Introduction
IMSL C Math Library
Organization of the Documentation
Finding the Right Function
Naming Conventions
Getting Started and the imsl.h file
Getting Started
The imsl.h File
Error Handling, Underflow, Overflow, and Document Examples
Memory Allocation for Output Arrays
Printing Results
Complex Arithmetic
Missing Values
Passing Data to User-Supplied Functions
Example
Return Values from User-Supplied Functions
Example
Thread Safe Usage
Error Handling
Routines that Produce Output
OpenMP Usage
Vendor Supplied Libraries Usage
C++ Usage
Output
Matrix Storage Modes
General Mode
Rectangular Mode
Symmetric Mode
Hermitian Mode
Sparse Coordinate Storage Format
Band Storage Format
Choosing Between Banded and Coordinate Forms
Compressed Sparse Column (CSC) Format
Chapter 1: Linear Systems
Functions
Usage Notes
Solving Systems of Linear Equations
Matrix Factorizations
Matrix Inversions
Multiple Right-Hand Sides
Least-Squares Solutions and QR Factorizations
Non-Negative Matrix Factorization
Singular Value Decompositions and Generalized Inverses
Ill-Conditioning and Singularity
lin_sol_gen
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Reconstruction of L-1 and U from factor:
Example 3
Output
Example 4
Output
Warning Errors
Fatal Errors
lin_sol_gen (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Warning Errors
Fatal Errors
lin_sol_posdef
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Warning Errors
Fatal Errors
lin_sol_posdef (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
lin_sol_gen_band
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
lin_sol_gen_band (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
lin_sol_posdef_band
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
lin_sol_posdef_band (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
lin_sol_gen_coordinate
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Example 3
Output
lin_sol_gen_coordinate (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
superlu
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
superlu (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
superlu_smp
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
superlu_smp (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
lin_sol_posdef_coordinate
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
lin_sol_posdef_coordinate (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
sparse_cholesky_smp
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Fatal Errors
sparse_cholesky_smp (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Fatal Errors
lin_sol_gen_min_residual
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Fatal Errors
lin_sol_def_cg
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Fatal Errors
lin_least_squares_gen
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Fatal Errors
nonneg_least_squares
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
lin_lsq_lin_constraints
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Fatal Errors
nonneg_matrix_factorization
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
lin_svd_gen
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Warning Errors
lin_svd_gen (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Warning Errors
lin_sol_nonnegdef
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Warning Errors
Chapter 2: Eigensystem Analysis
Functions
Usage Notes
Error Analysis and Accuracy
Reformulating Generalized Eigenvalue Problems
eig_gen
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
eig_gen (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Fatal Errors
eig_sym
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
eig_herm (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
eig_symgen
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
geneig
Synopsis
Required Arguments
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
geneig (complex)
Synopsis
Required Arguments
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Chapter 3: Interpolation and Approximation
Functions
Usage Notes
Piecewise Polynomials
Splines and B-Splines
Cubic Splines
Tensor Product Splines
Scattered Data Interpolation
Multi-dimensional Interpolation
Least Squares
Smoothing by Cubic Splines
Structures for Splines and Piecewise Polynomials
B-Splines
Example
Output
Piecewise Polynomials
Example
Output
cub_spline_interp_e_cnd
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Example 4
Output
Warning Errors
Fatal Errors
cub_spline_interp_shape
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
cub_spline_tcb
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
cub_spline_value
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
cub_spline_integral
Synopsis
Required Arguments
Return Value
Description
Example
Output
spline_interp
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
spline_knots
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
spline_2d_interp
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
spline_value
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Fatal Errors
spline_integral
Synopsis
Required Arguments
Return Value
Description
Example
Output
Warning Errors
Fatal Errors
spline_2d_value
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
spline_2d_integral
Synopsis
Required Arguments
Return Value
Description
Example
Output
Warning Errors
Fatal Errors
spline_nd_interp
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
Warning Errors
Fatal Errors
user_fcn_least_squares
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Remarks
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Warning Errors
Fatal Errors
spline_least_squares
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
spline_2d_least_squares
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
cub_spline_smooth
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
spline_lsq_constrained
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
smooth_1d_data
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
scattered_2d_interp
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Fatal Errors
radial_scattered_fit
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Fatal Errors
radial_evaluate
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
Chapter 4: Quadrature
Functions
Usage Notes
Univariate Quadrature
Multivariate Quadrature
Gauss Quadrature
int_fcn_sing
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
int_fcn_sing_1d
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Remarks
Examples
Example 1
Output
Example 2
Output
Fatal Errors
int_fcn
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
int_fcn_sing_pts
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
int_fcn_alg_log
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
int_fcn_inf
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
int_fcn_trig
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
int_fcn_fourier
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
int_fcn_cauchy
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
int_fcn_smooth
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Fatal Errors
int_fcn_2d
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
int_fcn_sing_2d
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Remarks
Example
Output
Fatal Errors
int_fcn_sing_3d
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Remarks
Example
Output
Fatal Errors
int_fcn_hyper_rect
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
Warning Errors
Fatal Errors
int_fcn_qmc
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
Fatal Errors
gauss_quad_rule
Synopsis
Required Arguments
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
fcn_derivative
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Fatal Errors
Chapter 5: Differential Equations
Functions
Usage Notes
Ordinary Differential Equations
Differential-algebraic Equations
Partial Differential Equations
ode_runge_kutta
Synopsis
Required Arguments for imsl_ f_ode_runge_kutta_mgr
Required Arguments for imsl_f_ode_runge_kutta
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Fatal Errors
ode_adams_gear
bvp_finite_difference
Synopsis
Required Arguments
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Fatal Errors
differential_algebraic_eqs
Synopsis
Required Arguments
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1 – Method of Lines PDE Problem
Output
Example 2 – Pendulum Problem
Output
Example 3 – User Solves Linear System
Output
Fatal Errors
dea_petzold_gear
ode_adams_2nd_order
ode_adams_krogh
Synopsis
Required Arguments
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
Introduction to pde_1d_mg
Description Summary
pde_1d_mg
Synopsis
Required Arguments for imsl_f_pde_1d_mg_mgr
Required Arguments for imsl_f_pde_1d_mg
Synopsis with Optional Arguments for imsl_f_pde_1d_mg_mgr
Optional Arguments
Synopsis with Optional Arguments for imsl_f_pde_1d_mg
Optional Arguments
Examples
Remarks on the Examples
Example 1 - Electrodynamics Model
Example 2 - Inviscid Flow on a Plate
Example 3 - Population Dynamics
Example 4 - A Model in Cylindrical Coordinates
Example 5 - A Flame Propagation Model
Example 6 - A ‘Hot Spot’ Model
Example 7 - Traveling Waves
Example 8 - Black-Scholes
Code for PV-WAVE Plotting
Fatal Errors
pde_method_of_lines
modified_method_of_lines
Synopsis
Required Arguments for imsl_f_modified_method_of_lines_mgr
Required Arguments for imsl_f_modified_method_of_lines
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Example 4
Output
Fatal Errors
feynman_kac
Synopsis
Required Arguments
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Example 4
Output
Fatal Errors
feynman_kac_evaluate
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
fast_poisson_2d
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
Fatal Errors
Chapter 6: Transforms
Functions
Usage Notes
Fast Fourier Transforms
Continuous Versus Discrete Fourier Transform
fft_real
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
fft_real_init
Synopsis
Required Arguments
Return Value
Description
Example
Output
fft_complex
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
fft_complex_init
Synopsis
Required Arguments
Return Value
Description
Example
Output
fft_cosine
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
fft_cosine_init
Synopsis
Required Arguments
Return Value
Description
Example
Output
fft_sine
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
fft_sine_init
Synopsis
Required Arguments
Return Value
Description
Example
Output
fft_2d_complex
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Erors
convolution
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
convolution (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
inverse_laplace
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Fatal Errors
Chapter 7: Nonlinear Equations
Functions
Usage Notes
Zeros of a Polynomial
Zeros of a Function
Root of System of Equations
zeros_poly
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
zeros_poly (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
zero_univariate
Synopsis
Required Arguments
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
Fatal Errors
zeros_function
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
zeros_sys_eqn
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
Chapter 8: Optimization
Functions
Usage Notes
Unconstrained Minimization
Linearly Constrained Minimization
Nonlinearly Constrained Minimization
Return Values from User-Supplied Functions
min_uncon
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
min_uncon_deriv
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
min_uncon_golden
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Remarks
Example
Output
Warning Errors
Fatal Errors
min_uncon_multivar
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Informational Errors
Warning Errors
Fatal Errors
nonlin_least_squares
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Informational Errors
Warning Errors
Fatal Errors
read_mps
Synopsis
Required Argument
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
MPS File Format
NAME Section
ROWS Section
COLUMNS Section
RHS Section
RANGES Section
BOUNDS Section
QUADRATIC Section
ENDATA Section
linear_programming
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Note Errors
Warning Errors
Fatal Errors
lin_prog
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
quadratic_prog
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
sparse_lin_prog
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
sparse_quadratic_prog
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
min_con_gen_lin
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Fatal Errors
bounded_least_squares
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Example 2
Output
Fatal Errors
constrained_nlp
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arugments
Optional Arguments
Description
Example
Output
Fatal Errors
jacobian
Synopsis
Required Arguments
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Example 4
Output
Example 5
Output
Chapter 9: Special Functions
Functions
Usage Notes
Additional Information
erf
Synopsis
Required Arguments
Return Value
Description
Example
Output
erfc
Synopsis
Required Arguments
Return Value
Description
Example
Output
Alert Errors
erfce
Synopsis
Required Arguments
Return Value
Description
Example
Output
erfe
Synopsis
Required Arguments
Return Value
Description
Example
Output
erf_inverse
Synopsis
Required Arguments
Return Value
Description
Example
Output
Warning Errors
Fatal Errors
erfc_inverse
Synopsis
Required Arguments
Return Value
Description
Example
Output
Alert Errors
Warning Errors
Fatal Errors
beta
Synopsis
Required Arguments
Return Value
Description
Example
Output
Alert Errors
Fatal Errors
log_beta
Synopsis
Required Arguments
Return Value
Description
Example
Output
Warning Errors
beta_incomplete
Synopsis
Required Arguments
Return Value
Description
Example
Output
gamma
Synopsis
Required Arguments
Return Value
Description
Example
Output
Alert Errors
Warning Errors
Fatal Errors
log_gamma
Synopsis
Required Arguments
Return Value
Description
Example
Output
Warning Errors
Fatal Errors
gamma_incomplete
Synopsis
Required Arguments
Return Value
Description
Example
Output
Fatal Errors
psi
Synopsis
Required Arguments
Return Values
Description
Example
Output
Warning Errors
psi1
Synopsis
Required Arguments
Return Value
Description
Example
Output
Warning Errors
bessel_J0
Synopsis
Required Arguments
Return Value
Description
Example
Output
Warning Errors
Fatal Errors
bessel_J1
Synopsis
Required Arguments
Return Value
Description
Example
Output
Alert Errors
Warning Errors
Fatal Errors
bessel_Jx
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
Fatal Errors
bessel_Y0
Synopsis
Required Arguments
Return Value
Description
Example
Output
Warning Errors
Fatal Errors
bessel_Y1
Synopsis
Required Arguments
Return Value
Description
Example
Output
Warning Errors
Fatal Errors
bessel_Yx
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
bessel_I0
Synopsis
Required Arguments
Return Value
Description
Example
Output
Fatal Errors
bessel_exp_I0
Synopsis
Required Arguments
Return Value
Description
Example
Output
bessel_I1
Synopsis
Required Arguments
Return Value
Description
Example
Output
Alert Errors
Fatal Errors
bessel_exp_I1
Synopsis
Required Arguments
Return Value
Description
Example
Output
bessel_Ix
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
bessel_K0
Synopsis
Required Arguments
Return Value
Description
Example
Output
Alert Errors
bessel_exp_K0
Synopsis
Required Arguments
Return Value
Description
Example
Output
bessel_K1
Synopsis
Required Arguments
Return Value
Description
Example
Output
Alert Errors
Fatal Errors
bessel_exp_K1
Synopsis
Required Arguments
Return Value
Description
Example
Output
bessel_Kx
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
elliptic_integral_K
Synopsis
Required Arguments
Return Value
Description
Example
Output
elliptic_integral_E
Synopsis
Required Arguments
Return Value
Description
Example
Output
elliptic_integral_RF
Synopsis
Required Arguments
Return Value
Description
Example
Output
elliptic_integral_RD
Synopsis
Required Arguments
Return Value
Description
Example
Output
elliptic_integral_RJ
Synopsis
Required Arguments
Return Value
Description
Example
Output
elliptic_integral_RC
Synopsis
Required Arguments
Return Value
Description
Example
Output
fresnel_integral_C
Synopsis
Required Arguments
Return Value
Description
Example
Output
fresnel_integral_S
Synopsis
Required Arguments
Return Value
Description
Example
Output
airy_Ai
Synopsis
Required Arguments
Return Value
Description
Example
Output
airy_Bi
Synopsis
Required Arguments
Return Value
Description
Example
Output
airy_Ai_derivative
Synopsis
Required Arguments
Return Value
Description
Example
Output
airy_Bi_derivative
Synopsis
Required Arguments
Return Value
Description
Example
Output
kelvin_ber0
Synopsis
Required Arguments
Return Value
Description
Example
Output
kelvin_bei0
Synopsis
Required Arguments
Return Value
Description
Example
Output
kelvin_ker0
Synopsis
Required Arguments
Return Value
Description
Example
Output
kelvin_kei0
Synopsis
Required Arguments
Return Value
Description
Example
Output
kelvin_ber0_derivative
Synopsis
Required Arguments
Return Value
Description
Example
Output
kelvin_bei0_derivative
Synopsis
Required Arguments
Return Value
Description
Example
Output
kelvin_ker0_derivative
Synopsis
Required Arguments
Return Value
Description
Example
Output
kelvin_kei0_derivative
Synopsis
Required Arguments
Return Value
Description
Example
Output
normal_cdf
Synopsis
Required Arguments
Return Value
Description
Example
Output
normal_inverse_cdf
Synopsis
Required Arguments
Return Value
Description
Example
Output
chi_squared_cdf
Synopsis
Required Arguments
Return Value
Description
Example
Output
Informational Errors
Alert Errors
chi_squared_inverse_cdf
Synopsis
Required Arguments
Return Value
Description
Example
Output
Warning Errors
F_cdf
Synopsis
Required Arguments
Return Value
Description
Example
Output
F_inverse_cdf
Synopsis
Required Arguments
Return Value
Description
Example
Output
Fatal Errors
t_cdf
Synopsis
Required Arguments
Return Value
Description
Example
Output
t_inverse_cdf
Synopsis
Required Arguments
Return Value
Description
Example
Output
Informational Errors
gamma_cdf
Synopsis
Required Arguments
Return Value
Description
Example
Output
Informational Errors
Fatal Errors
binomial_cdf
Synopsis
Required Arguments
Return Value
Description
Example
Output
Informational Errors
hypergeometric_cdf
Synopsis
Required Arguments
Return Value
Description
Example
Output
Informational Errors
Fatal Errors
poisson_cdf
Synopsis
Required Arguments
Return Value
Description
Example
Output
Informational Errors
beta_cdf
Synopsis
Required Arguments
Return Value
Description
Example
Output
beta_inverse_cdf
Synopsis
Required Arguments
Return Value
Description
Example
Output
bivariate_normal_cdf
Synopsis
Required Arguments
Return Value
Description
Example
Output
cumulative_interest
Synopsis
Required Arguments
Return Value
Description
Example
Output
cumulative_principal
Synopsis
Required Arguments
Return Value
Description
Example
Output
depreciation_db
Synopsis
Required Arguments
Return Value
Description
Example
Output
depreciation_ddb
Synopsis
Required Arguments
Return Value
Description
Example
Output
depreciation_sln
Synopsis
Required Arguments
Return Value
Description
Example
Output
depreciation_syd
Synopsis
Required Arguments
Return Value
Description
Example
Output
depreciation_vdb
Synopsis
Required Arguments
Return Value
Description
Example
Output
dollar_decimal
Synopsis
Required Arguments
Return Value
Description
Example
Output
dollar_fraction
Synopsis
Required Arguments
Return Value
Description
Example
Output
effective_rate
Synopsis
Required Arguments
Return Value
Description
Example
Output
future_value
Synopsis
Required Arguments
Return Value
Description
Example
Output
future_value_schedule
Synopsis
Required Arguments
Return Value
Description
Example
Output
interest_payment
Synopsis
Required Arguments
Return Value
Description
Example
Output
interest_rate_annuity
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
internal_rate_of_return
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
internal_rate_schedule
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
modified_internal_rate
Synopsis
Required Arguments
Return Value
Description
Example
Output
net_present_value
Synopsis
Required Arguments
Return Value
Description
Example
Output
nominal_rate
Synopsis
Required Arguments
Return Value
Description
Example
Output
number_of_periods
Synopsis
Required Arguments
Return Value
Description
Example
Output
payment
Synopsis
Required Arguments
Return Value
Description
Example
Output
present_value
Synopsis
Required Arguments
Return Value
Description
Example
Output
present_value_schedule
Synopsis
Required Arguments
Return Value
Description
Example
Output
principal_payment
Synopsis
Required Arguments
Return Value
Description
Example
Output
accr_interest_maturity
Synopsis
Required Arguments
Return Value
Description
Example
Output
accr_interest_periodic
Synopsis
Required Arguments
Return Value
Description
Example
Output
bond_equivalent_yield
Synopsis
Required Arguments
Return Value
Description
Example
Output
convexity
Synopsis
Required Arguments
Return Value
Description
Example
Output
coupon_days
Synopsis
Required Arguments
Return Value
Description
Example
Output
coupon_number
Synopsis
Required Arguments
Return Value
Description
Example
Output
days_before_settlement
Synopsis
Required Arguments
Return Value
Description
Example
Output
days_to_next_coupon
Synopsis
Required Arguments
Return Value
Description
Example
Output
depreciation_amordegrc
Synopsis
Required Arguments
Return Value
Description
Example
Output
depreciation_amorlinc
Synopsis
Required Arguments
Return Value
Description
Example
Output
discount_price
Synopsis
Required Arguments
Return Value
Description
Example
Output
discount_rate
Synopsis
Required Arguments
Return Value
Description
Example
Output
discount_yield
Synopsis
Required Arguments
Return Value
Description
Example
Output
duration
Synopsis
Required Arguments
Return Value
Description
Example
Output
interest_rate_security
Synopsis
Required Arguments
Return Value
Description
Example
Output
modified_duration
Synopsis
Required Arguments
Return Value
Description
Example
Output
next_coupon_date
Synopsis
Required Arguments
Return Value
Description
Example
Output
previous_coupon_date
Synopsis
Required Arguments
Return Value
Description
Example
Output
price
Synopsis
Required Arguments
Return Value
Description
Example
Output
price_maturity
Synopsis
Required Arguments
Return Value
Description
Example
Output
received_maturity
Synopsis
Required Arguments
Return Value
Description
Example
Output
treasury_bill_price
Synopsis
Required Arguments
Return Value
Description
Example
Output
treasury_bill_yield
Synopsis
Required Arguments
Return Value
Description
Example
Output
year_fraction
Synopsis
Required Arguments
Return Value
Description
Example
Output
yield_maturity
Synopsis
Required Arguments
Return Value
Description
Example
Output
yield_periodic
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
Chapter 10: Statistics and Random Number Generation
Functions
Usage Notes
Statistics
Overview of Random Number Generation
The Basic Uniform Generator
Shuffled Generators
Setting the Seed
simple_statistics
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Mean
Variance
Skewness
Excess or Kurtosis
Minimum
Maximum
Range
Coefficient of Variation
Median
Median Absolute Deviation
Simple Robust Estimate of Scale
Example
Output
table_oneway
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Example 4
Output
chi_squared_test
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Programming Notes
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Warning Errors
Fatal Errors
covariances
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Usage Notes
Examples
Example 1
Output
Example 2
Output
Warning Errors
regression
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
poly_regression
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
Fatal Errors
ranks
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Ties
The Scores
Examples
Example 1
Output
Example 2
Output
random_seed_get
Synopsis
Return Value
Description
Example
Output
random_seed_set
Synopsis
Required Arguments
Description
Example
random_option
Synopsis
Required Arguments
Description
Example
random_uniform
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
random_normal
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
Remark
random_poisson
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
random_gamma
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
random_beta
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
random_exponential
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
faure_next_point
Synopsis
Required Arguments for imsl_faure_sequence_init
Return Value for imsl_faure_sequence_init
Required Arguments for imsl_faure_next_point
Return Value for imsl_faure_next_point
Required Arguments for imsl_faure_sequence_free
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
Chapter 11: Printing Functions
Functions
write_matrix
Synopsis
Required Arguments
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Example 3
Output
page
Synopsis
Required Arguments
Example
Output
write_options
Synopsis
Required Arguments
Description
Example
Output
Chapter 12: Utilities
Functions
output_file
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
File myfile
Example 2
Output
Output
version
Synopsis
Required Arguments
Return Value
Description
Example
ctime
Synopsis
Return Value
Example
Output
date_to_days
Synopsis
Required Arguments
Return Value
Description
Example
Output
days_to_date
Synopsis
Required Arguments
Description
Example
Output
error_options
Synopsis with Optional Arguments
Optional Arguments
Return Value
Description
Examples
Example 1
Output
Example 2
Output
Example 3
Output
Example 4
Output
error_type
Synopsis
Return Value
Description
Example
error_message
Synopsis
Return Value
Description
Example
Output
error_code
Synopsis
Return Value
Example
Output
initialize_error_handler
Synopsis
Return Value
Description
Example
set_user_fcn_return_flag
Synopsis
Required Arguments
Description
Programming Notes
Examples
Example 1
Output
Example 2
Output
initialize
free
Synopsis
Required Arguments
Description
Example
Output
fopen
Synopsis
Required Arguments
Return Value
Description
Example
Output
fclose
Synopsis
Required Arguments
Return Value
Description
Example
omp_options
Synopsis with Optional Arguments
Return Value
Optional Arguments
Description
Example
Output
constant
Synopsis
Required Arguments
Return Value
Description
Examples
Example 1
Output
Example 2
Output
Warning Errors
machine (integer)
Synopsis
Required Arguments
Return Value
Description
Example
Output
machine (float)
Synopsis
Required Arguments
Return Value
Description
Example
Output
sort
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
sort (integer)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
vector_norm
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
vector_norm (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
mat_mul_rect
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
mat_mul_rect (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
mat_mul_rect_band
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
mat_mul_rect_band (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
mat_mul_rect_coordinate
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
mat_mul_rect_coordinate (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
mat_add_band
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
mat_add_band (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
mat_add_coordinate
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
mat_add_coordinate (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
matrix_norm
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
matrix_norm_band
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
matrix_norm_coordinate
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
generate_test_band
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
generate_test_band (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
generate_test_coordinate
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
generate_test_coordinate (complex)
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Examples
Example 1
Output
Example 2
Output
Programming Notes for Using NVIDIA® CUDA™ Toolkit
Rationale and General Algorithm
Implementation
Basic Linear Algebra Subprograms
Transforms
Utility Functions
Required NVIDIA Copyright Notice:
cuda_get
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Output
Warning Errors
cuda_set
Synopsis
Required Arguments
Return Value
Synopsis with Optional Arguments
Optional Arguments
Description
Example
Warning Errors
cuda_free
Synopsis
Return Value
Description
Example
Warning Errors
Reference Material
Contents
User Errors
What Determines Error Severity
Kinds of Errors and Default Actions
Errors in Lower-Level Functions
Functions for Error Handling
Threads and Error Handling
Use of Informational Error to Determine Program Action
Additional Examples
Complex Data Types and Functions
Single-Precision Complex Operations and Functions
Double-Precision Complex Operations and Functions
Example
Output
Appendix A: References
Abramowitz and Stegun
Ahrens and Dieter
Akima
Altman and Gondzio
Ashcraft
Ashcraft et al.
Atkinson (1979)
Atkinson (1978)
Barnett
Barrett and Healy
Bays and Durham
Beckers
Blom
Blom and Zegeling
Boisvert
Bosten and Battiste
Brenan, Campbell, and Petzold
Brent
Brigham
Burgoyne
Carlson
Carlson and Notis
Carlson and Foley
Cheng
Cohen and Taylor
Cooley and Tukey
Cooper
Courant and Hilbert
Craven and Wahba
Crowe et al.
Davis and Rabinowitz
de Boor
Demmel et al.
Dennis and Schnabel
Dongarra et al.
Doornik
Draper and Smith
DuCroz et al.
Duff et al.
Duff et al.
Duff and Reid
Enright and Pryce
Farebrother and Berry
Fisher
Fishman and Moore
Forsythe
Franke
Garbow et al.
Gautschi
Gear
Gentleman
George and Liu
Gill and Murray
Gill et al.
Goldfarb and Idnani
Golub
Golub and Van Loan
Golub and Welsch
Gondzio (1994)
Gondzio (1995)
Gregory and Karney
Griffin and Redfish
Grosse
Guerra and Tapia
Hageman and Young
Hanson
Hanson
Hanson and Krogh
Hardy
Hart et al.
Healy
Herraman
Higham
Hill
Hindmarsh
Hinkley
Huber
Hull et al.
Irvine et al.
Jackson et al.
Jenkins
Jenkins and Traub
Jöhnk
Kendall and Stuart
Kennedy and Gentle
Kernighan and Richtie
Kinnucan and Kuki
Knuth
Kochanek and Bartels
Krogh
Learmonth and Lewis
Lehmann
Levenberg
Leavenworth
Lentini and Pereyra
Lewis et al.
Liepman
Liu
Lyness and Giunta
Madsen and Sincovec
Maindonald
Marquardt
Marsaglia and Tsang
Martin and Wilkinson
Mayle
Michelli
Michelli et al.
Moler and Stewart
Moré et al.
Müller
Murtagh
Murty
Neter and Wasserman
Neter et al.
NVIDIA
Østerby and Zlatev
Owen
Parlett
Pennington and Berzins
Petro
Petzold
Piessens et al.
Powell
Ralston
Rauber et. al.
Reinsch
Rice
Saad and Schultz
Salane
Sallas and Lionti
Savage
Schmeiser
Schmeiser and Babu
Schmeiser and Kachitvichyanukul
Schmeiser and Lal
Seidler and Carmichael
Shampine
Shampine and Gear
Sincovec and Madsen
Singleton
Smith et al.
Smith
Spellucci, Peter
Stewart
Strecok
Stroud and Secrest
Temme
Tezuka
Thompson and Barnett
Tukey
Velleman and Hoaglin
Verwer et al
Walker
Watkins
Weeks
Wilmott et al
Appendix B: Alphabetical Summary of Functions
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Y
Z
Product Support
Contacting IMSL Support
A Component of the Rogue Wave IMSL® C Numerical Libraries
Product Support