 1
! 195: END IF
! 196: 10 CONTINUE
! 197: ELSE
! 198: *
! 199: * Q was determined by a call to DSPTRD with UPLO = 'L'.
! 200: *
! 201: FORWRD = ( LEFT .AND. .NOT.NOTRAN ) .OR.
! 202: $ ( .NOT.LEFT .AND. NOTRAN )
! 203: *
! 204: IF( FORWRD ) THEN
! 205: I1 = 1
! 206: I2 = NQ - 1
! 207: I3 = 1
! 208: II = 2
! 209: ELSE
! 210: I1 = NQ - 1
! 211: I2 = 1
! 212: I3 = -1
! 213: II = NQ*( NQ+1 ) / 2 - 1
! 214: END IF
! 215: *
! 216: IF( LEFT ) THEN
! 217: NI = N
! 218: JC = 1
! 219: ELSE
! 220: MI = M
! 221: IC = 1
! 222: END IF
! 223: *
! 224: DO 20 I = I1, I2, I3
! 225: AII = AP( II )
! 226: AP( II ) = ONE
! 227: IF( LEFT ) THEN
! 228: *
! 229: * H(i) is applied to C(i+1:m,1:n)
! 230: *
! 231: MI = M - I
! 232: IC = I + 1
! 233: ELSE
! 234: *
! 235: * H(i) is applied to C(1:m,i+1:n)
! 236: *
! 237: NI = N - I
! 238: JC = I + 1
! 239: END IF
! 240: *
! 241: * Apply H(i)
! 242: *
! 243: CALL DLARF( SIDE, MI, NI, AP( II ), 1, TAU( I ),
! 244: $ C( IC, JC ), LDC, WORK )
! 245: AP( II ) = AII
! 246: *
! 247: IF( FORWRD ) THEN
! 248: II = II + NQ - I + 1
! 249: ELSE
! 250: II = II - NQ + I - 2
! 251: END IF
! 252: 20 CONTINUE
! 253: END IF
! 254: RETURN
! 255: *
! 256: * End of DOPMTR
! 257: *
! 258: END
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