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Commit 407798c

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Provide state/error handling for linear algebra (#774)
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‎doc/specs/index.md‎

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@@ -22,6 +22,7 @@ This is an index/directory of the specifications (specs) for each new module/fea
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- [io](./stdlib_io.html) - Input/output helper & convenience
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- [kinds](./stdlib_kinds.html) - Kind parameters
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- [linalg](./stdlib_linalg.html) - Linear Algebra
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- [linalg_state_type](./stdlib_linalg_state_type.html) - Linear Algebra state and error handling
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- [logger](./stdlib_logger.html) - Runtime logging system
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- [math](./stdlib_math.html) - General purpose mathematical functions
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- [optval](./stdlib_optval.html) - Fallback value for optional arguments
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---
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title: linalg_state_type
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---
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# Linear Algebra -- State and Error Handling Module
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[TOC]
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## Introduction
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The `stdlib_linalg_state` module provides a derived type holding information on the
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state of linear algebra operations, and procedures for expert control of linear algebra workflows.
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All linear algebra procedures are engineered to support returning an optional `linalg_state_type`
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variable to holds such information, as a form of expert API. If the user does not require state
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information, but fatal errors are encountered during the execution of linear algebra routines, the
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program will undergo a hard stop.
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Instead, if the state argument is present, the program will never stop, but will return detailed error
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information into the state handler.
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## Derived types provided
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<!-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -->
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### The `linalg_state_type` derived type
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The `linalg_state_type` is defined as a derived type containing an integer error flag, and
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fixed-size character strings to store an error message and the location of the error state change.
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Fixed-size string storage was chosen to facilitate the compiler's memory allocation and ultimately
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ensure maximum computational performance.
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A similarly named generic interface, `linalg_state_type`, is provided to allow the developer to
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create diagnostic messages and raise error flags easily. The call starts with an error flag or
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the location of the event, and is followed by an arbitrary list of `integer`, `real`, `complex` or
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`character` variables. Numeric variables may be provided as either scalars or rank-1 (array) inputs.
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#### Type-bound procedures
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The following convenience type-bound procedures are provided:
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- `print()` returns an allocatable character string containing state location, message, and error flag;
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- `print_message()` returns an allocatable character string containing the state message;
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- `ok()` returns a `logical` flag that is `.true.` in case of successful state (`flag==LINALG_SUCCESS`);
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- `error()` returns a `logical` flag that is `.true.` in case of error state (`flag/=LINALG_SUCCESS`).
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#### Status
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Experimental
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#### Example
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```fortran
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{!example/linalg/example_state1.f90!}
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```
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## Error flags provided
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The module provides the following state flags:
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- `LINALG_SUCCESS`: Successful execution
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- `LINALG_VALUE_ERROR`: Numerical errors (such as infinity, not-a-number, range bounds) are encountered.
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- `LINALG_ERROR`: Linear Algebra errors are encountered, such as: non-converging iterations, impossible operations, etc.
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- `LINALG_INTERNAL_ERROR`: Provided as a developer safeguard for internal errors that should never occur.
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## Comparison operators provided
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The module provides overloaded comparison operators for all comparisons of a `linalg_state_type` variable
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with an integer error flag: `<`, `<=`, `==`, `>=`, `>`, `/=`.

‎example/linalg/CMakeLists.txt‎

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ADD_EXAMPLE(is_triangular)
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ADD_EXAMPLE(outer_product)
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ADD_EXAMPLE(trace)
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ADD_EXAMPLE(state1)
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ADD_EXAMPLE(state2)
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ADD_EXAMPLE(blas_gemv)
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ADD_EXAMPLE(lapack_getrf)

‎example/linalg/example_state1.f90‎

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program example_state1
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use stdlib_linalg_state, only: linalg_state_type, LINALG_SUCCESS, LINALG_VALUE_ERROR, &
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operator(/=)
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implicit none
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type(linalg_state_type) :: err
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! To create a state variable, we enter its integer state flag, followed by a list of variables
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! that will be automatically assembled into a formatted error message. No need to provide string formats
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err = linalg_state_type(LINALG_VALUE_ERROR,'just an example with scalar ',&
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'integer=',1,'real=',2.0,'complex=',(3.0,1.0),'and array ',[1,2,3],'inputs')
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! Print flag
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print *, err%print()
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! Check success
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print *, 'Check error: ',err%error()
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print *, 'Check flag : ',err /= LINALG_SUCCESS
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end program example_state1

‎example/linalg/example_state2.f90‎

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program example_state2
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!! This example shows how to set a `type(linalg_state_type)` variable to process output conditions
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!! out of a simple division routine. The example is meant to highlight:
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!! 1) the different mechanisms that can be used to initialize the `linalg_state` variable providing
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!! strings, scalars, or arrays, on input to it;
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!! 2) `pure` setup of the error control
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use stdlib_linalg_state, only: linalg_state_type, LINALG_VALUE_ERROR, LINALG_SUCCESS, &
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linalg_error_handling
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implicit none
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integer :: info
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type(linalg_state_type) :: err
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real :: a_div_b
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! OK
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call very_simple_division(0.0,2.0,a_div_b,err)
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print *, err%print()
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! Division by zero
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call very_simple_division(1.0,0.0,a_div_b,err)
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print *, err%print()
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! Out of bounds
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call very_simple_division(huge(0.0),0.001,a_div_b,err)
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print *, err%print()
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contains
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!> Simple division returning an integer flag (LAPACK style)
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elemental subroutine very_simple_division(a,b,a_div_b,err)
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real, intent(in) :: a,b
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real, intent(out) :: a_div_b
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type(linalg_state_type), optional, intent(out) :: err
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type(linalg_state_type) :: err0
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real, parameter :: MAXABS = huge(0.0)
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character(*), parameter :: this = 'simple division'
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!> Check a
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if (b==0.0) then
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! Division by zero
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err0 = linalg_state_type(this,LINALG_VALUE_ERROR,'Division by zero trying ',a,'/',b)
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elseif (.not.abs(b)<MAXABS) then
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! B is out of bounds
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err0 = linalg_state_type(this,LINALG_VALUE_ERROR,'B is infinity in a/b: ',[a,b]) ! use an array
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elseif (.not.abs(a)<MAXABS) then
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! A is out of bounds
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err0 = linalg_state_type(this,LINALG_VALUE_ERROR,'A is infinity in a/b: a=',a,' b=',b)
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else
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a_div_b = a/b
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if (.not.abs(a_div_b)<MAXABS) then
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! Result is out of bounds
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err0 = linalg_state_type(this,LINALG_VALUE_ERROR,'A/B is infinity in a/b: a=',a,' b=',b)
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else
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err0%state = LINALG_SUCCESS
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end if
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end if
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! Return error flag, or hard stop on failure
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call linalg_error_handling(err0,err)
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end subroutine very_simple_division
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end program example_state2

‎src/CMakeLists.txt‎

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stdlib_linalg_outer_product.fypp
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stdlib_linalg_kronecker.fypp
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stdlib_linalg_cross_product.fypp
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stdlib_linalg_state.fypp
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stdlib_optval.fypp
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stdlib_selection.fypp
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stdlib_sorting.fypp

‎src/stdlib_linalg_constants.fypp‎

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public
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! Integer size support for ILP64 builds should be done here
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integer, parameter :: ilp = int32
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private :: int32, int64

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