Annotation of rpl/lapack/lapack/zpstrf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZPSTRF( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2.2) --
! 4: *
! 5: * -- Contributed by Craig Lucas, University of Manchester / NAG Ltd. --
! 6: * -- June 2010 --
! 7: *
! 8: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 9: *
! 10: * .. Scalar Arguments ..
! 11: DOUBLE PRECISION TOL
! 12: INTEGER INFO, LDA, N, RANK
! 13: CHARACTER UPLO
! 14: * ..
! 15: * .. Array Arguments ..
! 16: COMPLEX*16 A( LDA, * )
! 17: DOUBLE PRECISION WORK( 2*N )
! 18: INTEGER PIV( N )
! 19: * ..
! 20: *
! 21: * Purpose
! 22: * =======
! 23: *
! 24: * ZPSTRF computes the Cholesky factorization with complete
! 25: * pivoting of a complex Hermitian positive semidefinite matrix A.
! 26: *
! 27: * The factorization has the form
! 28: * P' * A * P = U' * U , if UPLO = 'U',
! 29: * P' * A * P = L * L', if UPLO = 'L',
! 30: * where U is an upper triangular matrix and L is lower triangular, and
! 31: * P is stored as vector PIV.
! 32: *
! 33: * This algorithm does not attempt to check that A is positive
! 34: * semidefinite. This version of the algorithm calls level 3 BLAS.
! 35: *
! 36: * Arguments
! 37: * =========
! 38: *
! 39: * UPLO (input) CHARACTER*1
! 40: * Specifies whether the upper or lower triangular part of the
! 41: * symmetric matrix A is stored.
! 42: * = 'U': Upper triangular
! 43: * = 'L': Lower triangular
! 44: *
! 45: * N (input) INTEGER
! 46: * The order of the matrix A. N >= 0.
! 47: *
! 48: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 49: * On entry, the symmetric matrix A. If UPLO = 'U', the leading
! 50: * n by n upper triangular part of A contains the upper
! 51: * triangular part of the matrix A, and the strictly lower
! 52: * triangular part of A is not referenced. If UPLO = 'L', the
! 53: * leading n by n lower triangular part of A contains the lower
! 54: * triangular part of the matrix A, and the strictly upper
! 55: * triangular part of A is not referenced.
! 56: *
! 57: * On exit, if INFO = 0, the factor U or L from the Cholesky
! 58: * factorization as above.
! 59: *
! 60: * LDA (input) INTEGER
! 61: * The leading dimension of the array A. LDA >= max(1,N).
! 62: *
! 63: * PIV (output) INTEGER array, dimension (N)
! 64: * PIV is such that the nonzero entries are P( PIV(K), K ) = 1.
! 65: *
! 66: * RANK (output) INTEGER
! 67: * The rank of A given by the number of steps the algorithm
! 68: * completed.
! 69: *
! 70: * TOL (input) DOUBLE PRECISION
! 71: * User defined tolerance. If TOL < 0, then N*U*MAX( A(K,K) )
! 72: * will be used. The algorithm terminates at the (K-1)st step
! 73: * if the pivot <= TOL.
! 74: *
! 75: * WORK (workspace) DOUBLE PRECISION array, dimension (2*N)
! 76: * Work space.
! 77: *
! 78: * INFO (output) INTEGER
! 79: * < 0: If INFO = -K, the K-th argument had an illegal value,
! 80: * = 0: algorithm completed successfully, and
! 81: * > 0: the matrix A is either rank deficient with computed rank
! 82: * as returned in RANK, or is indefinite. See Section 7 of
! 83: * LAPACK Working Note #161 for further information.
! 84: *
! 85: * =====================================================================
! 86: *
! 87: * .. Parameters ..
! 88: DOUBLE PRECISION ONE, ZERO
! 89: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 90: COMPLEX*16 CONE
! 91: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
! 92: * ..
! 93: * .. Local Scalars ..
! 94: COMPLEX*16 ZTEMP
! 95: DOUBLE PRECISION AJJ, DSTOP, DTEMP
! 96: INTEGER I, ITEMP, J, JB, K, NB, PVT
! 97: LOGICAL UPPER
! 98: * ..
! 99: * .. External Functions ..
! 100: DOUBLE PRECISION DLAMCH
! 101: INTEGER ILAENV
! 102: LOGICAL LSAME, DISNAN
! 103: EXTERNAL DLAMCH, ILAENV, LSAME, DISNAN
! 104: * ..
! 105: * .. External Subroutines ..
! 106: EXTERNAL ZDSCAL, ZGEMV, ZHERK, ZLACGV, ZPSTF2, ZSWAP,
! 107: $ XERBLA
! 108: * ..
! 109: * .. Intrinsic Functions ..
! 110: INTRINSIC DBLE, DCONJG, MAX, MIN, SQRT, MAXLOC
! 111: * ..
! 112: * .. Executable Statements ..
! 113: *
! 114: * Test the input parameters.
! 115: *
! 116: INFO = 0
! 117: UPPER = LSAME( UPLO, 'U' )
! 118: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 119: INFO = -1
! 120: ELSE IF( N.LT.0 ) THEN
! 121: INFO = -2
! 122: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 123: INFO = -4
! 124: END IF
! 125: IF( INFO.NE.0 ) THEN
! 126: CALL XERBLA( 'ZPSTRF', -INFO )
! 127: RETURN
! 128: END IF
! 129: *
! 130: * Quick return if possible
! 131: *
! 132: IF( N.EQ.0 )
! 133: $ RETURN
! 134: *
! 135: * Get block size
! 136: *
! 137: NB = ILAENV( 1, 'ZPOTRF', UPLO, N, -1, -1, -1 )
! 138: IF( NB.LE.1 .OR. NB.GE.N ) THEN
! 139: *
! 140: * Use unblocked code
! 141: *
! 142: CALL ZPSTF2( UPLO, N, A( 1, 1 ), LDA, PIV, RANK, TOL, WORK,
! 143: $ INFO )
! 144: GO TO 230
! 145: *
! 146: ELSE
! 147: *
! 148: * Initialize PIV
! 149: *
! 150: DO 100 I = 1, N
! 151: PIV( I ) = I
! 152: 100 CONTINUE
! 153: *
! 154: * Compute stopping value
! 155: *
! 156: DO 110 I = 1, N
! 157: WORK( I ) = DBLE( A( I, I ) )
! 158: 110 CONTINUE
! 159: PVT = MAXLOC( WORK( 1:N ), 1 )
! 160: AJJ = DBLE( A( PVT, PVT ) )
! 161: IF( AJJ.EQ.ZERO.OR.DISNAN( AJJ ) ) THEN
! 162: RANK = 0
! 163: INFO = 1
! 164: GO TO 230
! 165: END IF
! 166: *
! 167: * Compute stopping value if not supplied
! 168: *
! 169: IF( TOL.LT.ZERO ) THEN
! 170: DSTOP = N * DLAMCH( 'Epsilon' ) * AJJ
! 171: ELSE
! 172: DSTOP = TOL
! 173: END IF
! 174: *
! 175: *
! 176: IF( UPPER ) THEN
! 177: *
! 178: * Compute the Cholesky factorization P' * A * P = U' * U
! 179: *
! 180: DO 160 K = 1, N, NB
! 181: *
! 182: * Account for last block not being NB wide
! 183: *
! 184: JB = MIN( NB, N-K+1 )
! 185: *
! 186: * Set relevant part of first half of WORK to zero,
! 187: * holds dot products
! 188: *
! 189: DO 120 I = K, N
! 190: WORK( I ) = 0
! 191: 120 CONTINUE
! 192: *
! 193: DO 150 J = K, K + JB - 1
! 194: *
! 195: * Find pivot, test for exit, else swap rows and columns
! 196: * Update dot products, compute possible pivots which are
! 197: * stored in the second half of WORK
! 198: *
! 199: DO 130 I = J, N
! 200: *
! 201: IF( J.GT.K ) THEN
! 202: WORK( I ) = WORK( I ) +
! 203: $ DBLE( DCONJG( A( J-1, I ) )*
! 204: $ A( J-1, I ) )
! 205: END IF
! 206: WORK( N+I ) = DBLE( A( I, I ) ) - WORK( I )
! 207: *
! 208: 130 CONTINUE
! 209: *
! 210: IF( J.GT.1 ) THEN
! 211: ITEMP = MAXLOC( WORK( (N+J):(2*N) ), 1 )
! 212: PVT = ITEMP + J - 1
! 213: AJJ = WORK( N+PVT )
! 214: IF( AJJ.LE.DSTOP.OR.DISNAN( AJJ ) ) THEN
! 215: A( J, J ) = AJJ
! 216: GO TO 220
! 217: END IF
! 218: END IF
! 219: *
! 220: IF( J.NE.PVT ) THEN
! 221: *
! 222: * Pivot OK, so can now swap pivot rows and columns
! 223: *
! 224: A( PVT, PVT ) = A( J, J )
! 225: CALL ZSWAP( J-1, A( 1, J ), 1, A( 1, PVT ), 1 )
! 226: IF( PVT.LT.N )
! 227: $ CALL ZSWAP( N-PVT, A( J, PVT+1 ), LDA,
! 228: $ A( PVT, PVT+1 ), LDA )
! 229: DO 140 I = J + 1, PVT - 1
! 230: ZTEMP = DCONJG( A( J, I ) )
! 231: A( J, I ) = DCONJG( A( I, PVT ) )
! 232: A( I, PVT ) = ZTEMP
! 233: 140 CONTINUE
! 234: A( J, PVT ) = DCONJG( A( J, PVT ) )
! 235: *
! 236: * Swap dot products and PIV
! 237: *
! 238: DTEMP = WORK( J )
! 239: WORK( J ) = WORK( PVT )
! 240: WORK( PVT ) = DTEMP
! 241: ITEMP = PIV( PVT )
! 242: PIV( PVT ) = PIV( J )
! 243: PIV( J ) = ITEMP
! 244: END IF
! 245: *
! 246: AJJ = SQRT( AJJ )
! 247: A( J, J ) = AJJ
! 248: *
! 249: * Compute elements J+1:N of row J.
! 250: *
! 251: IF( J.LT.N ) THEN
! 252: CALL ZLACGV( J-1, A( 1, J ), 1 )
! 253: CALL ZGEMV( 'Trans', J-K, N-J, -CONE, A( K, J+1 ),
! 254: $ LDA, A( K, J ), 1, CONE, A( J, J+1 ),
! 255: $ LDA )
! 256: CALL ZLACGV( J-1, A( 1, J ), 1 )
! 257: CALL ZDSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
! 258: END IF
! 259: *
! 260: 150 CONTINUE
! 261: *
! 262: * Update trailing matrix, J already incremented
! 263: *
! 264: IF( K+JB.LE.N ) THEN
! 265: CALL ZHERK( 'Upper', 'Conj Trans', N-J+1, JB, -ONE,
! 266: $ A( K, J ), LDA, ONE, A( J, J ), LDA )
! 267: END IF
! 268: *
! 269: 160 CONTINUE
! 270: *
! 271: ELSE
! 272: *
! 273: * Compute the Cholesky factorization P' * A * P = L * L'
! 274: *
! 275: DO 210 K = 1, N, NB
! 276: *
! 277: * Account for last block not being NB wide
! 278: *
! 279: JB = MIN( NB, N-K+1 )
! 280: *
! 281: * Set relevant part of first half of WORK to zero,
! 282: * holds dot products
! 283: *
! 284: DO 170 I = K, N
! 285: WORK( I ) = 0
! 286: 170 CONTINUE
! 287: *
! 288: DO 200 J = K, K + JB - 1
! 289: *
! 290: * Find pivot, test for exit, else swap rows and columns
! 291: * Update dot products, compute possible pivots which are
! 292: * stored in the second half of WORK
! 293: *
! 294: DO 180 I = J, N
! 295: *
! 296: IF( J.GT.K ) THEN
! 297: WORK( I ) = WORK( I ) +
! 298: $ DBLE( DCONJG( A( I, J-1 ) )*
! 299: $ A( I, J-1 ) )
! 300: END IF
! 301: WORK( N+I ) = DBLE( A( I, I ) ) - WORK( I )
! 302: *
! 303: 180 CONTINUE
! 304: *
! 305: IF( J.GT.1 ) THEN
! 306: ITEMP = MAXLOC( WORK( (N+J):(2*N) ), 1 )
! 307: PVT = ITEMP + J - 1
! 308: AJJ = WORK( N+PVT )
! 309: IF( AJJ.LE.DSTOP.OR.DISNAN( AJJ ) ) THEN
! 310: A( J, J ) = AJJ
! 311: GO TO 220
! 312: END IF
! 313: END IF
! 314: *
! 315: IF( J.NE.PVT ) THEN
! 316: *
! 317: * Pivot OK, so can now swap pivot rows and columns
! 318: *
! 319: A( PVT, PVT ) = A( J, J )
! 320: CALL ZSWAP( J-1, A( J, 1 ), LDA, A( PVT, 1 ), LDA )
! 321: IF( PVT.LT.N )
! 322: $ CALL ZSWAP( N-PVT, A( PVT+1, J ), 1,
! 323: $ A( PVT+1, PVT ), 1 )
! 324: DO 190 I = J + 1, PVT - 1
! 325: ZTEMP = DCONJG( A( I, J ) )
! 326: A( I, J ) = DCONJG( A( PVT, I ) )
! 327: A( PVT, I ) = ZTEMP
! 328: 190 CONTINUE
! 329: A( PVT, J ) = DCONJG( A( PVT, J ) )
! 330: *
! 331: *
! 332: * Swap dot products and PIV
! 333: *
! 334: DTEMP = WORK( J )
! 335: WORK( J ) = WORK( PVT )
! 336: WORK( PVT ) = DTEMP
! 337: ITEMP = PIV( PVT )
! 338: PIV( PVT ) = PIV( J )
! 339: PIV( J ) = ITEMP
! 340: END IF
! 341: *
! 342: AJJ = SQRT( AJJ )
! 343: A( J, J ) = AJJ
! 344: *
! 345: * Compute elements J+1:N of column J.
! 346: *
! 347: IF( J.LT.N ) THEN
! 348: CALL ZLACGV( J-1, A( J, 1 ), LDA )
! 349: CALL ZGEMV( 'No Trans', N-J, J-K, -CONE,
! 350: $ A( J+1, K ), LDA, A( J, K ), LDA, CONE,
! 351: $ A( J+1, J ), 1 )
! 352: CALL ZLACGV( J-1, A( J, 1 ), LDA )
! 353: CALL ZDSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
! 354: END IF
! 355: *
! 356: 200 CONTINUE
! 357: *
! 358: * Update trailing matrix, J already incremented
! 359: *
! 360: IF( K+JB.LE.N ) THEN
! 361: CALL ZHERK( 'Lower', 'No Trans', N-J+1, JB, -ONE,
! 362: $ A( J, K ), LDA, ONE, A( J, J ), LDA )
! 363: END IF
! 364: *
! 365: 210 CONTINUE
! 366: *
! 367: END IF
! 368: END IF
! 369: *
! 370: * Ran to completion, A has full rank
! 371: *
! 372: RANK = N
! 373: *
! 374: GO TO 230
! 375: 220 CONTINUE
! 376: *
! 377: * Rank is the number of steps completed. Set INFO = 1 to signal
! 378: * that the factorization cannot be used to solve a system.
! 379: *
! 380: RANK = J - 1
! 381: INFO = 1
! 382: *
! 383: 230 CONTINUE
! 384: RETURN
! 385: *
! 386: * End of ZPSTRF
! 387: *
! 388: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zpstrf.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack