m_qtlmap_math
NAME
m_qtlmap_math -- Mathematical subroutines
SYNOPSIS
This modules purposes an interface with NAG specification. In a NAG environment, the nag subroutines is called
otherwise an implementation of the subroutine using SLATEC is called
DESCRIPTION
NOTES
SEE ALSO
MATH_QTLMAP_F01ADF
[ Top ] [ m_qtlmap_math ] [ Subroutines ]
NAME
MATH_QTLMAP_F01ADF
DESCRIPTION
Calculates the approximate inverse of a real symmetric positive-definite matrix, using a Cholesky factorization.
NOTES
USe DPOTRF : LAPACK
MATH_QTLMAP_F03ABF
[ Top ] [ m_qtlmap_math ] [ Subroutines ]
NAME
MATH_QTLMAP_F03ABF
DESCRIPTION
Calculates the determinant of a real symmetric positive-definite matrix using a Cholesky factorization.
NOTES
MATH_QTLMAP_G01AAF
[ Top ] [ m_qtlmap_math ] [ Subroutines ]
NAME
MATH_QTLMAP_G01AAF
DESCRIPTION
Calculates the mean, standard deviation, coefficients of skewness and kurtosis, and the maximum and minimum values for a set of ungrouped data. Weighting may be used.
NOTES
MATH_QTLMAP_G01EAF
[ Top ] [ m_qtlmap_math ] [ Subroutines ]
NAME
MATH_QTLMAP_G01EAF
DESCRIPTION
Returns a one or two-tail probability for the standard Normal distribution, via the routine name.
The lower tail probability :
P(X<=x) = 1/2*derfc(-x/sqrt(2))
The upper tail probability :
P(X>=x) = P(X<=-x)
'S':P(X>=x)+P(X<=-|x|)
'C':P(X<=x)-P(X<=-|x|)
NOTES
MATH_QTLMAP_G01EBF
[ Top ] [ m_qtlmap_math ] [ Subroutines ]
NAME
MATH_QTLMAP_G01EBF
DESCRIPTION
Returns the lower tail, upper tail or two-tail probability for the Student’s t-distribution with real degrees of freedom, via the routine name.
NOTES
MATH_QTLMAP_G01ECF
[ Top ] [ m_qtlmap_math ] [ Subroutines ]
NAME
MATH_QTLMAP_G01ECF
DESCRIPTION
Returns the lower or upper tail probability for the 12 distribution with real degrees of freedom, via
the routine name
NOTES
SLATEC :
* DGAMI : incomplete gamma function
MATH_QTLMAP_G01EEF
[ Top ] [ m_qtlmap_math ] [ Subroutines ]
NAME
MATH_QTLMAP_G01EEF
DESCRIPTION
Computes the upper and lower tail probabilities and the probability density function of the beta distribution with parameters a and b.
NOTES
MATH_QTLMAP_G01FAF
[ Top ] [ m_qtlmap_math ] [ Subroutines ]
NAME
MATH_QTLMAP_G01FAF
DESCRIPTION
Returns the deviate associated with the given probability of the standard Normal distribution, via the routine name.
NOTES
MATH_QTLMAP_G03ACF
[ Top ] [ m_qtlmap_math ] [ Subroutines ]
NAME
MATH_QTLMAP_G05EHF
DESCRIPTION
Performs a canonical variate (canonical discrimination) analysis. INPUT WEIGHT : 'U' no weights ar used . ’W’ or ’V’, weights are used and must be supplied in WT. Constraint: WEIGHT 1⁄4 ’U’; ’W’ or ’V’. In the case of WEIGHT 1⁄4 ’W’, the weights are treated as frequencies and the effective number of observations is the sum of the weights. If WEIGHT 1⁄4 ’V’, the weights are treated as being inversely proportional to the variance of the observations and the effective number of observations is the number of observations with non-zero weights. N : the number of observations. Constraint: N >= NX + NG. M : the total number of variables. Constraint: M >= NX. X(LDX,M) : X(i,j) must contain the ith observation for the jth variable, 1<=i<=N, 1<=j<=M LDX : the first dimension of the array X LDX >= N ISX(M) : indicates whether or not the jth variable is to be included in the analysis. If ISX(j) > 0, then the variables contained in the jth column of X is included in the canonical variate analysis, NX : the number of variables in the analysis, nx .Constraint : NX >= 1 ING(N) : ING(i) indicates which group the ith observation is in, for i=1,2,...,n. The effective number of groups is the number of groups with non-zero membership. Constraint 1<=NG(i)<= NG i=1,..,N NG : the number of groups, ng . Constraint: NG >=2 WT : size(WT)>=N if WEIGHT='W' or 'V' , 1 otherwise. if WEIGHT=’W’ or ’V’, then the first n elements of WT must contain the weights to used in the analysis. if W(i)=0.0, then the ith observation is not included in the analysis. if WEIGHT=’U’, then WT is not referenced. Constraints: WT(i)>=0.0,for i=1,2,..,N , SOMME(WT(i))>=NX + effective number of groups , i=1,...,N LDCVM : the dimension of the array CVM as declared in the program. Constraint LDCVM >=NG LDE : the first dimension of the array E. Constraint: LDE >= min(NX,NG-1). LDCVX : the first dimension of the array CVX TOL : the value of TOL is used to decide if the variables are of full rank and, if not, what is the rank of the variables. The smaller the value of TOL the stricter the criterion for selecting the singular value decomposition. If a non-negative value of TOL less than machine precision is entered, then the square root of machine precision is used instead. OUTPUT NIG(NG) : NIG(j) gives the number of observations in group j, for j=1,2,...,ng. CVM(LDCVM,NX) : CVM(i,j) contains the mean of the jth canonical variate for the ith group, for i=1,2,...,ng ; j=1,2,...,l the remaining columns, if any, are used as workspace. E(LDE,6) : the statistics of the canonical variate analysis. E(i,1), the canonical correlations, deltai , for i=1,2,...,l. E(i,2), the eigenvalues of the within-group sum of squares matrix ,lambda2, for i=1,...,l. E(i,3), the proportion of variation explained by the ith canonical variate, for i=1,...,l. E(i,4), the Chi2 statistic for the ith canonical variate, for i=1,...,l. E(i,5), the degrees of freedom for Chi2 statistic for the ith canonical variate, for i=1,...,l. E(i,6), he significance level for the Chi2 statistic for the ith canonical variate, for i=1,...,l. NCV : he number of canonical variates, l. This will be the minimum of NG-1 and the rank of X. CVX(LDCVX,NG-1) : the canonical variate loadings. CVX(i,j) contains the loading coefficient for the ith variable on the jth canonical variate, for i=1,...,NX ; j=1,...,l; the remaining columns, if any, are used as workspace. IRANKX : the rank of the dependent variables. If the variables are of full rank then IRANKX 1⁄4 NX. If the variables are not of full rank then IRANKX is an estimate of the rank of the dependent variables. IRANKX is calculated as the number of singular values greater than TOLÂ (largest singular value).
NOTES
MATH_QTLMAP_G05EHF
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NAME
MATH_QTLMAP_G05EHF
DESCRIPTION
Performs a pseudo-random permutation of a vector of integers.
NOTES
Use order-pack module m_ctrper : Permute an array randomly, but leaving elements close to their initial locations (nearbyness is controled by PCLS).
MATH_QTLMAP_INFO
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NAME
MATH_QTLMAP_INFO
DESCRIPTION
Give some information about library used by this module
NOTES
MATH_QTLMAP_INVDETMAT
[ Top ] [ m_qtlmap_math ] [ Subroutines ]
NAME
MATH_QTLMAP_INVDETMAT
DESCRIPTION
Calculates the inverse and the derterminant of a real matrix
NOTES
Use DPOFA,DPODI : SLATEC
MATH_QTLMAP_INVDETMATSYM
[ Top ] [ m_qtlmap_math ] [ Subroutines ]
NAME
MATH_QTLMAP_F01ADF
DESCRIPTION
Calculates the inverse and the derterminant of a real symmetric positive-definite matrix
NOTES
MATH_QTLMAP_LOWERTAIL_BETA
[ Top ] [ m_qtlmap_math ] [ Subroutines ]
NAME
MATH_QTLMAP_LOWERTAIL_BETA
DESCRIPTION
Computes the lower of the beta distribution with parameters a and b.
NOTES
NAG : G01EEF
MATH_QTLMAP_M01CAF
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NAME
MATH_QTLMAP_M01CAF
DESCRIPTION
Rearranges a vector of real numbers into ascending or descending order.
NOTES
ORDERPACK
MATH_QTLMAP_M01DAF
[ Top ] [ m_qtlmap_math ] [ Subroutines ]
NAME
MATH_QTLMAP_M01DAF
DESCRIPTION
Ranks a vector of real numbers in ascending or descending order.
NOTES
ORDERPACK
MATH_QTLMAP_S15ADF
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NAME
MATH_QTLMAP_S15ADF
DESCRIPTION
Returns the value of the complementary error function, erfc x, via the routine name.
NOTES
Use DERFC from http://www.kurims.kyoto-u.ac.jp/~ooura/gamerf.html
MATH_QTLMAP_S15AEF
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NAME
MATH_QTLMAP_S15AEF
DESCRIPTION
Returns the value of the error function erf x, via the routine name.
NOTES
Use DERF from http://www.kurims.kyoto-u.ac.jp/~ooura/gamerf.html