Annotation of rpl/lapack/lapack/zpotf2.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZPOTF2( 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: COMPLEX*16 A( LDA, * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * ZPOTF2 computes the Cholesky factorization of a complex Hermitian
! 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: * Hermitian 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) COMPLEX*16 array, dimension (LDA,N)
! 42: * On entry, the Hermitian 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: COMPLEX*16 CONE
! 69: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
! 70: * ..
! 71: * .. Local Scalars ..
! 72: LOGICAL UPPER
! 73: INTEGER J
! 74: DOUBLE PRECISION AJJ
! 75: * ..
! 76: * .. External Functions ..
! 77: LOGICAL LSAME, DISNAN
! 78: COMPLEX*16 ZDOTC
! 79: EXTERNAL LSAME, ZDOTC, DISNAN
! 80: * ..
! 81: * .. External Subroutines ..
! 82: EXTERNAL XERBLA, ZDSCAL, ZGEMV, ZLACGV
! 83: * ..
! 84: * .. Intrinsic Functions ..
! 85: INTRINSIC DBLE, MAX, SQRT
! 86: * ..
! 87: * .. Executable Statements ..
! 88: *
! 89: * Test the input parameters.
! 90: *
! 91: INFO = 0
! 92: UPPER = LSAME( UPLO, 'U' )
! 93: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 94: INFO = -1
! 95: ELSE IF( N.LT.0 ) THEN
! 96: INFO = -2
! 97: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 98: INFO = -4
! 99: END IF
! 100: IF( INFO.NE.0 ) THEN
! 101: CALL XERBLA( 'ZPOTF2', -INFO )
! 102: RETURN
! 103: END IF
! 104: *
! 105: * Quick return if possible
! 106: *
! 107: IF( N.EQ.0 )
! 108: $ RETURN
! 109: *
! 110: IF( UPPER ) THEN
! 111: *
! 112: * Compute the Cholesky factorization A = U'*U.
! 113: *
! 114: DO 10 J = 1, N
! 115: *
! 116: * Compute U(J,J) and test for non-positive-definiteness.
! 117: *
! 118: AJJ = DBLE( A( J, J ) ) - ZDOTC( J-1, A( 1, J ), 1,
! 119: $ A( 1, J ), 1 )
! 120: IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
! 121: A( J, J ) = AJJ
! 122: GO TO 30
! 123: END IF
! 124: AJJ = SQRT( AJJ )
! 125: A( J, J ) = AJJ
! 126: *
! 127: * Compute elements J+1:N of row J.
! 128: *
! 129: IF( J.LT.N ) THEN
! 130: CALL ZLACGV( J-1, A( 1, J ), 1 )
! 131: CALL ZGEMV( 'Transpose', J-1, N-J, -CONE, A( 1, J+1 ),
! 132: $ LDA, A( 1, J ), 1, CONE, A( J, J+1 ), LDA )
! 133: CALL ZLACGV( J-1, A( 1, J ), 1 )
! 134: CALL ZDSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
! 135: END IF
! 136: 10 CONTINUE
! 137: ELSE
! 138: *
! 139: * Compute the Cholesky factorization A = L*L'.
! 140: *
! 141: DO 20 J = 1, N
! 142: *
! 143: * Compute L(J,J) and test for non-positive-definiteness.
! 144: *
! 145: AJJ = DBLE( A( J, J ) ) - ZDOTC( J-1, A( J, 1 ), LDA,
! 146: $ A( J, 1 ), LDA )
! 147: IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
! 148: A( J, J ) = AJJ
! 149: GO TO 30
! 150: END IF
! 151: AJJ = SQRT( AJJ )
! 152: A( J, J ) = AJJ
! 153: *
! 154: * Compute elements J+1:N of column J.
! 155: *
! 156: IF( J.LT.N ) THEN
! 157: CALL ZLACGV( J-1, A( J, 1 ), LDA )
! 158: CALL ZGEMV( 'No transpose', N-J, J-1, -CONE, A( J+1, 1 ),
! 159: $ LDA, A( J, 1 ), LDA, CONE, A( J+1, J ), 1 )
! 160: CALL ZLACGV( J-1, A( J, 1 ), LDA )
! 161: CALL ZDSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
! 162: END IF
! 163: 20 CONTINUE
! 164: END IF
! 165: GO TO 40
! 166: *
! 167: 30 CONTINUE
! 168: INFO = J
! 169: *
! 170: 40 CONTINUE
! 171: RETURN
! 172: *
! 173: * End of ZPOTF2
! 174: *
! 175: END
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