Annotation of rpl/lapack/lapack/dtftri.f, revision 1.7
1.7 ! bertrand 1: *> \brief \b DTFTRI
! 2: *
! 3: * =========== DOCUMENTATION ===========
1.1 bertrand 4: *
1.7 ! bertrand 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
1.1 bertrand 7: *
1.7 ! bertrand 8: *> \htmlonly
! 9: *> Download DTFTRI + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtftri.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtftri.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtftri.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER TRANSR, UPLO, DIAG
! 25: * INTEGER INFO, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * DOUBLE PRECISION A( 0: * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> DTFTRI computes the inverse of a triangular matrix A stored in RFP
! 38: *> format.
! 39: *>
! 40: *> This is a Level 3 BLAS version of the algorithm.
! 41: *> \endverbatim
! 42: *
! 43: * Arguments:
! 44: * ==========
! 45: *
! 46: *> \param[in] TRANSR
! 47: *> \verbatim
! 48: *> TRANSR is CHARACTER*1
! 49: *> = 'N': The Normal TRANSR of RFP A is stored;
! 50: *> = 'T': The Transpose TRANSR of RFP A is stored.
! 51: *> \endverbatim
! 52: *>
! 53: *> \param[in] UPLO
! 54: *> \verbatim
! 55: *> UPLO is CHARACTER*1
! 56: *> = 'U': A is upper triangular;
! 57: *> = 'L': A is lower triangular.
! 58: *> \endverbatim
! 59: *>
! 60: *> \param[in] DIAG
! 61: *> \verbatim
! 62: *> DIAG is CHARACTER*1
! 63: *> = 'N': A is non-unit triangular;
! 64: *> = 'U': A is unit triangular.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in] N
! 68: *> \verbatim
! 69: *> N is INTEGER
! 70: *> The order of the matrix A. N >= 0.
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in,out] A
! 74: *> \verbatim
! 75: *> A is DOUBLE PRECISION array, dimension (0:nt-1);
! 76: *> nt=N*(N+1)/2. On entry, the triangular factor of a Hermitian
! 77: *> Positive Definite matrix A in RFP format. RFP format is
! 78: *> described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'
! 79: *> then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
! 80: *> (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is
! 81: *> the transpose of RFP A as defined when
! 82: *> TRANSR = 'N'. The contents of RFP A are defined by UPLO as
! 83: *> follows: If UPLO = 'U' the RFP A contains the nt elements of
! 84: *> upper packed A; If UPLO = 'L' the RFP A contains the nt
! 85: *> elements of lower packed A. The LDA of RFP A is (N+1)/2 when
! 86: *> TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is
! 87: *> even and N is odd. See the Note below for more details.
! 88: *>
! 89: *> On exit, the (triangular) inverse of the original matrix, in
! 90: *> the same storage format.
! 91: *> \endverbatim
! 92: *>
! 93: *> \param[out] INFO
! 94: *> \verbatim
! 95: *> INFO is INTEGER
! 96: *> = 0: successful exit
! 97: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 98: *> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
! 99: *> matrix is singular and its inverse can not be computed.
! 100: *> \endverbatim
! 101: *
! 102: * Authors:
! 103: * ========
! 104: *
! 105: *> \author Univ. of Tennessee
! 106: *> \author Univ. of California Berkeley
! 107: *> \author Univ. of Colorado Denver
! 108: *> \author NAG Ltd.
! 109: *
! 110: *> \date November 2011
! 111: *
! 112: *> \ingroup doubleOTHERcomputational
! 113: *
! 114: *> \par Further Details:
! 115: * =====================
! 116: *>
! 117: *> \verbatim
! 118: *>
! 119: *> We first consider Rectangular Full Packed (RFP) Format when N is
! 120: *> even. We give an example where N = 6.
! 121: *>
! 122: *> AP is Upper AP is Lower
! 123: *>
! 124: *> 00 01 02 03 04 05 00
! 125: *> 11 12 13 14 15 10 11
! 126: *> 22 23 24 25 20 21 22
! 127: *> 33 34 35 30 31 32 33
! 128: *> 44 45 40 41 42 43 44
! 129: *> 55 50 51 52 53 54 55
! 130: *>
! 131: *>
! 132: *> Let TRANSR = 'N'. RFP holds AP as follows:
! 133: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
! 134: *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
! 135: *> the transpose of the first three columns of AP upper.
! 136: *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
! 137: *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
! 138: *> the transpose of the last three columns of AP lower.
! 139: *> This covers the case N even and TRANSR = 'N'.
! 140: *>
! 141: *> RFP A RFP A
! 142: *>
! 143: *> 03 04 05 33 43 53
! 144: *> 13 14 15 00 44 54
! 145: *> 23 24 25 10 11 55
! 146: *> 33 34 35 20 21 22
! 147: *> 00 44 45 30 31 32
! 148: *> 01 11 55 40 41 42
! 149: *> 02 12 22 50 51 52
! 150: *>
! 151: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
! 152: *> transpose of RFP A above. One therefore gets:
! 153: *>
! 154: *>
! 155: *> RFP A RFP A
! 156: *>
! 157: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
! 158: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
! 159: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
! 160: *>
! 161: *>
! 162: *> We then consider Rectangular Full Packed (RFP) Format when N is
! 163: *> odd. We give an example where N = 5.
! 164: *>
! 165: *> AP is Upper AP is Lower
! 166: *>
! 167: *> 00 01 02 03 04 00
! 168: *> 11 12 13 14 10 11
! 169: *> 22 23 24 20 21 22
! 170: *> 33 34 30 31 32 33
! 171: *> 44 40 41 42 43 44
! 172: *>
! 173: *>
! 174: *> Let TRANSR = 'N'. RFP holds AP as follows:
! 175: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
! 176: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
! 177: *> the transpose of the first two columns of AP upper.
! 178: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
! 179: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
! 180: *> the transpose of the last two columns of AP lower.
! 181: *> This covers the case N odd and TRANSR = 'N'.
! 182: *>
! 183: *> RFP A RFP A
! 184: *>
! 185: *> 02 03 04 00 33 43
! 186: *> 12 13 14 10 11 44
! 187: *> 22 23 24 20 21 22
! 188: *> 00 33 34 30 31 32
! 189: *> 01 11 44 40 41 42
! 190: *>
! 191: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
! 192: *> transpose of RFP A above. One therefore gets:
! 193: *>
! 194: *> RFP A RFP A
! 195: *>
! 196: *> 02 12 22 00 01 00 10 20 30 40 50
! 197: *> 03 13 23 33 11 33 11 21 31 41 51
! 198: *> 04 14 24 34 44 43 44 22 32 42 52
! 199: *> \endverbatim
! 200: *>
! 201: * =====================================================================
! 202: SUBROUTINE DTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
1.1 bertrand 203: *
1.7 ! bertrand 204: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 205: * -- LAPACK is a software package provided by Univ. of Tennessee, --
206: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.7 ! bertrand 207: * November 2011
1.1 bertrand 208: *
209: * .. Scalar Arguments ..
210: CHARACTER TRANSR, UPLO, DIAG
211: INTEGER INFO, N
212: * ..
213: * .. Array Arguments ..
214: DOUBLE PRECISION A( 0: * )
215: * ..
216: *
217: * =====================================================================
218: *
219: * .. Parameters ..
220: DOUBLE PRECISION ONE
221: PARAMETER ( ONE = 1.0D+0 )
222: * ..
223: * .. Local Scalars ..
224: LOGICAL LOWER, NISODD, NORMALTRANSR
225: INTEGER N1, N2, K
226: * ..
227: * .. External Functions ..
228: LOGICAL LSAME
229: EXTERNAL LSAME
230: * ..
231: * .. External Subroutines ..
232: EXTERNAL XERBLA, DTRMM, DTRTRI
233: * ..
234: * .. Intrinsic Functions ..
235: INTRINSIC MOD
236: * ..
237: * .. Executable Statements ..
238: *
239: * Test the input parameters.
240: *
241: INFO = 0
242: NORMALTRANSR = LSAME( TRANSR, 'N' )
243: LOWER = LSAME( UPLO, 'L' )
244: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
245: INFO = -1
246: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
247: INFO = -2
248: ELSE IF( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) )
1.6 bertrand 249: $ THEN
1.1 bertrand 250: INFO = -3
251: ELSE IF( N.LT.0 ) THEN
252: INFO = -4
253: END IF
254: IF( INFO.NE.0 ) THEN
255: CALL XERBLA( 'DTFTRI', -INFO )
256: RETURN
257: END IF
258: *
259: * Quick return if possible
260: *
261: IF( N.EQ.0 )
1.6 bertrand 262: $ RETURN
1.1 bertrand 263: *
264: * If N is odd, set NISODD = .TRUE.
265: * If N is even, set K = N/2 and NISODD = .FALSE.
266: *
267: IF( MOD( N, 2 ).EQ.0 ) THEN
268: K = N / 2
269: NISODD = .FALSE.
270: ELSE
271: NISODD = .TRUE.
272: END IF
273: *
274: * Set N1 and N2 depending on LOWER
275: *
276: IF( LOWER ) THEN
277: N2 = N / 2
278: N1 = N - N2
279: ELSE
280: N1 = N / 2
281: N2 = N - N1
282: END IF
283: *
284: *
285: * start execution: there are eight cases
286: *
287: IF( NISODD ) THEN
288: *
289: * N is odd
290: *
291: IF( NORMALTRANSR ) THEN
292: *
293: * N is odd and TRANSR = 'N'
294: *
295: IF( LOWER ) THEN
296: *
297: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
298: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
299: * T1 -> a(0), T2 -> a(n), S -> a(n1)
300: *
301: CALL DTRTRI( 'L', DIAG, N1, A( 0 ), N, INFO )
302: IF( INFO.GT.0 )
1.6 bertrand 303: $ RETURN
1.1 bertrand 304: CALL DTRMM( 'R', 'L', 'N', DIAG, N2, N1, -ONE, A( 0 ),
1.6 bertrand 305: $ N, A( N1 ), N )
1.1 bertrand 306: CALL DTRTRI( 'U', DIAG, N2, A( N ), N, INFO )
307: IF( INFO.GT.0 )
1.6 bertrand 308: $ INFO = INFO + N1
1.1 bertrand 309: IF( INFO.GT.0 )
1.6 bertrand 310: $ RETURN
1.1 bertrand 311: CALL DTRMM( 'L', 'U', 'T', DIAG, N2, N1, ONE, A( N ), N,
1.6 bertrand 312: $ A( N1 ), N )
1.1 bertrand 313: *
314: ELSE
315: *
316: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
317: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
318: * T1 -> a(n2), T2 -> a(n1), S -> a(0)
319: *
320: CALL DTRTRI( 'L', DIAG, N1, A( N2 ), N, INFO )
321: IF( INFO.GT.0 )
1.6 bertrand 322: $ RETURN
1.1 bertrand 323: CALL DTRMM( 'L', 'L', 'T', DIAG, N1, N2, -ONE, A( N2 ),
1.6 bertrand 324: $ N, A( 0 ), N )
1.1 bertrand 325: CALL DTRTRI( 'U', DIAG, N2, A( N1 ), N, INFO )
326: IF( INFO.GT.0 )
1.6 bertrand 327: $ INFO = INFO + N1
1.1 bertrand 328: IF( INFO.GT.0 )
1.6 bertrand 329: $ RETURN
1.1 bertrand 330: CALL DTRMM( 'R', 'U', 'N', DIAG, N1, N2, ONE, A( N1 ),
1.6 bertrand 331: $ N, A( 0 ), N )
1.1 bertrand 332: *
333: END IF
334: *
335: ELSE
336: *
337: * N is odd and TRANSR = 'T'
338: *
339: IF( LOWER ) THEN
340: *
341: * SRPA for LOWER, TRANSPOSE and N is odd
342: * T1 -> a(0), T2 -> a(1), S -> a(0+n1*n1)
343: *
344: CALL DTRTRI( 'U', DIAG, N1, A( 0 ), N1, INFO )
345: IF( INFO.GT.0 )
1.6 bertrand 346: $ RETURN
1.1 bertrand 347: CALL DTRMM( 'L', 'U', 'N', DIAG, N1, N2, -ONE, A( 0 ),
1.6 bertrand 348: $ N1, A( N1*N1 ), N1 )
1.1 bertrand 349: CALL DTRTRI( 'L', DIAG, N2, A( 1 ), N1, INFO )
350: IF( INFO.GT.0 )
1.6 bertrand 351: $ INFO = INFO + N1
1.1 bertrand 352: IF( INFO.GT.0 )
1.6 bertrand 353: $ RETURN
1.1 bertrand 354: CALL DTRMM( 'R', 'L', 'T', DIAG, N1, N2, ONE, A( 1 ),
1.6 bertrand 355: $ N1, A( N1*N1 ), N1 )
1.1 bertrand 356: *
357: ELSE
358: *
359: * SRPA for UPPER, TRANSPOSE and N is odd
360: * T1 -> a(0+n2*n2), T2 -> a(0+n1*n2), S -> a(0)
361: *
362: CALL DTRTRI( 'U', DIAG, N1, A( N2*N2 ), N2, INFO )
363: IF( INFO.GT.0 )
1.6 bertrand 364: $ RETURN
1.1 bertrand 365: CALL DTRMM( 'R', 'U', 'T', DIAG, N2, N1, -ONE,
1.6 bertrand 366: $ A( N2*N2 ), N2, A( 0 ), N2 )
1.1 bertrand 367: CALL DTRTRI( 'L', DIAG, N2, A( N1*N2 ), N2, INFO )
368: IF( INFO.GT.0 )
1.6 bertrand 369: $ INFO = INFO + N1
1.1 bertrand 370: IF( INFO.GT.0 )
1.6 bertrand 371: $ RETURN
1.1 bertrand 372: CALL DTRMM( 'L', 'L', 'N', DIAG, N2, N1, ONE,
1.6 bertrand 373: $ A( N1*N2 ), N2, A( 0 ), N2 )
1.1 bertrand 374: END IF
375: *
376: END IF
377: *
378: ELSE
379: *
380: * N is even
381: *
382: IF( NORMALTRANSR ) THEN
383: *
384: * N is even and TRANSR = 'N'
385: *
386: IF( LOWER ) THEN
387: *
388: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
389: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
390: * T1 -> a(1), T2 -> a(0), S -> a(k+1)
391: *
392: CALL DTRTRI( 'L', DIAG, K, A( 1 ), N+1, INFO )
393: IF( INFO.GT.0 )
1.6 bertrand 394: $ RETURN
1.1 bertrand 395: CALL DTRMM( 'R', 'L', 'N', DIAG, K, K, -ONE, A( 1 ),
1.6 bertrand 396: $ N+1, A( K+1 ), N+1 )
1.1 bertrand 397: CALL DTRTRI( 'U', DIAG, K, A( 0 ), N+1, INFO )
398: IF( INFO.GT.0 )
1.6 bertrand 399: $ INFO = INFO + K
1.1 bertrand 400: IF( INFO.GT.0 )
1.6 bertrand 401: $ RETURN
1.1 bertrand 402: CALL DTRMM( 'L', 'U', 'T', DIAG, K, K, ONE, A( 0 ), N+1,
1.6 bertrand 403: $ A( K+1 ), N+1 )
1.1 bertrand 404: *
405: ELSE
406: *
407: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
408: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
409: * T1 -> a(k+1), T2 -> a(k), S -> a(0)
410: *
411: CALL DTRTRI( 'L', DIAG, K, A( K+1 ), N+1, INFO )
412: IF( INFO.GT.0 )
1.6 bertrand 413: $ RETURN
1.1 bertrand 414: CALL DTRMM( 'L', 'L', 'T', DIAG, K, K, -ONE, A( K+1 ),
1.6 bertrand 415: $ N+1, A( 0 ), N+1 )
1.1 bertrand 416: CALL DTRTRI( 'U', DIAG, K, A( K ), N+1, INFO )
417: IF( INFO.GT.0 )
1.6 bertrand 418: $ INFO = INFO + K
1.1 bertrand 419: IF( INFO.GT.0 )
1.6 bertrand 420: $ RETURN
1.1 bertrand 421: CALL DTRMM( 'R', 'U', 'N', DIAG, K, K, ONE, A( K ), N+1,
1.6 bertrand 422: $ A( 0 ), N+1 )
1.1 bertrand 423: END IF
424: ELSE
425: *
426: * N is even and TRANSR = 'T'
427: *
428: IF( LOWER ) THEN
429: *
430: * SRPA for LOWER, TRANSPOSE and N is even (see paper)
431: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
432: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
433: *
434: CALL DTRTRI( 'U', DIAG, K, A( K ), K, INFO )
435: IF( INFO.GT.0 )
1.6 bertrand 436: $ RETURN
1.1 bertrand 437: CALL DTRMM( 'L', 'U', 'N', DIAG, K, K, -ONE, A( K ), K,
1.6 bertrand 438: $ A( K*( K+1 ) ), K )
1.1 bertrand 439: CALL DTRTRI( 'L', DIAG, K, A( 0 ), K, INFO )
440: IF( INFO.GT.0 )
1.6 bertrand 441: $ INFO = INFO + K
1.1 bertrand 442: IF( INFO.GT.0 )
1.6 bertrand 443: $ RETURN
1.1 bertrand 444: CALL DTRMM( 'R', 'L', 'T', DIAG, K, K, ONE, A( 0 ), K,
1.6 bertrand 445: $ A( K*( K+1 ) ), K )
1.1 bertrand 446: ELSE
447: *
448: * SRPA for UPPER, TRANSPOSE and N is even (see paper)
449: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
450: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
451: *
452: CALL DTRTRI( 'U', DIAG, K, A( K*( K+1 ) ), K, INFO )
453: IF( INFO.GT.0 )
1.6 bertrand 454: $ RETURN
1.1 bertrand 455: CALL DTRMM( 'R', 'U', 'T', DIAG, K, K, -ONE,
1.6 bertrand 456: $ A( K*( K+1 ) ), K, A( 0 ), K )
1.1 bertrand 457: CALL DTRTRI( 'L', DIAG, K, A( K*K ), K, INFO )
458: IF( INFO.GT.0 )
1.6 bertrand 459: $ INFO = INFO + K
1.1 bertrand 460: IF( INFO.GT.0 )
1.6 bertrand 461: $ RETURN
1.1 bertrand 462: CALL DTRMM( 'L', 'L', 'N', DIAG, K, K, ONE, A( K*K ), K,
1.6 bertrand 463: $ A( 0 ), K )
1.1 bertrand 464: END IF
465: END IF
466: END IF
467: *
468: RETURN
469: *
470: * End of DTFTRI
471: *
472: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dtftri.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack