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complib/zlar2v(3) -- from both sides to a sequence of 2-by-2 complex Hermitian matrices,
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ZLAR2V applies a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices, defined by the elements of the vectors x, y and z. For i = 1,2,...,n ( x(i) z(i) ) := ( conjg(z(i)) y(i) ) ( c(i) conjg(s(i)) ) ( x(i) z(i) ) ( c(i) -conjg(s(i)) ) ( -s(i) c(i) ) ( conjg(z(i)) y(i) ) ( s(i) c(i) ) |
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complib/zlarf(3) -- applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right
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ZLARF applies a complex elementary reflector H to a complex 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 complex scalar and v is a complex vector. If tau = 0, then H is taken to be the unit matrix. To apply H' (the conjugate transpose of H), supply conjg(tau) instead tau. |
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complib/zlarfb(3) -- complex M-by-N matrix C, from either the left or the right
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ZLARFB applies a complex block reflector H or its transpose H' to a complex M-by-N matrix C, from either the left or the right. |
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complib/zlarfg(3) -- generate a complex elementary reflector H of order n, such that H' * ( alpha ) = ( beta ), H' * H = I
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ZLARFG generates a complex elementary reflector H of order n, such that ( x ) ( 0 ) where alpha and beta are scalars, with beta real, and x is an (n-1)- element complex vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v' ) , ( v ) where tau is a complex scalar and v is a complex (n-1)-element vector. Note that H is not hermitian. If the elements of x are all zero and alpha is real, then tau = 0 and H is taken to be the unit matrix. Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1... |
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complib/zlarft(3) -- form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k ele
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ZLARFT forms the triangular factor T of a complex 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 ... |
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complib/zlarfx(3) -- applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right
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ZLARFX applies a complex elementary reflector H to a complex 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 complex scalar and v is a complex vector. If tau = 0, then H is taken to be the unit matrix This version uses inline code if H has order < 11. |
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complib/zlargv(3) -- generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors
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ZLARGV generates a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y. For i = 1,2,...,n ( c(i) s(i) ) ( x(i) ) = ( a(i) ) ( -conjg(s(i)) c(i) ) ( y(i) ) = ( 0 ) |
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complib/zlarnv(3) -- return a vector of n random complex numbers from a uniform or normal distribution
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ZLARNV returns a vector of n random complex numbers from a uniform or normal distribution. |
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complib/zlartg(3) -- generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ]
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ZLARTG generates a plane rotation so that [ -SN CS ] [ G ] [ 0 ] This is a faster version of the BLAS1 routine ZROTG, except for the following 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. |
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complib/zlartv(3) -- applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y
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ZLARTV applies a vector of complex plane rotations with real cosines to elements of the complex vectors x and y. For i = 1,2,...,n ( x(i) ) := ( c(i) s(i) ) ( x(i) ) ( y(i) ) ( -conjg(s(i)) c(i) ) ( y(i) ) |
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complib/zlascl(3) -- multiplie the M by N complex matrix A by the real scalar CTO/CFROM
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ZLASCL multiplies the M by N complex 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/zlaset(3) -- initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals
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ZLASET initializes a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals. |
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complib/zlasr(3) -- where A is an m by n complex matrix and P is an orthogonal matrix,
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ZLASR 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... |
