Annotation of rpl/lapack/lapack/dsytri_rook.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b DSYTRI_ROOK
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DSYTRI_ROOK + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytri_rook.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytri_rook.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytri_rook.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DSYTRI_ROOK( UPLO, N, A, LDA, IPIV, WORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER UPLO
! 25: * INTEGER INFO, LDA, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * INTEGER IPIV( * )
! 29: * DOUBLE PRECISION A( LDA, * ), WORK( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> DSYTRI_ROOK computes the inverse of a real symmetric
! 39: *> matrix A using the factorization A = U*D*U**T or A = L*D*L**T
! 40: *> computed by DSYTRF_ROOK.
! 41: *> \endverbatim
! 42: *
! 43: * Arguments:
! 44: * ==========
! 45: *
! 46: *> \param[in] UPLO
! 47: *> \verbatim
! 48: *> UPLO is CHARACTER*1
! 49: *> Specifies whether the details of the factorization are stored
! 50: *> as an upper or lower triangular matrix.
! 51: *> = 'U': Upper triangular, form is A = U*D*U**T;
! 52: *> = 'L': Lower triangular, form is A = L*D*L**T.
! 53: *> \endverbatim
! 54: *>
! 55: *> \param[in] N
! 56: *> \verbatim
! 57: *> N is INTEGER
! 58: *> The order of the matrix A. N >= 0.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in,out] A
! 62: *> \verbatim
! 63: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 64: *> On entry, the block diagonal matrix D and the multipliers
! 65: *> used to obtain the factor U or L as computed by DSYTRF_ROOK.
! 66: *>
! 67: *> On exit, if INFO = 0, the (symmetric) inverse of the original
! 68: *> matrix. If UPLO = 'U', the upper triangular part of the
! 69: *> inverse is formed and the part of A below the diagonal is not
! 70: *> referenced; if UPLO = 'L' the lower triangular part of the
! 71: *> inverse is formed and the part of A above the diagonal is
! 72: *> not referenced.
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] LDA
! 76: *> \verbatim
! 77: *> LDA is INTEGER
! 78: *> The leading dimension of the array A. LDA >= max(1,N).
! 79: *> \endverbatim
! 80: *>
! 81: *> \param[in] IPIV
! 82: *> \verbatim
! 83: *> IPIV is INTEGER array, dimension (N)
! 84: *> Details of the interchanges and the block structure of D
! 85: *> as determined by DSYTRF_ROOK.
! 86: *> \endverbatim
! 87: *>
! 88: *> \param[out] WORK
! 89: *> \verbatim
! 90: *> WORK is DOUBLE PRECISION array, dimension (N)
! 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, D(i,i) = 0; the matrix is singular and its
! 99: *> inverse could 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 April 2012
! 111: *
! 112: *> \ingroup doubleSYcomputational
! 113: *
! 114: *> \par Contributors:
! 115: * ==================
! 116: *>
! 117: *> \verbatim
! 118: *>
! 119: *> April 2012, Igor Kozachenko,
! 120: *> Computer Science Division,
! 121: *> University of California, Berkeley
! 122: *>
! 123: *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
! 124: *> School of Mathematics,
! 125: *> University of Manchester
! 126: *>
! 127: *> \endverbatim
! 128: *
! 129: * =====================================================================
! 130: SUBROUTINE DSYTRI_ROOK( UPLO, N, A, LDA, IPIV, WORK, INFO )
! 131: *
! 132: * -- LAPACK computational routine (version 3.4.1) --
! 133: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 134: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 135: * April 2012
! 136: *
! 137: * .. Scalar Arguments ..
! 138: CHARACTER UPLO
! 139: INTEGER INFO, LDA, N
! 140: * ..
! 141: * .. Array Arguments ..
! 142: INTEGER IPIV( * )
! 143: DOUBLE PRECISION A( LDA, * ), WORK( * )
! 144: * ..
! 145: *
! 146: * =====================================================================
! 147: *
! 148: * .. Parameters ..
! 149: DOUBLE PRECISION ONE, ZERO
! 150: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 151: * ..
! 152: * .. Local Scalars ..
! 153: LOGICAL UPPER
! 154: INTEGER K, KP, KSTEP
! 155: DOUBLE PRECISION AK, AKKP1, AKP1, D, T, TEMP
! 156: * ..
! 157: * .. External Functions ..
! 158: LOGICAL LSAME
! 159: DOUBLE PRECISION DDOT
! 160: EXTERNAL LSAME, DDOT
! 161: * ..
! 162: * .. External Subroutines ..
! 163: EXTERNAL DCOPY, DSWAP, DSYMV, XERBLA
! 164: * ..
! 165: * .. Intrinsic Functions ..
! 166: INTRINSIC ABS, MAX
! 167: * ..
! 168: * .. Executable Statements ..
! 169: *
! 170: * Test the input parameters.
! 171: *
! 172: INFO = 0
! 173: UPPER = LSAME( UPLO, 'U' )
! 174: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 175: INFO = -1
! 176: ELSE IF( N.LT.0 ) THEN
! 177: INFO = -2
! 178: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 179: INFO = -4
! 180: END IF
! 181: IF( INFO.NE.0 ) THEN
! 182: CALL XERBLA( 'DSYTRI_ROOK', -INFO )
! 183: RETURN
! 184: END IF
! 185: *
! 186: * Quick return if possible
! 187: *
! 188: IF( N.EQ.0 )
! 189: $ RETURN
! 190: *
! 191: * Check that the diagonal matrix D is nonsingular.
! 192: *
! 193: IF( UPPER ) THEN
! 194: *
! 195: * Upper triangular storage: examine D from bottom to top
! 196: *
! 197: DO 10 INFO = N, 1, -1
! 198: IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
! 199: $ RETURN
! 200: 10 CONTINUE
! 201: ELSE
! 202: *
! 203: * Lower triangular storage: examine D from top to bottom.
! 204: *
! 205: DO 20 INFO = 1, N
! 206: IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
! 207: $ RETURN
! 208: 20 CONTINUE
! 209: END IF
! 210: INFO = 0
! 211: *
! 212: IF( UPPER ) THEN
! 213: *
! 214: * Compute inv(A) from the factorization A = U*D*U**T.
! 215: *
! 216: * K is the main loop index, increasing from 1 to N in steps of
! 217: * 1 or 2, depending on the size of the diagonal blocks.
! 218: *
! 219: K = 1
! 220: 30 CONTINUE
! 221: *
! 222: * If K > N, exit from loop.
! 223: *
! 224: IF( K.GT.N )
! 225: $ GO TO 40
! 226: *
! 227: IF( IPIV( K ).GT.0 ) THEN
! 228: *
! 229: * 1 x 1 diagonal block
! 230: *
! 231: * Invert the diagonal block.
! 232: *
! 233: A( K, K ) = ONE / A( K, K )
! 234: *
! 235: * Compute column K of the inverse.
! 236: *
! 237: IF( K.GT.1 ) THEN
! 238: CALL DCOPY( K-1, A( 1, K ), 1, WORK, 1 )
! 239: CALL DSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
! 240: $ A( 1, K ), 1 )
! 241: A( K, K ) = A( K, K ) - DDOT( K-1, WORK, 1, A( 1, K ),
! 242: $ 1 )
! 243: END IF
! 244: KSTEP = 1
! 245: ELSE
! 246: *
! 247: * 2 x 2 diagonal block
! 248: *
! 249: * Invert the diagonal block.
! 250: *
! 251: T = ABS( A( K, K+1 ) )
! 252: AK = A( K, K ) / T
! 253: AKP1 = A( K+1, K+1 ) / T
! 254: AKKP1 = A( K, K+1 ) / T
! 255: D = T*( AK*AKP1-ONE )
! 256: A( K, K ) = AKP1 / D
! 257: A( K+1, K+1 ) = AK / D
! 258: A( K, K+1 ) = -AKKP1 / D
! 259: *
! 260: * Compute columns K and K+1 of the inverse.
! 261: *
! 262: IF( K.GT.1 ) THEN
! 263: CALL DCOPY( K-1, A( 1, K ), 1, WORK, 1 )
! 264: CALL DSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
! 265: $ A( 1, K ), 1 )
! 266: A( K, K ) = A( K, K ) - DDOT( K-1, WORK, 1, A( 1, K ),
! 267: $ 1 )
! 268: A( K, K+1 ) = A( K, K+1 ) -
! 269: $ DDOT( K-1, A( 1, K ), 1, A( 1, K+1 ), 1 )
! 270: CALL DCOPY( K-1, A( 1, K+1 ), 1, WORK, 1 )
! 271: CALL DSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
! 272: $ A( 1, K+1 ), 1 )
! 273: A( K+1, K+1 ) = A( K+1, K+1 ) -
! 274: $ DDOT( K-1, WORK, 1, A( 1, K+1 ), 1 )
! 275: END IF
! 276: KSTEP = 2
! 277: END IF
! 278: *
! 279: IF( KSTEP.EQ.1 ) THEN
! 280: *
! 281: * Interchange rows and columns K and IPIV(K) in the leading
! 282: * submatrix A(1:k+1,1:k+1)
! 283: *
! 284: KP = IPIV( K )
! 285: IF( KP.NE.K ) THEN
! 286: IF( KP.GT.1 )
! 287: $ CALL DSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
! 288: CALL DSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
! 289: TEMP = A( K, K )
! 290: A( K, K ) = A( KP, KP )
! 291: A( KP, KP ) = TEMP
! 292: END IF
! 293: ELSE
! 294: *
! 295: * Interchange rows and columns K and K+1 with -IPIV(K) and
! 296: * -IPIV(K+1)in the leading submatrix A(1:k+1,1:k+1)
! 297: *
! 298: KP = -IPIV( K )
! 299: IF( KP.NE.K ) THEN
! 300: IF( KP.GT.1 )
! 301: $ CALL DSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
! 302: CALL DSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
! 303: *
! 304: TEMP = A( K, K )
! 305: A( K, K ) = A( KP, KP )
! 306: A( KP, KP ) = TEMP
! 307: TEMP = A( K, K+1 )
! 308: A( K, K+1 ) = A( KP, K+1 )
! 309: A( KP, K+1 ) = TEMP
! 310: END IF
! 311: *
! 312: K = K + 1
! 313: KP = -IPIV( K )
! 314: IF( KP.NE.K ) THEN
! 315: IF( KP.GT.1 )
! 316: $ CALL DSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
! 317: CALL DSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
! 318: TEMP = A( K, K )
! 319: A( K, K ) = A( KP, KP )
! 320: A( KP, KP ) = TEMP
! 321: END IF
! 322: END IF
! 323: *
! 324: K = K + 1
! 325: GO TO 30
! 326: 40 CONTINUE
! 327: *
! 328: ELSE
! 329: *
! 330: * Compute inv(A) from the factorization A = L*D*L**T.
! 331: *
! 332: * K is the main loop index, increasing from 1 to N in steps of
! 333: * 1 or 2, depending on the size of the diagonal blocks.
! 334: *
! 335: K = N
! 336: 50 CONTINUE
! 337: *
! 338: * If K < 1, exit from loop.
! 339: *
! 340: IF( K.LT.1 )
! 341: $ GO TO 60
! 342: *
! 343: IF( IPIV( K ).GT.0 ) THEN
! 344: *
! 345: * 1 x 1 diagonal block
! 346: *
! 347: * Invert the diagonal block.
! 348: *
! 349: A( K, K ) = ONE / A( K, K )
! 350: *
! 351: * Compute column K of the inverse.
! 352: *
! 353: IF( K.LT.N ) THEN
! 354: CALL DCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
! 355: CALL DSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
! 356: $ ZERO, A( K+1, K ), 1 )
! 357: A( K, K ) = A( K, K ) - DDOT( N-K, WORK, 1, A( K+1, K ),
! 358: $ 1 )
! 359: END IF
! 360: KSTEP = 1
! 361: ELSE
! 362: *
! 363: * 2 x 2 diagonal block
! 364: *
! 365: * Invert the diagonal block.
! 366: *
! 367: T = ABS( A( K, K-1 ) )
! 368: AK = A( K-1, K-1 ) / T
! 369: AKP1 = A( K, K ) / T
! 370: AKKP1 = A( K, K-1 ) / T
! 371: D = T*( AK*AKP1-ONE )
! 372: A( K-1, K-1 ) = AKP1 / D
! 373: A( K, K ) = AK / D
! 374: A( K, K-1 ) = -AKKP1 / D
! 375: *
! 376: * Compute columns K-1 and K of the inverse.
! 377: *
! 378: IF( K.LT.N ) THEN
! 379: CALL DCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
! 380: CALL DSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
! 381: $ ZERO, A( K+1, K ), 1 )
! 382: A( K, K ) = A( K, K ) - DDOT( N-K, WORK, 1, A( K+1, K ),
! 383: $ 1 )
! 384: A( K, K-1 ) = A( K, K-1 ) -
! 385: $ DDOT( N-K, A( K+1, K ), 1, A( K+1, K-1 ),
! 386: $ 1 )
! 387: CALL DCOPY( N-K, A( K+1, K-1 ), 1, WORK, 1 )
! 388: CALL DSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
! 389: $ ZERO, A( K+1, K-1 ), 1 )
! 390: A( K-1, K-1 ) = A( K-1, K-1 ) -
! 391: $ DDOT( N-K, WORK, 1, A( K+1, K-1 ), 1 )
! 392: END IF
! 393: KSTEP = 2
! 394: END IF
! 395: *
! 396: IF( KSTEP.EQ.1 ) THEN
! 397: *
! 398: * Interchange rows and columns K and IPIV(K) in the trailing
! 399: * submatrix A(k-1:n,k-1:n)
! 400: *
! 401: KP = IPIV( K )
! 402: IF( KP.NE.K ) THEN
! 403: IF( KP.LT.N )
! 404: $ CALL DSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
! 405: CALL DSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
! 406: TEMP = A( K, K )
! 407: A( K, K ) = A( KP, KP )
! 408: A( KP, KP ) = TEMP
! 409: END IF
! 410: ELSE
! 411: *
! 412: * Interchange rows and columns K and K-1 with -IPIV(K) and
! 413: * -IPIV(K-1) in the trailing submatrix A(k-1:n,k-1:n)
! 414: *
! 415: KP = -IPIV( K )
! 416: IF( KP.NE.K ) THEN
! 417: IF( KP.LT.N )
! 418: $ CALL DSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
! 419: CALL DSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
! 420: *
! 421: TEMP = A( K, K )
! 422: A( K, K ) = A( KP, KP )
! 423: A( KP, KP ) = TEMP
! 424: TEMP = A( K, K-1 )
! 425: A( K, K-1 ) = A( KP, K-1 )
! 426: A( KP, K-1 ) = TEMP
! 427: END IF
! 428: *
! 429: K = K - 1
! 430: KP = -IPIV( K )
! 431: IF( KP.NE.K ) THEN
! 432: IF( KP.LT.N )
! 433: $ CALL DSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
! 434: CALL DSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
! 435: TEMP = A( K, K )
! 436: A( K, K ) = A( KP, KP )
! 437: A( KP, KP ) = TEMP
! 438: END IF
! 439: END IF
! 440: *
! 441: K = K - 1
! 442: GO TO 50
! 443: 60 CONTINUE
! 444: END IF
! 445: *
! 446: RETURN
! 447: *
! 448: * End of DSYTRI_ROOK
! 449: *
! 450: END
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