Annotation of rpl/lapack/lapack/dpotf2.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DPOTF2( UPLO, N, A, LDA, 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, LDA, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: DOUBLE PRECISION A( LDA, * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * DPOTF2 computes the Cholesky factorization of a real symmetric
! 20: * positive definite matrix A.
! 21: *
! 22: * The factorization has the form
! 23: * A = U' * U , if UPLO = 'U', or
! 24: * A = L * L', if UPLO = 'L',
! 25: * where U is an upper triangular matrix and L is lower triangular.
! 26: *
! 27: * This is the unblocked version of the algorithm, calling Level 2 BLAS.
! 28: *
! 29: * Arguments
! 30: * =========
! 31: *
! 32: * UPLO (input) CHARACTER*1
! 33: * Specifies whether the upper or lower triangular part of the
! 34: * symmetric matrix A is stored.
! 35: * = 'U': Upper triangular
! 36: * = 'L': Lower triangular
! 37: *
! 38: * N (input) INTEGER
! 39: * The order of the matrix A. N >= 0.
! 40: *
! 41: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
! 42: * On entry, the symmetric matrix A. If UPLO = 'U', the leading
! 43: * n by n upper triangular part of A contains the upper
! 44: * triangular part of the matrix A, and the strictly lower
! 45: * triangular part of A is not referenced. If UPLO = 'L', the
! 46: * leading n by n lower triangular part of A contains the lower
! 47: * triangular part of the matrix A, and the strictly upper
! 48: * triangular part of A is not referenced.
! 49: *
! 50: * On exit, if INFO = 0, the factor U or L from the Cholesky
! 51: * factorization A = U'*U or A = L*L'.
! 52: *
! 53: * LDA (input) INTEGER
! 54: * The leading dimension of the array A. LDA >= max(1,N).
! 55: *
! 56: * INFO (output) INTEGER
! 57: * = 0: successful exit
! 58: * < 0: if INFO = -k, the k-th argument had an illegal value
! 59: * > 0: if INFO = k, the leading minor of order k is not
! 60: * positive definite, and the factorization could not be
! 61: * completed.
! 62: *
! 63: * =====================================================================
! 64: *
! 65: * .. Parameters ..
! 66: DOUBLE PRECISION ONE, ZERO
! 67: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 68: * ..
! 69: * .. Local Scalars ..
! 70: LOGICAL UPPER
! 71: INTEGER J
! 72: DOUBLE PRECISION AJJ
! 73: * ..
! 74: * .. External Functions ..
! 75: LOGICAL LSAME, DISNAN
! 76: DOUBLE PRECISION DDOT
! 77: EXTERNAL LSAME, DDOT, DISNAN
! 78: * ..
! 79: * .. External Subroutines ..
! 80: EXTERNAL DGEMV, DSCAL, XERBLA
! 81: * ..
! 82: * .. Intrinsic Functions ..
! 83: INTRINSIC MAX, SQRT
! 84: * ..
! 85: * .. Executable Statements ..
! 86: *
! 87: * Test the input parameters.
! 88: *
! 89: INFO = 0
! 90: UPPER = LSAME( UPLO, 'U' )
! 91: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 92: INFO = -1
! 93: ELSE IF( N.LT.0 ) THEN
! 94: INFO = -2
! 95: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 96: INFO = -4
! 97: END IF
! 98: IF( INFO.NE.0 ) THEN
! 99: CALL XERBLA( 'DPOTF2', -INFO )
! 100: RETURN
! 101: END IF
! 102: *
! 103: * Quick return if possible
! 104: *
! 105: IF( N.EQ.0 )
! 106: $ RETURN
! 107: *
! 108: IF( UPPER ) THEN
! 109: *
! 110: * Compute the Cholesky factorization A = U'*U.
! 111: *
! 112: DO 10 J = 1, N
! 113: *
! 114: * Compute U(J,J) and test for non-positive-definiteness.
! 115: *
! 116: AJJ = A( J, J ) - DDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 )
! 117: IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
! 118: A( J, J ) = AJJ
! 119: GO TO 30
! 120: END IF
! 121: AJJ = SQRT( AJJ )
! 122: A( J, J ) = AJJ
! 123: *
! 124: * Compute elements J+1:N of row J.
! 125: *
! 126: IF( J.LT.N ) THEN
! 127: CALL DGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ),
! 128: $ LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA )
! 129: CALL DSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
! 130: END IF
! 131: 10 CONTINUE
! 132: ELSE
! 133: *
! 134: * Compute the Cholesky factorization A = L*L'.
! 135: *
! 136: DO 20 J = 1, N
! 137: *
! 138: * Compute L(J,J) and test for non-positive-definiteness.
! 139: *
! 140: AJJ = A( J, J ) - DDOT( J-1, A( J, 1 ), LDA, A( J, 1 ),
! 141: $ LDA )
! 142: IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
! 143: A( J, J ) = AJJ
! 144: GO TO 30
! 145: END IF
! 146: AJJ = SQRT( AJJ )
! 147: A( J, J ) = AJJ
! 148: *
! 149: * Compute elements J+1:N of column J.
! 150: *
! 151: IF( J.LT.N ) THEN
! 152: CALL DGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ),
! 153: $ LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 )
! 154: CALL DSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
! 155: END IF
! 156: 20 CONTINUE
! 157: END IF
! 158: GO TO 40
! 159: *
! 160: 30 CONTINUE
! 161: INFO = J
! 162: *
! 163: 40 CONTINUE
! 164: RETURN
! 165: *
! 166: * End of DPOTF2
! 167: *
! 168: END
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