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complib/dlarnv(3) -- return a vector of n random real numbers from a uniform or normal distribution
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DLARNV returns a vector of n random real numbers from a uniform or normal distribution. |
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complib/dlartg(3) -- generate a plane rotation so that [ CS SN ]
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DLARTG generate a plane rotation so that [ -SN CS ] [ G ] [ 0 ] This is a slower, more accurate version of the BLAS1 routine DROTG, with the following other differences: F and G are unchanged on return. If G=0, then CS=1 and SN=0. If F=0 and (G .ne. 0), then CS=0 and SN=1 without doing any floating point operations (saves work in DBDSQR when there are zeros on the diagonal). If F exceeds G in magnitude, CS will be positive.... |
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complib/dlartv(3) -- applie a vector of real plane rotations to elements of the real vectors x and y
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DLARTV applies a vector of real plane rotations to elements of the real vectors x and y. For i = 1,2,...,n ( x(i) ) := ( c(i) s(i) ) ( x(i) ) ( y(i) ) ( -s(i) c(i) ) ( y(i) ) |
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complib/dlaruv(3) -- return a vector of n random real numbers from a uniform (0,1)
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DLARUV returns a vector of n random real numbers from a uniform (0,1) distribution (n <= 128). This is an auxiliary routine called by DLARNV and ZLARNV. |
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complib/dlas2(3) -- compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]
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DLAS2 computes the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]. On return, SSMIN is the smaller singular value and SSMAX is the larger singular value. |
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complib/dlascl(3) -- multiplie the M by N real matrix A by the real scalar CTO/CFROM
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DLASCL multiplies the M by N real matrix A by the real scalar CTO/CFROM. This is done without over/underflow as long as the final result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that A may be full, upper triangular, lower triangular, upper Hessenberg, or banded. |
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complib/dlaset(3) -- initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals
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DLASET initializes an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals. |
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complib/dlasq1(3) -- matrix with diagonal D and off-diagonal E
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DLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E. The singular values are computed to high relative accuracy, barring over/underflow or denormalization. The algorithm is described in "Accurate singular values and differential qd algorithms," by K. V. Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230,1994. See also "Implementation of differential qd algorithms," by K. V. Fernando and B. N. Parlett, Technical Report, D... |
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complib/dlasq2(3) -- DLASQ2 computes the singular values of a real N-by-N unreduced bidiagonal matrix with squared diagonal element
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DLASQ2 computes the singular values of a real N-by-N unreduced bidiagonal matrix with squared diagonal elements in Q and squared off-diagonal elements in E. The singular values are computed to relative accuracy TOL, barring over/underflow or denormalization. |
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complib/dlasq3(3) -- DLASQ3 is the workhorse of the whole bidiagonal SVD algorithm
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DLASQ3 is the workhorse of the whole bidiagonal SVD algorithm. This can be described as the differential qd with shifts. |
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complib/dlasq4(3) -- DLASQ4 estimates TAU, the smallest eigenvalue of a matrix
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DLASQ4 estimates TAU, the smallest eigenvalue of a matrix. This routine improves the input value of SUP which is an upper bound for the smallest eigenvalue for this matrix . |
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complib/dlasr(3) -- where A is an m by n real matrix and P is an orthogonal matrix,
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DLASR performs the transformation consisting of a sequence of plane rotations determined by the parameters PIVOT and DIRECT as follows ( z = m when SIDE = 'L' or 'l' and z = n when SIDE = 'R' or 'r' ): When DIRECT = 'F' or 'f' ( Forward sequence ) then P = P( z - 1 )*...*P( 2 )*P( 1 ), and when DIRECT = 'B' or 'b' ( Backward sequence ) then P = P( 1 )*P( 2 )*...*P( z - 1 ), where P( k ) is a plane rotation matrix for the following planes: when PIVOT = 'V' or 'v' ( Variable pi... |
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complib/dlasrt(3) -- the numbers in D in increasing order (if ID = 'I') or in decreasing order (if ID = 'D' )
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Sort the numbers in D in increasing order (if ID = 'I') or in decreasing order (if ID = 'D' ). Use Quick Sort, reverting to Insertion sort on arrays of size <= 20. Dimension of STACK limits N to about 2**32. |
