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complib/clar2v(3) -- from both sides to a sequence of 2-by-2 complex Hermitian matrices,
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CLAR2V 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/clarf(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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CLARF 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/clarfb(3) -- complex M-by-N matrix C, from either the left or the right
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CLARFB 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/clarfg(3) -- generate a complex elementary reflector H of order n, such that H' * ( alpha ) = ( beta ), H' * H = I
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CLARFG 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/clarft(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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CLARFT 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/clarfx(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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CLARFX 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/clargv(3) -- generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors
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CLARGV 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/clarnv(3) -- return a vector of n random complex numbers from a uniform or normal distribution
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CLARNV returns a vector of n random complex numbers from a uniform or normal distribution. |
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complib/clartg(3) -- generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ]
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CLARTG generates a plane rotation so that [ -SN CS ] [ G ] [ 0 ] This is a faster version of the BLAS1 routine CROTG, 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/clartv(3) -- applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y
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CLARTV 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/clascl(3) -- multiplie the M by N complex matrix A by the real scalar CTO/CFROM
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CLASCL 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/claset(3) -- initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals
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CLASET initializes a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals. |
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complib/clasr(3) -- where A is an m by n complex matrix and P is an orthogonal matrix,
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CLASR 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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perl5/Class::Struct(3) -- declare struct-like datatypes as Perl classes
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Class::Struct exports a single function, struct. Given a list of element names and types, and optionally a class name, struct creates a Perl 5 class that implements a "struct-like" data structure. The new class is given a constructor method, new, for creating struct objects. Page 1 Class::Struct(3) Class::Struct(3) Each element in the struct data has an accessor method, which is used to assign to the element and to fetch its value. The default accessor can be overridden by declaring a sub of t... |
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complib/classq(3) -- )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
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CLASSQ returns the values scl and ssq such that where x( i ) = abs( X( 1 + ( i - 1 )*INCX ) ). The value of sumsq is assumed to be at least unity and the value of ssq will then satisfy 1.0 .le. ssq .le. ( sumsq + 2*n ). scale is assumed to be non-negative and scl returns the value scl = max( scale, abs( real( x( i ) ) ), abs( aimag( x( i ) ) ) ), i scale and sumsq must be supplied in SCALE and SUMSQ respectively. SCALE and SUMSQ are overwritten by scl and ssq respectively. The routine makes only... |
