Annotation of rpl/lapack/lapack/zpftrf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZPFTRF( TRANSR, UPLO, N, A, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2) --
! 4: *
! 5: * -- Contributed by Fred Gustavson of the IBM Watson Research Center --
! 6: * -- November 2008 --
! 7: *
! 8: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 9: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 10: *
! 11: * ..
! 12: * .. Scalar Arguments ..
! 13: CHARACTER TRANSR, UPLO
! 14: INTEGER N, INFO
! 15: * ..
! 16: * .. Array Arguments ..
! 17: COMPLEX*16 A( 0: * )
! 18: *
! 19: * Purpose
! 20: * =======
! 21: *
! 22: * ZPFTRF computes the Cholesky factorization of a complex Hermitian
! 23: * positive definite matrix A.
! 24: *
! 25: * The factorization has the form
! 26: * A = U**H * U, if UPLO = 'U', or
! 27: * A = L * L**H, if UPLO = 'L',
! 28: * where U is an upper triangular matrix and L is lower triangular.
! 29: *
! 30: * This is the block version of the algorithm, calling Level 3 BLAS.
! 31: *
! 32: * Arguments
! 33: * =========
! 34: *
! 35: * TRANSR (input) CHARACTER
! 36: * = 'N': The Normal TRANSR of RFP A is stored;
! 37: * = 'C': The Conjugate-transpose TRANSR of RFP A is stored.
! 38: *
! 39: * UPLO (input) CHARACTER
! 40: * = 'U': Upper triangle of RFP A is stored;
! 41: * = 'L': Lower triangle of RFP A is stored.
! 42: *
! 43: * N (input) INTEGER
! 44: * The order of the matrix A. N >= 0.
! 45: *
! 46: * A (input/output) COMPLEX array, dimension ( N*(N+1)/2 );
! 47: * On entry, the Hermitian matrix A in RFP format. RFP format is
! 48: * described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'
! 49: * then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
! 50: * (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is
! 51: * the Conjugate-transpose of RFP A as defined when
! 52: * TRANSR = 'N'. The contents of RFP A are defined by UPLO as
! 53: * follows: If UPLO = 'U' the RFP A contains the nt elements of
! 54: * upper packed A. If UPLO = 'L' the RFP A contains the elements
! 55: * of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR =
! 56: * 'C'. When TRANSR is 'N' the LDA is N+1 when N is even and N
! 57: * is odd. See the Note below for more details.
! 58: *
! 59: * On exit, if INFO = 0, the factor U or L from the Cholesky
! 60: * factorization RFP A = U**H*U or RFP A = L*L**H.
! 61: *
! 62: * INFO (output) INTEGER
! 63: * = 0: successful exit
! 64: * < 0: if INFO = -i, the i-th argument had an illegal value
! 65: * > 0: if INFO = i, the leading minor of order i is not
! 66: * positive definite, and the factorization could not be
! 67: * completed.
! 68: *
! 69: * Further Notes on RFP Format:
! 70: * ============================
! 71: *
! 72: * We first consider Standard Packed Format when N is even.
! 73: * We give an example where N = 6.
! 74: *
! 75: * AP is Upper AP is Lower
! 76: *
! 77: * 00 01 02 03 04 05 00
! 78: * 11 12 13 14 15 10 11
! 79: * 22 23 24 25 20 21 22
! 80: * 33 34 35 30 31 32 33
! 81: * 44 45 40 41 42 43 44
! 82: * 55 50 51 52 53 54 55
! 83: *
! 84: *
! 85: * Let TRANSR = 'N'. RFP holds AP as follows:
! 86: * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
! 87: * three columns of AP upper. The lower triangle A(4:6,0:2) consists of
! 88: * conjugate-transpose of the first three columns of AP upper.
! 89: * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
! 90: * three columns of AP lower. The upper triangle A(0:2,0:2) consists of
! 91: * conjugate-transpose of the last three columns of AP lower.
! 92: * To denote conjugate we place -- above the element. This covers the
! 93: * case N even and TRANSR = 'N'.
! 94: *
! 95: * RFP A RFP A
! 96: *
! 97: * -- -- --
! 98: * 03 04 05 33 43 53
! 99: * -- --
! 100: * 13 14 15 00 44 54
! 101: * --
! 102: * 23 24 25 10 11 55
! 103: *
! 104: * 33 34 35 20 21 22
! 105: * --
! 106: * 00 44 45 30 31 32
! 107: * -- --
! 108: * 01 11 55 40 41 42
! 109: * -- -- --
! 110: * 02 12 22 50 51 52
! 111: *
! 112: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
! 113: * transpose of RFP A above. One therefore gets:
! 114: *
! 115: *
! 116: * RFP A RFP A
! 117: *
! 118: * -- -- -- -- -- -- -- -- -- --
! 119: * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
! 120: * -- -- -- -- -- -- -- -- -- --
! 121: * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
! 122: * -- -- -- -- -- -- -- -- -- --
! 123: * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
! 124: *
! 125: *
! 126: * We next consider Standard Packed Format when N is odd.
! 127: * We give an example where N = 5.
! 128: *
! 129: * AP is Upper AP is Lower
! 130: *
! 131: * 00 01 02 03 04 00
! 132: * 11 12 13 14 10 11
! 133: * 22 23 24 20 21 22
! 134: * 33 34 30 31 32 33
! 135: * 44 40 41 42 43 44
! 136: *
! 137: *
! 138: * Let TRANSR = 'N'. RFP holds AP as follows:
! 139: * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
! 140: * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
! 141: * conjugate-transpose of the first two columns of AP upper.
! 142: * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
! 143: * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
! 144: * conjugate-transpose of the last two columns of AP lower.
! 145: * To denote conjugate we place -- above the element. This covers the
! 146: * case N odd and TRANSR = 'N'.
! 147: *
! 148: * RFP A RFP A
! 149: *
! 150: * -- --
! 151: * 02 03 04 00 33 43
! 152: * --
! 153: * 12 13 14 10 11 44
! 154: *
! 155: * 22 23 24 20 21 22
! 156: * --
! 157: * 00 33 34 30 31 32
! 158: * -- --
! 159: * 01 11 44 40 41 42
! 160: *
! 161: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
! 162: * transpose of RFP A above. One therefore gets:
! 163: *
! 164: *
! 165: * RFP A RFP A
! 166: *
! 167: * -- -- -- -- -- -- -- -- --
! 168: * 02 12 22 00 01 00 10 20 30 40 50
! 169: * -- -- -- -- -- -- -- -- --
! 170: * 03 13 23 33 11 33 11 21 31 41 51
! 171: * -- -- -- -- -- -- -- -- --
! 172: * 04 14 24 34 44 43 44 22 32 42 52
! 173: *
! 174: * =====================================================================
! 175: *
! 176: * .. Parameters ..
! 177: DOUBLE PRECISION ONE
! 178: COMPLEX*16 CONE
! 179: PARAMETER ( ONE = 1.0D+0, CONE = ( 1.0D+0, 0.0D+0 ) )
! 180: * ..
! 181: * .. Local Scalars ..
! 182: LOGICAL LOWER, NISODD, NORMALTRANSR
! 183: INTEGER N1, N2, K
! 184: * ..
! 185: * .. External Functions ..
! 186: LOGICAL LSAME
! 187: EXTERNAL LSAME
! 188: * ..
! 189: * .. External Subroutines ..
! 190: EXTERNAL XERBLA, ZHERK, ZPOTRF, ZTRSM
! 191: * ..
! 192: * .. Intrinsic Functions ..
! 193: INTRINSIC MOD
! 194: * ..
! 195: * .. Executable Statements ..
! 196: *
! 197: * Test the input parameters.
! 198: *
! 199: INFO = 0
! 200: NORMALTRANSR = LSAME( TRANSR, 'N' )
! 201: LOWER = LSAME( UPLO, 'L' )
! 202: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
! 203: INFO = -1
! 204: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
! 205: INFO = -2
! 206: ELSE IF( N.LT.0 ) THEN
! 207: INFO = -3
! 208: END IF
! 209: IF( INFO.NE.0 ) THEN
! 210: CALL XERBLA( 'ZPFTRF', -INFO )
! 211: RETURN
! 212: END IF
! 213: *
! 214: * Quick return if possible
! 215: *
! 216: IF( N.EQ.0 )
! 217: + RETURN
! 218: *
! 219: * If N is odd, set NISODD = .TRUE.
! 220: * If N is even, set K = N/2 and NISODD = .FALSE.
! 221: *
! 222: IF( MOD( N, 2 ).EQ.0 ) THEN
! 223: K = N / 2
! 224: NISODD = .FALSE.
! 225: ELSE
! 226: NISODD = .TRUE.
! 227: END IF
! 228: *
! 229: * Set N1 and N2 depending on LOWER
! 230: *
! 231: IF( LOWER ) THEN
! 232: N2 = N / 2
! 233: N1 = N - N2
! 234: ELSE
! 235: N1 = N / 2
! 236: N2 = N - N1
! 237: END IF
! 238: *
! 239: * start execution: there are eight cases
! 240: *
! 241: IF( NISODD ) THEN
! 242: *
! 243: * N is odd
! 244: *
! 245: IF( NORMALTRANSR ) THEN
! 246: *
! 247: * N is odd and TRANSR = 'N'
! 248: *
! 249: IF( LOWER ) THEN
! 250: *
! 251: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
! 252: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
! 253: * T1 -> a(0), T2 -> a(n), S -> a(n1)
! 254: *
! 255: CALL ZPOTRF( 'L', N1, A( 0 ), N, INFO )
! 256: IF( INFO.GT.0 )
! 257: + RETURN
! 258: CALL ZTRSM( 'R', 'L', 'C', 'N', N2, N1, CONE, A( 0 ), N,
! 259: + A( N1 ), N )
! 260: CALL ZHERK( 'U', 'N', N2, N1, -ONE, A( N1 ), N, ONE,
! 261: + A( N ), N )
! 262: CALL ZPOTRF( 'U', N2, A( N ), N, INFO )
! 263: IF( INFO.GT.0 )
! 264: + INFO = INFO + N1
! 265: *
! 266: ELSE
! 267: *
! 268: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
! 269: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
! 270: * T1 -> a(n2), T2 -> a(n1), S -> a(0)
! 271: *
! 272: CALL ZPOTRF( 'L', N1, A( N2 ), N, INFO )
! 273: IF( INFO.GT.0 )
! 274: + RETURN
! 275: CALL ZTRSM( 'L', 'L', 'N', 'N', N1, N2, CONE, A( N2 ), N,
! 276: + A( 0 ), N )
! 277: CALL ZHERK( 'U', 'C', N2, N1, -ONE, A( 0 ), N, ONE,
! 278: + A( N1 ), N )
! 279: CALL ZPOTRF( 'U', N2, A( N1 ), N, INFO )
! 280: IF( INFO.GT.0 )
! 281: + INFO = INFO + N1
! 282: *
! 283: END IF
! 284: *
! 285: ELSE
! 286: *
! 287: * N is odd and TRANSR = 'C'
! 288: *
! 289: IF( LOWER ) THEN
! 290: *
! 291: * SRPA for LOWER, TRANSPOSE and N is odd
! 292: * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
! 293: * T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
! 294: *
! 295: CALL ZPOTRF( 'U', N1, A( 0 ), N1, INFO )
! 296: IF( INFO.GT.0 )
! 297: + RETURN
! 298: CALL ZTRSM( 'L', 'U', 'C', 'N', N1, N2, CONE, A( 0 ), N1,
! 299: + A( N1*N1 ), N1 )
! 300: CALL ZHERK( 'L', 'C', N2, N1, -ONE, A( N1*N1 ), N1, ONE,
! 301: + A( 1 ), N1 )
! 302: CALL ZPOTRF( 'L', N2, A( 1 ), N1, INFO )
! 303: IF( INFO.GT.0 )
! 304: + INFO = INFO + N1
! 305: *
! 306: ELSE
! 307: *
! 308: * SRPA for UPPER, TRANSPOSE and N is odd
! 309: * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
! 310: * T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
! 311: *
! 312: CALL ZPOTRF( 'U', N1, A( N2*N2 ), N2, INFO )
! 313: IF( INFO.GT.0 )
! 314: + RETURN
! 315: CALL ZTRSM( 'R', 'U', 'N', 'N', N2, N1, CONE, A( N2*N2 ),
! 316: + N2, A( 0 ), N2 )
! 317: CALL ZHERK( 'L', 'N', N2, N1, -ONE, A( 0 ), N2, ONE,
! 318: + A( N1*N2 ), N2 )
! 319: CALL ZPOTRF( 'L', N2, A( N1*N2 ), N2, INFO )
! 320: IF( INFO.GT.0 )
! 321: + INFO = INFO + N1
! 322: *
! 323: END IF
! 324: *
! 325: END IF
! 326: *
! 327: ELSE
! 328: *
! 329: * N is even
! 330: *
! 331: IF( NORMALTRANSR ) THEN
! 332: *
! 333: * N is even and TRANSR = 'N'
! 334: *
! 335: IF( LOWER ) THEN
! 336: *
! 337: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
! 338: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
! 339: * T1 -> a(1), T2 -> a(0), S -> a(k+1)
! 340: *
! 341: CALL ZPOTRF( 'L', K, A( 1 ), N+1, INFO )
! 342: IF( INFO.GT.0 )
! 343: + RETURN
! 344: CALL ZTRSM( 'R', 'L', 'C', 'N', K, K, CONE, A( 1 ), N+1,
! 345: + A( K+1 ), N+1 )
! 346: CALL ZHERK( 'U', 'N', K, K, -ONE, A( K+1 ), N+1, ONE,
! 347: + A( 0 ), N+1 )
! 348: CALL ZPOTRF( 'U', K, A( 0 ), N+1, INFO )
! 349: IF( INFO.GT.0 )
! 350: + INFO = INFO + K
! 351: *
! 352: ELSE
! 353: *
! 354: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
! 355: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
! 356: * T1 -> a(k+1), T2 -> a(k), S -> a(0)
! 357: *
! 358: CALL ZPOTRF( 'L', K, A( K+1 ), N+1, INFO )
! 359: IF( INFO.GT.0 )
! 360: + RETURN
! 361: CALL ZTRSM( 'L', 'L', 'N', 'N', K, K, CONE, A( K+1 ),
! 362: + N+1, A( 0 ), N+1 )
! 363: CALL ZHERK( 'U', 'C', K, K, -ONE, A( 0 ), N+1, ONE,
! 364: + A( K ), N+1 )
! 365: CALL ZPOTRF( 'U', K, A( K ), N+1, INFO )
! 366: IF( INFO.GT.0 )
! 367: + INFO = INFO + K
! 368: *
! 369: END IF
! 370: *
! 371: ELSE
! 372: *
! 373: * N is even and TRANSR = 'C'
! 374: *
! 375: IF( LOWER ) THEN
! 376: *
! 377: * SRPA for LOWER, TRANSPOSE and N is even (see paper)
! 378: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
! 379: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
! 380: *
! 381: CALL ZPOTRF( 'U', K, A( 0+K ), K, INFO )
! 382: IF( INFO.GT.0 )
! 383: + RETURN
! 384: CALL ZTRSM( 'L', 'U', 'C', 'N', K, K, CONE, A( K ), N1,
! 385: + A( K*( K+1 ) ), K )
! 386: CALL ZHERK( 'L', 'C', K, K, -ONE, A( K*( K+1 ) ), K, ONE,
! 387: + A( 0 ), K )
! 388: CALL ZPOTRF( 'L', K, A( 0 ), K, INFO )
! 389: IF( INFO.GT.0 )
! 390: + INFO = INFO + K
! 391: *
! 392: ELSE
! 393: *
! 394: * SRPA for UPPER, TRANSPOSE and N is even (see paper)
! 395: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
! 396: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
! 397: *
! 398: CALL ZPOTRF( 'U', K, A( K*( K+1 ) ), K, INFO )
! 399: IF( INFO.GT.0 )
! 400: + RETURN
! 401: CALL ZTRSM( 'R', 'U', 'N', 'N', K, K, CONE,
! 402: + A( K*( K+1 ) ), K, A( 0 ), K )
! 403: CALL ZHERK( 'L', 'N', K, K, -ONE, A( 0 ), K, ONE,
! 404: + A( K*K ), K )
! 405: CALL ZPOTRF( 'L', K, A( K*K ), K, INFO )
! 406: IF( INFO.GT.0 )
! 407: + INFO = INFO + K
! 408: *
! 409: END IF
! 410: *
! 411: END IF
! 412: *
! 413: END IF
! 414: *
! 415: RETURN
! 416: *
! 417: * End of ZPFTRF
! 418: *
! 419: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zpftrf.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack