Annotation of rpl/lapack/lapack/dpptrf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DPPTRF( UPLO, N, AP, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: CHARACTER UPLO
! 10: INTEGER INFO, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: DOUBLE PRECISION AP( * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * DPPTRF computes the Cholesky factorization of a real symmetric
! 20: * positive definite matrix A stored in packed format.
! 21: *
! 22: * The factorization has the form
! 23: * A = U**T * U, if UPLO = 'U', or
! 24: * A = L * L**T, if UPLO = 'L',
! 25: * where U is an upper triangular matrix and L is lower triangular.
! 26: *
! 27: * Arguments
! 28: * =========
! 29: *
! 30: * UPLO (input) CHARACTER*1
! 31: * = 'U': Upper triangle of A is stored;
! 32: * = 'L': Lower triangle of A is stored.
! 33: *
! 34: * N (input) INTEGER
! 35: * The order of the matrix A. N >= 0.
! 36: *
! 37: * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 38: * On entry, the upper or lower triangle of the symmetric matrix
! 39: * A, packed columnwise in a linear array. The j-th column of A
! 40: * is stored in the array AP as follows:
! 41: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 42: * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
! 43: * See below for further details.
! 44: *
! 45: * On exit, if INFO = 0, the triangular factor U or L from the
! 46: * Cholesky factorization A = U**T*U or A = L*L**T, in the same
! 47: * storage format as A.
! 48: *
! 49: * INFO (output) INTEGER
! 50: * = 0: successful exit
! 51: * < 0: if INFO = -i, the i-th argument had an illegal value
! 52: * > 0: if INFO = i, the leading minor of order i is not
! 53: * positive definite, and the factorization could not be
! 54: * completed.
! 55: *
! 56: * Further Details
! 57: * ======= =======
! 58: *
! 59: * The packed storage scheme is illustrated by the following example
! 60: * when N = 4, UPLO = 'U':
! 61: *
! 62: * Two-dimensional storage of the symmetric matrix A:
! 63: *
! 64: * a11 a12 a13 a14
! 65: * a22 a23 a24
! 66: * a33 a34 (aij = aji)
! 67: * a44
! 68: *
! 69: * Packed storage of the upper triangle of A:
! 70: *
! 71: * AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
! 72: *
! 73: * =====================================================================
! 74: *
! 75: * .. Parameters ..
! 76: DOUBLE PRECISION ONE, ZERO
! 77: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 78: * ..
! 79: * .. Local Scalars ..
! 80: LOGICAL UPPER
! 81: INTEGER J, JC, JJ
! 82: DOUBLE PRECISION AJJ
! 83: * ..
! 84: * .. External Functions ..
! 85: LOGICAL LSAME
! 86: DOUBLE PRECISION DDOT
! 87: EXTERNAL LSAME, DDOT
! 88: * ..
! 89: * .. External Subroutines ..
! 90: EXTERNAL DSCAL, DSPR, DTPSV, XERBLA
! 91: * ..
! 92: * .. Intrinsic Functions ..
! 93: INTRINSIC SQRT
! 94: * ..
! 95: * .. Executable Statements ..
! 96: *
! 97: * Test the input parameters.
! 98: *
! 99: INFO = 0
! 100: UPPER = LSAME( UPLO, 'U' )
! 101: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 102: INFO = -1
! 103: ELSE IF( N.LT.0 ) THEN
! 104: INFO = -2
! 105: END IF
! 106: IF( INFO.NE.0 ) THEN
! 107: CALL XERBLA( 'DPPTRF', -INFO )
! 108: RETURN
! 109: END IF
! 110: *
! 111: * Quick return if possible
! 112: *
! 113: IF( N.EQ.0 )
! 114: $ RETURN
! 115: *
! 116: IF( UPPER ) THEN
! 117: *
! 118: * Compute the Cholesky factorization A = U'*U.
! 119: *
! 120: JJ = 0
! 121: DO 10 J = 1, N
! 122: JC = JJ + 1
! 123: JJ = JJ + J
! 124: *
! 125: * Compute elements 1:J-1 of column J.
! 126: *
! 127: IF( J.GT.1 )
! 128: $ CALL DTPSV( 'Upper', 'Transpose', 'Non-unit', J-1, AP,
! 129: $ AP( JC ), 1 )
! 130: *
! 131: * Compute U(J,J) and test for non-positive-definiteness.
! 132: *
! 133: AJJ = AP( JJ ) - DDOT( J-1, AP( JC ), 1, AP( JC ), 1 )
! 134: IF( AJJ.LE.ZERO ) THEN
! 135: AP( JJ ) = AJJ
! 136: GO TO 30
! 137: END IF
! 138: AP( JJ ) = SQRT( AJJ )
! 139: 10 CONTINUE
! 140: ELSE
! 141: *
! 142: * Compute the Cholesky factorization A = L*L'.
! 143: *
! 144: JJ = 1
! 145: DO 20 J = 1, N
! 146: *
! 147: * Compute L(J,J) and test for non-positive-definiteness.
! 148: *
! 149: AJJ = AP( JJ )
! 150: IF( AJJ.LE.ZERO ) THEN
! 151: AP( JJ ) = AJJ
! 152: GO TO 30
! 153: END IF
! 154: AJJ = SQRT( AJJ )
! 155: AP( JJ ) = AJJ
! 156: *
! 157: * Compute elements J+1:N of column J and update the trailing
! 158: * submatrix.
! 159: *
! 160: IF( J.LT.N ) THEN
! 161: CALL DSCAL( N-J, ONE / AJJ, AP( JJ+1 ), 1 )
! 162: CALL DSPR( 'Lower', N-J, -ONE, AP( JJ+1 ), 1,
! 163: $ AP( JJ+N-J+1 ) )
! 164: JJ = JJ + N - J + 1
! 165: END IF
! 166: 20 CONTINUE
! 167: END IF
! 168: GO TO 40
! 169: *
! 170: 30 CONTINUE
! 171: INFO = J
! 172: *
! 173: 40 CONTINUE
! 174: RETURN
! 175: *
! 176: * End of DPPTRF
! 177: *
! 178: END
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