Routines

[A] [B] [C] [D] [E] [F] [G] [H] [ I ] [J] [K] [L] [M]
[N] [O] [P] [Q] [R] [S] [T] [U] [V] [W] [X] [Y] [Z]

Function Purpose Statement

ACBCB	Adds two complex band matrices, both in band storage mode.
ACHAR	Returns a character given its ASCII value.
AMACH	Retrieves single-precision machine constants.
ARBRB	Adds two band matrices, both in band storage mode.

BCLSF	Solves a nonlinear least squares problem subject to bounds on the variables using a modified Levenberg-Marquardt algorithm and a finite-difference Jacobian.
BCLSJ	Solves a nonlinear least squares problem subject to bounds on the variables using a modified Levenberg-Marquardt algorithm and a user-supplied Jacobian.
BCNLS	Solves a nonlinear least-squares problem subject to bounds on the variables and general linear constraints.
BCOAH	Minimizes a function of N variables subject to bounds the variables using a modified Newton method and a user-supplied Hessian.
BCODH	Minimizes a function of N variables subject to bounds the variables using a modified Newton method and a finite-difference Hessian.
BCONF	Minimizes a function of N variables subject to bounds the variables using a quasi-Newton method and a finite-difference gradient.
BCONG	Minimizes a function of N variables subject to bounds the variables using a quasi-Newton method and a user-supplied gradient.
BCPOL	Minimizes a function of N variables subject to bounds the variables using a direct search complex algorithm.
BLINF	Computes the bilinear form xTAy.
BS1GD	Evaluates the derivative of a spline on a grid, given its B-spline representation.
BS2DR	Evaluates the derivative of a two-dimensional tensor-product spline, given its tensor-product B-spline representation.
BS2GD	Evaluates the derivative of a two-dimensional tensor-product spline, given its tensor-product B-spline representation on a grid.
BS2IG	Evaluates the integral of a tensor-product spline on a rectangular domain, given its tensor-product B-spline representation.
BS2IN	Computes a two-dimensional tensor-product spline interpolant, returning the tensor-product B-spline coefficients.
BS2VL	Evaluates a two-dimensional tensor-product spline, given its tensor-product B-spline representation.
BS3DR	Evaluates the derivative of a three-dimensional tensor-product spline, given its tensor-product B-spline representation.
BS3GD	Evaluates the derivative of a three-dimensional tensor-product spline, given its tensor-product B-spline representation on a grid.
BS3IG	Evaluates the integral of a tensor-product spline in three dimensions over a three-dimensional rectangle, given its tensorproduct B-spline representation.
BS3IN	Computes a three-dimensional tensor-product spline interpolant, returning the tensor-product B-spline coefficients.
BS3VL	Evaluates a three-dimensional tensor-product spline, given its tensor-product B-spline representation
BSCPP	Converts a spline in B-spline representation to piecewise polynomial representation.
BSDER	Evaluates the derivative of a spline, given its B-spline representation.
BSINT	Computes the spline interpolant, returning the B-spline coefficients.
BSITG	Evaluates the integral of a spline, given its B-spline representation.
BSLS2	Computes a two-dimensional tensor-product spline approximant using least squares, returning the tensor-product B-spline coefficients.
BSLS3	Computes a three-dimensional tensor-product spline approximant using least squares, returning the tensor-product B-spline coefficients.
BSLSQ	Computes the least-squares spline approximation, and return the B-spline coefficients.
BSNAK	Computes the ‘not-a-knot' spline knot sequence.
BSOPK	Computes the ‘optimal' spline knot sequence.
BSVAL	Evaluates a spline, given its B-spline representation.
BSVLS	Computes the variable knot B-spline least squares approximation to given data.
BVPFD	Solves a (parameterized) system of differential equations with boundary conditions at two points, using a variable order, variable step size finite-difference method with deferred corrections.
BVPMS	Solves a (parameterized) system of differential equations with boundary conditions at two points, using a multiple-shooting method.

CADD	Adds a scalar to each component of a vector, x ¬ x + a, all complex.
CAXPY	Computes the scalar times a vector plus a vector, y ¬ ax + y, all complex.
CCBCB	Copies a complex band matrix stored in complex band storage mode.
CCBCG	Converts a complex matrix in band storage mode to a complex matrix in full storage mode.
CCGCB	Converts a complex general matrix to a matrix in complex band storage mode.
CCGCG	Copies a complex general matrix.
CCONV	Computes the convolution of two complex vectors.
CCOPY	Copies a vector x to a vector y, both complex.
CCORL	Computes the correlation of two complex vectors.
CDGRD	Approximates the gradient using central differences.
CDOTC	Computes the complex conjugate dot product, .
CDOTU	Computes the complex dot product xTy.
CGBMV	Computes one of the matrix-vector operations: , where A is a matrix stored in band storage mode.
CGEMM	Computes one of the matrix-matrix operations:
CGEMV	Computes one of the matrix-vector operations: ,
CGERC	Computes the rank-one update of a complex general matrix: .
CGERU	Computes the rank-one update of a complex general matrix: .
CHBCB	Copies a complex Hermitian band matrix stored in band Hermitian storage mode to a complex band matrix stored in band storage mode.
CHBMV	Computes the matrix-vector operation ,where A is an Hermitian band matrix in band Hermitian storage.
CHEMM	Computes one of the matrix-matrix operations: , where A is an Hermitian matrix and B and C are m by n matrices.
CHEMV	Computes the matrix-vector operation , where A is an Hermitian matrix.
CHER	Computes the rank-one update of an Hermitian matrix: with x complex and a real.
CHER2	Computes a rank-two update of an Hermitian matrix: .
CHER2K	Computes one of the Hermitian rank 2k operations: , where C is an n by n Hermitian matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.
CHERK	Computes one of the Hermitian rank k operations: , where C is an n by n Hermitian matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.
CHFCG	Extends a complex Hermitian matrix defined in its upper triangle to its lower triangle.
CHGRD	Checks a user-supplied gradient of a function.
CHHES	Checks a user-supplied Hessian of an analytic function.
CHJAC	Checks a user-supplied Hessian of an analytic function.
CHOL	Checks a user-supplied Jacobian of a system of equations with M functions in N unknowns.
COND	Computes the condition number of a matrix.
CONFT	Computes the condition number of a rectangular matrix, A.
CONST	Computes the least-squares constrained spline approximation, returning the B-spline coefficients.
CPSEC	Returns the value of various mathematical and physical constants.
CRBCB	Returns CPU time used in seconds.
CRBRB	Converts a real matrix in band storage mode to a complex matrix in band storage mode.
CRBRG	Copies a real band matrix stored in band storage mode.
CRGCG	Converts a real matrix in band storage mode to a real general matrix.
CRGRB	Copies a real general matrix to a complex general matrix.
CRGRG	Converts a real general matrix to a matrix in band storage mode.
CRRCR	Copies a real general matrix.
CS1GD	Copies a real rectangular matrix to a complex rectangular matrix.
CSAKM	Evaluates the derivative of a cubic spline on a grid.
CSBRB	Computes the Akima cubic spline interpolant.
CSCAL	Copies a real symmetric band matrix stored in band symmetric storage mode to a real band matrix stored in band storage mode.
CSCON	Multiplies a vector by a scalar, y ¬ ay, both complex.
CSDEC	Computes a cubic spline interpolant that is consistent with the concavity of the data.
CSDER	Computes the cubic spline interpolant with specified derivative endpoint conditions.
CSET	Evaluates the derivative of a cubic spline.
CSFRG	Sets the components of a vector to a scalar, all complex.
CSHER	Extends a real symmetric matrix defined in its upper triangle to its lower triangle.
CSIEZ	Computes the cubic spline interpolant with the ‘not-a-knot' condition and return values of the interpolant at specified points.
CSINT	Computes the cubic spline interpolant with the ‘not-a-knot' condition.
CSITG	Evaluates the integral of a cubic spline.
CSPER	Computes the cubic spline interpolant with periodic boundary conditions.
CSROT	Applies a complex Givens plane rotation.
CSROTM	Applies a complex modified Givens plane rotation.
CSSCAL	Multiplies a complex vector by a single-precision scalar, y ¬ ay.
CSSCV	Computes a smooth cubic spline approximation to noisy data using cross-validation to estimate the smoothing parameter.
CSSED	Smooths one-dimensional data by error detection.
CSSMH	Computes a smooth cubic spline approximation to noisy data.
CSUB	Subtracts each component of a vector from a scalar, x ¬ a - x, all complex.
CSVAL	Evaluates a cubic spline.
CSVCAL	Multiplies a complex vector by a single-precision scalar and store the result in another complex vector, y ¬ ax.
CSWAP	Interchanges vectors x and y, both complex.
CSYMM	Computes one of the matrix-matrix operations: , where A is a symmetric matrix and B and C are m by n matrices.
CSYR2K	Computes one of the symmetric rank 2k operations: , where C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.
CSYRK	Computes one of the symmetric rank k operations: , where C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.
CTBMV	Computes one of the matrix-vector operations: , where A is a triangular matrix in band storage mode.
CTBSV	Solves one of the complex triangular systems: , where A is a triangular matrix in band storage mode.
CTRMM	Computes one of the matrix-matrix operations: where B is an m by n matrix and A is a triangular matrix.
CTRMV	Computes one of the matrix-vector operations: , where A is a triangular matrix.
CTRSM	Solves one of the complex matrix equations: where A is a traiangular matrix.
CTRSV	Solves one of the complex triangular systems: , where A is a triangular matrix.
CUNIT	Converts X in units XUNITS to Y in units YUNITS.
CVCAL	Multiplies a vector by a scalar and store the result in another vector, y ¬ ax, all complex.
CVTSI	Converts a character string containing an integer number into the corresponding integer form.
CZCDOT	Computes the sum of a complex scalar plus a complex conjugate dot product, , using a double-precision accumulator.
CZDOTA	Computes the sum of a complex scalar, a complex dot product and the double-complex accumulator, which is set to the result ACC ¬ ACC + a + xTy.
CZDOTC	Computes the complex conjugate dot product, , using a double-precision accumulator.
CZDOTI	Computes the sum of a complex scalar plus a complex dot product using a double-complex accumulator, which is set to the result ACC ¬ a + xTy.
CZDOTU	Computes the complex dot product xTy using a double-precision accumulator.
CZUDOT	Computes the sum of a complex scalar plus a complex dot product, a + xTy, using a double-precision accumulator.

DASPG	Solves a first order differential-algebraic system of equations, g(t, y, y¢) = 0, using Petzold−Gear BDF method.
DENSE_LP	Solves a linear programming problem.
DERIV	Computes the first, second or third derivative of a user-supplied function.
DET	Computes the determinant of a rectangular matrix, A.
DIAG	Constructs a square diagonal matrix from a rank-1 array or several diagonal matrices from a rank-2 array.
DIAGONALS	Extracts a rank-1 array whose values are the diagonal terms of a rank-2 array argument.
DISL1	Computes the 1-norm distance between two points.
DISL2	Computes the Euclidean (2-norm) distance between two points.
DISLI	Computes the infinity norm distance between two points.
DLPRS	Solves a linear programming problem via the revised simplex algorithm.
DMACH	See AMACH.
DQADD (See Extended Precision Arithmetic Chapter 9 )	Adds a double-precision scalar to the accumulator in extended precision.
DQINI (See Extended Precision Arithmetic Chapter 9 )	Initializes an extended-precision accumulator with a double-precision scalar.
DQMUL (See Extended Precision Arithmetic Chapter 9 )	Multiplies double-precision scalars in extended precision.
DQSTO (See Extended Precision Arithmetic Chapter 9 )	Stores a double-precision approximation to an extended-precision scalar.
DSDOT(See Chapter 9 )	Computes the single-precision dot product xTy using a double precision accumulator. This routine handles MATH/LIBRARY and STAT/LIBRARY type DOUBLE PRECISION options.
SUMAG/DUMAG	This routine handles MATH/LIBRARY and STAT/LIBRARY type DOUBLE PRECISION options.

EIG	Computes the eigenvalue-eigenvector decomposition of an ordinary or generalized eigenvalue problem.
EPICG	Computes the performance index for a complex eigensystem.
EPIHF	Computes the performance index for a complex Hermitian eigensystem.
EPIRG	Computes the performance index for a real eigensystem.
EPISB	Computes the performance index for a real symmetric eigensystem in band symmetric storage mode.
EPISF	Computes the performance index for a real symmetric eigensystem.
ERROR_POST	Prints error messages that are generated by IMSL routines using EPACK.
ERSET	Sets error handler default print and stop actions.
EVAHF	Computes the largest or smallest eigenvalues of a complex Hermitian matrix.
EVASB	Computes the largest or smallest eigenvalues of a real symmetric matrix in band symmetric storage mode.
EVASF	Computes the largest or smallest eigenvalues of a real symmetric matrix.
EVBHF	Computes the eigenvalues in a given range of a complex Hermitian matrix.
EVBSB	Computes the eigenvalues in a given interval of a real symmetric matrix stored in band symmetric storage mode.
EVBSF	Computes selected eigenvalues of a real symmetric matrix.
EVCCG	Computes all of the eigenvalues and eigenvectors of a complex matrix.
EVCCH	Computes all of the eigenvalues and eigenvectors of a complex upper Hessenberg matrix.
EVCHF	Computes all of the eigenvalues and eigenvectors of a complex Hermitian matrix.
EVCRG	Computes all of the eigenvalues and eigenvectors of a real matrix.
EVCRH	Computes all of the eigenvalues and eigenvectors of a real upper Hessenberg matrix.
EVCSB	Computes all of the eigenvalues and eigenvectors of a real symmetric matrix in band symmetric storage mode.
EVCSF	Computes all of the eigenvalues and eigenvectors of a real symmetric matrix.
EVEHF	Computes the largest or smallest eigenvalues and the corresponding eigenvectors of a complex Hermitian matrix.
EVESB	Computes the largest or smallest eigenvalues and the corresponding eigenvectors of a real symmetric matrix in band symmetric storage mode.
EVESF	Computes the largest or smallest eigenvalues and the corresponding eigenvectors of a real symmetric matrix.
EVFHF	Computes the eigenvalues in a given range and the corresponding eigenvectors of a complex Hermitian matrix.
EVFSB	Computes the eigenvalues in a given interval and the corresponding eigenvectors of a real symmetric matrix stored in band symmetric storage mode.
EVFSF	Computes selected eigenvalues and eigenvectors of a real symmetric matrix.
EVLCG	Computes all of the eigenvalues of a complex matrix.
EVLCH	Computes all of the eigenvalues of a complex upper Hessenberg matrix.
EVLHF	Computes all of the eigenvalues of a complex Hermitian matrix.
EVLRG	Computes all of the eigenvalues of a real matrix.
EVLRH	Computes all of the eigenvalues of a real upper Hessenberg matrix.
EVLSB	Computes all of the eigenvalues of a real symmetric matrix in band symmetric storage mode.
EVLSF	Computes all of the eigenvalues of a real symmetric matrix.
EYE	Creates a rank-2 square array whose diagonals are all the value one.

FAURE_FREE	Frees the structure containing information about the Faure sequence.
FAURE_INIT	Shuffled Faure sequence initialization.
FAURE_NEXT	Computes a shuffled Faure sequence.
FAST_DFT	Computes the Discrete Fourier Transform of a rank-1 complex array, x.
FAST_2DFT	Computes the Discrete Fourier Transform (2DFT) of a rank-2 complex array, x.
FAST_3DFT	Computes the Discrete Fourier Transform (2DFT) of a rank-3 complex array, x.
FCOSI	Computes parameters needed by FCOST.
FCOST	Computes the discrete Fourier cosine transformation of an even sequence.
FDGRD	Approximates the gradient using forward differences.
FDHES	Approximates the Hessian using forward differences and function values.
FDJAC	Approximates the Jacobian of M functions in N unknowns using forward differences.
FFT	The Discrete Fourier Transform of a complex sequence and its inverse transform.
FFT_BOX	The Discrete Fourier Transform of several complex or real sequences.
FFT2B	Computes the inverse Fourier transform of a complex periodic two-dimensional array.
FFT2D	Computes Fourier coefficients of a complex periodic two-dimensional array.
FFT3B	Computes the inverse Fourier transform of a complex periodic three-dimensional array.
FFT3F	Computes Fourier coefficients of a complex periodic threedimensional array.
FFTCB	Computes the complex periodic sequence from its Fourier coefficients.
FFTCF	Computes the Fourier coefficients of a complex periodic sequence.
FFTCI	Computes parameters needed by FFTCF and FFTCB.
FFTRB	Computes the real periodic sequence from its Fourier coefficients.
FFTRF	Computes the Fourier coefficients of a real periodic sequence.
FFTRI	Computes parameters needed by FFTRF and FFTRB.
FNLSQ	Computes a least-squares approximation with user-supplied basis functions.
FPS2H	Solves Poisson's or Helmholtz's equation on a two-dimensional rectangle using a fast Poisson solver based on the HODIE finite-difference scheme on a uni mesh.
FPS3H	Solves Poisson's or Helmholtz's equation on a three-dimensional box using a fast Poisson solver based on the HODIE finite-difference scheme on a uniform mesh.
FQRUL	Computes a Fejér quadrature rule with various classical weight functions.
FSINI	Computes parameters needed by FSINT.
FSINT	Computes the discrete Fourier sine transformation of an odd sequence.

GDHES	Approximates the Hessian using forward differences and a user-supplied gradient.
GGUES	Generates points in an N-dimensional space.
GMRES	Uses restarted GMRES with reverse communication to generate an approximate solution of Ax = b.
GPICG	Computes the performance index for a generalized complex eigensystem Az = lBz.
GPIRG	Computes the performance index for a generalized real eigensystem Az = lBz.
GPISP	Computes the performance index for a generalized real symmetric eigensystem problem.
GQRCF	Computes a Gauss, Gauss-Radau or Gauss-Lobatto quadrature rule given the recurrence coefficients for the monic polynomials orthogonal with respect to the weight function.
GQRUL	Computes a Gauss, Gauss-Radau, or Gauss-Lobatto quadrature rule with various classical weight functions.
GVCCG	Computes all of the eigenvalues and eigenvectors of a generalized complex eigensystem Az = lBz.
GVCRG	Computes all of the eigenvalues and eigenvectors of a generalized real eigensystem Az = lBz.
GVCSP	Computes all of the eigenvalues and eigenvectors of the generalized real symmetric eigenvalue problem Az = lBz, with B symmetric positive definite.
GVLCG	Computes all of the eigenvalues of a generalized complex eigensystem Az = lBz.
GVLRG	Computes all of the eigenvalues of a generalized real eigensystem Az = lBz.
GVLSP	Computes all of the eigenvalues of the generalized real symmetric eigenvalue problem Az = lBz, with B symmetric positive definite.

HRRRR	Computes the Hadamard product of two real rectangular matrices.
HYPOT	Computes without underflow or overflow.

IACHAR	Returns the integer ASCII value of a character argument.
IADD	Adds a scalar to each component of a vector, x ¬ x + a, all integer. Finds the smallest index of the component of a complex vector having maximum magnitude.
ICAMAX	Finds the smallest index of the component of a complex vector having minimum magnitude.
ICAMIN	Returns the ASCII value of a character converted to uppercase.
ICASE	Copies a vector x to a vector y, both integer.
ICOPY	Computes the day of the week for a given date.
IDYWK	Retrieves the code for an informational error.
IERCD and N1RTY	The inverse of the Discrete Fourier Transform of a complex sequence.
IFFT	The inverse of the Discrete Fourier Transform of a complex sequence.
IFFT_BOX	The inverse Discrete Fourier Transform of several complex or real sequences.
IFNAN(X)	Checks if a value is NaN (not a number).
IICSR	Compares two character strings using the ASCII collating sequence but without regard to case.
IIDEX	Determines the position in a string at which a given character sequence begins without regard to case.
IIMAX	Finds the smallest index of the maximum component of a integer vector.
IIMIN	Finds the smallest index of the minimum of an integer vector.
IMACH	Retrieves integer machine constants.
INLAP	Computes the inverse Laplace transform of a complex function.
ISAMAX	Finds the smallest index of the component of a single-precision vector having maximum absolute value.
ISAMIN	Finds the smallest index of the component of a single-precision vector having minimum absolute value.
ISET	Sets the components of a vector to a scalar, all integer.
ISMAX	Finds the smallest index of the component of a single-precision vector having maximum value.
ISMIN	Finds the smallest index of the component of a single-precision vector having minimum value.
ISNAN	This is a generic logical function used to test scalars or arrays for occurrence of an IEEE 754 Standard format of floating point (ANSI/IEEE 1985) NaN, or not-a-number.
ISRCH	Searches a sorted integer vector for a given integer and return its index.
ISUB	Subtracts each component of a vector from a scalar, x ¬ a - x, all integer.
ISUM	Sums the values of an integer vector.
ISWAP	Interchanges vectors x and y, both integer.
IUMAG	Sets or retrieves MATH/LIBRARY integer options.
IVMRK	Solves an initial-value problem y¢ = f(t, y) for ordinary differential equations using Runge-Kutta pairs of various orders.
IVPAG	Solves an initial-value problem for ordinary differential equations using either Adams-Moulton's or Gear's BDF method.
IVPRK	Solves an initial-value problem for ordinary differential equations using the Runge-Kutta-Verner fifth-order and sixth-order method.

JCGRC

Solves a real symmetric definite linear system using the Jacobi preconditioned conjugate gradient method with reverse communication.

LCHRG	Computes the Cholesky decomposition of a symmetric positive semidefinite matrix with optional column pivoting.
LCLSQ	Solves a linear least-squares problem with linear constraints.
LCONF	Minimizes a general objective function subject to linear equality/inequality constraints.
LCONG	Minimizes a general objective function subject to linear equality/inequality constraints.
LDNCH	Downdates the RTR Cholesky factorization of a real symmetric positive definite matrix after a rank-one matrix is removed
LFCCB	Computes the LU factorization of a complex matrix in band storage mode and estimate its L1condition number.
LFCCG	Computes the LU factorization of a complex general matrix and estimate its L1 condition number.
LFCCT	Estimates the condition number of a complex triangular matrix.
LFCDH	Computes the RH R factorization of a complex Hermitian positive definite matrix and estimate its L1 condition number.
LFCDS	Computes the RT R Cholesky factorization of a real symmetric positive definite matrix and estimate its L1condition number.
LFCHF	Computes the U DUH factorization of a complex Hermitian matrix and estimate its L1 condition number.
LFCQH	Computes the RH R factorization of a complex Hermitian positive definite matrix in band Hermitian storage mode and estimate its L1 condition number.
LFCQS	Computes the RT R Cholesky factorization of a real symmetric positive definite matrix in band symmetric storage mode and estimate its L1 condition number.
LFCRB	Computes the LU factorization of a real matrix in band storage mode and estimate its L1 condition number.
LFCRG	Computes the LU factorization of a real general matrix and estimate its L1 condition number.
LFCRT	Estimates the condition number of a real triangular matrix.
LFCSF	Computes the U DUT factorization of a real symmetric matrix and estimate its L1condition number.
LFDCB	Computes the determinant of a complex matrix given the LU factorization of the matrix in band storage mode.
LFDCG	Computes the determinant of a complex general matrix given the LU factorization of the matrix.
LFDCT	Computes the determinant of a complex triangular matrix.
LFDDH	Computes the determinant of a complex Hermitian positive definite matrix given the RH R Cholesky factorization of the matrix.
LFDDS	Computes the determinant of a real symmetric positive definite matrix given the RH R Cholesky factorization of the matrix.
LFDHF	Computes the determinant of a complex Hermitian matrix given the U DUH factorization of the matrix.
LFDQH	Computes the determinant of a complex Hermitian positive definite matrix given the RH R Cholesky factorization in band Hermitian storage mode.
LFDQS	Computes the determinant of a real symmetric positive definite matrix given the RT R Cholesky factorization of the band symmetric storage mode.
LFDRB	Computes the determinant of a real matrix in band storage mode given the LU factorization of the matrix.
LFDRG	Computes the determinant of a real general matrix given the LU factorization of the matrix.
LFDRT	Computes the determinant of a real triangular matrix.
LFDSF	Computes the determinant of a real symmetric matrix given the U DUT factorization of the matrix.
LFICB	Uses iterative refinement to improve the solution of a complex system of linear equations in band storage mode.
LFICG	Uses iterative refinement to improve the solution of a complex general system of linear equations.
LFIDH	Uses iterative refinement to improve the solution of a complex Hermitian positive definite system of linear equations.
LFIDS	Uses iterative refinement to improve the solution of a real symmetric positive definite system of linear equations.
LFIHF	Uses iterative refinement to improve the solution of a complex Hermitian system of linear equations.
LFIQH	Uses iterative refinement to improve the solution of a complex Hermitian positive definite system of linear equations in band Hermitian storage mode.
LFIQS	Uses iterative refinement to improve the solution of a real symmetric positive definite system of linear equations in band symmetric storage mode.
LFIRB	Uses iterative refinement to improve the solution of a real system of linear equations in band storage mode.
LFIRG	Uses iterative refinement to improve the solution of a real general system of linear equations.
LFISF	Uses iterative refinement to improve the solution of a real symmetric system of linear equations.
LFSCB	Solves a complex system of linear equations given the LU factorization of the coefficient matrix in band storage mode.
LFSCG	Solves a complex general system of linear equations given the LU factorization of the coefficient matrix.
LFSDH	Solves a complex Hermitian positive definite system of linear equations given the RH R factorization of the coefficient matrix.
LFSDS	Solves a real symmetric positive definite system of linear equations given the RT R Choleksy factorization of the coefficient matrix.
LFSHF	Solves a complex Hermitian system of linear equations given the U DUH factorization of the coefficient matrix.
LFSQH	Solves a complex Hermitian positive definite system of linear equations given the factorization of the coefficient matrix in band Hermitian storage mode.
LFSQS	Solves a real symmetric positive definite system of linear equations given the factorization of the coefficient matrix in band symmetric storage mode.
LFSRB	Solves a real system of linear equations given the LU factorization of the coefficient matrix in band storage mode.
LFSRG	Solves a real general system of linear equations given the LU factorization of the coefficient matrix.
LFSSF	Solves a real symmetric system of linear equations given the U DUT factorization of the coefficient matrix.
LFSXD	Solves a real sparse symmetric positive definite system of linear equations, given the Cholesky factorization of the coefficient matrix.
LFSXG	Solves a sparse system of linear equations given the LU factorization of the coefficient matrix.
LFSZD	Solves a complex sparse Hermitian positive definite system of linear equations, given the Cholesky factorization of the coefficient matrix.
LFSZG	Solves a complex sparse system of linear equations given the LU factorization of the coefficient matrix.
LFTCB	Computes the LU factorization of a complex matrix in band storage mode.
LFTCG	Computes the LU factorization of a complex general matrix.
LFTDH	Computes the RH R factorization of a complex Hermitian positive definite matrix.
LFTDS	Computes the RT R Cholesky factorization of a real symmetric positive definite matrix.
LFTHF	Computes the U DUH factorization of a complex Hermitian matrix.
LFTQH	Computes the RH R factorization of a complex Hermitian positive definite matrix in band Hermitian storage mode.
LFTQS	Computes the RT R Cholesky factorization of a real symmetric positive definite matrix in band symmetric storage mode.
LFTRB	Computes the LU factorization of a real matrix in band storage mode.
LFTRG	Computes the LU factorization of a real general matrix.
LFTSF	Computes the U DUT factorization of a real symmetric matrix.
LFTXG	Computes the LU factorization of a real general sparse matrix.
LFTZG	Computes the LU factorization of a complex general sparse matrix.
LINCG	Computes the inverse of a complex general matrix.
LINCT	Computes the inverse of a complex triangular matrix.
LINDS	Computes the inverse of a real symmetric positive definite matrix.
LINRG	Computes the inverse of a real general matrix.
LINRT	Computes the inverse of a real triangular matrix.
LIN_EIG_GEN	Computes the eigenvalues of a self-adjoint matrix, A.
LIN_EIG_SELF	Computes the eigenvalues of a self-adjoint matrix, A.
LIN_GEIG_GEN	Computes the generalized eigenvalues of an n ´ n matrix pencil, Av = lBv.
LIN_SOL_GEN	Solves a general system of linear equations Ax = b.
LIN_SOL_LSQ	Solves a rectangular system of linear equations Ax @ b, in a least-squares sense.
LIN_SOL_SELF	Solves a system of linear equations Ax = b, where A is a self-adjoint matrix.
LIN_SOL_SVD	Solves a rectangular least-squares system of linear equations Ax @ b using singular value decomposition.
LIN_SOL_TRI	Solves multiple systems of linear equations.
LIN_SVD	Computes the singular value decomposition (SVD) of a rectangular matrix, A.
LNFXD	Computes the numerical Cholesky factorization of a sparse symmetrical matrix A.
LNFZD	Computes the numerical Cholesky factorization of a sparse Hermitian matrix A.
LQERR	Accumulates the orthogonal matrix Q from its factored form given the QR factorization of a rectangular matrix A.
LQRRR	Computes the QR decomposition, AP = QR, using Householder transformations.
LQRRV	Computes the least-squares solution using Householder transformations applied in blocked form.
LQRSL	Computes the coordinate transformation, projection, and complete the solution of the least-squares problem Ax = b.
LSACB	Solves a complex system of linear equations in band storage mode with iterative refinement.
LSACG	Solves a complex general system of linear equations with iterative refinement.
LSADH	Solves a Hermitian positive definite system of linear equations with iterative refinement.
LSADS	Solves a real symmetric positive definite system of linear equations with iterative refinement.
LSAHF	Solves a complex Hermitian system of linear equations with iterative refinement.
LSAQH	Solves a complex Hermitian positive definite system of linear equations in band Hermitian storage mode with iterative refinement.
LSAQS	Solves a real symmetric positive definite system of linear equations in band symmetric storage mode with iterative refinement.
LSARB	Solves a real system of linear equations in band storage mode with iterative refinement.
LSARG	Solves a real general system of linear equations with iterative refinement.
LSASF	Solves a real symmetric system of linear equations with iterative refinement.
LSBRR	Solves a linear least-squares problem with iterative refinement.
LSCXD	Performs the symbolic Cholesky factorization for a sparse symmetric matrix using a minimum degree ordering or a userspecified ordering, and set up the data structure for the numerical Cholesky factorization.
LSGRR	Computes the generalized inverse of a real matrix.
LSLCB	Solves a complex system of linear equations in band storage mode without iterative refinement.
LSLCC	Solves a complex circulant linear system.
LSLCG	Solves a complex general system of linear equations without iterative refinement.
LSLCQ	Computes the LDU factorization of a complex tridiagonal matrix A using a cyclic reduction algorithm.
LSLCR	Computes the LDU factorization of a real tridiagonal matrix A using a cyclic reduction algorithm.
LSLCT	Solves a complex triangular system of linear equations.
LSLDH	Solves a complex Hermitian positive definite system of linear equations without iterative refinement.
LSLDS	Solves a real symmetric positive definite system of linear equations without iterative refinement.
LSLHF	Solves a complex Hermitian system of linear equations without iterative refinement.
LSLPB	Computes the RT DR Cholesky factorization of a real symmetric positive definite matrix A in codiagonal band symmetric storage mode. Solve a system Ax = b.
LSLQB	Computes the RH DR Cholesky factorization of a complex hermitian positive-definite matrix A in codiagonal band hermitian storage mode. Solve a system Ax = b.
LSLQH	Solves a complex Hermitian positive definite system of linearequations in band Hermitian storage mode without iterative refinement.
LSLQS	Solves a real symmetric positive definite system of linear equations in band symmetric storage mode without iterative refinement.
LSLRB	Solves a real system of linear equations in band storage mode without iterative refinement.
LSLRG	Solves a real general system of linear equations without iterative refinement.
LSLRT	Solves a real triangular system of linear equations.
LSLSF	Solves a real symmetric system of linear equations without iterative refinement.
LSLTC	Solves a complex Toeplitz linear system.
LSLTO	Solves a real Toeplitz linear system.
LSLTQ	Solves a complex tridiagonal system of linear equations.
LSLTR	Solves a real tridiagonal system of linear equations.
LSLXD	Solves a sparse system of symmetric positive definite linear algebraic equations by Gaussian elimination.
LSLXG	Solves a sparse system of linear algebraic equations by Gaussian elimination.
LSLZD	Solves a complex sparse Hermitian positive definite system of linear equations by Gaussian elimination.
LSLZG	Solves a complex sparse system of linear equations by Gaussian elimination.
LSQRR	Solves a linear least-squares problem without iterative refinement.
LSVCR	Computes the singular value decomposition of a complex matrix.
LSVRR	Computes the singular value decomposition of a real matrix.
LUPCH	Updates the RTR Cholesky factorization of a real symmetric positive definite matrix after a rank-one matrix is added.
LUPQR	Computes an updated QR factorization after the rank-one matrix axyT is added.

MCRCR	Multiplies two complex rectangular matrices, AB.
MOLCH	Solves a system of partial differential equations of the form ut = f(x, t, u, ux, uxx) using the method of lines. The solution is represented with cubic Hermite polynomials.
MP_SETUP	Initializes or finalizes MPI.
MPS_FREE	Deallocates the space allocated for the IMSL derived type s_MPS. This routine is usually used in conjunction with READ_MPS.
MRRRR	Multiplies two real rectangular matrices, AB.
MUCBV	Multiplies a complex band matrix in band storage mode by a complex vector.
MUCRV	Multiplies a complex rectangular matrix by a complex vector.
MURBV	Multiplies a real band matrix in band storage mode by a real vector.
MURRV	Multiplies a real rectangular matrix by a vector.
MXTXF	Computes the transpose product of a matrix, ATA.
MXTYF	Multiplies the transpose of matrix A by matrix B, ATB.
MXYTF	Multiplies a matrx A by the transpose of a matrix B, ABT.

NAN	Returns, as a scalar function, a value corresponding to the IEEE 754 Standard format of floating point (ANSI/IEEE 1985) for NaN.
IERCD and N1RTY	Retrieves an error type for the most recently called IMSL routine.
NDAYS	Computes the number of days from January 1, 1900, to the given date.
NDYIN	Gives the date corresponding to the number of days since January 1, 1900.
NEQBF	Solves a system of nonlinear equations using factored secant update with a finite-difference approximation to the Jacobian.
NEQBJ	Solves a system of nonlinear equations using factored secant update with a user-supplied Jacobian.
NEQNF	Solves a system of nonlinear equations using a modified Powell hybrid algorithm and a finite-difference approximation to the Jacobian.
NEQNJ	Solves a system of nonlinear equations using a modified Powell hybrid algorithm with a user-supplied Jacobian.
NNLPF	Uses a sequential equality constrained QP method.
NNLPG	Uses a sequential equality constrained QP method.
NORM	Computes the norm of a rank-1 or rank-2 array. For rank-3 arrays, the norms of each rank-2 array, in dimension 3, are computed.
NR1CB	Computes the 1-norm of a complex band matrix in band storage mode.
NR1RB	Computes the 1-norm of a real band matrix in band storage mode.
NR1RR	Computes the 1-norm of a real matrix.
NR2RR	Computes the Frobenius norm of a real rectangular matrix.
NRIRR	Computes the infinity norm of a real matrix.

OPERATORS:
.h.	Computes transpose and conjugate transpose of a matrix.
.hx.	Computes matrix-vector and matrix-matrix products.
.i.	Computes the inverse matrix, for square non-singular matrices.
.ix.	Computes the inverse matrix times a vector or matrix for square non-singular matrices.
.t.	Computes transpose and conjugate transpose of a matrix.
.tx.	Computes matrix-vector and matrix-matrix products.
.x.	Computes matrix-vector and matrix-matrix products.
.xh.	Computes matrix-vector and matrix-matrix products.
.xi.	Computes the inverse matrix times a vector or matrix for square non-singular matrices.
.xt.	Computes matrix-vector and matrix-matrix products.
ORTH	Orthogonalizes the columns of a rank-2 or rank-3 array.

PCGRC	Solves a real symmetric definite linear system using a preconditioned conjugate gradient method with reverse communication.
PARALLEL_NONNEGATIVE_LSQ	Solves a linear, non-negative constrained least-squares system.
PARALLEL_BOUNDED_LSQ	Solves a linear least-squares system with bounds on the unknowns.
PDE_1D_MG	Method of lines with Variable Griddings.
PERMA	Permutes the rows or columns of a matrix.
PERMU	Rearranges the elements of an array as specified by a permutation.
PGOPT	Prints a plot of up to 10 sets of points.
PLOTP	Prints a plot of up to 10 sets of points.
POLRG	Evaluates a real general matrix polynomial.
PP1GD	Evaluates the derivative of a piecewise polynomial on a grid.
PPDER	Evaluates the derivative of a piecewise polynomial.
PPITG	Evaluates the integral of a piecewise polynomial.
PPVAL	Evaluates a piecewise polynomial.
PRIME	Decomposes an integer into its prime factors.

QAND	Integrates a function on a hyper-rectangle.
QCOSB	Computes a sequence from its cosine Fourier coefficients with only odd wave numbers.
QCOSF	Computes the coefficients of the cosine Fourier transform with only odd wave numbers.
QCOSI	Computes parameters needed by QCOSF and QCOSB.
QD2DR	Evaluates the derivative of a function defined on a rectangular grid using quadratic interpolation.
QD2VL	Evaluates a function defined on a rectangular grid using quadratic interpolation.
QD3DR	Evaluates the derivative of a function defined on a rectangular three-dimensional grid using quadratic interpolation.
QD3VL	Evaluates a function defined on a rectangular three-dimensional grid using quadratic interpolation.
QDAG	Integrates a function using a globally adaptive scheme based on Gauss-Kronrod rules.
QDAGI	Integrates a function over an infinite or semi-infinite interval.
QDAGP	Integrates a function with singularity points given.
QDAGS	Integrates a function (which may have endpoint singularities).
QDAWC	Integrates a function F(X)/(X - C) in the Cauchy principal value sense.
QDAWF	Computes a Fourier integral.
QDAWO	Integrates a function containing a sine or a cosine.
QDAWS	Integrates a function with algebraic-logarithmic singularities.
QDDER	Evaluates the derivative of a function defined on a set of points using quadratic interpolation.
QDNG	Integrates a smooth function using a nonadaptive rule.
QDVAL	Evaluates a function defined on a set of points using quadratic interpolation.
QMC	Integrates a function over a hyperrectangle using a quasi-Monte Carlo method.
QPROG	Solves a quadratic programming problem subject to linear equality/inequality constraints.
QSINB	Computes a sequence from its sine Fourier coefficients with only odd wave numbers.
QSINF	Computes the coefficients of the sine Fourier transform with only odd wave numbers.
QSINI	Computes parameters needed by QSINF and QSINB.

RAND	Computes a scalar, rank-1, rank-2 or rank-3 array of random numbers.
RAND_GEN	Generates a rank-1 array of random numbers.
RANK	Computes the mathematical rank of a rank-2 or rank-3 array.
RATCH	Computes a rational weighted Chebyshev approximation to a continuous function on an interval.
RCONV	Computes the convolution of two real vectors.
RCORL	Computes the correlation of two real vectors.
RCURV	Fits a polynomial curve using least squares.
READ_MPS	Reads an MPS file containing a linear program problem or a quadratic programming problem.
RECCF	Computes recurrence coefficients for various monic polynomials.
RECQR	Computes recurrence coefficients for monic polynomials given a quadrature rule.
RLINE	Fits a line to a set of data points using least squares.
RNGET	Retrieves the current value of the seed used in the IMSL random number generators.
RNIN32	Initializes the 32-bit Merseene Twister generator using an array.
RNGE32	Retrieves the current table used in the 32-bit Mersenne Twister generator.
RNSE32	Sets the current table used in the 32-bit Mersenne Twister generator.
RNIN64	Initializes the 32-bit Merseene Twister generator using an array.
RNGE64	Retrieves the current table used in the 64-bit Mersenne Twister generator
RNSE64	Sets the current table used in the 64-bit Mersenne Twister generator.
RNOPT	Selects the uniform (0, 1) multiplicative congruential pseudorandom number generator.
RNSET	Initializes a random seed for use in the IMSL random number generators.
RNUN	Generates pseudorandom numbers from a uniform (0, 1) distribution.
RNUNF	Generates a pseudorandom number from a uniform (0, 1) distribution.

SADD	Adds a scalar to each component of a vector, x ¬ x + a, all single precision.
SASUM	Sums the absolute values of the components of a single-precision vector.
SAXPY	Computes the scalar times a vector plus a vector, y ¬ ax + y, all single precision.
ScaLAPACK_EXIT	Exits ScaLAPACK mode for the IMSL Library routines.
ScaLAPACK_GETDIM	Calculates the row and column dimensions of a local distributed array based on the size of the array to be distributed and the row and column blocking factors to be used.
ScaLAPACK_MAP	Maps array data from a global array to local arrays in the two-dimensional block-cyclic form required by ScaLAPACK routines.
ScaLAPACK_READ	Reads matrix data from a file and transmits it into the two-dimensional block-cyclic form required by ScaLAPACK routines.
ScaLAPACK_SETUP	Sets up a processor grid and calculates default values for use in mapping arrays to the processor grid
ScaLAPACK_UNMAP	Unmaps array data from local distributed arrays to a global array.
ScaLAPACK_WRITE	Writes the matrix data to a file.
SCASUM	Sums the absolute values of the real part together with the absolute values of the imaginary part of the components of a complex vector.
SCNRM2	Computes the Euclidean norm of a complex vector.
SCOPY	Copies a vector x to a vector y, both single precision.
SDDOTA	Computes the sum of a single-precision scalar, a single-precision dot product and the double-precision accumulator, which is set to the result ACC ¬ ACC + a + xTy.
SDDOTI	Computes the sum of a single-precision scalar plus a singleprecision dot product using a double-precision accumulator, which is set to the result ACC ¬ a + xTy.
SDOT	Computes the single-precision dot product xTy.
SDSDOT	Computes the sum of a single-precision scalar and a single precision dot product, a + xTy, using a double-precision accumulator.
SGBMV	Computes one of the matrix-vector operations: , where A is a matrix stored in band storage mode.
SGEMM	Computes one of the matrix-matrix operations: .
SGEMV	Computes one of the matrix-vector operations: ,
SGER	Computes the rank-one update of a real general matrix: .
SHOW	Prints rank-1 or rank-2 arrays of numbers in a readable format.
SHPROD	Computes the Hadamard product of two single-precision vectors.
SINLP	Computes the inverse Laplace transform of a complex function.
SLCNT	Calculates the indices of eigenvalues of a Sturm-Liouville problem with boundary conditions (at regular points) in a specified subinterval of the real line, [a, b].
SLEIG	Determines eigenvalues, eigenfunctions and/or spectral density functions for Sturm-Liouville problems in the form with boundary conditions (at regular points).
SLPRS	Solves a sparse linear programming problem via the revised simplex algorithm.
SNRM2	Computes the Euclidean length or L2 norm of a single-precision vector.
SORT_REAL	Sorts a rank-1 array of real numbers x so the y results are algebraically nondecreasing, y1 £ y2 £ ¼ yn.
SPLEZ	Computes the values of a spline that either interpolates or fits user-supplied data.
SPLINE_CONSTRAINTS	Returns the derived type array result.
SPLINE_FITTING	Weighted least-squares fitting by B-splines to discrete One-Dimensional data is performed.
SPLINE_VALUES	Returns an array result, given an array of input
SPRDCT	Multiplies the components of a single-precision vector.
SRCH	Searches a sorted vector for a given scalar and return its index.
SROT	Applies a Givens plane rotation in single precision.
SROTG	Constructs a Givens plane rotation in single precision.
SROTM	Applies a modified Givens plane rotation in single precision.
SROTMG	Constructs a modified Givens plane rotation in single precision.
SSBMV	Computes the matrix-vector operation , where A is a symmetric matrix in band symmetric storage mode.
SSCAL	Multiplies a vector by a scalar, y ¬ ay, both single precision.
SSET	Sets the components of a vector to a scalar, all single precision.
SSRCH	Searches a character vector, sorted in ascending ASCII order, for a given string and return its index.
SSUB	Subtracts each component of a vector from a scalar, x ¬ a - x, all single precision.
SSUM	Sums the values of a single-precision vector.
SSWAP	Interchanges vectors x and y, both single precision.
SSYMM	Computes one of the matrix-matrix operations: , where A is a symmetric matrix and B and C are m by n matrices.
SSYMV	Computes the matrix-vector operation , where A is a symmetric matrix.
SSYR	Computes the rank-one update of a real symmetric matrix: .
SSYR2	Computes the rank-two update of a real symmetric matrix: .
SSYR2K	Computes one of the symmetric rank 2k operations: , where C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.
SSYRK	Computes one of the symmetric rank k operations: , where C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.
STBMV	Computes one of the matrix-vector operations: , where A is a triangular matrix in band storage mode.
STBSV	Solves one of the triangular systems: , where A is a triangular matrix in band storage mode.
STRMM	Computes one of the matrix-matrix operations: where B is an m by n matrix and A is a triangular matrix.
STRMV	Computes one of the matrix-vector operations: , where A is a triangular matrix.
STRSM	Solves one of the matrix equations: where B is an m by n matrix and A is a triangular matrix.
STRSV	Solves one of the triangular linear systems: where A is a triangular matrix.
SUMAG/DUMAG	Sets or retrieves MATH/LIBRARY single-precision options.
SURF	Computes a smooth bivariate interpolant to scattered data that is locally a quintic polynomial in two variables.
SURFACE_CONSTRAINTS	Returns the derived type array result given optional input.
SURFACE_FITTING	Weighted least-squares fitting by tensor product B-splines to discrete two-dimensional data is performed.
SURFACE_VALUES	Returns a tensor product array result, given two arrays of independent variable values.
SVCAL	Multiplies a vector by a scalar and store the result in another vector, y ¬ ax, all single precision.
SVD	Computes the singular value decomposition of a rank-2 or rank-3 array, .
SVIBN	Sorts an integer array by nondecreasing absolute value.
SVIGN	Sorts an integer array by algebraically increasing value.
SVIGP	Sorts an integer array by algebraically increasing value and returns the permutation that rearranges the array.
SVRBN	Sorts a real array by nondecreasing absolute value.
SVRBP	Sorts a real array by nondecreasing absolute value and returns the permutation that rearranges the array.
SVRGN	Sorts a real array by algebraically increasing value.
SVRGP	Sorts a real array by algebraically increasing value and returns the permutation that rearranges the array.
SXYZ	Computes a single-precision xyz product.

TDATE	Gets today's date.
TIMDY	Gets time of day.
TRNRR	Transposes a rectangular matrix.
TWODQ	Computes a two-dimensional iterated integral.

UMACH	Sets or retrieves input or output device unit numbers.
UMAG	Handles MATH/LIBRARY and STAT/LIBRARY type REAL and double precision options.
UMCGF	Minimizes a function of N variables using a conjugate gradient algorithm and a finite-difference gradient.
UMCGG	Minimizes a function of N variables using a conjugate gradient algorithm and a user-supplied gradient.
UMIAH	Minimizes a function of N variables using a modified Newton method and a user-supplied Hessian.
UMIDH	Minimizes a function of N variables using a modified Newton method and a finite-difference Hessian.
UMINF	Minimizes a function of N variables using a modified Newton method and a finite-difference Hessian.
UMING	Minimizes a function of N variables using a quasi-New method and a finite-difference gradient.
UMPOL	Minimizes a function of N variables using a direct search polytope algorithm.
UNIT	Normalizes the columns of a rank-2 or rank-3 array so each has Euclidean length of value one.
UNLSF	Solves a nonlinear least squares problem using a modified Levenberg-Marquardt algorithm and a finite-difference Jacobian.
UNLSJ	Solves a nonlinear least squares problem using a modified Levenberg-Marquardt algorithm and a user-supplied Jacobian.
UVMGS	Finds the minimum point of a nonsmooth function of a single variable.
UVMID	Finds the minimum point of a smooth function of a single variable using both function evaluations and first derivative evaluations.
UVMIF	Finds the minimum point of a smooth function of a single variable using only function evaluations.

VCONC	Computes the convolution of two complex vectors.
VCONR	Computes the convolution of two real vectors.
VERML	Obtains IMSL MATH/LIBRARY-related version, system and license numbers.

WRCRL	Prints a complex rectangular matrix with a given format and labels.
WRCRN	Prints a complex rectangular matrix with integer row and column labels.
WRIRL	Prints an integer rectangular matrix with a given format and labels.
WRIRN	Prints an integer rectangular matrix with integer row and column labels.
WROPT	Sets or retrieves an option for printing a matrix.
WRRRL	Prints a real rectangular matrix with a given format and labels.
WRRRN	Prints a real rectangular matrix with integer row and column labels.

ZANLY	Finds the zeros of a univariate complex function using Müller's method.
ZBREN	Finds a zero of a real function that changes sign in a given interval.
ZPLRC	Finds the zeros of a polynomial with real coefficients using Laguerre's method.
ZPOCC	Finds the zeros of a polynomial with complex coefficients using the Jenkins-Traub three-stage algorithm.
ZPORC	Finds the zeros of a polynomial with real coefficients using the Jenkins-Traub three-stage algorithm.
ZQADD	Adds a double complex scalar to the accumulator in extended precision.
ZQINI	Initializes an extended-precision complex accumulator to a double complex scalar.
ZQMUL	Multiplies double complex scalars using extended precision.
ZQSTO	Stores a double complex approximation to an extended-precision complex scalar.
ZREAL	Finds the real zeros of a real function using Müller's method.

Visual Numerics, Inc.
Visual Numerics - Developers of IMSL and PV-WAVE
http://www.vni.com/
PHONE: 713.784.3131
FAX:713.781.9260