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complib/dlapll(3) -- two column vectors X and Y, let A = ( X Y )
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Given two column vectors X and Y, let The subroutine first computes the QR factorization of A = Q*R, and then computes the SVD of the 2-by-2 upper triangular matrix R. The smaller singular value of R is returned in SSMIN, which is used as the measurement of the linear dependency of the vectors X and Y. |
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complib/dlapmt(3) -- rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integer
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DLAPMT rearranges the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N. If FORWRD = .TRUE., forward permutation: X(*,K(J)) is moved X(*,J) for J = 1,2,...,N. If FORWRD = .FALSE., backward permutation: X(*,J) is moved to X(*,K(J)) for J = 1,2,...,N. |
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complib/dlapy2(3) -- return sqrt(x**2+y**2), taking care not to cause unnecessary overflow
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DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary overflow. |
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complib/dlapy3(3) -- return sqrt(x**2+y**2+z**2), taking care not to cause unnecessary overflow
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DLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause unnecessary overflow. |
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complib/dlaqgb(3) -- equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scalin
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DLAQGB equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C. |
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complib/dlaqge(3) -- equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
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DLAQGE equilibrates a general M by N matrix A using the row and scaling factors in the vectors R and C. |
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complib/dlaqsb(3) -- equilibrate a symmetric band matrix A using the scaling factors in the vector S
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DLAQSB equilibrates a symmetric band matrix A using the scaling factors in the vector S. |
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complib/dlaqsp(3) -- equilibrate a symmetric matrix A using the scaling factors in the vector S
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DLAQSP equilibrates a symmetric matrix A using the scaling factors in the vector S. |
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complib/dlaqsy(3) -- equilibrate a symmetric matrix A using the scaling factors in the vector S
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DLAQSY equilibrates a symmetric matrix A using the scaling factors in the vector S. |
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complib/dlaqtr(3) -- solve the real quasi-triangular system op(T)*p = scale*c, if LREAL = .TRUE
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DLAQTR solves the real quasi-triangular system or the complex quasi-triangular systems op(T + iB)*(p+iq) = scale*(c+id), if LREAL = .FALSE. in real arithmetic, where T is upper quasi-triangular. If LREAL = .FALSE., then the first diagonal block of T must be 1 by 1, B is the specially structured matrix B = [ b(1) b(2) ... b(n) ] [ w ] [ w ] [ . ] [ w ] op(A) = A or A', A' denotes the conjugate transpose of matrix A. On input, X = [ c ]. On output, X = [ p ]. [ d ] [ q ] This subroutine is desig... |
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complib/dlar2v(3) -- sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z
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DLAR2V applies a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z. For i = 1,2,...,n ( x(i) z(i) ) := ( c(i) s(i) ) ( x(i) z(i) ) ( c(i) -s(i) ) ( z(i) y(i) ) ( -s(i) c(i) ) ( z(i) y(i) ) ( s(i) c(i) ) |
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complib/dlarf(3) -- applie a real elementary reflector H to a real m by n matrix C, from either the left or the right
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DLARF applies a real elementary reflector H to a real m by n matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v' where tau is a real scalar and v is a real vector. If tau = 0, then H is taken to be the unit matrix. |
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complib/dlarfb(3) -- applie a real block reflector H or its transpose H' to a real m by n matrix C, from either the left or the rig
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DLARFB applies a real block reflector H or its transpose H' to a real m by n matrix C, from either the left or the right. |
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complib/dlarfg(3) -- generate a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H' * H = I
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DLARFG generates a real elementary reflector H of order n, such that ( x ) ( 0 ) where alpha and beta are scalars, and x is an (n-1)-element real vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v' ) , ( v ) where tau is a real scalar and v is a real (n-1)-element vector. If the elements of x are all zero, then tau = 0 and H is taken to be the unit matrix. Otherwise 1 <= tau <= 2. |
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complib/dlarft(3) -- form the triangular factor T of a real block reflector H of order n, which is defined as a product of k elemen
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DLARFT forms the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and H = I - V * T * V' If STOREV = 'R', the vector which defines the elementary reflector H(i) is sto... |
