Annotation of rpl/lapack/lapack/dlagtm.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DLAGTM
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLAGTM + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlagtm.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlagtm.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlagtm.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
! 22: * B, LDB )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER TRANS
! 26: * INTEGER LDB, LDX, N, NRHS
! 27: * DOUBLE PRECISION ALPHA, BETA
! 28: * ..
! 29: * .. Array Arguments ..
! 30: * DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ),
! 31: * $ X( LDX, * )
! 32: * ..
! 33: *
! 34: *
! 35: *> \par Purpose:
! 36: * =============
! 37: *>
! 38: *> \verbatim
! 39: *>
! 40: *> DLAGTM performs a matrix-vector product of the form
! 41: *>
! 42: *> B := alpha * A * X + beta * B
! 43: *>
! 44: *> where A is a tridiagonal matrix of order N, B and X are N by NRHS
! 45: *> matrices, and alpha and beta are real scalars, each of which may be
! 46: *> 0., 1., or -1.
! 47: *> \endverbatim
! 48: *
! 49: * Arguments:
! 50: * ==========
! 51: *
! 52: *> \param[in] TRANS
! 53: *> \verbatim
! 54: *> TRANS is CHARACTER*1
! 55: *> Specifies the operation applied to A.
! 56: *> = 'N': No transpose, B := alpha * A * X + beta * B
! 57: *> = 'T': Transpose, B := alpha * A'* X + beta * B
! 58: *> = 'C': Conjugate transpose = Transpose
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in] N
! 62: *> \verbatim
! 63: *> N is INTEGER
! 64: *> The order of the matrix A. N >= 0.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in] NRHS
! 68: *> \verbatim
! 69: *> NRHS is INTEGER
! 70: *> The number of right hand sides, i.e., the number of columns
! 71: *> of the matrices X and B.
! 72: *> \endverbatim
! 73: *>
! 74: *> \param[in] ALPHA
! 75: *> \verbatim
! 76: *> ALPHA is DOUBLE PRECISION
! 77: *> The scalar alpha. ALPHA must be 0., 1., or -1.; otherwise,
! 78: *> it is assumed to be 0.
! 79: *> \endverbatim
! 80: *>
! 81: *> \param[in] DL
! 82: *> \verbatim
! 83: *> DL is DOUBLE PRECISION array, dimension (N-1)
! 84: *> The (n-1) sub-diagonal elements of T.
! 85: *> \endverbatim
! 86: *>
! 87: *> \param[in] D
! 88: *> \verbatim
! 89: *> D is DOUBLE PRECISION array, dimension (N)
! 90: *> The diagonal elements of T.
! 91: *> \endverbatim
! 92: *>
! 93: *> \param[in] DU
! 94: *> \verbatim
! 95: *> DU is DOUBLE PRECISION array, dimension (N-1)
! 96: *> The (n-1) super-diagonal elements of T.
! 97: *> \endverbatim
! 98: *>
! 99: *> \param[in] X
! 100: *> \verbatim
! 101: *> X is DOUBLE PRECISION array, dimension (LDX,NRHS)
! 102: *> The N by NRHS matrix X.
! 103: *> \endverbatim
! 104: *>
! 105: *> \param[in] LDX
! 106: *> \verbatim
! 107: *> LDX is INTEGER
! 108: *> The leading dimension of the array X. LDX >= max(N,1).
! 109: *> \endverbatim
! 110: *>
! 111: *> \param[in] BETA
! 112: *> \verbatim
! 113: *> BETA is DOUBLE PRECISION
! 114: *> The scalar beta. BETA must be 0., 1., or -1.; otherwise,
! 115: *> it is assumed to be 1.
! 116: *> \endverbatim
! 117: *>
! 118: *> \param[in,out] B
! 119: *> \verbatim
! 120: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
! 121: *> On entry, the N by NRHS matrix B.
! 122: *> On exit, B is overwritten by the matrix expression
! 123: *> B := alpha * A * X + beta * B.
! 124: *> \endverbatim
! 125: *>
! 126: *> \param[in] LDB
! 127: *> \verbatim
! 128: *> LDB is INTEGER
! 129: *> The leading dimension of the array B. LDB >= max(N,1).
! 130: *> \endverbatim
! 131: *
! 132: * Authors:
! 133: * ========
! 134: *
! 135: *> \author Univ. of Tennessee
! 136: *> \author Univ. of California Berkeley
! 137: *> \author Univ. of Colorado Denver
! 138: *> \author NAG Ltd.
! 139: *
! 140: *> \date November 2011
! 141: *
! 142: *> \ingroup doubleOTHERauxiliary
! 143: *
! 144: * =====================================================================
1.1 bertrand 145: SUBROUTINE DLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
146: $ B, LDB )
147: *
1.9 ! bertrand 148: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 149: * -- LAPACK is a software package provided by Univ. of Tennessee, --
150: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 151: * November 2011
1.1 bertrand 152: *
153: * .. Scalar Arguments ..
154: CHARACTER TRANS
155: INTEGER LDB, LDX, N, NRHS
156: DOUBLE PRECISION ALPHA, BETA
157: * ..
158: * .. Array Arguments ..
159: DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ),
160: $ X( LDX, * )
161: * ..
162: *
163: * =====================================================================
164: *
165: * .. Parameters ..
166: DOUBLE PRECISION ONE, ZERO
167: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
168: * ..
169: * .. Local Scalars ..
170: INTEGER I, J
171: * ..
172: * .. External Functions ..
173: LOGICAL LSAME
174: EXTERNAL LSAME
175: * ..
176: * .. Executable Statements ..
177: *
178: IF( N.EQ.0 )
179: $ RETURN
180: *
181: * Multiply B by BETA if BETA.NE.1.
182: *
183: IF( BETA.EQ.ZERO ) THEN
184: DO 20 J = 1, NRHS
185: DO 10 I = 1, N
186: B( I, J ) = ZERO
187: 10 CONTINUE
188: 20 CONTINUE
189: ELSE IF( BETA.EQ.-ONE ) THEN
190: DO 40 J = 1, NRHS
191: DO 30 I = 1, N
192: B( I, J ) = -B( I, J )
193: 30 CONTINUE
194: 40 CONTINUE
195: END IF
196: *
197: IF( ALPHA.EQ.ONE ) THEN
198: IF( LSAME( TRANS, 'N' ) ) THEN
199: *
200: * Compute B := B + A*X
201: *
202: DO 60 J = 1, NRHS
203: IF( N.EQ.1 ) THEN
204: B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
205: ELSE
206: B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
207: $ DU( 1 )*X( 2, J )
208: B( N, J ) = B( N, J ) + DL( N-1 )*X( N-1, J ) +
209: $ D( N )*X( N, J )
210: DO 50 I = 2, N - 1
211: B( I, J ) = B( I, J ) + DL( I-1 )*X( I-1, J ) +
212: $ D( I )*X( I, J ) + DU( I )*X( I+1, J )
213: 50 CONTINUE
214: END IF
215: 60 CONTINUE
216: ELSE
217: *
1.8 bertrand 218: * Compute B := B + A**T*X
1.1 bertrand 219: *
220: DO 80 J = 1, NRHS
221: IF( N.EQ.1 ) THEN
222: B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
223: ELSE
224: B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
225: $ DL( 1 )*X( 2, J )
226: B( N, J ) = B( N, J ) + DU( N-1 )*X( N-1, J ) +
227: $ D( N )*X( N, J )
228: DO 70 I = 2, N - 1
229: B( I, J ) = B( I, J ) + DU( I-1 )*X( I-1, J ) +
230: $ D( I )*X( I, J ) + DL( I )*X( I+1, J )
231: 70 CONTINUE
232: END IF
233: 80 CONTINUE
234: END IF
235: ELSE IF( ALPHA.EQ.-ONE ) THEN
236: IF( LSAME( TRANS, 'N' ) ) THEN
237: *
238: * Compute B := B - A*X
239: *
240: DO 100 J = 1, NRHS
241: IF( N.EQ.1 ) THEN
242: B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
243: ELSE
244: B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
245: $ DU( 1 )*X( 2, J )
246: B( N, J ) = B( N, J ) - DL( N-1 )*X( N-1, J ) -
247: $ D( N )*X( N, J )
248: DO 90 I = 2, N - 1
249: B( I, J ) = B( I, J ) - DL( I-1 )*X( I-1, J ) -
250: $ D( I )*X( I, J ) - DU( I )*X( I+1, J )
251: 90 CONTINUE
252: END IF
253: 100 CONTINUE
254: ELSE
255: *
1.8 bertrand 256: * Compute B := B - A**T*X
1.1 bertrand 257: *
258: DO 120 J = 1, NRHS
259: IF( N.EQ.1 ) THEN
260: B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
261: ELSE
262: B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
263: $ DL( 1 )*X( 2, J )
264: B( N, J ) = B( N, J ) - DU( N-1 )*X( N-1, J ) -
265: $ D( N )*X( N, J )
266: DO 110 I = 2, N - 1
267: B( I, J ) = B( I, J ) - DU( I-1 )*X( I-1, J ) -
268: $ D( I )*X( I, J ) - DL( I )*X( I+1, J )
269: 110 CONTINUE
270: END IF
271: 120 CONTINUE
272: END IF
273: END IF
274: RETURN
275: *
276: * End of DLAGTM
277: *
278: END
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