Adds two complex band matrices, both in band storage mode.

Returns a character given its ASCII value.

Retrieves single-precision machine constants.

Adds two band matrices, both in band storage mode.

Compute some eigenvalues and eigenvectors of the generalized eigenvalue problem Ax = Bx.

Compute some eigenvalues and eigenvectors of the generalized eigenvalue problem Ax = Bx.

Computes some eigenvalues and eigenvectors of the generalized real symmetric eigenvalue problem Ax = Bx.

Solves a nonlinear least squares problem subject to bounds on the variables using a modified Levenberg-Marquardt algorithm and a finite-difference Jacobian.

Solves a nonlinear least squares problem subject to bounds on the variables using a modified Levenberg-Marquardt algorithm and a user-supplied Jacobian.

Solves a nonlinear least-squares problem subject to bounds on the variables and general linear constraints.

Minimizes a function of N variables subject to bounds the variables using a modified Newton method and a user-supplied Hessian.

Minimizes a function of N variables subject to bounds the variables using a modified Newton method and a finite-difference Hessian.

Minimizes a function of N variables subject to bounds the variables using a quasi-Newton method and a finite-difference gradient.

Minimizes a function of N variables subject to bounds the variables using a quasi-Newton method and a user-supplied gradient.

Minimizes a function of N variables subject to bounds the variables using a direct search complex algorithm.

Computes the bilinear form xTAy.

Evaluates the derivative of a spline on a grid, given its B-spline representation.

Evaluates the derivative of a two-dimensional tensor-product spline, given its tensor-product B-spline representation.

Evaluates the derivative of a two-dimensional tensor-product spline, given its tensor-product B-spline representation on a grid.

Evaluates the integral of a tensor-product spline on a rectangular domain, given its tensor-product B-spline representation.

Computes a two-dimensional tensor-product spline interpolant, returning the tensor-product B-spline coefficients.

Evaluates a two-dimensional tensor-product spline, given its tensor-product B-spline representation.

Evaluates the derivative of a three-dimensional tensor-product spline, given its tensor-product B-spline representation.

Evaluates the derivative of a three-dimensional tensor-product spline, given its tensor-product B-spline representation on a grid.

Evaluates the integral of a tensor-product spline in three dimensions over a three-dimensional rectangle, given its tensorproduct B-spline representation.

Computes a three-dimensional tensor-product spline interpolant, returning the tensor-product B-spline coefficients.

Evaluates a three-dimensional tensor-product spline, given its tensor-product B-spline representation

Converts a spline in B-spline representation to piecewise polynomial representation.

Evaluates the derivative of a spline, given its B-spline representation.

Computes the spline interpolant, returning the B-spline coefficients.

Evaluates the integral of a spline, given its B-spline representation.

Computes a two-dimensional tensor-product spline approximant using least squares, returning the tensor-product B-spline coefficients.

Computes a three-dimensional tensor-product spline approximant using least squares, returning the tensor-product B-spline coefficients.

Computes the least-squares spline approximation, and return the B-spline coefficients.

Computes the ‘not-a-knot’ spline knot sequence.

Computes the ‘optimal’ spline knot sequence.

Evaluates a spline, given its B-spline representation.

Computes the variable knot B-spline least squares approximation to given data.

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.

Adds a scalar to each component of a vector, x ← x + a, all complex.

Computes the scalar times a vector plus a vector, y ← ax + y, all complex.

Copies a complex band matrix stored in complex band storage mode.

Converts a complex matrix in band storage mode to a complex matrix in full storage mode.

Converts a complex general matrix to a matrix in complex band storage mode.

Copies a complex general matrix.

Computes the convolution of two complex vectors.

Copies a vector x to a vector y, both complex.

Computes the correlation of two complex vectors.

Approximates the gradient using central differences.

Computes the complex conjugate dot product, .

Computes the complex dot product xTy.

Computes one of the matrix-vector operations: , where A is a matrix stored in band storage mode.

Computes one of the matrix-matrix operations:

Computes one of the matrix-vector operations:

Computes the rank-one update of a complex general matrix: .

Computes the rank-one update of a complex general matrix: .

Copies a complex Hermitian band matrix stored in band Hermitian storage mode to a complex band matrix stored in band storage mode.

Computes the matrix-vector operation , where A is an Hermitian band matrix in band Hermitian storage.

Computes one of the matrix-matrix operations: , where A is an Hermitian matrix and B and C are m by n matrices.

Computes the matrix-vector operation , where A is an Hermitian matrix.

Computes the rank-one update of an Hermitian matrix: with x complex and α real.

Computes a rank-two update of an Hermitian matrix: .

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.

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.

Extends a complex Hermitian matrix defined in its upper triangle to its lower triangle.

Checks a user-supplied gradient of a function.

Checks a user-supplied Hessian of an analytic function.

Checks a user-supplied Hessian of an analytic function.

Checks a user-supplied Jacobian of a system of equations with M functions in N unknowns.

Computes the matrix-vector operation y ← αAx + βy where A is an Hermitian matrix.

Performs the matrix-vector operation: , where A is a triangular packed Hermitian.

Computes the condition number of a matrix.

Computes the least-squares constrained spline approximation, returning the B-spline coefficients.

Returns the value of various mathematical and physical constants.

Returns CPU time used in seconds.

Converts a real matrix in band storage mode to a complex matrix in band storage mode.

Copies a real band matrix stored in band storage mode.

Converts a real matrix in band storage mode to a real general matrix.

Copies a real general matrix to a complex general matrix.

Converts a real general matrix to a matrix in band storage mode.

Copies a real general matrix.

Copies a real rectangular matrix to a complex rectangular matrix.

Evaluates the derivative of a cubic spline on a grid.

Computes the Akima cubic spline interpolant.

Copies a real symmetric band matrix stored in band symmetric storage mode to a real band matrix stored in band storage mode.

Multiplies a vector by a scalar, y ← ay, both complex.

Computes a cubic spline interpolant that is consistent with the concavity of the data.

Computes the cubic spline interpolant with specified derivative endpoint conditions.

Evaluates the derivative of a cubic spline.

Sets the components of a vector to a scalar, all complex.

Extends a real symmetric matrix defined in its upper triangle to its lower triangle.

Computes the Hermite cubic spline interpolant.

Computes the cubic spline interpolant with the ‘not-a-knot’ condition and return values of the interpolant at specified points.

Computes the cubic spline interpolant with the ‘not-a-knot’ condition.

Evaluates the integral of a cubic spline.

Computes the cubic spline interpolant with periodic boundary conditions.

Applies a complex Givens plane rotation.

Applies a complex modified Givens plane rotation.

Multiplies a complex vector by a single-precision scalar, y ← ay.

Computes a smooth cubic spline approximation to noisy data using cross-validation to estimate the smoothing parameter.

Smooths one-dimensional data by error detection.

Computes a smooth cubic spline approximation to noisy data.

Subtracts each component of a vector from a scalar, x ← a ‑ x, all complex.

Evaluates a cubic spline.

Multiplies a complex vector by a single-precision scalar and store the result in another complex vector, y ← ax.

Interchanges vectors x and y, both complex.

Computes one of the matrix-matrix operations: , where A is a symmetric matrix and B and C are m by n matrices.

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.

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.

Computes one of the matrix-vector operations: , where A is a triangular matrix in band storage mode.

Solves one of the complex triangular systems: , where A is a triangular matrix in band storage mode.

Solves one of the system of equations: where A is a packed upper or lower triangular matrix.

Performes the matrix-vector operation, , where A is a packed triangular matrix.

Computes one of the matrix-matrix operations:

where B is an m by n matrix and A is a triangular matrix.

Computes one of the matrix-vector operations: , where A is a triangular matrix.

Solves one of the complex matrix equations:

where A is a traiangular matrix

Solves one of the complex triangular systems: ,

where A is a triangular matrix.

Converts X in units XUNITS to Y in units YUNITS.

Multiplies a vector by a scalar and store the result in another vector, y ← ax, all complex.

Converts a character string containing an integer number into the corresponding integer form.

Computes the sum of a complex scalar plus a complex conjugate dot product, , using a double-precision accumulator.

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.

Computes the complex conjugate dot product, , using a double-precision accumulator.

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.

Computes the complex dot product xTy using a double-precision accumulator.

Solves a first order differential-algebraic system of equations, g(t, y, yʹ) = 0, possibly with additional constraints.

Approximates the Jacobian of m functions in n unknowns using divided differences

Solves a linear programming problem.

Computes the first, second or third derivative of a user-supplied function.

Computes the determinant of a rectangular matrix, A.

Constructs a square diagonal matrix from a rank-1 array or several diagonal matrices from a rank-2 array.

Extracts a rank-1 array whose values are the diagonal terms of a rank-2 array argument.

Computes the 1-norm distance between two points.

Computes the Euclidean (2-norm) distance between two points.

Computes the infinity norm distance between two points.

Solves a linear programming problem via the revised simplex algorithm.

See AMACH.

Adds a double-precision scalar to the accumulator in extended precision.

Initializes an extended-precision accumulator with a double-precision scalar.

Multiplies double-precision scalars in extended precision.

Stores a double-precision approximation to an extended-precision scalar.

Computes the single-precision dot product xTy using a double precision accumulator.

Computes the eigenvalue-eigenvector decomposition of an ordinary or generalized eigenvalue problem.

Computes the performance index for a complex eigensystem.

Computes the performance index for a complex Hermitian eigensystem.

Computes the performance index for a real eigensystem.

Computes the performance index for a real symmetric eigensystem in band symmetric storage mode.

Computes the performance index for a real symmetric eigensystem.

Prints error messages that are generated by IMSL routines using EPACK.

Sets error handler default print and stop actions.

Computes the largest or smallest eigenvalues of a complex Hermitian matrix.

Computes the largest or smallest eigenvalues of a real symmetric matrix in band symmetric storage mode.

Computes the largest or smallest eigenvalues of a real symmetric matrix.

Computes the eigenvalues in a given range of a complex Hermitian matrix.

Computes the eigenvalues in a given interval of a real symmetric matrix stored in band symmetric storage mode.

Computes selected eigenvalues of a real symmetric matrix.

Computes all of the eigenvalues and eigenvectors of a complex matrix.

Computes all of the eigenvalues and eigenvectors of a complex upper Hessenberg matrix.

Computes all of the eigenvalues and eigenvectors of a complex Hermitian matrix.

Computes all of the eigenvalues and eigenvectors of a real matrix.

Computes all of the eigenvalues and eigenvectors of a real upper Hessenberg matrix.

Computes all of the eigenvalues and eigenvectors of a real symmetric matrix in band symmetric storage mode.

Computes all of the eigenvalues and eigenvectors of a real symmetric matrix.

Computes the largest or smallest eigenvalues and the corresponding eigenvectors of a complex Hermitian matrix.

Computes the largest or smallest eigenvalues and the corresponding eigenvectors of a real symmetric matrix in band symmetric storage mode.

Computes the largest or smallest eigenvalues and the corresponding eigenvectors of a real symmetric matrix.

Computes the eigenvalues in a given range and the corresponding eigenvectors of a complex Hermitian matrix.

Computes the eigenvalues in a given interval and the corresponding eigenvectors of a real symmetric matrix stored in band symmetric storage mode.

Computes selected eigenvalues and eigenvectors of a real symmetric matrix.

Computes all of the eigenvalues of a complex matrix.

Computes all of the eigenvalues of a complex upper Hessenberg matrix.

Computes all of the eigenvalues of a complex Hermitian matrix.

Computes all of the eigenvalues of a real matrix.

Computes all of the eigenvalues of a real upper Hessenberg matrix.

Computes all of the eigenvalues of a real symmetric matrix in band symmetric storage mode.

Computes all of the eigenvalues of a real symmetric matrix.

Frees the structure containing information about the Faure sequence.

Shuffled Faure sequence initialization.

Computes a shuffled Faure sequence.

Computes the Discrete Fourier Transform of a rank-1 complex array, x.

Computes the Discrete Fourier Transform (2DFT) of a rank-2 complex array, x.

Computes the Discrete Fourier Transform (2DFT) of a rank-3 complex array, x.

Computes parameters needed by FCOST.

Computes the discrete Fourier cosine transformation of an even sequence.

Approximates the gradient using forward differences.

Approximates the Hessian using forward differences and function values.

Approximates the Jacobian of M functions in N unknowns using forward differences.

Solves the generalized Feynman-Kac PDE on a rectangular grid using a finite element Galerkin method. Initial and boundary conditions are provided.

The Discrete Fourier Transform of a complex sequence and its inverse transform.

The Discrete Fourier Transform of several complex or real sequences.

Computes the inverse Fourier transform of a complex periodic two-dimensional array.

Computes Fourier coefficients of a complex periodic two-dimensional array.

Computes the inverse Fourier transform of a complex periodic three-dimensional array.

Computes Fourier coefficients of a complex periodic three-dimensional array.

Computes the complex periodic sequence from its Fourier coefficients.

Computes the Fourier coefficients of a complex periodic sequence.

Computes parameters needed by FFTCF and FFTCB.

Computes the real periodic sequence from its Fourier coefficients.

Computes the Fourier coefficients of a real periodic sequence.

Computes parameters needed by FFTRF and FFTRB.

Computes a least-squares approximation with user-supplied basis functions.

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.

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.

Computes a Fejér quadrature rule with various classical weight functions.

Computes parameters needed by FSINT.

Approximates the Hessian using forward differences and a user-supplied gradient.

Generates points in an N-dimensional space.

Uses restarted GMRES with reverse communication to generate an approximate solution of Ax = b.

Computes the performance index for a generalized complex eigensystem Az = λBz.

Computes the performance index for a generalized real eigensystem Az = λBz.

Computes the performance index for a generalized real symmetric eigensystem problem.

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.

Computes a Gauss, Gauss-Radau, or Gauss-Lobatto quadrature rule with various classical weight functions.

Computes all of the eigenvalues and eigenvectors of a generalized complex eigensystem Az = λBz.

Computes all of the eigenvalues and eigenvectors of a generalized real eigensystem Az = λBz.

Computes all of the eigenvalues and eigenvectors of the generalized real symmetric eigenvalue problem Az = λBz, with B symmetric positive definite.

Computes all of the eigenvalues of a generalized complex eigensystem Az = λBz.

Computes all of the eigenvalues of a generalized real eigensystem Az = λBz.

Computes the Hadamard product of two real rectangular matrices.

Returns the integer ASCII value of a character argument.

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.

Finds the smallest index of the component of a complex vector having minimum magnitude.

Returns the ASCII value of a character converted to uppercase.

Copies a vector x to a vector y, both integer.

Computes the day of the week for a given date.

Retrieves the code for an informational error.

The inverse of the Discrete Fourier Transform of a complex sequence.

The inverse Discrete Fourier Transform of several complex or real sequences.

Checks if a value is NaN (not a number).

Compares two character strings using the ASCII collating sequence but without regard to case.

Determines the position in a string at which a given character sequence begins without regard to case.

Finds the smallest index of the maximum component of a integer vector.

Finds the smallest index of the minimum of an integer vector.

Retrieves integer machine constants.

Computes the inverse Laplace transform of a complex function.

Finds the smallest index of the component of a single-precision vector having maximum absolute value.

Finds the smallest index of the component of a single-precision vector having minimum absolute value.

Sets the components of a vector to a scalar, all integer.

Finds the smallest index of the component of a single-precision vector having maximum value.

Finds the smallest index of the component of a single-precision vector having minimum value.

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.

Searches a sorted integer vector for a given integer and return its index.

Subtracts each component of a vector from a scalar, x ← a ‑ x, all integer.

Sums the values of an integer vector.

Interchanges vectors x and y, both integer.

Sets or retrieves MATH/LIBRARY integer options.

Solves an initial-value problem y′ = f(t, y) for ordinary differential equations using Runge-Kutta pairs of various orders.

Solves an initial-value problem for a system of ordinary differential equations of order one or two using a variable order Adams method.

Solves an initial-value problem for ordinary differential equations using either Adams-Moulton’s or Gear’s BDF method.

Computes the Cholesky decomposition of a symmetric positive semidefinite matrix with optional column pivoting.

Solves a linear least-squares problem with linear constraints.

Minimizes a general objective function subject to linear equality/inequality constraints.

Minimizes a general objective function subject to linear equality/inequality constraints.

Downdates the RT R Cholesky factorization of a real symmetric positive definite matrix after a rank-one matrix is removed

Computes the LU factorization of a complex matrix in band storage mode and estimate its L1⋅ condition number.

Computes the LU factorization of a complex general matrix and estimate its L1 condition number.

Estimates the condition number of a complex triangular matrix.

Computes the RH R factorization of a complex Hermitian positive definite matrix and estimate its L1 condition number.

Computes the RT R Cholesky factorization of a real symmetric positive definite matrix and estimate its L1condition number.

Computes the U DUH factorization of a complex Hermitian matrix and estimate its L1 condition number.

Computes the RH R factorization of a complex Hermitian positive definite matrix in band Hermitian storage mode and estimate its L1 condition number.

Computes the RT R Cholesky factorization of a real symmetric positive definite matrix in band symmetric storage mode and estimate its L1 condition number.

Computes the LU factorization of a real matrix in band storage mode and estimate its L1 condition number.

Computes the LU factorization of a real general matrix and estimate its L1 condition number.

Estimates the condition number of a real triangular matrix.

Computes the U DUT factorization of a real symmetric matrix and estimate its L1 condition number.

Computes the determinant of a complex matrix given the LU factorization of the matrix in band storage mode.

Computes the determinant of a complex general matrix given the LU factorization of the matrix.

Computes the determinant of a complex triangular matrix.

Computes the determinant of a complex Hermitian positive definite matrix given the RH R Cholesky factorization of the matrix.

Computes the determinant of a real symmetric positive definite matrix given the RH R Cholesky factorization of the matrix.

Computes the determinant of a complex Hermitian matrix given the U DUH factorization of the matrix.

Computes the determinant of a complex Hermitian positive definite matrix given the RH R Cholesky factorization in band Hermitian storage mode.

Computes the determinant of a real symmetric positive definite matrix given the RT R Cholesky factorization of the band symmetric storage mode.

Computes the determinant of a real matrix in band storage mode given the LU factorization of the matrix.

Computes the determinant of a real general matrix given the LU factorization of the matrix.

Computes the determinant of a real triangular matrix.

Computes the determinant of a real symmetric matrix given the U DUT factorization of the matrix.

Uses iterative refinement to improve the solution of a complex system of linear equations in band storage mode.

Uses iterative refinement to improve the solution of a complex general system of linear equations.

Uses iterative refinement to improve the solution of a complex Hermitian positive definite system of linear equations.

Uses iterative refinement to improve the solution of a real symmetric positive definite system of linear equations.

Uses iterative refinement to improve the solution of a complex Hermitian system of linear equations.

Uses iterative refinement to improve the solution of a complex Hermitian positive definite system of linear equations in band Hermitian storage mode.

Uses iterative refinement to improve the solution of a real symmetric positive definite system of linear equations in band symmetric storage mode.

Uses iterative refinement to improve the solution of a real system of linear equations in band storage mode.

Uses iterative refinement to improve the solution of a real general system of linear equations.

Uses iterative refinement to improve the solution of a real symmetric system of linear equations.

Solves a complex system of linear equations given the LU factorization of the coefficient matrix in band storage mode.

Solves a complex general system of linear equations given the LU factorization of the coefficient matrix.

Solves a complex Hermitian positive definite system of linear equations given the RH R factorization of the coefficient matrix.

Solves a real symmetric positive definite system of linear equations given the RT R Choleksy factorization of the coefficient matrix.

Solves a complex Hermitian system of linear equations given the U DUH factorization of the coefficient matrix.

Solves a complex Hermitian positive definite system of linear equations given the factorization of the coefficient matrix in band Hermitian storage mode.

Solves a real symmetric positive definite system of linear equations given the factorization of the coefficient matrix in band symmetric storage mode.

Solves a real system of linear equations given the LU factorization of the coefficient matrix in band storage mode.

Solves a real general system of linear equations given the LU factorization of the coefficient matrix.

Solves a real symmetric system of linear equations given the U DUT factorization of the coefficient matrix.

Solves a real sparse symmetric positive definite system of linear equations, given the Cholesky factorization of the coefficient matrix.

Solves a sparse system of linear equations given the LU factorization of the coefficient matrix.

Solves a complex sparse Hermitian positive definite system of linear equations, given the Cholesky factorization of the coefficient matrix.

Solves a complex sparse system of linear equations given the LU factorization of the coefficient matrix.

Computes the LU factorization of a complex matrix in band storage mode.

Computes the LU factorization of a complex general matrix.

Computes the RH R factorization of a complex Hermitian positive definite matrix.

Computes the RT R Cholesky factorization of a real symmetric positive definite matrix.

Computes the U DUH factorization of a complex Hermitian matrix.

Computes the RH R factorization of a complex Hermitian positive definite matrix in band Hermitian storage mode.

Computes the RT R Cholesky factorization of a real symmetric positive definite matrix in band symmetric storage mode.

Computes the LU factorization of a real matrix in band storage mode.

Computes the LU factorization of a real general matrix.

Computes the U DUT factorization of a real symmetric matrix.

Computes the LU factorization of a real general sparse matrix.

Computes the LU factorization of a complex general sparse matrix.

Computes the inverse of a complex general matrix.

Computes the inverse of a complex triangular matrix.

Computes the inverse of a real symmetric positive definite matrix.

Computes the inverse of a real general matrix.

Computes the inverse of a real triangular matrix.

Computes the eigenvalues of a self-adjoint matrix, A.

Computes the eigenvalues of a self-adjoint matrix, A.

Computes the generalized eigenvalues of an n ×  n matrix pencil, Av = λBv.

Solves a general system of linear equations Ax = b.

Solves a rectangular system of linear equations Ax≅b, in a least-squares sense.

Solves a system of linear equations Ax = b, where A is a self-adjoint matrix.

Solves a rectangular least-squares system of linear equations Ax ≅ b using singular value decomposition.

Solves multiple systems of linear equations.

Computes the singular value decomposition (SVD) of a rectangular matrix, A.

Computes the numerical Cholesky factorization of a sparse symmetrical matrix A.

Computes the numerical Cholesky factorization of a sparse Hermitian matrix A.

Accumulates the orthogonal matrix Q from its factored form given the QR factorization of a rectangular matrix A.

Computes the QR decomposition, AP = QR, using Householder transformations.

Computes the least-squares solution using Householder transformations applied in blocked form.

Computes the coordinate transformation, projection, and complete the solution of the least-squares problem Ax = b.

Solves a complex system of linear equations in band storage mode with iterative refinement.

Solves a complex general system of linear equations with iterative refinement.

Solves a Hermitian positive definite system of linear equations with iterative refinement.

Solves a real symmetric positive definite system of linear equations with iterative refinement.

Solves a complex Hermitian system of linear equations with iterative refinement.

Solves a complex Hermitian positive definite system of linear equations in band Hermitian storage mode with iterative refinement.

Solves a real symmetric positive definite system of linear equations in band symmetric storage mode with iterative refinement.

Solves a real system of linear equations in band storage mode with iterative refinement.

Solves a real general system of linear equations with iterative refinement.

Solves a real symmetric system of linear equations with iterative refinement.

Solves a linear least-squares problem with iterative refinement.

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.

Computes the generalized inverse of a real matrix.

Solves a complex system of linear equations in band storage mode without iterative refinement.

Solves a complex circulant linear system.

Solves a complex general system of linear equations without iterative refinement.

Computes the LDU factorization of a complex tridiagonal matrix A using a cyclic reduction algorithm.

Computes the LDU factorization of a real tridiagonal matrix A using a cyclic reduction algorithm.

Solves a complex triangular system of linear equations.

Solves a complex Hermitian positive definite system of linear equations without iterative refinement.

Solves a real symmetric positive definite system of linear equations without iterative refinement.

Solves a complex Hermitian system of linear equations without iterative refinement.

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.

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.

Solves a complex Hermitian positive definite system of linearequations in band Hermitian storage mode without iterative refinement.

Solves a real symmetric positive definite system of linear equations in band symmetric storage mode without iterative refinement.

Solves a real system of linear equations in band storage mode without iterative refinement.

Solves a real general system of linear equations without iterative refinement.

Solves a real triangular system of linear equations.

Solves a real symmetric system of linear equations without iterative refinement.

Solves a complex Toeplitz linear system.

Solves a real Toeplitz linear system.

Solves a complex tridiagonal system of linear equations.

Solves a real tridiagonal system of linear equations.

Solves a sparse system of symmetric positive definite linear algebraic equations by Gaussian elimination.

Solves a sparse system of linear algebraic equations by Gaussian elimination.

Solves a complex sparse Hermitian positive definite system of linear equations by Gaussian elimination.

Solves a complex sparse system of linear equations by Gaussian elimination.

Solves a linear least-squares problem without iterative refinement.

Computes the singular value decomposition of a complex matrix.

Computes the singular value decomposition of a real matrix.

Updates the RT R Cholesky factorization of a real symmetric positive definite matrix after a rank-one matrix is added.

Multiplies two complex rectangular matrices, AB.

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.

Initializes or finalizes MPI.

Deallocates the space allocated for the IMSL derived type s_MPS. This routine is usually used in conjunction with READ_MPS.

Multiplies two real rectangular matrices, AB.

Multiplies a complex band matrix in band storage mode by a complex vector.

Multiplies a complex rectangular matrix by a complex vector.

Multiplies a real band matrix in band storage mode by a real vector.

Multiplies a real rectangular matrix by a vector.

Computes the transpose product of a matrix, ATA.

Multiplies the transpose of matrix A by matrix B, ATB.

Returns, as a scalar function, a value corresponding to the IEEE 754 Standard format of floating point (ANSI/IEEE 1985) for NaN.

Retrieves an error type for the most recently called IMSL routine.

Computes the number of days from January 1, 1900, to the given date.

Gives the date corresponding to the number of days since January 1, 1900.

Solves a system of nonlinear equations using factored secant update with a finite-difference approximation to the Jacobian.

Solves a system of nonlinear equations using factored secant update with a user-supplied Jacobian.

Solves a system of nonlinear equations using a modified Powell hybrid algorithm and a finite-difference approximation to the Jacobian.

Solves a system of nonlinear equations using a modified Powell hybrid algorithm with a user-supplied Jacobian.

Uses a sequential equality constrained QP method.

Uses a sequential equality constrained QP method.

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.

Computes the 1-norm of a complex band matrix in band storage mode.

Computes the 1-norm of a real band matrix in band storage mode.

Computes the 1-norm of a real matrix.

Computes the Frobenius norm of a real rectangular matrix.

Computes transpose and conjugate transpose of a matrix.

Computes matrix-vector and matrix-matrix products.

Computes the inverse matrix, for square non-singular matrices.

Computes the inverse matrix times a vector or matrix for square non-singular matrices.

Computes transpose and conjugate transpose of a matrix.

Computes matrix-vector and matrix-matrix products.

Computes matrix-vector and matrix-matrix products.

Computes matrix-vector and matrix-matrix products.

Computes the inverse matrix times a vector or matrix for square non-singular matrices.

Computes matrix-vector and matrix-matrix products.

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

Solves a linear, non-negative constrained least-squares system.

Solves a linear least-squares system with bounds on the unknowns.

Method of lines with Variable Griddings.

Permutes the rows or columns of a matrix.

Rearranges the elements of an array as specified by a permutation.

Prints a plot of up to 10 sets of points.

Prints a plot of up to 10 sets of points.

Evaluates a real general matrix polynomial.

Evaluates the derivative of a piecewise polynomial on a grid.

Evaluates the derivative of a piecewise polynomial.

Evaluates the integral of a piecewise polynomial.

Evaluates a piecewise polynomial.

Integrates a function on a hyper-rectangle.

Computes a sequence from its cosine Fourier coefficients with only odd wave numbers.

Computes the coefficients of the cosine Fourier transform with only odd wave numbers.

Computes parameters needed by QCOSF and QCOSB.

Evaluates the derivative of a function defined on a rectangular grid using quadratic interpolation.

Evaluates a function defined on a rectangular grid using quadratic interpolation.

Evaluates the derivative of a function defined on a rectangular three-dimensional grid using quadratic interpolation.

Evaluates a function defined on a rectangular three-dimensional grid using quadratic interpolation.

Integrates a function using a globally adaptive scheme based on Gauss-Kronrod rules.

Integrates a function over an infinite or semi-infinite interval.

Integrates a function with singularity points given.

Integrates a function with a possible internal or endpoint singularity.

Integrates a function of two variables with a possible internal or end point singularity.

Integrates a function of three variables with a possible internal or endpoint singularity.

Integrates a function (which may have endpoint singularities).

Integrates a function F(X)/(X ‑ C) in the Cauchy principal value sense.

Computes a Fourier integral.

Integrates a function containing a sine or a cosine.

Integrates a function with algebraic-logarithmic singularities.

Evaluates the derivative of a function defined on a set of points using quadratic interpolation.

Integrates a smooth function using a nonadaptive rule.

Evaluates a function defined on a set of points using quadratic interpolation.

Integrates a function over a hyperrectangle using a quasi-Monte Carlo method.

Solves a quadratic programming problem subject to linear equality/inequality constraints.

Computes a sequence from its sine Fourier coefficients with only odd wave numbers.

Computes the coefficients of the sine Fourier transform with only odd wave numbers.

Computes a scalar, rank-1, rank-2 or rank-3 array of random numbers.

Generates a rank-1 array of random numbers.

Computes the mathematical rank of a rank-2 or rank-3 array.

Computes a rational weighted Chebyshev approximation to a continuous function on an interval.

Computes the convolution of two real vectors.

Computes the correlation of two real vectors.

Fits a polynomial curve using least squares.

Reads an MPS file containing a linear program problem or a quadratic programming problem.

Computes recurrence coefficients for various monic polynomials.

Computes recurrence coefficients for monic polynomials given a quadrature rule.

Fits a line to a set of data points using least squares.

Retrieves the current value of the seed used in the IMSL random number generators.

Initializes the 32-bit Merseene Twister generator using an array.

Retrieves the current table used in the 32-bit Mersenne Twister generator.

Sets the current table used in the 32-bit Mersenne Twister generator.

Initializes the 32-bit Merseene Twister generator using an array.

Retrieves the current table used in the 64-bit Mersenne Twister generator

Sets the current table used in the 64-bit Mersenne Twister generator.

Selects the uniform (0, 1) multiplicative congruential pseudorandom number generator.

Initializes a random seed for use in the IMSL random number generators.

Generates pseudorandom numbers from a uniform (0, 1) distribution.

Adds a scalar to each component of a vector, x ← x + a, all single precision.

Sums the absolute values of the components of a single-precision vector.

Computes the scalar times a vector plus a vector, y ← ax + y, all single precision.

Exits ScaLAPACK mode for the IMSL Library routines.

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.

Maps array data from a global array to local arrays in the two-dimensional block-cyclic form required by ScaLAPACK routines.

Reads matrix data from a file and transmits it into the two-dimensional block-cyclic form required by ScaLAPACK routines.

Sets up a processor grid and calculates default values for use in mapping arrays to the processor grid

Unmaps array data from local distributed arrays to a global array.

Writes the matrix data to a file.

Sums the absolute values of the real part together with the absolute values of the imaginary part of the components of a complex vector.

Computes the Euclidean norm of a complex vector.

Copies a vector x to a vector y, both single precision.

Computes the sum of a single-precision scalar, a single-precision dot product and the double-precision accumulator, which is set to the result ACCACC + a + xTy.

Computes the sum of a single-precision scalar plus a singleprecision dot product using a double-precision accumulator, which is set to the result ACCa + xTy.

Computes the single-precision dot product xTy.

Computes the sum of a single-precision scalar and a single precision dot product, a + xTy, using a double-precision accumulator.

Computes one of the matrix-vector operations: , where A is a matrix stored in band storage mode.

Computes one of the matrix-matrix operations:

Computes one of the matrix-vector operations:

Computes the rank-one update of a real general matrix:

Prints rank-1 or rank-2 arrays of numbers in a readable format.

Computes the Hadamard product of two single-precision vectors.

Computes the inverse Laplace transform of a complex function.

Calculates the indices of eigenvalues of a Sturm-Liouville problem with boundary conditions (at regular points) in a specified subinterval of the real line, [α, β].

Determines eigenvalues, eigenfunctions and/or spectral density functions for Sturm-Liouville problems in the form with boundary conditions (at regular points).

Solves a sparse linear programming problem via the revised simplex algorithm.

Computes the Euclidean length or L2 norm of a single-precision vector.

Sorts a rank-1 array of real numbers x so the y results are algebraically nondecreasing, y1 ≤ y2 ≤ … yn.

Computes the values of a spline that either interpolates or fits user-supplied data.

Returns the derived type array result.

Weighted least-squares fitting by B-splines to discrete One-Dimensional data is performed.

Returns an array result, given an array of input

Multiplies the components of a single-precision vector.

Searches a sorted vector for a given scalar and return its index.

Applies a Givens plane rotation in single precision.

Constructs a Givens plane rotation in single precision.

Applies a modified Givens plane rotation in single precision.

Constructs a modified Givens plane rotation in single precision.

Computes the matrix-vector operation , where A is a symmetric matrix in band symmetric storage mode.

Multiplies a vector by a scalar, y ← ay, both single precision.

Sets the components of a vector to a scalar, all single precision.

Performs the matrix-vector operation y := α *A * x + β * y.

Performs the matrix-vector operation, A ← A + αxxT where A is a packed symmetric matrix.

Performs the symmetric rank 2 operation,A ← A + αxyT + αyxT where A is a packed symmetric matrix.

Searches a character vector, sorted in ascending ASCII order, for a given string and return its index.

Subtracts each component of a vector from a scalar, x ← a ‑ x, all single precision.

Sums the values of a single-precision vector.

Interchanges vectors x and y, both single precision.

Computes one of the matrix-matrix operations: , where A is a symmetric matrix and B and C are m by n matrices.

Computes the matrix-vector operation , where A is a symmetric matrix.

Computes the rank-one update of a real symmetric matrix: .

Computes the rank-two update of a real symmetric matrix: .

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.

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.

Computes one of the matrix-vector operations: , where A is a triangular matrix in band storage mode.

Solves one of the triangular systems: , where A is a triangular matrix in band storage mode.

Performs one of the matrix-vector operations, x ← Ax, x ← ATx where A is an N × N packed triangular matrix.

Solves one of the systems of equations, x ← A-1x, x ← (A-1)Tx where A is an N × N packed triangular matrix.

Computes one of the matrix-matrix operations: where B is an m by n matrix and A is a triangular matrix.

Computes one of the matrix-vector operations: , where A is a triangular matrix.

Solves one of the matrix equations:

where B is an m by n matrix and A is a triangular matrix.

Solves one of the triangular linear systems: where A is a triangular matrix.

Computes a smooth bivariate interpolant to scattered data that is locally a quintic polynomial in two variables.

Multidimensional interpolation and differentiation.

Returns the derived type array result given optional input.

Weighted least-squares fitting by tensor product B-splines to discrete two-dimensional data is performed.

Returns a tensor product array result, given two arrays of independent variable values.

Multiplies a vector by a scalar and store the result in another vector, y ← ax, all single precision.

Computes the singular value decomposition of a rank-2 or rank-3 array, .

Sorts an integer array by nondecreasing absolute value.

Sorts an integer array by algebraically increasing value.

Sorts an integer array by algebraically increasing value and returns the permutation that rearranges the array.

Sorts a real array by nondecreasing absolute value.

Sorts a real array by nondecreasing absolute value and returns the permutation that rearranges the array.

Sorts a real array by algebraically increasing value.

Sorts a real array by algebraically increasing value and returns the permutation that rearranges the array.

Gets today’s date.

Gets time of day.

Solves a transportation problem.

Transposes a rectangular matrix.

Sets or retrieves input or output device unit numbers.

Handles MATH/LIBRARY and STAT/LIBRARY type REAL and double precision options.

Minimizes a function of N variables using a conjugate gradient algorithm and a finite-difference gradient.

Minimizes a function of N variables using a conjugate gradient algorithm and a user-supplied gradient.

Minimizes a function of N variables using a modified Newton method and a user-supplied Hessian.

Minimizes a function of N variables using a modified Newton method and a finite-difference Hessian.

Minimizes a function of N variables using a modified Newton method and a finite-difference Hessian.

Minimizes a function of N variables using a quasi-Newton method and a finite-difference gradient.

Minimizes a function of N variables using a direct search polytope algorithm.

Normalizes the columns of a rank-2 or rank-3 array so each has Euclidean length of value one.

Solves a nonlinear least squares problem using a modified Levenberg-Marquardt algorithm and a finite-difference Jacobian.

Solves a nonlinear least squares problem using a modified Levenberg-Marquardt algorithm and a user-supplied Jacobian.

Finds the minimum point of a nonsmooth function of a single variable.

Finds the minimum point of a smooth function of a single variable using both function evaluations and first derivative evaluations.

Computes the convolution of two complex vectors.

Computes the convolution of two real vectors.

Prints a complex rectangular matrix with a given format and labels.

Prints a complex rectangular matrix with integer row and column labels.

Prints an integer rectangular matrix with a given format and labels.

Prints an integer rectangular matrix with integer row and column labels.

Sets or retrieves an option for printing a matrix.

Prints a real rectangular matrix with a given format and labels.

Finds the zeros of a univariate complex function using Müller’s method.

Finds a zero of a real function that changes sign in a given interval.

Finds the zeros of a polynomial with real coefficients using Laguerre’s method.

Finds the zeros of a polynomial with complex coefficients using the Jenkins-Traub three-stage algorithm.

Finds the zeros of a polynomial with real coefficients using the Jenkins-Traub three-stage algorithm.

Adds a double complex scalar to the accumulator in extended precision.

Initializes an extended-precision complex accumulator to a double complex scalar.

Multiplies double complex scalars using extended precision.

Stores a double complex approximation to an extended-precision complex scalar.

Finds the real zeros of a real function using Müller’s method.