Annotation of rpl/lapack/lapack/ztftri.f, revision 1.7
1.7 ! bertrand 1: *> \brief \b ZTFTRI
! 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 ZTFTRI + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztftri.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztftri.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztftri.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER TRANSR, UPLO, DIAG
! 25: * INTEGER INFO, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * COMPLEX*16 A( 0: * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> ZTFTRI 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: *> = 'C': The Conjugate-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 COMPLEX*16 array, dimension ( N*(N+1)/2 );
! 76: *> On entry, the triangular matrix A in RFP format. RFP format
! 77: *> is described by TRANSR, UPLO, and N as follows: If TRANSR =
! 78: *> 'N' then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
! 79: *> (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is
! 80: *> the Conjugate-transpose of RFP A as defined when
! 81: *> TRANSR = 'N'. The contents of RFP A are defined by UPLO as
! 82: *> follows: If UPLO = 'U' the RFP A contains the nt elements of
! 83: *> upper packed A; If UPLO = 'L' the RFP A contains the nt
! 84: *> elements of lower packed A. The LDA of RFP A is (N+1)/2 when
! 85: *> TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is
! 86: *> even and N is odd. See the Note below for more details.
! 87: *>
! 88: *> On exit, the (triangular) inverse of the original matrix, in
! 89: *> the same storage format.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[out] INFO
! 93: *> \verbatim
! 94: *> INFO is INTEGER
! 95: *> = 0: successful exit
! 96: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 97: *> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
! 98: *> matrix is singular and its inverse can not be computed.
! 99: *> \endverbatim
! 100: *
! 101: * Authors:
! 102: * ========
! 103: *
! 104: *> \author Univ. of Tennessee
! 105: *> \author Univ. of California Berkeley
! 106: *> \author Univ. of Colorado Denver
! 107: *> \author NAG Ltd.
! 108: *
! 109: *> \date November 2011
! 110: *
! 111: *> \ingroup complex16OTHERcomputational
! 112: *
! 113: *> \par Further Details:
! 114: * =====================
! 115: *>
! 116: *> \verbatim
! 117: *>
! 118: *> We first consider Standard Packed Format when N is even.
! 119: *> We give an example where N = 6.
! 120: *>
! 121: *> AP is Upper AP is Lower
! 122: *>
! 123: *> 00 01 02 03 04 05 00
! 124: *> 11 12 13 14 15 10 11
! 125: *> 22 23 24 25 20 21 22
! 126: *> 33 34 35 30 31 32 33
! 127: *> 44 45 40 41 42 43 44
! 128: *> 55 50 51 52 53 54 55
! 129: *>
! 130: *>
! 131: *> Let TRANSR = 'N'. RFP holds AP as follows:
! 132: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
! 133: *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
! 134: *> conjugate-transpose of the first three columns of AP upper.
! 135: *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
! 136: *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
! 137: *> conjugate-transpose of the last three columns of AP lower.
! 138: *> To denote conjugate we place -- above the element. This covers the
! 139: *> case N even and TRANSR = 'N'.
! 140: *>
! 141: *> RFP A RFP A
! 142: *>
! 143: *> -- -- --
! 144: *> 03 04 05 33 43 53
! 145: *> -- --
! 146: *> 13 14 15 00 44 54
! 147: *> --
! 148: *> 23 24 25 10 11 55
! 149: *>
! 150: *> 33 34 35 20 21 22
! 151: *> --
! 152: *> 00 44 45 30 31 32
! 153: *> -- --
! 154: *> 01 11 55 40 41 42
! 155: *> -- -- --
! 156: *> 02 12 22 50 51 52
! 157: *>
! 158: *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
! 159: *> transpose of RFP A above. One therefore gets:
! 160: *>
! 161: *>
! 162: *> RFP A RFP A
! 163: *>
! 164: *> -- -- -- -- -- -- -- -- -- --
! 165: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
! 166: *> -- -- -- -- -- -- -- -- -- --
! 167: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
! 168: *> -- -- -- -- -- -- -- -- -- --
! 169: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
! 170: *>
! 171: *>
! 172: *> We next consider Standard Packed Format when N is odd.
! 173: *> We give an example where N = 5.
! 174: *>
! 175: *> AP is Upper AP is Lower
! 176: *>
! 177: *> 00 01 02 03 04 00
! 178: *> 11 12 13 14 10 11
! 179: *> 22 23 24 20 21 22
! 180: *> 33 34 30 31 32 33
! 181: *> 44 40 41 42 43 44
! 182: *>
! 183: *>
! 184: *> Let TRANSR = 'N'. RFP holds AP as follows:
! 185: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
! 186: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
! 187: *> conjugate-transpose of the first two columns of AP upper.
! 188: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
! 189: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
! 190: *> conjugate-transpose of the last two columns of AP lower.
! 191: *> To denote conjugate we place -- above the element. This covers the
! 192: *> case N odd and TRANSR = 'N'.
! 193: *>
! 194: *> RFP A RFP A
! 195: *>
! 196: *> -- --
! 197: *> 02 03 04 00 33 43
! 198: *> --
! 199: *> 12 13 14 10 11 44
! 200: *>
! 201: *> 22 23 24 20 21 22
! 202: *> --
! 203: *> 00 33 34 30 31 32
! 204: *> -- --
! 205: *> 01 11 44 40 41 42
! 206: *>
! 207: *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
! 208: *> transpose of RFP A above. One therefore gets:
! 209: *>
! 210: *>
! 211: *> RFP A RFP A
! 212: *>
! 213: *> -- -- -- -- -- -- -- -- --
! 214: *> 02 12 22 00 01 00 10 20 30 40 50
! 215: *> -- -- -- -- -- -- -- -- --
! 216: *> 03 13 23 33 11 33 11 21 31 41 51
! 217: *> -- -- -- -- -- -- -- -- --
! 218: *> 04 14 24 34 44 43 44 22 32 42 52
! 219: *> \endverbatim
! 220: *>
! 221: * =====================================================================
! 222: SUBROUTINE ZTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
1.1 bertrand 223: *
1.7 ! bertrand 224: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 225: * -- LAPACK is a software package provided by Univ. of Tennessee, --
226: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.7 ! bertrand 227: * November 2011
1.1 bertrand 228: *
229: * .. Scalar Arguments ..
230: CHARACTER TRANSR, UPLO, DIAG
231: INTEGER INFO, N
232: * ..
233: * .. Array Arguments ..
234: COMPLEX*16 A( 0: * )
235: * ..
236: *
237: * =====================================================================
238: *
239: * .. Parameters ..
240: COMPLEX*16 CONE
241: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
242: * ..
243: * .. Local Scalars ..
244: LOGICAL LOWER, NISODD, NORMALTRANSR
245: INTEGER N1, N2, K
246: * ..
247: * .. External Functions ..
248: LOGICAL LSAME
249: EXTERNAL LSAME
250: * ..
251: * .. External Subroutines ..
252: EXTERNAL XERBLA, ZTRMM, ZTRTRI
253: * ..
254: * .. Intrinsic Functions ..
255: INTRINSIC MOD
256: * ..
257: * .. Executable Statements ..
258: *
259: * Test the input parameters.
260: *
261: INFO = 0
262: NORMALTRANSR = LSAME( TRANSR, 'N' )
263: LOWER = LSAME( UPLO, 'L' )
264: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
265: INFO = -1
266: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
267: INFO = -2
268: ELSE IF( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) )
1.6 bertrand 269: $ THEN
1.1 bertrand 270: INFO = -3
271: ELSE IF( N.LT.0 ) THEN
272: INFO = -4
273: END IF
274: IF( INFO.NE.0 ) THEN
275: CALL XERBLA( 'ZTFTRI', -INFO )
276: RETURN
277: END IF
278: *
279: * Quick return if possible
280: *
281: IF( N.EQ.0 )
1.6 bertrand 282: $ RETURN
1.1 bertrand 283: *
284: * If N is odd, set NISODD = .TRUE.
285: * If N is even, set K = N/2 and NISODD = .FALSE.
286: *
287: IF( MOD( N, 2 ).EQ.0 ) THEN
288: K = N / 2
289: NISODD = .FALSE.
290: ELSE
291: NISODD = .TRUE.
292: END IF
293: *
294: * Set N1 and N2 depending on LOWER
295: *
296: IF( LOWER ) THEN
297: N2 = N / 2
298: N1 = N - N2
299: ELSE
300: N1 = N / 2
301: N2 = N - N1
302: END IF
303: *
304: *
305: * start execution: there are eight cases
306: *
307: IF( NISODD ) THEN
308: *
309: * N is odd
310: *
311: IF( NORMALTRANSR ) THEN
312: *
313: * N is odd and TRANSR = 'N'
314: *
315: IF( LOWER ) THEN
316: *
317: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
318: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
319: * T1 -> a(0), T2 -> a(n), S -> a(n1)
320: *
321: CALL ZTRTRI( 'L', DIAG, N1, A( 0 ), N, INFO )
322: IF( INFO.GT.0 )
1.6 bertrand 323: $ RETURN
1.1 bertrand 324: CALL ZTRMM( 'R', 'L', 'N', DIAG, N2, N1, -CONE, A( 0 ),
1.6 bertrand 325: $ N, A( N1 ), N )
1.1 bertrand 326: CALL ZTRTRI( 'U', DIAG, N2, A( N ), N, INFO )
327: IF( INFO.GT.0 )
1.6 bertrand 328: $ INFO = INFO + N1
1.1 bertrand 329: IF( INFO.GT.0 )
1.6 bertrand 330: $ RETURN
1.1 bertrand 331: CALL ZTRMM( 'L', 'U', 'C', DIAG, N2, N1, CONE, A( N ), N,
1.6 bertrand 332: $ A( N1 ), N )
1.1 bertrand 333: *
334: ELSE
335: *
336: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
337: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
338: * T1 -> a(n2), T2 -> a(n1), S -> a(0)
339: *
340: CALL ZTRTRI( 'L', DIAG, N1, A( N2 ), N, INFO )
341: IF( INFO.GT.0 )
1.6 bertrand 342: $ RETURN
1.1 bertrand 343: CALL ZTRMM( 'L', 'L', 'C', DIAG, N1, N2, -CONE, A( N2 ),
1.6 bertrand 344: $ N, A( 0 ), N )
1.1 bertrand 345: CALL ZTRTRI( 'U', DIAG, N2, A( N1 ), N, INFO )
346: IF( INFO.GT.0 )
1.6 bertrand 347: $ INFO = INFO + N1
1.1 bertrand 348: IF( INFO.GT.0 )
1.6 bertrand 349: $ RETURN
1.1 bertrand 350: CALL ZTRMM( 'R', 'U', 'N', DIAG, N1, N2, CONE, A( N1 ),
1.6 bertrand 351: $ N, A( 0 ), N )
1.1 bertrand 352: *
353: END IF
354: *
355: ELSE
356: *
357: * N is odd and TRANSR = 'C'
358: *
359: IF( LOWER ) THEN
360: *
361: * SRPA for LOWER, TRANSPOSE and N is odd
362: * T1 -> a(0), T2 -> a(1), S -> a(0+n1*n1)
363: *
364: CALL ZTRTRI( 'U', DIAG, N1, A( 0 ), N1, INFO )
365: IF( INFO.GT.0 )
1.6 bertrand 366: $ RETURN
1.1 bertrand 367: CALL ZTRMM( 'L', 'U', 'N', DIAG, N1, N2, -CONE, A( 0 ),
1.6 bertrand 368: $ N1, A( N1*N1 ), N1 )
1.1 bertrand 369: CALL ZTRTRI( 'L', DIAG, N2, A( 1 ), N1, INFO )
370: IF( INFO.GT.0 )
1.6 bertrand 371: $ INFO = INFO + N1
1.1 bertrand 372: IF( INFO.GT.0 )
1.6 bertrand 373: $ RETURN
1.1 bertrand 374: CALL ZTRMM( 'R', 'L', 'C', DIAG, N1, N2, CONE, A( 1 ),
1.6 bertrand 375: $ N1, A( N1*N1 ), N1 )
1.1 bertrand 376: *
377: ELSE
378: *
379: * SRPA for UPPER, TRANSPOSE and N is odd
380: * T1 -> a(0+n2*n2), T2 -> a(0+n1*n2), S -> a(0)
381: *
382: CALL ZTRTRI( 'U', DIAG, N1, A( N2*N2 ), N2, INFO )
383: IF( INFO.GT.0 )
1.6 bertrand 384: $ RETURN
1.1 bertrand 385: CALL ZTRMM( 'R', 'U', 'C', DIAG, N2, N1, -CONE,
1.6 bertrand 386: $ A( N2*N2 ), N2, A( 0 ), N2 )
1.1 bertrand 387: CALL ZTRTRI( 'L', DIAG, N2, A( N1*N2 ), N2, INFO )
388: IF( INFO.GT.0 )
1.6 bertrand 389: $ INFO = INFO + N1
1.1 bertrand 390: IF( INFO.GT.0 )
1.6 bertrand 391: $ RETURN
1.1 bertrand 392: CALL ZTRMM( 'L', 'L', 'N', DIAG, N2, N1, CONE,
1.6 bertrand 393: $ A( N1*N2 ), N2, A( 0 ), N2 )
1.1 bertrand 394: END IF
395: *
396: END IF
397: *
398: ELSE
399: *
400: * N is even
401: *
402: IF( NORMALTRANSR ) THEN
403: *
404: * N is even and TRANSR = 'N'
405: *
406: IF( LOWER ) THEN
407: *
408: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
409: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
410: * T1 -> a(1), T2 -> a(0), S -> a(k+1)
411: *
412: CALL ZTRTRI( 'L', DIAG, K, A( 1 ), N+1, INFO )
413: IF( INFO.GT.0 )
1.6 bertrand 414: $ RETURN
1.1 bertrand 415: CALL ZTRMM( 'R', 'L', 'N', DIAG, K, K, -CONE, A( 1 ),
1.6 bertrand 416: $ N+1, A( K+1 ), N+1 )
1.1 bertrand 417: CALL ZTRTRI( 'U', DIAG, K, A( 0 ), N+1, INFO )
418: IF( INFO.GT.0 )
1.6 bertrand 419: $ INFO = INFO + K
1.1 bertrand 420: IF( INFO.GT.0 )
1.6 bertrand 421: $ RETURN
1.1 bertrand 422: CALL ZTRMM( 'L', 'U', 'C', DIAG, K, K, CONE, A( 0 ), N+1,
1.6 bertrand 423: $ A( K+1 ), N+1 )
1.1 bertrand 424: *
425: ELSE
426: *
427: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
428: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
429: * T1 -> a(k+1), T2 -> a(k), S -> a(0)
430: *
431: CALL ZTRTRI( 'L', DIAG, K, A( K+1 ), N+1, INFO )
432: IF( INFO.GT.0 )
1.6 bertrand 433: $ RETURN
1.1 bertrand 434: CALL ZTRMM( 'L', 'L', 'C', DIAG, K, K, -CONE, A( K+1 ),
1.6 bertrand 435: $ N+1, A( 0 ), N+1 )
1.1 bertrand 436: CALL ZTRTRI( 'U', DIAG, K, A( K ), N+1, INFO )
437: IF( INFO.GT.0 )
1.6 bertrand 438: $ INFO = INFO + K
1.1 bertrand 439: IF( INFO.GT.0 )
1.6 bertrand 440: $ RETURN
1.1 bertrand 441: CALL ZTRMM( 'R', 'U', 'N', DIAG, K, K, CONE, A( K ), N+1,
1.6 bertrand 442: $ A( 0 ), N+1 )
1.1 bertrand 443: END IF
444: ELSE
445: *
446: * N is even and TRANSR = 'C'
447: *
448: IF( LOWER ) THEN
449: *
450: * SRPA for LOWER, TRANSPOSE and N is even (see paper)
451: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
452: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
453: *
454: CALL ZTRTRI( 'U', DIAG, K, A( K ), K, INFO )
455: IF( INFO.GT.0 )
1.6 bertrand 456: $ RETURN
1.1 bertrand 457: CALL ZTRMM( 'L', 'U', 'N', DIAG, K, K, -CONE, A( K ), K,
1.6 bertrand 458: $ A( K*( K+1 ) ), K )
1.1 bertrand 459: CALL ZTRTRI( 'L', DIAG, K, A( 0 ), K, INFO )
460: IF( INFO.GT.0 )
1.6 bertrand 461: $ INFO = INFO + K
1.1 bertrand 462: IF( INFO.GT.0 )
1.6 bertrand 463: $ RETURN
1.1 bertrand 464: CALL ZTRMM( 'R', 'L', 'C', DIAG, K, K, CONE, A( 0 ), K,
1.6 bertrand 465: $ A( K*( K+1 ) ), K )
1.1 bertrand 466: ELSE
467: *
468: * SRPA for UPPER, TRANSPOSE and N is even (see paper)
469: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
470: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
471: *
472: CALL ZTRTRI( 'U', DIAG, K, A( K*( K+1 ) ), K, INFO )
473: IF( INFO.GT.0 )
1.6 bertrand 474: $ RETURN
1.1 bertrand 475: CALL ZTRMM( 'R', 'U', 'C', DIAG, K, K, -CONE,
1.6 bertrand 476: $ A( K*( K+1 ) ), K, A( 0 ), K )
1.1 bertrand 477: CALL ZTRTRI( 'L', DIAG, K, A( K*K ), K, INFO )
478: IF( INFO.GT.0 )
1.6 bertrand 479: $ INFO = INFO + K
1.1 bertrand 480: IF( INFO.GT.0 )
1.6 bertrand 481: $ RETURN
1.1 bertrand 482: CALL ZTRMM( 'L', 'L', 'N', DIAG, K, K, CONE, A( K*K ), K,
1.6 bertrand 483: $ A( 0 ), K )
1.1 bertrand 484: END IF
485: END IF
486: END IF
487: *
488: RETURN
489: *
490: * End of ZTFTRI
491: *
492: END
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