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 Section All Sections 1 - General Commands 2 - System Calls 3 - Subroutines 4 - Special Files 5 - File Formats 6 - Games 7 - Macros and Conventions 8 - Maintenance Commands 9 - Kernel Interface n - New Commands
 complib/zlarfx(3) -- applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right 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. complib/zlargv(3) -- generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors 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 )
complib/zlarnv(3) -- return a vector of n random complex numbers from a uniform or normal distribution
ZLARNV returns a vector of n random complex numbers from a uniform or normal distribution.
complib/zlartg(3) -- generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ]
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.
complib/zlartv(3) -- applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y
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) )
complib/zlascl(3) -- multiplie the M by N complex matrix A by the real scalar CTO/CFROM
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.
complib/zlaset(3) -- initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals
ZLASET initializes a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals.
complib/zlasr(3) -- where A is an m by n complex matrix and P is an orthogonal matrix,
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...
complib/zlassq(3) -- )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
ZLASSQ 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...
complib/zlaswp(3) -- perform a series of row interchanges on the matrix A
ZLASWP performs a series of row interchanges on the matrix A. One row interchange is initiated for each of rows K1 through K2 of A.
complib/zlasyf(3) -- using the Bunch-Kaufman diagonal pivoting method
ZLASYF computes a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method. The partial factorization has the form: A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: ( 0 U22 ) ( 0 D ) ( U12' U22' ) A = ( L11 0 ) ( D 0 ) ( L11' L21' ) if UPLO = 'L' ( L21 I ) ( 0 A22 ) ( 0 I ) where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. Note that U' denotes the transpose of U....
complib/zlatbs(3) -- s*b, or A**H * x = s*b,
ZLATBS solves one of the triangular systems with scaling to prevent overflow, where A is an upper or lower triangular band matrix. Here A' denotes the transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine ZTBSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 a...
complib/zlatps(3) -- s*b, or A**H * x = s*b,
ZLATPS solves one of the triangular systems with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form. Here A**T denotes the transpose of A, A**H denotes the conjugate transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine ZTPSV is called. If the matri...
complib/zlatrd(3) -- reduce NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary similari
ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A. If UPLO = 'U', ZLATRD reduces the last NB rows and columns of a matrix, of which the upper triangle is supplied; if UPLO = 'L', ZLATRD reduces the first NB rows and columns of a matrix, of which the lower triangle is supplied. This is an aux...
complib/zlatrs(3) -- s*b, or A**H * x = s*b,
ZLATRS solves one of the triangular systems with scaling to prevent overflow. Here A is an upper or lower triangular matrix, A**T denotes the transpose of A, A**H denotes the conjugate transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine ZTRSV is called. If the matrix A is singular (A(j,j) = 0 ...
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