Annotation of rpl/lapack/lapack/dpftrf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DPFTRF( TRANSR, UPLO, N, A, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2.2) --
! 4: *
! 5: * -- Contributed by Fred Gustavson of the IBM Watson Research Center --
! 6: * -- June 2010 --
! 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: DOUBLE PRECISION A( 0: * )
! 18: *
! 19: * Purpose
! 20: * =======
! 21: *
! 22: * DPFTRF computes the Cholesky factorization of a real symmetric
! 23: * positive definite matrix A.
! 24: *
! 25: * The factorization has the form
! 26: * A = U**T * U, if UPLO = 'U', or
! 27: * A = L * L**T, 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: * = 'T': The 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) DOUBLE PRECISION array, dimension ( N*(N+1)/2 );
! 47: * On entry, the symmetric 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 = 'T' then RFP is
! 51: * the 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: * 'T'. 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**T*U or RFP A = L*L**T.
! 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 Details
! 70: * ===============
! 71: *
! 72: * We first consider Rectangular Full Packed (RFP) Format when N is
! 73: * even. 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: * the 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: * the transpose of the last three columns of AP lower.
! 92: * This covers the case N even and TRANSR = 'N'.
! 93: *
! 94: * RFP A RFP A
! 95: *
! 96: * 03 04 05 33 43 53
! 97: * 13 14 15 00 44 54
! 98: * 23 24 25 10 11 55
! 99: * 33 34 35 20 21 22
! 100: * 00 44 45 30 31 32
! 101: * 01 11 55 40 41 42
! 102: * 02 12 22 50 51 52
! 103: *
! 104: * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
! 105: * transpose of RFP A above. One therefore gets:
! 106: *
! 107: *
! 108: * RFP A RFP A
! 109: *
! 110: * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
! 111: * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
! 112: * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
! 113: *
! 114: *
! 115: * We then consider Rectangular Full Packed (RFP) Format when N is
! 116: * odd. We give an example where N = 5.
! 117: *
! 118: * AP is Upper AP is Lower
! 119: *
! 120: * 00 01 02 03 04 00
! 121: * 11 12 13 14 10 11
! 122: * 22 23 24 20 21 22
! 123: * 33 34 30 31 32 33
! 124: * 44 40 41 42 43 44
! 125: *
! 126: *
! 127: * Let TRANSR = 'N'. RFP holds AP as follows:
! 128: * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
! 129: * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
! 130: * the transpose of the first two columns of AP upper.
! 131: * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
! 132: * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
! 133: * the transpose of the last two columns of AP lower.
! 134: * This covers the case N odd and TRANSR = 'N'.
! 135: *
! 136: * RFP A RFP A
! 137: *
! 138: * 02 03 04 00 33 43
! 139: * 12 13 14 10 11 44
! 140: * 22 23 24 20 21 22
! 141: * 00 33 34 30 31 32
! 142: * 01 11 44 40 41 42
! 143: *
! 144: * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
! 145: * transpose of RFP A above. One therefore gets:
! 146: *
! 147: * RFP A RFP A
! 148: *
! 149: * 02 12 22 00 01 00 10 20 30 40 50
! 150: * 03 13 23 33 11 33 11 21 31 41 51
! 151: * 04 14 24 34 44 43 44 22 32 42 52
! 152: *
! 153: * =====================================================================
! 154: *
! 155: * .. Parameters ..
! 156: DOUBLE PRECISION ONE
! 157: PARAMETER ( ONE = 1.0D+0 )
! 158: * ..
! 159: * .. Local Scalars ..
! 160: LOGICAL LOWER, NISODD, NORMALTRANSR
! 161: INTEGER N1, N2, K
! 162: * ..
! 163: * .. External Functions ..
! 164: LOGICAL LSAME
! 165: EXTERNAL LSAME
! 166: * ..
! 167: * .. External Subroutines ..
! 168: EXTERNAL XERBLA, DSYRK, DPOTRF, DTRSM
! 169: * ..
! 170: * .. Intrinsic Functions ..
! 171: INTRINSIC MOD
! 172: * ..
! 173: * .. Executable Statements ..
! 174: *
! 175: * Test the input parameters.
! 176: *
! 177: INFO = 0
! 178: NORMALTRANSR = LSAME( TRANSR, 'N' )
! 179: LOWER = LSAME( UPLO, 'L' )
! 180: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
! 181: INFO = -1
! 182: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
! 183: INFO = -2
! 184: ELSE IF( N.LT.0 ) THEN
! 185: INFO = -3
! 186: END IF
! 187: IF( INFO.NE.0 ) THEN
! 188: CALL XERBLA( 'DPFTRF', -INFO )
! 189: RETURN
! 190: END IF
! 191: *
! 192: * Quick return if possible
! 193: *
! 194: IF( N.EQ.0 )
! 195: + RETURN
! 196: *
! 197: * If N is odd, set NISODD = .TRUE.
! 198: * If N is even, set K = N/2 and NISODD = .FALSE.
! 199: *
! 200: IF( MOD( N, 2 ).EQ.0 ) THEN
! 201: K = N / 2
! 202: NISODD = .FALSE.
! 203: ELSE
! 204: NISODD = .TRUE.
! 205: END IF
! 206: *
! 207: * Set N1 and N2 depending on LOWER
! 208: *
! 209: IF( LOWER ) THEN
! 210: N2 = N / 2
! 211: N1 = N - N2
! 212: ELSE
! 213: N1 = N / 2
! 214: N2 = N - N1
! 215: END IF
! 216: *
! 217: * start execution: there are eight cases
! 218: *
! 219: IF( NISODD ) THEN
! 220: *
! 221: * N is odd
! 222: *
! 223: IF( NORMALTRANSR ) THEN
! 224: *
! 225: * N is odd and TRANSR = 'N'
! 226: *
! 227: IF( LOWER ) THEN
! 228: *
! 229: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
! 230: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
! 231: * T1 -> a(0), T2 -> a(n), S -> a(n1)
! 232: *
! 233: CALL DPOTRF( 'L', N1, A( 0 ), N, INFO )
! 234: IF( INFO.GT.0 )
! 235: + RETURN
! 236: CALL DTRSM( 'R', 'L', 'T', 'N', N2, N1, ONE, A( 0 ), N,
! 237: + A( N1 ), N )
! 238: CALL DSYRK( 'U', 'N', N2, N1, -ONE, A( N1 ), N, ONE,
! 239: + A( N ), N )
! 240: CALL DPOTRF( 'U', N2, A( N ), N, INFO )
! 241: IF( INFO.GT.0 )
! 242: + INFO = INFO + N1
! 243: *
! 244: ELSE
! 245: *
! 246: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
! 247: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
! 248: * T1 -> a(n2), T2 -> a(n1), S -> a(0)
! 249: *
! 250: CALL DPOTRF( 'L', N1, A( N2 ), N, INFO )
! 251: IF( INFO.GT.0 )
! 252: + RETURN
! 253: CALL DTRSM( 'L', 'L', 'N', 'N', N1, N2, ONE, A( N2 ), N,
! 254: + A( 0 ), N )
! 255: CALL DSYRK( 'U', 'T', N2, N1, -ONE, A( 0 ), N, ONE,
! 256: + A( N1 ), N )
! 257: CALL DPOTRF( 'U', N2, A( N1 ), N, INFO )
! 258: IF( INFO.GT.0 )
! 259: + INFO = INFO + N1
! 260: *
! 261: END IF
! 262: *
! 263: ELSE
! 264: *
! 265: * N is odd and TRANSR = 'T'
! 266: *
! 267: IF( LOWER ) THEN
! 268: *
! 269: * SRPA for LOWER, TRANSPOSE and N is odd
! 270: * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
! 271: * T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
! 272: *
! 273: CALL DPOTRF( 'U', N1, A( 0 ), N1, INFO )
! 274: IF( INFO.GT.0 )
! 275: + RETURN
! 276: CALL DTRSM( 'L', 'U', 'T', 'N', N1, N2, ONE, A( 0 ), N1,
! 277: + A( N1*N1 ), N1 )
! 278: CALL DSYRK( 'L', 'T', N2, N1, -ONE, A( N1*N1 ), N1, ONE,
! 279: + A( 1 ), N1 )
! 280: CALL DPOTRF( 'L', N2, A( 1 ), N1, INFO )
! 281: IF( INFO.GT.0 )
! 282: + INFO = INFO + N1
! 283: *
! 284: ELSE
! 285: *
! 286: * SRPA for UPPER, TRANSPOSE and N is odd
! 287: * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
! 288: * T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
! 289: *
! 290: CALL DPOTRF( 'U', N1, A( N2*N2 ), N2, INFO )
! 291: IF( INFO.GT.0 )
! 292: + RETURN
! 293: CALL DTRSM( 'R', 'U', 'N', 'N', N2, N1, ONE, A( N2*N2 ),
! 294: + N2, A( 0 ), N2 )
! 295: CALL DSYRK( 'L', 'N', N2, N1, -ONE, A( 0 ), N2, ONE,
! 296: + A( N1*N2 ), N2 )
! 297: CALL DPOTRF( 'L', N2, A( N1*N2 ), N2, INFO )
! 298: IF( INFO.GT.0 )
! 299: + INFO = INFO + N1
! 300: *
! 301: END IF
! 302: *
! 303: END IF
! 304: *
! 305: ELSE
! 306: *
! 307: * N is even
! 308: *
! 309: IF( NORMALTRANSR ) THEN
! 310: *
! 311: * N is even and TRANSR = 'N'
! 312: *
! 313: IF( LOWER ) THEN
! 314: *
! 315: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
! 316: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
! 317: * T1 -> a(1), T2 -> a(0), S -> a(k+1)
! 318: *
! 319: CALL DPOTRF( 'L', K, A( 1 ), N+1, INFO )
! 320: IF( INFO.GT.0 )
! 321: + RETURN
! 322: CALL DTRSM( 'R', 'L', 'T', 'N', K, K, ONE, A( 1 ), N+1,
! 323: + A( K+1 ), N+1 )
! 324: CALL DSYRK( 'U', 'N', K, K, -ONE, A( K+1 ), N+1, ONE,
! 325: + A( 0 ), N+1 )
! 326: CALL DPOTRF( 'U', K, A( 0 ), N+1, INFO )
! 327: IF( INFO.GT.0 )
! 328: + INFO = INFO + K
! 329: *
! 330: ELSE
! 331: *
! 332: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
! 333: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
! 334: * T1 -> a(k+1), T2 -> a(k), S -> a(0)
! 335: *
! 336: CALL DPOTRF( 'L', K, A( K+1 ), N+1, INFO )
! 337: IF( INFO.GT.0 )
! 338: + RETURN
! 339: CALL DTRSM( 'L', 'L', 'N', 'N', K, K, ONE, A( K+1 ),
! 340: + N+1, A( 0 ), N+1 )
! 341: CALL DSYRK( 'U', 'T', K, K, -ONE, A( 0 ), N+1, ONE,
! 342: + A( K ), N+1 )
! 343: CALL DPOTRF( 'U', K, A( K ), N+1, INFO )
! 344: IF( INFO.GT.0 )
! 345: + INFO = INFO + K
! 346: *
! 347: END IF
! 348: *
! 349: ELSE
! 350: *
! 351: * N is even and TRANSR = 'T'
! 352: *
! 353: IF( LOWER ) THEN
! 354: *
! 355: * SRPA for LOWER, TRANSPOSE and N is even (see paper)
! 356: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
! 357: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
! 358: *
! 359: CALL DPOTRF( 'U', K, A( 0+K ), K, INFO )
! 360: IF( INFO.GT.0 )
! 361: + RETURN
! 362: CALL DTRSM( 'L', 'U', 'T', 'N', K, K, ONE, A( K ), N1,
! 363: + A( K*( K+1 ) ), K )
! 364: CALL DSYRK( 'L', 'T', K, K, -ONE, A( K*( K+1 ) ), K, ONE,
! 365: + A( 0 ), K )
! 366: CALL DPOTRF( 'L', K, A( 0 ), K, INFO )
! 367: IF( INFO.GT.0 )
! 368: + INFO = INFO + K
! 369: *
! 370: ELSE
! 371: *
! 372: * SRPA for UPPER, TRANSPOSE and N is even (see paper)
! 373: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
! 374: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
! 375: *
! 376: CALL DPOTRF( 'U', K, A( K*( K+1 ) ), K, INFO )
! 377: IF( INFO.GT.0 )
! 378: + RETURN
! 379: CALL DTRSM( 'R', 'U', 'N', 'N', K, K, ONE,
! 380: + A( K*( K+1 ) ), K, A( 0 ), K )
! 381: CALL DSYRK( 'L', 'N', K, K, -ONE, A( 0 ), K, ONE,
! 382: + A( K*K ), K )
! 383: CALL DPOTRF( 'L', K, A( K*K ), K, INFO )
! 384: IF( INFO.GT.0 )
! 385: + INFO = INFO + K
! 386: *
! 387: END IF
! 388: *
! 389: END IF
! 390: *
! 391: END IF
! 392: *
! 393: RETURN
! 394: *
! 395: * End of DPFTRF
! 396: *
! 397: END
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