Annotation of rpl/lapack/lapack/zsyconvf.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b ZSYCONVF
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZSYCONVF + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsyconvf.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsyconvf.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsyconvf.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZSYCONVF( UPLO, WAY, N, A, LDA, IPIV, E, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER UPLO, WAY
! 25: * INTEGER INFO, LDA, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * INTEGER IPIV( * )
! 29: * COMPLEX*16 A( LDA, * ), E( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *> If parameter WAY = 'C':
! 38: *> ZSYCONVF converts the factorization output format used in
! 39: *> ZSYTRF provided on entry in parameter A into the factorization
! 40: *> output format used in ZSYTRF_RK (or ZSYTRF_BK) that is stored
! 41: *> on exit in parameters A and E. It also coverts in place details of
! 42: *> the intechanges stored in IPIV from the format used in ZSYTRF into
! 43: *> the format used in ZSYTRF_RK (or ZSYTRF_BK).
! 44: *>
! 45: *> If parameter WAY = 'R':
! 46: *> ZSYCONVF performs the conversion in reverse direction, i.e.
! 47: *> converts the factorization output format used in ZSYTRF_RK
! 48: *> (or ZSYTRF_BK) provided on entry in parametes A and E into
! 49: *> the factorization output format used in ZSYTRF that is stored
! 50: *> on exit in parameter A. It also coverts in place details of
! 51: *> the intechanges stored in IPIV from the format used in ZSYTRF_RK
! 52: *> (or ZSYTRF_BK) into the format used in ZSYTRF.
! 53: *>
! 54: *> ZSYCONVF can also convert in Hermitian matrix case, i.e. between
! 55: *> formats used in ZHETRF and ZHETRF_RK (or ZHETRF_BK).
! 56: *> \endverbatim
! 57: *
! 58: * Arguments:
! 59: * ==========
! 60: *
! 61: *> \param[in] UPLO
! 62: *> \verbatim
! 63: *> UPLO is CHARACTER*1
! 64: *> Specifies whether the details of the factorization are
! 65: *> stored as an upper or lower triangular matrix A.
! 66: *> = 'U': Upper triangular
! 67: *> = 'L': Lower triangular
! 68: *> \endverbatim
! 69: *>
! 70: *> \param[in] WAY
! 71: *> \verbatim
! 72: *> WAY is CHARACTER*1
! 73: *> = 'C': Convert
! 74: *> = 'R': Revert
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[in] N
! 78: *> \verbatim
! 79: *> N is INTEGER
! 80: *> The order of the matrix A. N >= 0.
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[in,out] A
! 84: *> \verbatim
! 85: *> A is COMPLEX*16 array, dimension (LDA,N)
! 86: *>
! 87: *> 1) If WAY ='C':
! 88: *>
! 89: *> On entry, contains factorization details in format used in
! 90: *> ZSYTRF:
! 91: *> a) all elements of the symmetric block diagonal
! 92: *> matrix D on the diagonal of A and on superdiagonal
! 93: *> (or subdiagonal) of A, and
! 94: *> b) If UPLO = 'U': multipliers used to obtain factor U
! 95: *> in the superdiagonal part of A.
! 96: *> If UPLO = 'L': multipliers used to obtain factor L
! 97: *> in the superdiagonal part of A.
! 98: *>
! 99: *> On exit, contains factorization details in format used in
! 100: *> ZSYTRF_RK or ZSYTRF_BK:
! 101: *> a) ONLY diagonal elements of the symmetric block diagonal
! 102: *> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
! 103: *> (superdiagonal (or subdiagonal) elements of D
! 104: *> are stored on exit in array E), and
! 105: *> b) If UPLO = 'U': factor U in the superdiagonal part of A.
! 106: *> If UPLO = 'L': factor L in the subdiagonal part of A.
! 107: *>
! 108: *> 2) If WAY = 'R':
! 109: *>
! 110: *> On entry, contains factorization details in format used in
! 111: *> ZSYTRF_RK or ZSYTRF_BK:
! 112: *> a) ONLY diagonal elements of the symmetric block diagonal
! 113: *> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
! 114: *> (superdiagonal (or subdiagonal) elements of D
! 115: *> are stored on exit in array E), and
! 116: *> b) If UPLO = 'U': factor U in the superdiagonal part of A.
! 117: *> If UPLO = 'L': factor L in the subdiagonal part of A.
! 118: *>
! 119: *> On exit, contains factorization details in format used in
! 120: *> ZSYTRF:
! 121: *> a) all elements of the symmetric block diagonal
! 122: *> matrix D on the diagonal of A and on superdiagonal
! 123: *> (or subdiagonal) of A, and
! 124: *> b) If UPLO = 'U': multipliers used to obtain factor U
! 125: *> in the superdiagonal part of A.
! 126: *> If UPLO = 'L': multipliers used to obtain factor L
! 127: *> in the superdiagonal part of A.
! 128: *> \endverbatim
! 129: *>
! 130: *> \param[in] LDA
! 131: *> \verbatim
! 132: *> LDA is INTEGER
! 133: *> The leading dimension of the array A. LDA >= max(1,N).
! 134: *> \endverbatim
! 135: *>
! 136: *> \param[in,out] E
! 137: *> \verbatim
! 138: *> E is COMPLEX*16 array, dimension (N)
! 139: *>
! 140: *> 1) If WAY ='C':
! 141: *>
! 142: *> On entry, just a workspace.
! 143: *>
! 144: *> On exit, contains the superdiagonal (or subdiagonal)
! 145: *> elements of the symmetric block diagonal matrix D
! 146: *> with 1-by-1 or 2-by-2 diagonal blocks, where
! 147: *> If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0;
! 148: *> If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.
! 149: *>
! 150: *> 2) If WAY = 'R':
! 151: *>
! 152: *> On entry, contains the superdiagonal (or subdiagonal)
! 153: *> elements of the symmetric block diagonal matrix D
! 154: *> with 1-by-1 or 2-by-2 diagonal blocks, where
! 155: *> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
! 156: *> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
! 157: *>
! 158: *> On exit, is not changed
! 159: *> \endverbatim
! 160: *.
! 161: *> \param[in,out] IPIV
! 162: *> \verbatim
! 163: *> IPIV is INTEGER array, dimension (N)
! 164: *>
! 165: *> 1) If WAY ='C':
! 166: *> On entry, details of the interchanges and the block
! 167: *> structure of D in the format used in ZSYTRF.
! 168: *> On exit, details of the interchanges and the block
! 169: *> structure of D in the format used in ZSYTRF_RK
! 170: *> ( or ZSYTRF_BK).
! 171: *>
! 172: *> 1) If WAY ='R':
! 173: *> On entry, details of the interchanges and the block
! 174: *> structure of D in the format used in ZSYTRF_RK
! 175: *> ( or ZSYTRF_BK).
! 176: *> On exit, details of the interchanges and the block
! 177: *> structure of D in the format used in ZSYTRF.
! 178: *> \endverbatim
! 179: *>
! 180: *> \param[out] INFO
! 181: *> \verbatim
! 182: *> INFO is INTEGER
! 183: *> = 0: successful exit
! 184: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 185: *> \endverbatim
! 186: *
! 187: * Authors:
! 188: * ========
! 189: *
! 190: *> \author Univ. of Tennessee
! 191: *> \author Univ. of California Berkeley
! 192: *> \author Univ. of Colorado Denver
! 193: *> \author NAG Ltd.
! 194: *
! 195: *> \date December 2016
! 196: *
! 197: *> \ingroup complex16SYcomputational
! 198: *
! 199: *> \par Contributors:
! 200: * ==================
! 201: *>
! 202: *> \verbatim
! 203: *>
! 204: *> December 2016, Igor Kozachenko,
! 205: *> Computer Science Division,
! 206: *> University of California, Berkeley
! 207: *>
! 208: *> \endverbatim
! 209: * =====================================================================
! 210: SUBROUTINE ZSYCONVF( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
! 211: *
! 212: * -- LAPACK computational routine (version 3.7.0) --
! 213: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 214: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 215: * December 2016
! 216: *
! 217: * .. Scalar Arguments ..
! 218: CHARACTER UPLO, WAY
! 219: INTEGER INFO, LDA, N
! 220: * ..
! 221: * .. Array Arguments ..
! 222: INTEGER IPIV( * )
! 223: COMPLEX*16 A( LDA, * ), E( * )
! 224: * ..
! 225: *
! 226: * =====================================================================
! 227: *
! 228: * .. Parameters ..
! 229: COMPLEX*16 ZERO
! 230: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
! 231: * ..
! 232: * .. External Functions ..
! 233: LOGICAL LSAME
! 234: EXTERNAL LSAME
! 235: *
! 236: * .. External Subroutines ..
! 237: EXTERNAL ZSWAP, XERBLA
! 238: * .. Local Scalars ..
! 239: LOGICAL UPPER, CONVERT
! 240: INTEGER I, IP
! 241: * ..
! 242: * .. Executable Statements ..
! 243: *
! 244: INFO = 0
! 245: UPPER = LSAME( UPLO, 'U' )
! 246: CONVERT = LSAME( WAY, 'C' )
! 247: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 248: INFO = -1
! 249: ELSE IF( .NOT.CONVERT .AND. .NOT.LSAME( WAY, 'R' ) ) THEN
! 250: INFO = -2
! 251: ELSE IF( N.LT.0 ) THEN
! 252: INFO = -3
! 253: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 254: INFO = -5
! 255:
! 256: END IF
! 257: IF( INFO.NE.0 ) THEN
! 258: CALL XERBLA( 'ZSYCONVF', -INFO )
! 259: RETURN
! 260: END IF
! 261: *
! 262: * Quick return if possible
! 263: *
! 264: IF( N.EQ.0 )
! 265: $ RETURN
! 266: *
! 267: IF( UPPER ) THEN
! 268: *
! 269: * Begin A is UPPER
! 270: *
! 271: IF ( CONVERT ) THEN
! 272: *
! 273: * Convert A (A is upper)
! 274: *
! 275: *
! 276: * Convert VALUE
! 277: *
! 278: * Assign superdiagonal entries of D to array E and zero out
! 279: * corresponding entries in input storage A
! 280: *
! 281: I = N
! 282: E( 1 ) = ZERO
! 283: DO WHILE ( I.GT.1 )
! 284: IF( IPIV( I ).LT.0 ) THEN
! 285: E( I ) = A( I-1, I )
! 286: E( I-1 ) = ZERO
! 287: A( I-1, I ) = ZERO
! 288: I = I - 1
! 289: ELSE
! 290: E( I ) = ZERO
! 291: END IF
! 292: I = I - 1
! 293: END DO
! 294: *
! 295: * Convert PERMUTATIONS and IPIV
! 296: *
! 297: * Apply permutaions to submatrices of upper part of A
! 298: * in factorization order where i decreases from N to 1
! 299: *
! 300: I = N
! 301: DO WHILE ( I.GE.1 )
! 302: IF( IPIV( I ).GT.0 ) THEN
! 303: *
! 304: * 1-by-1 pivot interchange
! 305: *
! 306: * Swap rows i and IPIV(i) in A(1:i,N-i:N)
! 307: *
! 308: IP = IPIV( I )
! 309: IF( I.LT.N ) THEN
! 310: IF( IP.NE.I ) THEN
! 311: CALL ZSWAP( N-I, A( I, I+1 ), LDA,
! 312: $ A( IP, I+1 ), LDA )
! 313: END IF
! 314: END IF
! 315: *
! 316: ELSE
! 317: *
! 318: * 2-by-2 pivot interchange
! 319: *
! 320: * Swap rows i-1 and IPIV(i) in A(1:i,N-i:N)
! 321: *
! 322: IP = -IPIV( I )
! 323: IF( I.LT.N ) THEN
! 324: IF( IP.NE.(I-1) ) THEN
! 325: CALL ZSWAP( N-I, A( I-1, I+1 ), LDA,
! 326: $ A( IP, I+1 ), LDA )
! 327: END IF
! 328: END IF
! 329: *
! 330: * Convert IPIV
! 331: * There is no interchnge of rows i and and IPIV(i),
! 332: * so this should be reflected in IPIV format for
! 333: * *SYTRF_RK ( or *SYTRF_BK)
! 334: *
! 335: IPIV( I ) = I
! 336: *
! 337: I = I - 1
! 338: *
! 339: END IF
! 340: I = I - 1
! 341: END DO
! 342: *
! 343: ELSE
! 344: *
! 345: * Revert A (A is upper)
! 346: *
! 347: *
! 348: * Revert PERMUTATIONS and IPIV
! 349: *
! 350: * Apply permutaions to submatrices of upper part of A
! 351: * in reverse factorization order where i increases from 1 to N
! 352: *
! 353: I = 1
! 354: DO WHILE ( I.LE.N )
! 355: IF( IPIV( I ).GT.0 ) THEN
! 356: *
! 357: * 1-by-1 pivot interchange
! 358: *
! 359: * Swap rows i and IPIV(i) in A(1:i,N-i:N)
! 360: *
! 361: IP = IPIV( I )
! 362: IF( I.LT.N ) THEN
! 363: IF( IP.NE.I ) THEN
! 364: CALL ZSWAP( N-I, A( IP, I+1 ), LDA,
! 365: $ A( I, I+1 ), LDA )
! 366: END IF
! 367: END IF
! 368: *
! 369: ELSE
! 370: *
! 371: * 2-by-2 pivot interchange
! 372: *
! 373: * Swap rows i-1 and IPIV(i) in A(1:i,N-i:N)
! 374: *
! 375: I = I + 1
! 376: IP = -IPIV( I )
! 377: IF( I.LT.N ) THEN
! 378: IF( IP.NE.(I-1) ) THEN
! 379: CALL ZSWAP( N-I, A( IP, I+1 ), LDA,
! 380: $ A( I-1, I+1 ), LDA )
! 381: END IF
! 382: END IF
! 383: *
! 384: * Convert IPIV
! 385: * There is one interchange of rows i-1 and IPIV(i-1),
! 386: * so this should be recorded in two consecutive entries
! 387: * in IPIV format for *SYTRF
! 388: *
! 389: IPIV( I ) = IPIV( I-1 )
! 390: *
! 391: END IF
! 392: I = I + 1
! 393: END DO
! 394: *
! 395: * Revert VALUE
! 396: * Assign superdiagonal entries of D from array E to
! 397: * superdiagonal entries of A.
! 398: *
! 399: I = N
! 400: DO WHILE ( I.GT.1 )
! 401: IF( IPIV( I ).LT.0 ) THEN
! 402: A( I-1, I ) = E( I )
! 403: I = I - 1
! 404: END IF
! 405: I = I - 1
! 406: END DO
! 407: *
! 408: * End A is UPPER
! 409: *
! 410: END IF
! 411: *
! 412: ELSE
! 413: *
! 414: * Begin A is LOWER
! 415: *
! 416: IF ( CONVERT ) THEN
! 417: *
! 418: * Convert A (A is lower)
! 419: *
! 420: *
! 421: * Convert VALUE
! 422: * Assign subdiagonal entries of D to array E and zero out
! 423: * corresponding entries in input storage A
! 424: *
! 425: I = 1
! 426: E( N ) = ZERO
! 427: DO WHILE ( I.LE.N )
! 428: IF( I.LT.N .AND. IPIV(I).LT.0 ) THEN
! 429: E( I ) = A( I+1, I )
! 430: E( I+1 ) = ZERO
! 431: A( I+1, I ) = ZERO
! 432: I = I + 1
! 433: ELSE
! 434: E( I ) = ZERO
! 435: END IF
! 436: I = I + 1
! 437: END DO
! 438: *
! 439: * Convert PERMUTATIONS and IPIV
! 440: *
! 441: * Apply permutaions to submatrices of lower part of A
! 442: * in factorization order where k increases from 1 to N
! 443: *
! 444: I = 1
! 445: DO WHILE ( I.LE.N )
! 446: IF( IPIV( I ).GT.0 ) THEN
! 447: *
! 448: * 1-by-1 pivot interchange
! 449: *
! 450: * Swap rows i and IPIV(i) in A(i:N,1:i-1)
! 451: *
! 452: IP = IPIV( I )
! 453: IF ( I.GT.1 ) THEN
! 454: IF( IP.NE.I ) THEN
! 455: CALL ZSWAP( I-1, A( I, 1 ), LDA,
! 456: $ A( IP, 1 ), LDA )
! 457: END IF
! 458: END IF
! 459: *
! 460: ELSE
! 461: *
! 462: * 2-by-2 pivot interchange
! 463: *
! 464: * Swap rows i+1 and IPIV(i) in A(i:N,1:i-1)
! 465: *
! 466: IP = -IPIV( I )
! 467: IF ( I.GT.1 ) THEN
! 468: IF( IP.NE.(I+1) ) THEN
! 469: CALL ZSWAP( I-1, A( I+1, 1 ), LDA,
! 470: $ A( IP, 1 ), LDA )
! 471: END IF
! 472: END IF
! 473: *
! 474: * Convert IPIV
! 475: * There is no interchnge of rows i and and IPIV(i),
! 476: * so this should be reflected in IPIV format for
! 477: * *SYTRF_RK ( or *SYTRF_BK)
! 478: *
! 479: IPIV( I ) = I
! 480: *
! 481: I = I + 1
! 482: *
! 483: END IF
! 484: I = I + 1
! 485: END DO
! 486: *
! 487: ELSE
! 488: *
! 489: * Revert A (A is lower)
! 490: *
! 491: *
! 492: * Revert PERMUTATIONS and IPIV
! 493: *
! 494: * Apply permutaions to submatrices of lower part of A
! 495: * in reverse factorization order where i decreases from N to 1
! 496: *
! 497: I = N
! 498: DO WHILE ( I.GE.1 )
! 499: IF( IPIV( I ).GT.0 ) THEN
! 500: *
! 501: * 1-by-1 pivot interchange
! 502: *
! 503: * Swap rows i and IPIV(i) in A(i:N,1:i-1)
! 504: *
! 505: IP = IPIV( I )
! 506: IF ( I.GT.1 ) THEN
! 507: IF( IP.NE.I ) THEN
! 508: CALL ZSWAP( I-1, A( IP, 1 ), LDA,
! 509: $ A( I, 1 ), LDA )
! 510: END IF
! 511: END IF
! 512: *
! 513: ELSE
! 514: *
! 515: * 2-by-2 pivot interchange
! 516: *
! 517: * Swap rows i+1 and IPIV(i) in A(i:N,1:i-1)
! 518: *
! 519: I = I - 1
! 520: IP = -IPIV( I )
! 521: IF ( I.GT.1 ) THEN
! 522: IF( IP.NE.(I+1) ) THEN
! 523: CALL ZSWAP( I-1, A( IP, 1 ), LDA,
! 524: $ A( I+1, 1 ), LDA )
! 525: END IF
! 526: END IF
! 527: *
! 528: * Convert IPIV
! 529: * There is one interchange of rows i+1 and IPIV(i+1),
! 530: * so this should be recorded in consecutive entries
! 531: * in IPIV format for *SYTRF
! 532: *
! 533: IPIV( I ) = IPIV( I+1 )
! 534: *
! 535: END IF
! 536: I = I - 1
! 537: END DO
! 538: *
! 539: * Revert VALUE
! 540: * Assign subdiagonal entries of D from array E to
! 541: * subgiagonal entries of A.
! 542: *
! 543: I = 1
! 544: DO WHILE ( I.LE.N-1 )
! 545: IF( IPIV( I ).LT.0 ) THEN
! 546: A( I + 1, I ) = E( I )
! 547: I = I + 1
! 548: END IF
! 549: I = I + 1
! 550: END DO
! 551: *
! 552: END IF
! 553: *
! 554: * End A is LOWER
! 555: *
! 556: END IF
! 557:
! 558: RETURN
! 559: *
! 560: * End of ZSYCONVF
! 561: *
! 562: END
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