Annotation of rpl/lapack/lapack/zpotrf2.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b ZPOTRF2
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: * Definition:
! 9: * ===========
! 10: *
! 11: * RECURSIVE SUBROUTINE ZPOTRF2( UPLO, N, A, LDA, INFO )
! 12: *
! 13: * .. Scalar Arguments ..
! 14: * CHARACTER UPLO
! 15: * INTEGER INFO, LDA, N
! 16: * ..
! 17: * .. Array Arguments ..
! 18: * COMPLEX*16 A( LDA, * )
! 19: * ..
! 20: *
! 21: *
! 22: *> \par Purpose:
! 23: * =============
! 24: *>
! 25: *> \verbatim
! 26: *>
! 27: *> ZPOTRF2 computes the Cholesky factorization of a real symmetric
! 28: *> positive definite matrix A using the recursive algorithm.
! 29: *>
! 30: *> The factorization has the form
! 31: *> A = U**H * U, if UPLO = 'U', or
! 32: *> A = L * L**H, if UPLO = 'L',
! 33: *> where U is an upper triangular matrix and L is lower triangular.
! 34: *>
! 35: *> This is the recursive version of the algorithm. It divides
! 36: *> the matrix into four submatrices:
! 37: *>
! 38: *> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2
! 39: *> A = [ -----|----- ] with n1 = n/2
! 40: *> [ A21 | A22 ] n2 = n-n1
! 41: *>
! 42: *> The subroutine calls itself to factor A11. Update and scale A21
! 43: *> or A12, update A22 then call itself to factor A22.
! 44: *>
! 45: *> \endverbatim
! 46: *
! 47: * Arguments:
! 48: * ==========
! 49: *
! 50: *> \param[in] UPLO
! 51: *> \verbatim
! 52: *> UPLO is CHARACTER*1
! 53: *> = 'U': Upper triangle of A is stored;
! 54: *> = 'L': Lower triangle of A is stored.
! 55: *> \endverbatim
! 56: *>
! 57: *> \param[in] N
! 58: *> \verbatim
! 59: *> N is INTEGER
! 60: *> The order of the matrix A. N >= 0.
! 61: *> \endverbatim
! 62: *>
! 63: *> \param[in,out] A
! 64: *> \verbatim
! 65: *> A is COMPLEX*16 array, dimension (LDA,N)
! 66: *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
! 67: *> N-by-N upper triangular part of A contains the upper
! 68: *> triangular part of the matrix A, and the strictly lower
! 69: *> triangular part of A is not referenced. If UPLO = 'L', the
! 70: *> leading N-by-N lower triangular part of A contains the lower
! 71: *> triangular part of the matrix A, and the strictly upper
! 72: *> triangular part of A is not referenced.
! 73: *>
! 74: *> On exit, if INFO = 0, the factor U or L from the Cholesky
! 75: *> factorization A = U**H*U or A = L*L**H.
! 76: *> \endverbatim
! 77: *>
! 78: *> \param[in] LDA
! 79: *> \verbatim
! 80: *> LDA is INTEGER
! 81: *> The leading dimension of the array A. LDA >= max(1,N).
! 82: *> \endverbatim
! 83: *>
! 84: *> \param[out] INFO
! 85: *> \verbatim
! 86: *> INFO is INTEGER
! 87: *> = 0: successful exit
! 88: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 89: *> > 0: if INFO = i, the leading minor of order i is not
! 90: *> positive definite, and the factorization could not be
! 91: *> completed.
! 92: *> \endverbatim
! 93: *
! 94: * Authors:
! 95: * ========
! 96: *
! 97: *> \author Univ. of Tennessee
! 98: *> \author Univ. of California Berkeley
! 99: *> \author Univ. of Colorado Denver
! 100: *> \author NAG Ltd.
! 101: *
! 102: *> \date November 2015
! 103: *
! 104: *> \ingroup complex16POcomputational
! 105: *
! 106: * =====================================================================
! 107: RECURSIVE SUBROUTINE ZPOTRF2( UPLO, N, A, LDA, INFO )
! 108: *
! 109: * -- LAPACK computational routine (version 3.6.0) --
! 110: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 111: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 112: * November 2015
! 113: *
! 114: * .. Scalar Arguments ..
! 115: CHARACTER UPLO
! 116: INTEGER INFO, LDA, N
! 117: * ..
! 118: * .. Array Arguments ..
! 119: COMPLEX*16 A( LDA, * )
! 120: * ..
! 121: *
! 122: * =====================================================================
! 123: *
! 124: * .. Parameters ..
! 125: DOUBLE PRECISION ONE, ZERO
! 126: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 127: COMPLEX*16 CONE
! 128: PARAMETER ( CONE = (1.0D+0, 0.0D+0) )
! 129: * ..
! 130: * .. Local Scalars ..
! 131: LOGICAL UPPER
! 132: INTEGER N1, N2, IINFO
! 133: DOUBLE PRECISION AJJ
! 134: * ..
! 135: * .. External Functions ..
! 136: LOGICAL LSAME, DISNAN
! 137: EXTERNAL LSAME, DISNAN
! 138: * ..
! 139: * .. External Subroutines ..
! 140: EXTERNAL ZHERK, ZTRSM, XERBLA
! 141: * ..
! 142: * .. Intrinsic Functions ..
! 143: INTRINSIC MAX, DBLE, SQRT
! 144: * ..
! 145: * .. Executable Statements ..
! 146: *
! 147: * Test the input parameters
! 148: *
! 149: INFO = 0
! 150: UPPER = LSAME( UPLO, 'U' )
! 151: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 152: INFO = -1
! 153: ELSE IF( N.LT.0 ) THEN
! 154: INFO = -2
! 155: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 156: INFO = -4
! 157: END IF
! 158: IF( INFO.NE.0 ) THEN
! 159: CALL XERBLA( 'ZPOTRF2', -INFO )
! 160: RETURN
! 161: END IF
! 162: *
! 163: * Quick return if possible
! 164: *
! 165: IF( N.EQ.0 )
! 166: $ RETURN
! 167: *
! 168: * N=1 case
! 169: *
! 170: IF( N.EQ.1 ) THEN
! 171: *
! 172: * Test for non-positive-definiteness
! 173: *
! 174: AJJ = DBLE( A( 1, 1 ) )
! 175: IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
! 176: INFO = 1
! 177: RETURN
! 178: END IF
! 179: *
! 180: * Factor
! 181: *
! 182: A( 1, 1 ) = SQRT( AJJ )
! 183: *
! 184: * Use recursive code
! 185: *
! 186: ELSE
! 187: N1 = N/2
! 188: N2 = N-N1
! 189: *
! 190: * Factor A11
! 191: *
! 192: CALL ZPOTRF2( UPLO, N1, A( 1, 1 ), LDA, IINFO )
! 193: IF ( IINFO.NE.0 ) THEN
! 194: INFO = IINFO
! 195: RETURN
! 196: END IF
! 197: *
! 198: * Compute the Cholesky factorization A = U**H*U
! 199: *
! 200: IF( UPPER ) THEN
! 201: *
! 202: * Update and scale A12
! 203: *
! 204: CALL ZTRSM( 'L', 'U', 'C', 'N', N1, N2, CONE,
! 205: $ A( 1, 1 ), LDA, A( 1, N1+1 ), LDA )
! 206: *
! 207: * Update and factor A22
! 208: *
! 209: CALL ZHERK( UPLO, 'C', N2, N1, -ONE, A( 1, N1+1 ), LDA,
! 210: $ ONE, A( N1+1, N1+1 ), LDA )
! 211: CALL ZPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
! 212: IF ( IINFO.NE.0 ) THEN
! 213: INFO = IINFO + N1
! 214: RETURN
! 215: END IF
! 216: *
! 217: * Compute the Cholesky factorization A = L*L**H
! 218: *
! 219: ELSE
! 220: *
! 221: * Update and scale A21
! 222: *
! 223: CALL ZTRSM( 'R', 'L', 'C', 'N', N2, N1, CONE,
! 224: $ A( 1, 1 ), LDA, A( N1+1, 1 ), LDA )
! 225: *
! 226: * Update and factor A22
! 227: *
! 228: CALL ZHERK( UPLO, 'N', N2, N1, -ONE, A( N1+1, 1 ), LDA,
! 229: $ ONE, A( N1+1, N1+1 ), LDA )
! 230: CALL ZPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
! 231: IF ( IINFO.NE.0 ) THEN
! 232: INFO = IINFO + N1
! 233: RETURN
! 234: END IF
! 235: END IF
! 236: END IF
! 237: RETURN
! 238: *
! 239: * End of ZPOTRF2
! 240: *
! 241: END
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