Calcpad Language Reference for Claude Code

Description

Calcpad is free software for mathematical and engineering calculations. It represents a flexible and modern programmable calculator with Html report generator. It is simple and easy to use, but it also includes many advanced features:

real and complex numbers (rectangular and polar-phasor formats);
units of measurement (SI, Imperial and USCS);
vectors and matrices: rectangular, symmetric, column, diagonal, upper/lower triangular;
custom variables and units;
built-in library with common math functions;
vectors and matrix functions:
- data functions: search, lookup, sort, count, etc.;
- aggregate functions: min, max, sum, sumsq, srss, average, product (geometric) mean, etc.;
- math functions: norm, condition, determinant, rank, trace, transpose, adjugate and cofactor, inverse, factorization (cholesky, ldlt, lu, qr and svd), eigenvalues/vectors and linear systems of equations;
custom functions of multiple parameters f(x; y; z; …);
powerful numerical methods for root and extremum finding, numerical integration and differentiation;
finite sum, product and iteration procedures, Fourier series and FFT;
modules, macros and string variables;
reading and writing data from/to text, CSV and Excel files;
program flow control with conditions and loops;
"titles" and 'text' comments in quotes;
support for Html and CSS in comments for rich formatting;
function plotting, images, tables, parametric SVG drawings, etc.;
automatic generation of Html forms for data input;
professional looking Html reports for viewing and printing;
export to Word (*.docx) and PDF documents;
variable substitution and smart rounding of numbers;
output visibility control and content folding;
support for plain text (*.txt, *.cpd) and binary (*.cpdz) file formats.

Language specification

Primitives:

Real numbers: digits 0 - 9 and decimal point ".", e.g.
```
3.14
```
Complex numbers: re ± imi, e.g.
```
3 - 2i
```
Vectors:
```
[v₁; v₂; v₃; …; vₙ]
```

Matrices:

[M₁₁; M₁₂; … ; M₁ₙ | M₂₁; M₂₂; … ; M₂ₙ | … | Mₘ₁; Mₘ₂; … ; Mₘₙ]

Variables:

all Unicode letters
digits: 0 - 9
comma: " , "
special symbols: ′ , ″ , ‴ , ⁗ , ‾ , ø , Ø , ° , ∡
superscripts: ⁰ , ¹ , ² , ³ , ⁴ , ⁵ , ⁶ , ⁷ , ⁸ , ⁹ , ⁿ , ⁺ , ⁻
subscripts: ₀ , ₁ , ₂ , ₃ , ₄ , ₅ , ₆ , ₇ , ₈ , ₉ , ₊ , ₋ , ₌ , ₍ , ₎
" _ " for subscript
Any variable name must start with a letter. Names are case sensitive.

Operators:

- factorial

- exponent

- division

÷

- force division bar in inline mode and slash in pro mode (//)

\ - integer division

⦼

- modulo (remainder)

* - multiplication

- minus

- plus

≡

- equal to

≠

- not equal to

- less than

- greater than

≤

- less or equal

≥

- greater or equal

∧

- logical "AND"

∨

- logical "OR"

⊕

- logical "XOR"

∠

- phasor A∠φ (<<)

- assignment

Custom functions:

Definition:

f(x; y; z; ... ) = expression

Delimiter for arguments: semicolon

Built-in functions:

Trigonometric:

sin(x)

- sine

cos(x)

- cosine

tan(x)

- tangent

csc(x)

- cosecant

sec(x)

- secant

cot(x)

- cotangent

Hyperbolic:

sinh(x)

- hyperbolic sine

cosh(x)

- hyperbolic cosine

tanh(x)

- hyperbolic tangent

csch(x)

- hyperbolic cosecant

sech(x)

- hyperbolic secant

coth(x)

- hyperbolic cotangent

Inverse trigonometric:

asin(x)

- inverse sine

acos(x)

- inverse cosine

atan(x)

- inverse tangent

atan2(x; y)

- the angle whose tangent is the quotient of y and x

acsc(x)

- inverse cosecant

asec(x)

- inverse secant

acot(x)

- inverse cotangent

Inverse hyperbolic:

asinh(x)

- inverse hyperbolic sine

acosh(x)

- inverse hyperbolic cosine

atanh(x)

- inverse hyperbolic tangent

acsch(x)

- inverse hyperbolic cosecant

asech(x)

- inverse hyperbolic secant

acoth(x)

- inverse hyperbolic cotangent

Logarithmic, exponential and roots:

log(x)

- decimal logarithm

ln(x)

- natural logarithm

log_2(x)

- binary logarithm

exp(x)

- natural exponent

sqr(x)

sqrt(x)

- square root

cbrt(x)

- cubic root

root(x; n)

- n-th root

Rounding:

round(x)

- round to the nearest integer

floor(x)

- round to the smaller integer (towards -∞)

ceiling(x)

- round to the greater integer (towards +∞)

trunc(x)

- round to the smaller integer (towards zero)

Integer:

mod(x; y)

- the remainder of an integer division

gcd(x; y; z...)

- the greatest common divisor of several integers

lcm(x; y; z...)

- the least common multiple of several integers

Complex:

re(z)

- the real part of a complex number

im(z)

- the imaginary part of a complex number

abs(z)

- absolute value/magnitude

phase(z)

- the phase of a complex number

conj(z)

- the conjugate of a complex number

Aggregate and interpolation:

min(x; y; z...)

- minimum of multiple values

max(x; y; z...)

- maximum of multiple values

sum(x; y; z...)

- sum of multiple values = x + y + z...

sumsq(x; y; z...)

- sum of squares = x² + y² + z²...

srss(x; y; z...)

- square root of sum of squares = sqrt(x² + y² + z²...)

average(x; y; z...)

- average of multiple values = (x + y + z...)/n

product(x; y; z...)

- product of multiple values = x·y·z...

mean(x; y; z...)

- geometric mean = n-th root(x·y·z...)

take(n; a; b; c...)

- returns the n-th element from the list

line(x; a; b; c...)

- linear interpolation

spline(x; a; b; c...)

- Hermite spline interpolation

Conditional and logical:

if(condition; value-if-true; value-if-false)

- conditional evaluation

switch(condition1; value1; condition2; value2; … ; default)

- selective evaluation

not(x)

- logical "NOT"

and(x; y; z...)

- logical "AND"

or(x; y; z...)

- logical "OR"

xor(x; y; z...)

- logical "XOR"

Other:

sign(x)

- the sign of a number

random(x)

- random number between 0 and x

getunits(x)

- gets the units of x without the value. Returns 1 if x is unitless

setunits(x; u)

- sets the units u to x where x can be scalar, vector or matrix

clrunits(x)

- clears the units from a scalar, vector or matrix x

hp(x)

- converts x to its high performance (hp) equivalent type

ishp(x)

- checks if the type of x is a high-performance (hp) vector or matrix

Vector:

Creational:

vector(n)

- creates an empty vector with length n

vector_hp(n)

- creates an empty high performance (hp) vector with length n

range(x1; xn; s)

- creates a vector with values spanning from x1 to xn with step s

range_hp(x1; xn; s)

- creates a high performance (hp) from a range of values as above

Structural:

len(v)

- returns the length of vector v

size(v)

- the actual size of vector v - the index of the last non-zero element

resize(v; n)

- sets a new length n of vector v

fill(v; x)

- fills vector v with value x

join(A; b; c…)

- creates a vector by joining the arguments: matrices, vectors and scalars

slice(v; i₁; i₂)

- returns the part of vector v bounded by indexes i₁ and i₂ inclusive

first(v; n)

- the first n elements of vector v

last(v; n)

- the last n elements of vector v

extract(v; i)

- extracts the elements from v which indexes are contained in i

Data:

sort(v)

- sorts the elements of vector v in ascending order

rsort(v)

- sorts the elements of vector v in descending order

order(v)

- the indexes of vector v, arranged by the ascending order of its elements

revorder(v)

- the indexes of vector v, arranged by the descending order of its elements

reverse(v)

- a new vector containing the elements of v in reverse order

count(v; x; i)

- the number of elements in v, after the i-th one, that are equal to x

search(v; x; i)

- the index of the first element in v, after the i-th one, that is equal to x

find(v; x; i) or

find_eq(v; x; i)

- the indexes of all elements in v, after the i-th one, that are = x

find_ne(v; x; i)

- the indexes of all elements in v, after the i-th one, that are ≠ x

find_lt(v; x; i)

- the indexes of all elements in v, after the i-th one, that are < x

find_le(v; x; i)

- the indexes of all elements in v, after the i-th one, that are ≤ x

find_gt(v; x; i)

- the indexes of all elements in v, after the i-th one, that are > x

find_ge(v; x; i)

- the indexes of all elements in v, after the i-th one, that are ≥ x

lookup(a; b; x) or

lookup_eq(a; b; x)

- all elements in a for which the respective elements in b are = x

lookup_ne(a; b; x)

- all elements in a for which the respective elements in b are ≠ x

lookup_lt(a; b; x)

- all elements in a for which the respective elements in b are < x

lookup_le(a; b; x)

- all elements in a for which the respective elements in b are ≤ x

lookup_gt(a; b; x)

- all elements in a for which the respective elements in b are > x

lookup_ge(a; b; x)

- all elements in a for which the respective elements in b are ≥ x

Math:

norm_1(v)

- L1 (Manhattan) norm of vector v

norm(v) or

norm_2(v) or

norm_e(v)

- L2 (Euclidean) norm of vector v

norm_p(v; p)

- Lp norm of vector v

norm_i(v)

- L∞ (infinity) norm of vector v

unit(v)

- the normalized vector v (with L2 norm = 1)

dot(a; b)

- scalar product of two vectors a and b

cross(a; b)

- cross product of two vectors a and b (with length 2 or 3)

Matrix:

Creational:

matrix(m; n)

- creates an empty matrix with dimensions m⨯n

identity(n)

- creates an identity matrix with dimensions n⨯n

diagonal(n; d)

- creates a n⨯n diagonal matrix and fills the diagonal with value d

column(m; c)

- creates a column matrix with dimensions m⨯1, filled with value c

utriang(n)

- creates an upper triangular matrix with dimensions n⨯n

ltriang(n)

- creates a lower triangular matrix with dimensions n⨯n

symmetric(n)

- creates a symmetric matrix with dimensions n⨯n

matrix_hp(m; n)

- creates a high-performance matrix with dimensions m⨯n

identity_hp(n)

- creates a high-performance identity matrix with dimensions n⨯n

diagonal_hp(n; d)

- creates a high-performance n⨯n diagonal matrix filled with value d

column_hp(m; c)

- creates a high-performance m⨯1 column matrix filled with value c

utriang_hp(n)

- creates a high-performance n⨯n upper triangular matrix

ltriang_hp(n)

- creates a high-performance n⨯n lower triangular matrix

symmetric_hp(n)

- creates a high-performance symmetric matrix with dimensions n⨯n

vec2diag(v)

- creates a diagonal matrix from the elements of vector v

vec2row(v)

- creates a row matrix from the elements of vector v

vec2col(v)

- creates a column matrix from the elements of vector v

join_cols(c₁; c₂; c₃…)

- creates a new matrix by joining column vectors

join_rows(r₁; r₂; r₃…)

- creates a new matrix by joining row vectors

augment(A; B; C…)

- creates a new matrix by appending matrices A; B; C side by side

stack(A; B; C…)

- creates a new matrix by stacking matrices A; B; C one below the other

Structural:

n_rows(M)

- number of rows in matrix M

n_cols(M)

- number of columns in matrix M

mresize(M; m; n)

- sets new dimensions m and n for matrix M

mfill(M; x)

- fills matrix M with value x

fill_row(M; i; x)

- fills the i-th row of matrix M with value x

fill_col(M; j; x)

- fills the j-th column of matrix M with value x

copy(A; B; i; j)

- copies all elements from A to B, starting from indexes i and j of B

add(A; B; i; j)

- adds all elements from A to those of B, starting from indexes i and j of B

row(M; i)

- extracts the i-th row of matrix M as a vector

col(M; j)

- extracts the j-th column of matrix M as a vector

extract_rows(M; i)

- extracts the rows from matrix M whose indexes are contained in vector i

extract_cols(M; j)

- extracts the columns from matrix M whose indexes are contained in vector j

diag2vec(M)

- extracts the diagonal elements of matrix M to a vector

submatrix(M; i₁; i₂; j₁; j₂)

- extracts a submatrix of M, bounded by rows i₁ and i₂ and columns j₁ and j₂, incl.

Data:

sort_cols(M; i)

- sorts the columns of M based on the values in row i in ascending order

rsort_cols(M; i)

- sorts the columns of M based on the values in row i in descending order

sort_rows(M; j)

- sorts the rows of M based on the values in column j in ascending order

rsort_rows(M; j)

- sorts the rows of M based on the values in column j in descending order

order_cols(M; i)

- the indexes of the columns of M based on the ordering of the values from row i in ascending order

revorder_cols(M; i)

- the indexes of the columns of M based on the ordering of the values from row i in descending order

order_rows(M; j)

- the indexes of the rows of M based on the ordering of the values in column j in ascending order

revorder_rows(M; j)

- the indexes of the rows of M based on the ordering of the values in column j in descending order

mcount(M; x)

- number of occurrences of value x in matrix M

msearch(M; x; i; j)

- vector with the two indexes of the first occurrence of x in matrix M, starting from indexes i and j

mfind(M; x) or

mfind_eq(M; x)

- the indexes of all elements in M that are = x

mfind_ne(M; x)

- the indexes of all elements in M that are ≠ x

mfind_lt(M; x)

- the indexes of all elements in M that are < x

mfind_le(M; x)

- the indexes of all elements in M that are ≤ x

mfind_gt(M; x)

- the indexes of all elements in M that are > x

mfind_ge(M; x)

- the indexes of all elements in M that are ≥ x

hlookup(M; x; i₁; i₂) or

hlookup_eq(M; x; i₁; i₂)

- the values from row i₂ of M, for which the elements in row i₁ are = x

hlookup_ne(M; x; i₁; i₂)

- the values from row i₂ of M, for which the elements in row i₁ are ≠ x

hlookup_lt(M; x; i₁; i₂)

- the values from row i₂ of M, for which the elements in row i₁ are < x

hlookup_le(M; x; i₁; i₂)

- the values from row i₂ of M, for which the elements in row i₁ are ≤ x

hlookup_gt(M; x; i₁; i₂)

- the values from row i₂ of M, for which the elements in row i₁ are > x

hlookup_ge(M; x; i₁; i₂)

- the values from row i₂ of M, for which the elements in row i₁ are ≥ x

vlookup(M; x; j₁; j₂) or

vlookup_eq(M; x; j₁; j₂)

- the values from column j₂ of M, for which the elements in column j₁ are = x

vlookup_ne(M; x; j₁; j₂)

- the values from column j₂ of M, for which the elements in column j₁ are ≠ x

vlookup_lt(M; x; j₁; j₂)

- the values from column j₂ of M, for which the elements in column j₁ are < x

vlookup_le(M; x; j₁; j₂)

- the values from column j₂ of M, for which the elements in column j₁ are ≤ x

vlookup_gt(M; x; j₁; j₂)

- the values from column j₂ of M, for which the elements in column j₁ are > x

vlookup_ge(M; x; j₁; j₂)` - the values from column j₂ of M, for which the elements in column j₁ are ≥ x

Math:

hprod(A; B)

- Hadamard product of matrices A and B

fprod(A; B)

- Frobenius product of matrices A and B

kprod(A; B)

- Kronecker product of matrices A and B

mnorm_1(M)

- L1 norm of matrix M

mnorm(M) or

mnorm_2(M)

- L2 norm of matrix M

mnorm_e(M)

- Frobenius norm of matrix M

mnorm_i(M)

- L∞ norm of matrix M

cond_1(M)

- condition number of M based on the L1 norm

cond(M) or

cond_2(M)

- condition number of M based on the L2 norm

cond_e(M)

- condition number of M based on the Frobenius norm

cond_i(M)

- condition number of M based on the L∞ norm

det(M)

- determinant of matrix M

rank(M)

- rank of matrix M

trace(M)

- trace of matrix M

transp(M)

- transpose of matrix M

adj(M)

- adjugate of matrix M

cofactor(M)

- cofactor matrix of M

eigenvals(M; n_e)

- the first n_e eigenvalues of symmetric matrix M (or all if omitted) as a vector

eigenvecs(M; n_e)

- the first n_e eigenvectors of symmetric matrix M (or all if omitted) along the rows of the returned matrix

eigen(M; n_e)

- the first n_e eigenvalues and eigenvectors of symmetric matrix M (or all if omitted). Each row of the returned matrix contains the eigenvalue, followed by the respective egienvector elements

cholesky(M)

- Cholesky decomposition of a symmetric, positive-definite matrix M

lu(M)

- LU decomposition of matrix M

qr(M)

- QR decomposition of matrix M

svd(M)

- singular value decomposition of M

inverse(M)

- inverse of matrix M

lsolve(A; b)

- solves the system of linear equations Ax = b using LDLT decomposition for symmetric matrices, and LU for non-symmetric

clsolve(A; b)

- solves the linear matrix equation Ax = b with symmetric, positive-definite matrix A using Cholesky decomposition

slsolve(A; b)

- solves the linear matrix equation Ax = b with high-performance symmetric, positive-definite matrix A using preconditioned conjugate gradient (PCG) method

msolve(A; B)

- solves the generalized matrix equation AX = B using LDLT decomposition for symmetric matrices, and LU for non-symmetric

cmsolve(A; B)

- solves the generalized matrix equation AX = B with symmetric, positive-definite matrix A using Cholesky decomposition

smsolve(A; B)

- solves the generalized matrix equation AX = B with high-performance symmetric, positive-definite matrix A using PCG method

matmul(A; B)

- fast multiplication of square hp matrices using parallel Winograd algorithm. The multiplication operator A*B uses it automatically for square hp matrices of size 10 and larger;

fft(M)

- performs fast Fourier transform of row-major matrix M. It must have one row for real data and two rows for complex

ift(M)

- performs inverse Fourier transform of row-major matrix M. It must have one row for real data and two rows for complex

Double interpolation:

take(x; y; M)

- returns the element of matrix M at indexes x and y

line(x; y; M)

- double linear interpolation from the elements of matrix M based on the values of x and y

spline(x; y; M)

- double Hermite spline interpolation from the elements of matrix M based on the values of x and y

Tol

- target tolerance for the iterative PCG solver

Comments:

"Title" or 'text' in double or single quotes, respectively. HTML, CSS, JS and SVG are allowed inside comments.

Graphing and plotting:

$Plot{f(x) @ x = a : b}

- simple plot

$Plot{x(t) | y(t) @ t = a : b}

- parametric plot

$Plot{f1(x) & f2(x) & ... @ x = a : b}

- multiple plot

$Plot{x1(t) | y1(t) & x2(t) | y2(t) & ... @ x = a : b}

- multiple parametric plot

$Map{f(x; y) @ x = a : b & y = c : d}

- 2D color map of a 3D surface

PlotHeight

- height of plot area in pixels

PlotWidth

- width of plot area in pixels

PlotSVG

- draw plots in vector (SVG) format

PlotAdaptive

- use adaptive mesh (= 1) for function plotting or uniform (= 0)

PlotStep

- the size of the mesh for map plotting

PlotPalette

- the number of color palette to be used for surface plots (0-9)

PlotShadows

- draw surface plots with shadows

PlotSmooth

- smooth transition of colors (= 1) or isobands (= 0) for surface plots

PlotLightDir

- direction to light source (0-7) clockwise.

Iterative and numerical methods:

$Root{f(x) = const @ x = a : b}

- root finding for f(x) = const

$Root{f(x) @ x = a : b}

- root finding for f(x) = 0

$Find{f(x) @ x = a : b}

- similar to above, but x is not required to be a precise solution

$Sup{f(x) @ x = a : b}

- local maximum of a function. The location is implicitly assigned to a variable

x_sup

$Inf{f(x) @ x = a : b}

- local minimum of a function. The location is implicitly assigned to a variable

x_inf

$Area{f(x) @ x = a : b}

- adaptive Gauss-Lobatto numerical integration

$Integral{f(x) @ x = a : b}

- Tanh-Sinh numerical integration

$Slope{f(x) @ x = a}

- numerical differentiation by Richardson extrapolation (approximate)

$Derivative{f(x) @ x = a}

- numerical differentiation by complex step method (precise)

$Sum{f(k) @ k = a : b}

- iterative sum

$Product{f(k) @ k = a : b}

- iterative product

$Repeat{f(k) @ k = a : b}

- iterative expression block with counter

$While{condition; expressions}

- iterative expression block with condition

$Block{expressions}

- multi-line expression block

$Inline{expressions}

- inline expression block

Precision

- relative precision for numerical methods [10^-2; 10^-16] (default is 10^-12)

Program flow control:

Simple:

#if *condition*  
  '*Your code goes here* 
#end if

Alternative:

#if *condition*  
  '*Your code goes here*  
#else  
  '*Some other code*  
#end if

Complete:

#if *condition1*  
  '*Your code goes here*  
#else if *condition2*  
  '*Your code goes here*  
#else  
  '*Some other code*  
#end if

You can add or omit as many "#else if's" as needed. Only one "#else" is allowed. You can omit this too.

Iteration blocks:

Simple:

#repeat *number of repetitions*  
  '*Your code goes here*  
#loop

With conditional break/coutinue:

#repeat *number of repetitions*  
  '*Your code goes here*  
  #if *condition*  
  	#break or #continue  
  #end if  
  '*Some more code*  
#loop

With counter:

#for counter = start : end  
  '*Your code goes here*  
#loop

With condition:

#while *condition*  
  '*Your code goes here*  
#loop

Modules and macros/string variables:

Modules:

#include filename

- include external file (module)

#local

- start local section (not to be included)

#global

- start global section (to be included)

Inline string variable:

#def variable_name$ = content

Multiline string variable:

#def *variable_name$*  
  '*content line 1*  
  '*content line 2*  
  '...  
#end def

Inline string macro:

  #def macro_name$(param1$; param2$;...) = content

Multiline string macro:

#def macro_name$(param1$; param2$;...)  
  '*content line 1*  
  '*content line 2*  
  '...  
#end def

Import/Export of external data:

Text/CSV files:

#read M from filename.txt@R1C1:R2C2 TYPE=R SEP=','

- read matrix M from a text/CSV file

#write M to filename.txt@R1C1:R2C2 TYPE=N SEP=','

- write matrix M to a text/CSV file

#append M to filename.txt@R1C1:R2C2 TYPE=N SEP=','

- append matrix M to a text/CSV file

Excel files (xlsx and xlsm):

#read M from filename.xlsx@Sheet1!A1:B2 TYPE=R

- read matrix M from an Excel file

#write M to filename.xlsx@Sheet1!A1:B2 TYPE=N

- write matrix M to an Excel file

#append M to filename.xlsx@Sheet1!A1:B2 TYPE=N

- append matrix M to an Excel file (same as write)
Sheet, range, TYPE and SEP can be omitted.
For #read command, TYPE can be either of [R|D|C|S|U|L|V].
For #write and #append commands, TYPE can be Y or N.

Output control:

#hide

- hide the report contents

#show

- always show the contents (default)

#pre

- show the next contents only before calculations

#post

- show the next contents only after calculations

#val

- show only the final result, without the equation

#equ

- show complete equations and results (default)

#noc

- show only equations without results (no calculations)

#nosub

- do not substitute variables (no substitution)

#novar

- show equations only with substituted values (no variables)

#varsub

- show equations with variables and substituted values (default)

#split

- split equations that do not fit on a single line

#wrap

- wrap equations that do not fit on a single line (default)

#round n

- rounds the output to n digits after the decimal point

#round default

- restores rounding to the default settings

#format FFFF

- specifies custom format string

#format default

- restores the default formatting

#md on

- enables markdown in comments

#md off

- disables markdown in comments

#phasor

- sets output format of complex numbers to polar phasor: A∠φ

#complex

- sets output format of complex numbers to Cartesian algebraic: a + bi.
Each of the above commands is effective after the current line until the end of the report or another command that overwrites it.

Breakpoints for step-by-step execution:

#pause

- calculates to the current line and waits until resumed manually

#input

- renders an input form to the current line and waits for user input.

Switches for trigonometric units:

#deg

- degrees

#rad

- radians

#gra

- gradians

Separator for target units:

, for example:

3ft + 12in|cm

will show 121.92 cm

Dimensionless:

‰

‱

pcm

ppm

ppb

ppt

ppq

Angle units:

°

′

″

deg

rad

grad

rev

Metric units (SI and compatible):

Mass:

hg

kg

kt

Mt

Gt

dg

cg

mg

μg

Da

Length:

km

dm

cm

mm

μm

nm

pm

AU

ly

Time:

ms

μs

ns

ps

min

Frequency:

Hz

kHz

MHz

GHz

THz

mHz

μHz

nHz

pHz

rpm

Speed:

kmh

Electric current:

kA

MA

GA

TA

mA

μA

nA

pA

Temperature:

°C

Δ°C

Amount of substance:

mol

Luminous intensity:

cd

Area:

daa

ha

Volume:

daL

hL

dL

cL

mL

μL

nL

pL

Force:

dyn N

daN

hN

kN

MN

GN

TN

gf

kgf

tf

Moment:

Nm

kNm

Pressure:

Pa

daPa

hPa

kPa

MPa

GPa

TPa

dPa

cPa

mPa

μPa

nPa

pPa

bar

mbar

μbar

atm

at

Torr

mmHg

Viscosity:

cP

St

cSt

Energy work:

kJ

MJ

GJ

TJ

mJ

μJ

nJ

pJ

Wh

kWh

MWh

GWh

TWh

mWh

μWh

nWh

pWh

eV

keV

MeV

GeV

TeV

PeV

EeV

cal

kcal

erg     Power:

μW

hpM

VA

kVA

MVA

GVA

TVA

mVA

μVA

nVA

pVA

VAR

kVAR

MVAR

GVAR

TVAR

mVAR

μVAR

nVAR

pVAR

hpM

ks

,
Electric charge:

kC

MC

GC

TC

mC

μC

nC

pC

Ah

mAh

Potential:

kV

MV

GV

TV

mV

μV

nV

pV

Capacitance:

kF

MF

GF

TF

mF

μF

nF

pF

Resistance:

Ω

kΩ

MΩ

GΩ

TΩ

mΩ

μΩ

nΩ

pΩ

Conductance:

kS

MS

GS

TS

mS

μS

nS

pS

℧

k℧

M℧

G℧

T℧

m℧

μ℧

n℧

p℧

Magnetic flux:

Wb

kWb

MWb

GWb

TWb

mWb

μWb

nWb

pWb

Magnetic flux density:

kT

MT

GT

TT

mT

μT

nT

pT

Inductance:

kH

MH

GH

TH

mH

μH

nH

pH

Luminous flux:

lm

Illuminance:

lx

Radioactivity:

Bq

kBq

MBq

GBq

TBq

mBq

μBq

nBq

pBq

Ci

Rd

Absorbed dose:

Gy

kGy

MGy

GGy

TGy

mGy

μGy

nGy

pGy

Equivalent dose:

Sv

kSv

MSv

GSv

TSv

mSv

μSv

nSv

pSv

Catalytic activity:

kat

Non-metric units (Imperial/US):

Mass:

gr

dr

oz

lb

(or

lbm

lb_m

klb

kipm

(or

kip_m

st

qr

cwt

(or

cwt_UK

cwt_US

ton

(or

ton_UK

ton_US

slug

Length:

th

in

ft

yd

ch

fur

mi

ftm (or ftm_UK

ftm_US)

cable

(or

cable_UK

cable_US

nmi

li

rod

pole

perch

lea

Speed:

mph

knot

Temperature:

°F

Δ°F

°R

Area:

rood

ac

Volume, fluid:

fl_oz

gi

pt

qt

gal

bbl

, or

fl_oz_UK

gi_UK

pt_UK

qt_UK

gal_UK

bbl_UK

fl_oz_US

gi_US

pt_US

qt_US

gal_US

bbl_US

,
Volume, dry: (US)

pt_dry

, (US)

qt_dry

, (US)

gal_dry

, (US)

bbl_dry

pk

(or

pk_UK

pk_US

bu

(or

bu_UK

bu_US

)
Force:

ozf

(or

oz_f

lbf

(or

lb_f

kip

(or

kipf

kip_f

tonf

(or

ton_f

pdl

Pressure:

osi

osf psi

psf

ksi

ksf

tsi

tsf

inHg

Energy/work:

BTU

therm

(or therm_UK

therm_US)

quad

Power:

hp

hpE

hpS

Custom units:

.Name = expression

Unit names can include currency symbols:

€

£

₤

¥

¢

₽

₹

₩

, `₪'

ADDITIONAL NOTES ABOUT MATRICES AND VECTORS

Individual vector elements are accessed by the indexing
```
.
```
"dot" operator. For example:
```
a.1 = 5
```
,
```
a_k = a.k
```
,
```
a.(k + 1) = 6
```
.
Matrix elements are accessed by the indexing operator followed by two indexes in brackets: For example:
```
A.(1; 1) = 5
```
,
```
A_ij = A.(i; j)
```
,
```
A.(i + 1; j + 2) = 6
```
.
Calcpad automatically maintains the structure of special matrices (diagonal, triangular, symmetric, column).
Assigning a value to the off-diagonal or off-triangle element throws an error.
Reading a value from the off-diagonal or off-triangle element returns zero.
Matrices created by
```
_hp
```
suffixed functions or the
```
hp()
```
function are of "hp" type.
All elements in an "hp" vector or matrix must have the same or consistent units (or no units at all).
The other non-"hp" types can contain different units, but the should be consistent for all operations you perform on them. For example, you cannot sum elements with inconsistent units.
"Hp" types are much faster and more memory efficient. Always prefer "hp" types when there are no units or units are equal/consistent or the vectors/matrices are larger than 1000 even if you will have to remove the units before that and restore them later.

COMMON MISTAKES TO AVOID

Assignment vs. equality
- Use
```
=
```
  for assignment:
```
a = 5
```
- Use
```
≡
```
  or
```
==
```
  for comparison:
```
#if a ≡ 5
```
Semicolons as delimiters in functions
- Parameters separated by
```
;
```
  not
```
,
```
- Correct:
```
f(x; y; z)
```
- Wrong:
```
f(x, y, z)
```
Line continuation
- Use
```
 _
```
  at end of line for continuation
- Or end line with opening bracket or delimiter

Comments required for multiple expressions on a line

a = 5'comment'b = 10    'Correct'
a = 5 b = 10            'Wrong - syntax error'

Angle units
- Set
```
#deg
```
  ,
```
#rad
```
  , or
```
#gra
```
  before using trigonometric functions. The default angle units are
```
#deg
```
- Or attach units directly:
```
sin(45*deg)
```
- Angle units, including
```
rad
```
  are not consistent with dimensionless values and
```
rpm
```
  units. You will have to remove them manually in such cases by dividing to them.

QUICK REFERENCE EXAMPLES

Simple Calculation

'Beam Moment Calculation'
'Span -'L = 6m             
'Load -'q = 10kN/m         
'Moment -'M = w*L^2/8

With Function

stress(P; A) = P/A
P = 100kN
A = 0.01m^2
σ = stress(P; A) | MPa

With Conditional

#if σ > 250*MPa
  'The check is NOT satisfied ✖'
#else
  'heck is satisfied ✔'
#end if

With Loop

'Sum of squares'
sum = 0
#for i = 1 : 10
  sum = sum + i^2
#loop

With Plot

'Visualize function'
$Plot{x^2 - 4*x + 3 @ x = 0 : 5}

With Numerical Method

'Find root of equation'
x = $Root{x^2 - 10 @ x = 0 : 5}
'Result: 'x' ≈ 3.162'

SYNTAX SUMMARY

Element	Syntax	Example
Variable	`name = value`	`x = 5`
Function	`f(params) = expr`	`f(x) = x^2`
Comment	`'text'` or `"title"`	`'Length'`
If	`#if ... #end if`	`#if x > 0 ... #end if`
For loop	`#for i = a : b`	`#for i = 1 : 10`
Include	`#include file.cpd`	`#include materials.cpd`
Plot	`$Plot{f(x) @ x=a:b}`	`$Plot{sin(x) @ x=0:π}`
Root	`$Root{f(x) @ x=a:b}`	`$Root{x^2-5 @ x=0:10}`
Integral	`$Area{f(x) @ x=a:b}`	`$Area{sin(x) @ x=0:π}`

RESOURCES

Official Site: https://calcpad.eu/
GitHub: https://github.com/Proektsoftbg/Calcpad
Documentation: https://calcpad.eu/help/
Examples: https://github.com/Proektsoftbg/Calcpad/tree/main/Examples
Blog: https://calcpad.blog/

FILE EXTENSION

Use
```
.cpd
```
for Calcpad source files.

EXECUTION

Press Ctrl+Shift+B to run in VS Code or the command
```
Calcpad: Run Calcpad File
```
.

Calcpad Language Reference for Claude Code

Description

real and complex numbers (rectangular and polar-phasor formats);
units of measurement (SI, Imperial and USCS);
vectors and matrices: rectangular, symmetric, column, diagonal, upper/lower triangular;
custom variables and units;
built-in library with common math functions;
vectors and matrix functions:
- data functions: search, lookup, sort, count, etc.;
- aggregate functions: min, max, sum, sumsq, srss, average, product (geometric) mean, etc.;
- math functions: norm, condition, determinant, rank, trace, transpose, adjugate and cofactor, inverse, factorization (cholesky, ldlt, lu, qr and svd), eigenvalues/vectors and linear systems of equations;
custom functions of multiple parameters f(x; y; z; …);
powerful numerical methods for root and extremum finding, numerical integration and differentiation;
finite sum, product and iteration procedures, Fourier series and FFT;
modules, macros and string variables;
reading and writing data from/to text, CSV and Excel files;
program flow control with conditions and loops;
"titles" and 'text' comments in quotes;
support for Html and CSS in comments for rich formatting;
function plotting, images, tables, parametric SVG drawings, etc.;
automatic generation of Html forms for data input;
professional looking Html reports for viewing and printing;
export to Word (*.docx) and PDF documents;
variable substitution and smart rounding of numbers;
output visibility control and content folding;
support for plain text (*.txt, *.cpd) and binary (*.cpdz) file formats.

Language specification

Primitives:

Real numbers: digits 0 - 9 and decimal point ".", e.g.
```
3.14
```
Complex numbers: re ± imi, e.g.
```
3 - 2i
```
Vectors:
```
[v₁; v₂; v₃; …; vₙ]
```

Matrices:

[M₁₁; M₁₂; … ; M₁ₙ | M₂₁; M₂₂; … ; M₂ₙ | … | Mₘ₁; Mₘ₂; … ; Mₘₙ]

Variables:

all Unicode letters
digits: 0 - 9
comma: " , "
special symbols: ′ , ″ , ‴ , ⁗ , ‾ , ø , Ø , ° , ∡
superscripts: ⁰ , ¹ , ² , ³ , ⁴ , ⁵ , ⁶ , ⁷ , ⁸ , ⁹ , ⁿ , ⁺ , ⁻
subscripts: ₀ , ₁ , ₂ , ₃ , ₄ , ₅ , ₆ , ₇ , ₈ , ₉ , ₊ , ₋ , ₌ , ₍ , ₎
" _ " for subscript
Any variable name must start with a letter. Names are case sensitive.

Operators:

- factorial

- exponent

- division

÷

- force division bar in inline mode and slash in pro mode (//)

\ - integer division

⦼

- modulo (remainder)

* - multiplication

- minus

- plus

≡

- equal to

≠

- not equal to

- less than

- greater than

≤

- less or equal

≥

- greater or equal

∧

- logical "AND"

∨

- logical "OR"

⊕

- logical "XOR"

∠

- phasor A∠φ (<<)

- assignment

Custom functions:

Definition:

f(x; y; z; ... ) = expression

Delimiter for arguments: semicolon

Built-in functions:

Trigonometric:

sin(x)

- sine

cos(x)

- cosine

tan(x)

- tangent

csc(x)

- cosecant

sec(x)

- secant

cot(x)

- cotangent

Hyperbolic:

sinh(x)

- hyperbolic sine

cosh(x)

- hyperbolic cosine

tanh(x)

- hyperbolic tangent

csch(x)

- hyperbolic cosecant

sech(x)

- hyperbolic secant

coth(x)

- hyperbolic cotangent

Inverse trigonometric:

asin(x)

- inverse sine

acos(x)

- inverse cosine

atan(x)

- inverse tangent

atan2(x; y)

- the angle whose tangent is the quotient of y and x

acsc(x)

- inverse cosecant

asec(x)

- inverse secant

acot(x)

- inverse cotangent

Inverse hyperbolic:

asinh(x)

- inverse hyperbolic sine

acosh(x)

- inverse hyperbolic cosine

atanh(x)

- inverse hyperbolic tangent

acsch(x)

- inverse hyperbolic cosecant

asech(x)

- inverse hyperbolic secant

acoth(x)

- inverse hyperbolic cotangent

Logarithmic, exponential and roots:

log(x)

- decimal logarithm

ln(x)

- natural logarithm

log_2(x)

- binary logarithm

exp(x)

- natural exponent

sqr(x)

sqrt(x)

- square root

cbrt(x)

- cubic root

root(x; n)

- n-th root

Rounding:

round(x)

- round to the nearest integer

floor(x)

- round to the smaller integer (towards -∞)

ceiling(x)

- round to the greater integer (towards +∞)

trunc(x)

- round to the smaller integer (towards zero)

Integer:

mod(x; y)

- the remainder of an integer division

gcd(x; y; z...)

- the greatest common divisor of several integers

lcm(x; y; z...)

- the least common multiple of several integers

Complex:

re(z)

- the real part of a complex number

im(z)

- the imaginary part of a complex number

abs(z)

- absolute value/magnitude

phase(z)

- the phase of a complex number

conj(z)

- the conjugate of a complex number

Aggregate and interpolation:

min(x; y; z...)

- minimum of multiple values

max(x; y; z...)

- maximum of multiple values

sum(x; y; z...)

- sum of multiple values = x + y + z...

sumsq(x; y; z...)

- sum of squares = x² + y² + z²...

srss(x; y; z...)

- square root of sum of squares = sqrt(x² + y² + z²...)

average(x; y; z...)

- average of multiple values = (x + y + z...)/n

product(x; y; z...)

- product of multiple values = x·y·z...

mean(x; y; z...)

- geometric mean = n-th root(x·y·z...)

take(n; a; b; c...)

- returns the n-th element from the list

line(x; a; b; c...)

- linear interpolation

spline(x; a; b; c...)

- Hermite spline interpolation

Conditional and logical:

if(condition; value-if-true; value-if-false)

- conditional evaluation

switch(condition1; value1; condition2; value2; … ; default)

- selective evaluation

not(x)

- logical "NOT"

and(x; y; z...)

- logical "AND"

or(x; y; z...)

- logical "OR"

xor(x; y; z...)

- logical "XOR"

Other:

sign(x)

- the sign of a number

random(x)

- random number between 0 and x

getunits(x)

- gets the units of x without the value. Returns 1 if x is unitless

setunits(x; u)

- sets the units u to x where x can be scalar, vector or matrix

clrunits(x)

- clears the units from a scalar, vector or matrix x

hp(x)

- converts x to its high performance (hp) equivalent type

ishp(x)

- checks if the type of x is a high-performance (hp) vector or matrix

Vector:

Creational:

vector(n)

- creates an empty vector with length n

vector_hp(n)

- creates an empty high performance (hp) vector with length n

range(x1; xn; s)

- creates a vector with values spanning from x1 to xn with step s

range_hp(x1; xn; s)

- creates a high performance (hp) from a range of values as above

Structural:

len(v)

- returns the length of vector v

size(v)

- the actual size of vector v - the index of the last non-zero element

resize(v; n)

- sets a new length n of vector v

fill(v; x)

- fills vector v with value x

join(A; b; c…)

- creates a vector by joining the arguments: matrices, vectors and scalars

slice(v; i₁; i₂)

- returns the part of vector v bounded by indexes i₁ and i₂ inclusive

first(v; n)

- the first n elements of vector v

last(v; n)

- the last n elements of vector v

extract(v; i)

- extracts the elements from v which indexes are contained in i

Data:

sort(v)

- sorts the elements of vector v in ascending order

rsort(v)

- sorts the elements of vector v in descending order

order(v)

- the indexes of vector v, arranged by the ascending order of its elements

revorder(v)

- the indexes of vector v, arranged by the descending order of its elements

reverse(v)

- a new vector containing the elements of v in reverse order

count(v; x; i)

- the number of elements in v, after the i-th one, that are equal to x

search(v; x; i)

- the index of the first element in v, after the i-th one, that is equal to x

find(v; x; i) or

find_eq(v; x; i)

- the indexes of all elements in v, after the i-th one, that are = x

find_ne(v; x; i)

- the indexes of all elements in v, after the i-th one, that are ≠ x

find_lt(v; x; i)

- the indexes of all elements in v, after the i-th one, that are < x

find_le(v; x; i)

- the indexes of all elements in v, after the i-th one, that are ≤ x

find_gt(v; x; i)

- the indexes of all elements in v, after the i-th one, that are > x

find_ge(v; x; i)

- the indexes of all elements in v, after the i-th one, that are ≥ x

lookup(a; b; x) or

lookup_eq(a; b; x)

- all elements in a for which the respective elements in b are = x

lookup_ne(a; b; x)

- all elements in a for which the respective elements in b are ≠ x

lookup_lt(a; b; x)

- all elements in a for which the respective elements in b are < x

lookup_le(a; b; x)

- all elements in a for which the respective elements in b are ≤ x

lookup_gt(a; b; x)

- all elements in a for which the respective elements in b are > x

lookup_ge(a; b; x)

- all elements in a for which the respective elements in b are ≥ x

Math:

norm_1(v)

- L1 (Manhattan) norm of vector v

norm(v) or

norm_2(v) or

norm_e(v)

- L2 (Euclidean) norm of vector v

norm_p(v; p)

- Lp norm of vector v

norm_i(v)

- L∞ (infinity) norm of vector v

unit(v)

- the normalized vector v (with L2 norm = 1)

dot(a; b)

- scalar product of two vectors a and b

cross(a; b)

- cross product of two vectors a and b (with length 2 or 3)

Matrix:

Creational:

matrix(m; n)

- creates an empty matrix with dimensions m⨯n

identity(n)

- creates an identity matrix with dimensions n⨯n

diagonal(n; d)

- creates a n⨯n diagonal matrix and fills the diagonal with value d

column(m; c)

- creates a column matrix with dimensions m⨯1, filled with value c

utriang(n)

- creates an upper triangular matrix with dimensions n⨯n

ltriang(n)

- creates a lower triangular matrix with dimensions n⨯n

symmetric(n)

- creates a symmetric matrix with dimensions n⨯n

matrix_hp(m; n)

- creates a high-performance matrix with dimensions m⨯n

identity_hp(n)

- creates a high-performance identity matrix with dimensions n⨯n

diagonal_hp(n; d)

- creates a high-performance n⨯n diagonal matrix filled with value d

column_hp(m; c)

- creates a high-performance m⨯1 column matrix filled with value c

utriang_hp(n)

- creates a high-performance n⨯n upper triangular matrix

ltriang_hp(n)

- creates a high-performance n⨯n lower triangular matrix

symmetric_hp(n)

- creates a high-performance symmetric matrix with dimensions n⨯n

vec2diag(v)

- creates a diagonal matrix from the elements of vector v

vec2row(v)

- creates a row matrix from the elements of vector v

vec2col(v)

- creates a column matrix from the elements of vector v

join_cols(c₁; c₂; c₃…)

- creates a new matrix by joining column vectors

join_rows(r₁; r₂; r₃…)

- creates a new matrix by joining row vectors

augment(A; B; C…)

- creates a new matrix by appending matrices A; B; C side by side

stack(A; B; C…)

- creates a new matrix by stacking matrices A; B; C one below the other

Structural:

n_rows(M)

- number of rows in matrix M

n_cols(M)

- number of columns in matrix M

mresize(M; m; n)

- sets new dimensions m and n for matrix M

mfill(M; x)

- fills matrix M with value x

fill_row(M; i; x)

- fills the i-th row of matrix M with value x

fill_col(M; j; x)

- fills the j-th column of matrix M with value x

copy(A; B; i; j)

- copies all elements from A to B, starting from indexes i and j of B

add(A; B; i; j)

- adds all elements from A to those of B, starting from indexes i and j of B

row(M; i)

- extracts the i-th row of matrix M as a vector

col(M; j)

- extracts the j-th column of matrix M as a vector

extract_rows(M; i)

- extracts the rows from matrix M whose indexes are contained in vector i

extract_cols(M; j)

- extracts the columns from matrix M whose indexes are contained in vector j

diag2vec(M)

- extracts the diagonal elements of matrix M to a vector

submatrix(M; i₁; i₂; j₁; j₂)

- extracts a submatrix of M, bounded by rows i₁ and i₂ and columns j₁ and j₂, incl.

Data:

sort_cols(M; i)

- sorts the columns of M based on the values in row i in ascending order

rsort_cols(M; i)

- sorts the columns of M based on the values in row i in descending order

sort_rows(M; j)

- sorts the rows of M based on the values in column j in ascending order

rsort_rows(M; j)

- sorts the rows of M based on the values in column j in descending order

order_cols(M; i)

- the indexes of the columns of M based on the ordering of the values from row i in ascending order

revorder_cols(M; i)

- the indexes of the columns of M based on the ordering of the values from row i in descending order

order_rows(M; j)

- the indexes of the rows of M based on the ordering of the values in column j in ascending order

revorder_rows(M; j)

- the indexes of the rows of M based on the ordering of the values in column j in descending order

mcount(M; x)

- number of occurrences of value x in matrix M

msearch(M; x; i; j)

- vector with the two indexes of the first occurrence of x in matrix M, starting from indexes i and j

mfind(M; x) or

mfind_eq(M; x)

- the indexes of all elements in M that are = x

mfind_ne(M; x)

- the indexes of all elements in M that are ≠ x

mfind_lt(M; x)

- the indexes of all elements in M that are < x

mfind_le(M; x)

- the indexes of all elements in M that are ≤ x

mfind_gt(M; x)

- the indexes of all elements in M that are > x

mfind_ge(M; x)

- the indexes of all elements in M that are ≥ x

hlookup(M; x; i₁; i₂) or

hlookup_eq(M; x; i₁; i₂)

- the values from row i₂ of M, for which the elements in row i₁ are = x

hlookup_ne(M; x; i₁; i₂)

- the values from row i₂ of M, for which the elements in row i₁ are ≠ x

hlookup_lt(M; x; i₁; i₂)

- the values from row i₂ of M, for which the elements in row i₁ are < x

hlookup_le(M; x; i₁; i₂)

- the values from row i₂ of M, for which the elements in row i₁ are ≤ x

hlookup_gt(M; x; i₁; i₂)

- the values from row i₂ of M, for which the elements in row i₁ are > x

hlookup_ge(M; x; i₁; i₂)

- the values from row i₂ of M, for which the elements in row i₁ are ≥ x

vlookup(M; x; j₁; j₂) or

vlookup_eq(M; x; j₁; j₂)

- the values from column j₂ of M, for which the elements in column j₁ are = x

vlookup_ne(M; x; j₁; j₂)

- the values from column j₂ of M, for which the elements in column j₁ are ≠ x

vlookup_lt(M; x; j₁; j₂)

- the values from column j₂ of M, for which the elements in column j₁ are < x

vlookup_le(M; x; j₁; j₂)

- the values from column j₂ of M, for which the elements in column j₁ are ≤ x

vlookup_gt(M; x; j₁; j₂)

- the values from column j₂ of M, for which the elements in column j₁ are > x

vlookup_ge(M; x; j₁; j₂)` - the values from column j₂ of M, for which the elements in column j₁ are ≥ x

Math:

hprod(A; B)

- Hadamard product of matrices A and B

fprod(A; B)

- Frobenius product of matrices A and B

kprod(A; B)

- Kronecker product of matrices A and B

mnorm_1(M)

- L1 norm of matrix M

mnorm(M) or

mnorm_2(M)

- L2 norm of matrix M

mnorm_e(M)

- Frobenius norm of matrix M

mnorm_i(M)

- L∞ norm of matrix M

cond_1(M)

- condition number of M based on the L1 norm

cond(M) or

cond_2(M)

- condition number of M based on the L2 norm

cond_e(M)

- condition number of M based on the Frobenius norm

cond_i(M)

- condition number of M based on the L∞ norm

det(M)

- determinant of matrix M

rank(M)

- rank of matrix M

trace(M)

- trace of matrix M

transp(M)

- transpose of matrix M

adj(M)

- adjugate of matrix M

cofactor(M)

- cofactor matrix of M

eigenvals(M; n_e)

- the first n_e eigenvalues of symmetric matrix M (or all if omitted) as a vector

eigenvecs(M; n_e)

- the first n_e eigenvectors of symmetric matrix M (or all if omitted) along the rows of the returned matrix

eigen(M; n_e)

- the first n_e eigenvalues and eigenvectors of symmetric matrix M (or all if omitted). Each row of the returned matrix contains the eigenvalue, followed by the respective egienvector elements

cholesky(M)

- Cholesky decomposition of a symmetric, positive-definite matrix M

lu(M)

- LU decomposition of matrix M

qr(M)

- QR decomposition of matrix M

svd(M)

- singular value decomposition of M

inverse(M)

- inverse of matrix M

lsolve(A; b)

- solves the system of linear equations Ax = b using LDLT decomposition for symmetric matrices, and LU for non-symmetric

clsolve(A; b)

- solves the linear matrix equation Ax = b with symmetric, positive-definite matrix A using Cholesky decomposition

slsolve(A; b)

- solves the linear matrix equation Ax = b with high-performance symmetric, positive-definite matrix A using preconditioned conjugate gradient (PCG) method

msolve(A; B)

- solves the generalized matrix equation AX = B using LDLT decomposition for symmetric matrices, and LU for non-symmetric

cmsolve(A; B)

- solves the generalized matrix equation AX = B with symmetric, positive-definite matrix A using Cholesky decomposition

smsolve(A; B)

- solves the generalized matrix equation AX = B with high-performance symmetric, positive-definite matrix A using PCG method

matmul(A; B)

- fast multiplication of square hp matrices using parallel Winograd algorithm. The multiplication operator A*B uses it automatically for square hp matrices of size 10 and larger;

fft(M)

- performs fast Fourier transform of row-major matrix M. It must have one row for real data and two rows for complex

ift(M)

- performs inverse Fourier transform of row-major matrix M. It must have one row for real data and two rows for complex

Double interpolation:

take(x; y; M)

- returns the element of matrix M at indexes x and y

line(x; y; M)

- double linear interpolation from the elements of matrix M based on the values of x and y

spline(x; y; M)

- double Hermite spline interpolation from the elements of matrix M based on the values of x and y

Tol

- target tolerance for the iterative PCG solver

Comments:

"Title" or 'text' in double or single quotes, respectively. HTML, CSS, JS and SVG are allowed inside comments.

Graphing and plotting:

$Plot{f(x) @ x = a : b}

- simple plot

$Plot{x(t) | y(t) @ t = a : b}

- parametric plot

$Plot{f1(x) & f2(x) & ... @ x = a : b}

- multiple plot

$Plot{x1(t) | y1(t) & x2(t) | y2(t) & ... @ x = a : b}

- multiple parametric plot

$Map{f(x; y) @ x = a : b & y = c : d}

- 2D color map of a 3D surface

PlotHeight

- height of plot area in pixels

PlotWidth

- width of plot area in pixels

PlotSVG

- draw plots in vector (SVG) format

PlotAdaptive

- use adaptive mesh (= 1) for function plotting or uniform (= 0)

PlotStep

- the size of the mesh for map plotting

PlotPalette

- the number of color palette to be used for surface plots (0-9)

PlotShadows

- draw surface plots with shadows

PlotSmooth

- smooth transition of colors (= 1) or isobands (= 0) for surface plots

PlotLightDir

- direction to light source (0-7) clockwise.

Iterative and numerical methods:

$Root{f(x) = const @ x = a : b}

- root finding for f(x) = const

$Root{f(x) @ x = a : b}

- root finding for f(x) = 0

$Find{f(x) @ x = a : b}

- similar to above, but x is not required to be a precise solution

$Sup{f(x) @ x = a : b}

- local maximum of a function. The location is implicitly assigned to a variable

x_sup

$Inf{f(x) @ x = a : b}

- local minimum of a function. The location is implicitly assigned to a variable

x_inf

$Area{f(x) @ x = a : b}

- adaptive Gauss-Lobatto numerical integration

$Integral{f(x) @ x = a : b}

- Tanh-Sinh numerical integration

$Slope{f(x) @ x = a}

- numerical differentiation by Richardson extrapolation (approximate)

$Derivative{f(x) @ x = a}

- numerical differentiation by complex step method (precise)

$Sum{f(k) @ k = a : b}

- iterative sum

$Product{f(k) @ k = a : b}

- iterative product

$Repeat{f(k) @ k = a : b}

- iterative expression block with counter

$While{condition; expressions}

- iterative expression block with condition

$Block{expressions}

- multi-line expression block

$Inline{expressions}

- inline expression block

Precision

- relative precision for numerical methods [10^-2; 10^-16] (default is 10^-12)

Program flow control:

Simple:

#if *condition*  
  '*Your code goes here* 
#end if

Alternative:

#if *condition*  
  '*Your code goes here*  
#else  
  '*Some other code*  
#end if

Complete:

#if *condition1*  
  '*Your code goes here*  
#else if *condition2*  
  '*Your code goes here*  
#else  
  '*Some other code*  
#end if

You can add or omit as many "#else if's" as needed. Only one "#else" is allowed. You can omit this too.

Iteration blocks:

Simple:

#repeat *number of repetitions*  
  '*Your code goes here*  
#loop

With conditional break/coutinue:

#repeat *number of repetitions*  
  '*Your code goes here*  
  #if *condition*  
  	#break or #continue  
  #end if  
  '*Some more code*  
#loop

With counter:

#for counter = start : end  
  '*Your code goes here*  
#loop

With condition:

#while *condition*  
  '*Your code goes here*  
#loop

Modules and macros/string variables:

Modules:

#include filename

- include external file (module)

#local

- start local section (not to be included)

#global

- start global section (to be included)

Inline string variable:

#def variable_name$ = content

Multiline string variable:

#def *variable_name$*  
  '*content line 1*  
  '*content line 2*  
  '...  
#end def

Inline string macro:

  #def macro_name$(param1$; param2$;...) = content

Multiline string macro:

#def macro_name$(param1$; param2$;...)  
  '*content line 1*  
  '*content line 2*  
  '...  
#end def

Import/Export of external data:

Text/CSV files:

#read M from filename.txt@R1C1:R2C2 TYPE=R SEP=','

- read matrix M from a text/CSV file

#write M to filename.txt@R1C1:R2C2 TYPE=N SEP=','

- write matrix M to a text/CSV file

#append M to filename.txt@R1C1:R2C2 TYPE=N SEP=','

- append matrix M to a text/CSV file

Excel files (xlsx and xlsm):

#read M from filename.xlsx@Sheet1!A1:B2 TYPE=R

- read matrix M from an Excel file

#write M to filename.xlsx@Sheet1!A1:B2 TYPE=N

- write matrix M to an Excel file

#append M to filename.xlsx@Sheet1!A1:B2 TYPE=N

Output control:

#hide

- hide the report contents

#show

- always show the contents (default)

#pre

- show the next contents only before calculations

#post

- show the next contents only after calculations

#val

- show only the final result, without the equation

#equ

- show complete equations and results (default)

#noc

- show only equations without results (no calculations)

#nosub

- do not substitute variables (no substitution)

#novar

- show equations only with substituted values (no variables)

#varsub

- show equations with variables and substituted values (default)

#split

- split equations that do not fit on a single line

#wrap

- wrap equations that do not fit on a single line (default)

#round n

- rounds the output to n digits after the decimal point

#round default

- restores rounding to the default settings

#format FFFF

- specifies custom format string

#format default

- restores the default formatting

#md on

- enables markdown in comments

#md off

- disables markdown in comments

#phasor

- sets output format of complex numbers to polar phasor: A∠φ

#complex

Breakpoints for step-by-step execution:

#pause

- calculates to the current line and waits until resumed manually

#input

- renders an input form to the current line and waits for user input.

Switches for trigonometric units:

#deg

- degrees

#rad

- radians

#gra

- gradians

Separator for target units:

, for example:

3ft + 12in|cm

will show 121.92 cm

Dimensionless:

‰

‱

pcm

ppm

ppb

ppt

ppq

Angle units:

°

′

″

deg

rad

grad

rev

Metric units (SI and compatible):

Mass:

hg

kg

kt

Mt

Gt

dg

cg

mg

μg

Da

Length:

km

dm

cm

mm

μm

nm

pm

AU

ly

Time:

ms

μs

ns

ps

min

Frequency:

Hz

kHz

MHz

GHz

THz

mHz

μHz

nHz

pHz

rpm

Speed:

kmh

Electric current:

kA

MA

GA

TA

mA

μA

nA

pA

Temperature:

°C

Δ°C

Amount of substance:

mol

Luminous intensity:

cd

Area:

daa

ha

Volume:

daL

hL

dL

cL

mL

μL

nL

pL

Force:

dyn N

daN

hN

kN

MN

GN

TN

gf

kgf

tf

Moment:

Nm

kNm

Pressure:

Pa

daPa

hPa

kPa

MPa

GPa

TPa

dPa

cPa

mPa

μPa

nPa

pPa

bar

mbar

μbar

atm

at

Torr

mmHg

Viscosity:

cP

St

cSt

Energy work:

kJ

MJ

GJ

TJ

mJ

μJ

nJ

pJ

Wh

kWh

MWh

GWh

TWh

mWh

μWh

nWh

pWh

eV

keV

MeV

GeV

TeV

PeV

EeV

cal

kcal

erg     Power:

μW

hpM

VA

kVA

MVA

GVA

TVA

mVA

μVA

nVA

pVA

VAR

kVAR

MVAR

GVAR

TVAR

mVAR

μVAR

nVAR

pVAR

hpM

ks

,
Electric charge:

kC

MC

GC

TC

mC

μC

nC

pC

Ah

mAh

Potential:

kV

MV

GV

TV

mV

μV

nV

pV

Capacitance:

kF

MF

GF

TF

mF

μF

nF

pF

Resistance:

Ω

kΩ

MΩ

GΩ

TΩ

mΩ

μΩ

nΩ

pΩ

Conductance:

kS

MS

GS

TS

mS

μS

nS

pS

℧

k℧

M℧

G℧

T℧

m℧

μ℧

n℧

p℧

Magnetic flux:

Wb

kWb

MWb

GWb

TWb

mWb

μWb

nWb

pWb

Magnetic flux density:

kT

MT

GT

TT

mT

μT

nT

pT

Inductance:

kH

MH

GH

TH

mH

μH

nH

pH

Luminous flux:

lm

Illuminance:

lx

Radioactivity:

Bq

kBq

MBq

GBq

TBq

mBq

μBq

nBq

pBq

Ci

Rd

Absorbed dose:

Gy

kGy

MGy

GGy

TGy

mGy

μGy

nGy

pGy

Equivalent dose:

Sv

kSv

MSv

GSv

TSv

mSv

μSv

nSv

pSv

Catalytic activity:

kat

Non-metric units (Imperial/US):

Mass:

gr

dr

oz

lb

(or

lbm

lb_m

klb

kipm

(or

kip_m

st

qr

cwt

(or

cwt_UK

cwt_US

ton

(or

ton_UK

ton_US

slug

Length:

th

in

ft

yd

ch

fur

mi

ftm (or ftm_UK

ftm_US)

cable

(or

cable_UK

cable_US

nmi

li

rod

pole

perch

lea

Speed:

mph

knot

Temperature:

°F

Δ°F

°R

Area:

rood

ac

Volume, fluid:

fl_oz

gi

pt

qt

gal

bbl

, or

fl_oz_UK

gi_UK

pt_UK

qt_UK

gal_UK

bbl_UK

fl_oz_US

gi_US

pt_US

qt_US

gal_US

bbl_US

,
Volume, dry: (US)

pt_dry

, (US)

qt_dry

, (US)

gal_dry

, (US)

bbl_dry

pk

(or

pk_UK

pk_US

bu

(or

bu_UK

bu_US

)
Force:

ozf

(or

oz_f

lbf

(or

lb_f

kip

(or

kipf

kip_f

tonf

(or

ton_f

pdl

Pressure:

osi

osf psi

psf

ksi

ksf

tsi

tsf

inHg

Energy/work:

BTU

therm

(or therm_UK

therm_US)

quad

Power:

hp

hpE

hpS

Custom units:

.Name = expression

Unit names can include currency symbols:

€

£

₤

¥

¢

₽

₹

₩

, `₪'

ADDITIONAL NOTES ABOUT MATRICES AND VECTORS

Individual vector elements are accessed by the indexing
```
.
```
"dot" operator. For example:
```
a.1 = 5
```
,
```
a_k = a.k
```
,
```
a.(k + 1) = 6
```
.
Matrix elements are accessed by the indexing operator followed by two indexes in brackets: For example:
```
A.(1; 1) = 5
```
,
```
A_ij = A.(i; j)
```
,
```
A.(i + 1; j + 2) = 6
```
.
Calcpad automatically maintains the structure of special matrices (diagonal, triangular, symmetric, column).
Assigning a value to the off-diagonal or off-triangle element throws an error.
Reading a value from the off-diagonal or off-triangle element returns zero.
Matrices created by
```
_hp
```
suffixed functions or the
```
hp()
```
function are of "hp" type.
All elements in an "hp" vector or matrix must have the same or consistent units (or no units at all).
The other non-"hp" types can contain different units, but the should be consistent for all operations you perform on them. For example, you cannot sum elements with inconsistent units.
"Hp" types are much faster and more memory efficient. Always prefer "hp" types when there are no units or units are equal/consistent or the vectors/matrices are larger than 1000 even if you will have to remove the units before that and restore them later.

COMMON MISTAKES TO AVOID

Assignment vs. equality
- Use
```
=
```
  for assignment:
```
a = 5
```
- Use
```
≡
```
  or
```
==
```
  for comparison:
```
#if a ≡ 5
```
Semicolons as delimiters in functions
- Parameters separated by
```
;
```
  not
```
,
```
- Correct:
```
f(x; y; z)
```
- Wrong:
```
f(x, y, z)
```
Line continuation
- Use
```
 _
```
  at end of line for continuation
- Or end line with opening bracket or delimiter

Comments required for multiple expressions on a line

a = 5'comment'b = 10    'Correct'
a = 5 b = 10            'Wrong - syntax error'

Angle units
- Set
```
#deg
```
  ,
```
#rad
```
  , or
```
#gra
```
  before using trigonometric functions. The default angle units are
```
#deg
```
- Or attach units directly:
```
sin(45*deg)
```
- Angle units, including
```
rad
```
  are not consistent with dimensionless values and
```
rpm
```
  units. You will have to remove them manually in such cases by dividing to them.

QUICK REFERENCE EXAMPLES

Simple Calculation

'Beam Moment Calculation'
'Span -'L = 6m             
'Load -'q = 10kN/m         
'Moment -'M = w*L^2/8

With Function

stress(P; A) = P/A
P = 100kN
A = 0.01m^2
σ = stress(P; A) | MPa

With Conditional

#if σ > 250*MPa
  'The check is NOT satisfied ✖'
#else
  'heck is satisfied ✔'
#end if

With Loop

'Sum of squares'
sum = 0
#for i = 1 : 10
  sum = sum + i^2
#loop

With Plot

'Visualize function'
$Plot{x^2 - 4*x + 3 @ x = 0 : 5}

With Numerical Method

'Find root of equation'
x = $Root{x^2 - 10 @ x = 0 : 5}
'Result: 'x' ≈ 3.162'

SYNTAX SUMMARY

Element	Syntax	Example
Variable	`name = value`	`x = 5`
Function	`f(params) = expr`	`f(x) = x^2`
Comment	`'text'` or `"title"`	`'Length'`
If	`#if ... #end if`	`#if x > 0 ... #end if`
For loop	`#for i = a : b`	`#for i = 1 : 10`
Include	`#include file.cpd`	`#include materials.cpd`
Plot	`$Plot{f(x) @ x=a:b}`	`$Plot{sin(x) @ x=0:π}`
Root	`$Root{f(x) @ x=a:b}`	`$Root{x^2-5 @ x=0:10}`
Integral	`$Area{f(x) @ x=a:b}`	`$Area{sin(x) @ x=0:π}`

RESOURCES

Official Site: https://calcpad.eu/
GitHub: https://github.com/Proektsoftbg/Calcpad
Documentation: https://calcpad.eu/help/
Examples: https://github.com/Proektsoftbg/Calcpad/tree/main/Examples
Blog: https://calcpad.blog/

FILE EXTENSION

Use
```
.cpd
```
for Calcpad source files.

EXECUTION

Press Ctrl+Shift+B to run in VS Code or the command
```
Calcpad: Run Calcpad File
```
.

Calcpad Language Reference for Claude Code

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