# FUNCTION

# Public

# DET (MATRIX)

Determinant of a matrix. If you need the log of this, use LOGDET
directly.

# EIGENVALUES (A &KEY (ABSTOL 0))

Return the eigenvalues of A. See the documentation of
SPECTRAL-FACTORIZATION about ABSTOL.

# GEMM! (ALPHA A B BETA C &KEY TRANSPOSE-A? TRANSPOSE-B? M N K LDA LDB LDC)

Basically C = ALPHA * A' * B' + BETA * C. A' is A or its transpose depending on TRANSPOSE-A?. B' is B or its transpose depending on TRANSPOSE-B?. Returns C.
A' is an MxK matrix. B' is a KxN matrix. C is an MxN matrix.
LDA is the width of the matrix A (not of A'). If A is not transposed, then K <= LDA, if it's transposed then M <= LDA.
LDB is the width of the matrix B (not of B'). If B is not transposed, then N <= LDB, if it's transposed then K <= LDB.
In the example below M=3, N=2, K=5, LDA=6, LDB=3, LDC=4. The cells marked with + do not feature in the calculation.
N
--+
--+
K -B+
--+
--+
+++
K
-----+ --++
M --A--+ -C++
-----+ --++
++++++ ++++

# MMM (&REST MATRICES)

Multiply arguments from left to right using MM.

# QR-R (QR)

Return the R part of a QR factorization.

# SCAL! (ALPHA X &KEY N (INCX 1))

X = alpha * X.

# SPECTRAL-FACTORIZATION (A &KEY (ABSTOL 0))

Return a spectral factorization of A.
The LAPACK manual says the following about ABSTOL:
The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to
ABSTOL + EPS * max( |a|,|b| ) ,
where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing A to tridiagonal form.
See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3.
If high relative accuracy is important, set ABSTOL to DLAMCH( 'Safe minimum'). Doing so will guarantee that eigenvalues are computed to high relative accuracy when possible in future releases. The current code does not make any guarantees about high relative accuracy, but furutre releases will. See J. Barlow and J. Demmel, "Computing Accurate Eigensystems of Scaled Diagonally Dominant Matrices", LAPACK Working Note #7, for a discussion of which matrices define their eigenvalues to high relative accuracy.

# SPECTRAL-FACTORIZATION-W (INSTANCE)

@arg[extid]{A @class{extid}}
@return[sytemid]{puri:uri or nil}
Returns the System ID part of this External ID.

# SPECTRAL-FACTORIZATION-Z (INSTANCE)

@arg[extid]{A @class{extid}}
@return[sytemid]{puri:uri or nil}
Returns the System ID part of this External ID.

# SVD-D (INSTANCE)

@arg[extid]{A @class{extid}}
@return[sytemid]{puri:uri or nil}
Returns the System ID part of this External ID.

# SVD-U (INSTANCE)

# SVD-VT (INSTANCE)

# XX (LEFT-SQUARE-ROOT)

Convenience function to create a matrix from a left square root.

# Undocumented

# AXPY! (ALPHA X Y &KEY N (INCX 1) (INCY 1))

# COPY! (X Y &KEY N (INCX 1) (INCY 1))

# LEAST-SQUARES (Y X &REST REST &KEY (METHOD QR) &ALLOW-OTHER-KEYS)

# SETFSPECTRAL-FACTORIZATION-W (NEW-VALUE INSTANCE)

# SETFSPECTRAL-FACTORIZATION-Z (NEW-VALUE INSTANCE)

# SETFSVD-D (NEW-VALUE INSTANCE)

# SETFSVD-U (NEW-VALUE INSTANCE)

# SETFSVD-VT (NEW-VALUE INSTANCE)

# Private

# ABSOLUTE-SQUARE-TYPE (INTERNAL-TYPE)

Type of (* x (conjugate x)).

# ALL-FROM-SPECIFICATIONS%

Return an optimization specification for all functions that copy from foreign memory.

# ALL-TO-SPECIFICATIONS%

Return an optimization specification for all functions that copy to foreign memory.

# ARGUMENT-POINTERS (ARGUMENTS)

Return the list of pointers for all the arguments.

# ARGUMENTS-FOR-CFFI (ARGUMENTS)

Return a list that can be use in a CFFI call.

# ARRAY-FLOAT-TYPE (ARRAY)

Return an (internal) float type for an array. O(1) when the type can be detected from the specialized array element type, O(n) otherwise.

# ASSERT-SINGLE-LAPACK-INFO (ARGUMENTS)

Assert that there is at most one LAPACK-INFO in ARGUMENTS.

# BACKING-ARRAY (ARRAY)

Return the array in which the contents of ARRAY are stored. For simple arrays, this is always the array itself. The second value is the displacement.

# BLAS-LAPACK-CALL-FORM (TYPE-VAR NAME ARGUMENTS)

Return a form BLAS/LAPACK calls, conditioning on TYPE-VAR. See BLAS-LAPACK-FUNCTION-NAME for the interpretation of FIXME

# BLAS-LAPACK-FUNCTION-NAME (TYPE NAME)

Return the BLAS/LAPACK foreign function name. TYPE is the internal type, NAME is one of the following: NAME, (NAME), which are used for both complex and real names, or (REAL-NAME COMPLEX-NAME).

# CHOLESKY-LEFT (INSTANCE)

# COMMON-FLOAT-TYPE (&REST ARRAYS-OR-NUMBERS)

Return the common (internal) float type for the arguments.

# COMPLEX? (INTERNAL-TYPE)

True iff the internal type is complex.

# COPY-ARRAY-FROM-MEMORY (ARRAY POINTER INTERNAL-TYPE)

Copy the memory area of type INTERNAL-TYPE at POINTER to ARRAY.

# COPY-ARRAY-TO-MEMORY (ARRAY POINTER INTERNAL-TYPE)

Copy the contents of ARRAY to the memory area of type INTERNAL-TYPE at POINTER.

# COUNT-PERMUTATIONS% (IPIV)

Count the permutations in a pivoting vector.

# CREATE-ARRAY-FROM-MEMORY (POINTER INTERNAL-TYPE DIMENSIONS &OPTIONAL (ELEMENT-TYPE (LISP-TYPE INTERNAL-TYPE)))

Create an array from contents at POINTER.

# CREATE-TRANSPOSED-MATRIX-FROM-MEMORY (POINTER INTERNAL-TYPE DIMENSIONS &OPTIONAL (ELEMENT-TYPE (LISP-TYPE INTERNAL-TYPE)))

Create a matrix from transposed contents at POINTER.

# DEFAULT-LIBRARIES

Return a list of libraries. The source conditions on the platform, relying TRIVIAL-FEATURES. This function is only called when the libraries were not configured by the user, see the documentation on how to do that.

# DIAGONAL-LOG-SUM% (MATRIX &OPTIONAL (SIGN-CHANGES 0))

Sum of the log of the elements in the diagonal. Sign-changes counts the negative values, and may be started at something else than 0 (eg in case of pivoting). Return (values NIL 0) in case of encountering a 0.

# DIMENSIONS-AS-MATRIX (ARRAY ORIENTATION)

If ARRAY is a vector, return its dimensions as a matrix with given ORIENTATION (:ROW or :COLUMN) as multiple values, and T as the third value. If it is matrix, just return the dimensions and NIL. Used for considering vectors as conforming matrices (eg see MM).

# EPSILON (INTERNAL-TYPE)

Return the float epsilon for the given internal float type.

# EXPAND-SPECIFICATIONS% (CLAUSE SPECIFICATIONS)

Expand specifications using (clause internal-type element-type).

# FOREIGN-AREF (POINTER INTERNAL-TYPE &OPTIONAL (INDEX 0))

Accessing 1d arrays in memory.

# SETFFOREIGN-AREF (VALUE POINTER INTERNAL-TYPE &OPTIONAL (INDEX 0))

Setf expander for FOREIGN-AREF.

# FOREIGN-SIZE (TYPE)

Return the size of an internal type in bytes.

# FORTRAN-ARGUMENT/NEW-VARIABLE (FORM)

If FORM is (&NEW VARIABLE), return VARIABLE, otherwise NIL.

# INVERT-TRIANGULAR% (A UPPER? UNIT-DIAG?)

Invert a dense (triangular) matrix using the LAPACK routine *TRTRI. UPPER? indicates if the matrix is in the upper or the lower triangle of a matrix, UNIT-DIAG? indicates whether the diagonal is supposed to consist of 1s. For internal use, not exported.

# LAPACK-INFO-WRAP-ARGUMENT (ARGUMENT BODY)

Generate a wrapper for a LAPACK INFO argument, also checking the result and raising a condition if applicable. Useful for WRAP-ARGUMENT.

# LAST-ROWS-SS (MATRIX NRHS COMMON-TYPE)

Calculate the sum of squares of the last rows of MATRIX columnwise,
omitting the first NRHS rows. If MATRIX is a vector, just do this for the last elements. Used for interfacing with xGELS.

# LEAST-SQUARES-QR (Y X &KEY &ALLOW-OTHER-KEYS)

Least squares using QR decomposition. Additional values returned: the QR decomposition of X. See LEAST-SQUARES for additional documentation. Usage note: SVD-based methods are recommended over this one, unless X is well-conditioned.

# LU-L (LU)

Return the L part of an LU factorization.

# LU-U (LU)

Return the U part of an LU factorization.

# MATRIX-SQUARE-ROOT-LEFT (INSTANCE)

# MAYBE-DEFAULT-TYPE (TYPE PARAMETERS)

Return default type from PARAMETERS when TYPE is NIL.

# MM-HERMITIAN% (A TRANSPOSE-LEFT?)

Calculate A*op(A) if TRANSPOSE-LEFT? is NIL, and op(A)*A otherwise. op() is always conjugate transpose, but may be implemented as a transpose if A is real, in which case the two are equivalent. This function is meant to be used internally, and is not exported.

# NUMBER-FLOAT-TYPE (NUMBER)

Return an (internal) float type for a number.

# OUTPUT-ARRAY-FORM (FORM)

Return a form that can be passed to WITH-OUTPUT-ARRAY (or similar) as an output. The variable is extracted from &NEW forms, otherwise the form is passed as is.

# PROCESS-FORMS (FORMS ENVIRONMENT)

Process forms and return a list of argument specifications. A form may correspond to multiple arguments.

# QUERY-CONFIGURATION (INDICATOR &OPTIONAL DEFAULT)

Return the property for INDICATOR from the configuration variable, with an optional default, which can be a function (called on demand).

# SET-FEATURE (SYMBOL SET?)

Ensure that symbol is in *FEATURES* iff SET?. Returns no values.

# SUM-DIAGONAL% (ARRAY)

Sum diagonal of array, checking that it is square.

# TRANSPOSE-MATRIX-FROM-MEMORY (MATRIX POINTER INTERNAL-TYPE)

Transpose the contents of ARRAY to the memory area of type INTERNAL-TYPE at POINTER. VECTORs are also handled.

# TRANSPOSE-MATRIX-TO-MEMORY (MATRIX POINTER INTERNAL-TYPE)

Transpose the contents of ARRAY to the memory area of type INTERNAL-TYPE at POINTER. VECTORs are also handled.

# TRSM% (A A-UPPER? B)

Wrapper for BLAS routine xTRSM. Solve AX=B, where A is triangular.

# VALUE-FROM-MEMORY% (INTERNAL-TYPE)

Return a (LAMBDA (POINTER INDEX) ...) form that can be used to read an element from an array in memory.

# VALUE-TO-MEMORY% (INTERNAL-TYPE)

Return a (LAMBDA (POINTER INDEX VALUE) ...) form that can be used to write an element to an array in memory.

# WRAP-ARGUMENTS (ARGUMENTS PASS PARAMETERS BODY)

Wrap BODY in arguments. Convenience function used to implement the expansion.

# Undocumented

# SETFCHOLESKY-LEFT (NEW-VALUE INSTANCE)

# CHOLESKY-P (OBJECT)

# COPY-CHOLESKY (INSTANCE)

# COPY-MATRIX-SQUARE-ROOT (INSTANCE)

# COPY-SPECTRAL-FACTORIZATION (INSTANCE)

# COPY-SVD (INSTANCE)

# LISP-TYPE (INTERNAL-TYPE)

# MAKE-CHOLESKY (LEFT)

# MAKE-CHOLESKY% (LEFT)

# MAKE-MATRIX-SQUARE-ROOT (LEFT)

# MAKE-SPECTRAL-FACTORIZATION (&KEY ((Z DUM237) NIL) ((W DUM238) NIL))

# MAKE-SVD (&KEY ((U DUM275) NIL) ((D DUM276) NIL) ((VT DUM277) NIL))

# SETFMATRIX-SQUARE-ROOT-LEFT (NEW-VALUE INSTANCE)

# MATRIX-SQUARE-ROOT-P (OBJECT)

# SPECTRAL-FACTORIZATION-P (OBJECT)

# SVD-P (OBJECT)

# MACRO

# Public

# Undocumented

# WITH-FP-TRAPS-MASKED (&BODY BODY)

# Private

# &ARRAY-IN (INPUT &KEY TYPE TRANSPOSE? FORCE-COPY?)

Array which serves as an input. See FORTRAN-INPUT-ARRAY.

# &ARRAY-IN/OUT ((&KEY INPUT ((TYPE INPUT-TYPE) NIL) ((TRANSPOSE? INPUT-TRANSPOSE?) NIL) ((FORCE-COPY? INPUT-FORCE-COPY?) NIL INPUT-FORCE-COPY?-SPECIFIED?)) (&KEY (OUTPUT INPUT) ((DIMENSIONS OUTPUT-DIMENSIONS) NIL) ((TYPE OUTPUT-TYPE) INPUT-TYPE) ((TRANSPOSE? OUTPUT-TRANSPOSE?) NIL)))

Input/output array. See FORTRAN-INPUT-OUTPUT-ARRAY.

# &ARRAY-OUT (OUTPUT &KEY DIMENSIONS TYPE TRANSPOSE?)

Output array. See FORTRAN-OUTPUT-ARRAY.

# &ATOM (VALUE &KEY TYPE OUTPUT)

Atoms passed to FORTRAN. When not given, TYPE is inferred from the call's default. VALUE is coerced to the desired type. When OUTPUT is given, value is read after the call and placed there.

# &CHAR (CHARACTER)

Shorthand for character.

# &INFO (&OPTIONAL (CONDITION ''LAPACK-FAILURE))

Argument for checking whether the call was executed without an error. Automatically takes care of raising the appropriate condition if it wasn't. CONDITION specifies the condition to raise in case of positive error codes.

# &INTEGER (VALUE &KEY OUTPUT &ENVIRONMENT ENV)

Shorthand for integer atom.

# &INTEGERS (&REST VALUES &ENVIRONMENT ENV)

Shorthand for integer atoms (which are not modified). Useful for combining arguments.

# &NEW (VARIABLE)

Placeholder macro for newly allocated output variables. Using (&NEW VARIABLE) allocates a new array within the scope of the outer macro, and is usually used for output. See &ARRAY-OUT and &ARRAY-IN/OUT.

# &WORK (SIZE &OPTIONAL TYPE)

Allocate a work area of SIZE. When TYPE is not given, the call's default is used.

# &WORK-QUERY (&OPTIONAL TYPE)

Work area query, takes the place of TWO fortran arguments.

# ARRAY-CLAUSE% ((ARRAY INTERNAL-TYPE CLAUSE-ELEMENT-TYPE CLAUSE-INTERNAL-TYPE) &BODY BODY)

Macro that generates a lambda form that can bed used in EXPAND-SPECIFICATIONS%.

# BLAS-CALL ((NAME TYPE VALUE) &BODY FORMS &ENVIRONMENT ENV)

BLAS call. NAME is either a string or a list of two strings (real/complex). TYPE (internal-type) selects the function to call. VALUE is the form returned after the call.

# DEFINE-FACTORIZATION-EOPS% (TYPE CONVERSION)

Define elementwise operations for TYPE, trying to convert into arrays.

# LAPACK-CALL ((NAME TYPE VALUE) &BODY FORMS &ENVIRONMENT ENV)

LAPACK call, takes an &info argument. NAME is either a string or a list of two strings (real/complex). TYPE (internal-type) selects the function to call. VALUE is the form returned after the call.

# LAPACK-CALL-W/QUERY ((NAME TYPE VALUE) &BODY FORMS &ENVIRONMENT ENV)

LAPACK call which also takes &work-query arguments (in place of two FORTRAN arguments).

# LOG-WITH-SIGN% (VALUE SIGN-CHANGES BLOCK-NAME)

Log of (ABS VALUE), increments SIGN-CHANGES when negative, return-from block-name (values nil 0) when zero.

# WITH-ARRAY-INPUT (((POINTER &OPTIONAL (COPIED? (GENSYM COPIED?))) ARRAY INTERNAL-TYPE TRANSPOSE? FORCE-COPY?) &BODY BODY)

Ensure that ARRAY is mapped to a corresponding memory area for the duration of BODY (see below for details of semantics). POINTER is bound to the start of the memory address. The representation of values in the memory is determined by INTERNAL-TYPE. When TRANSPOSE?, transpose the array before BODY (only works for matrices, otherwise signal an error).
If FORCE-COPY? is false, POINTER may or may not point to the memory backing ARRAY.
If FORCE-COPY? is true, POINTER always points to a copy of the contents of ARRAY.
COPIED? is bound to indicate whether POINTER points to a copy or the actual array contents.
The value of the expression is always the value of BODY.

# WITH-ARRAY-INPUT-OUTPUT (((POINTER &OPTIONAL (COPIED? (GENSYM COPIED?))) INPUT-ARRAY INPUT-INTERNAL-TYPE INPUT-TRANSPOSE? INPUT-FORCE-COPY? OUTPUT-ARRAY OUTPUT-INTERNAL-TYPE OUTPUT-TRANSPOSE?) &BODY BODY)

Similar to WITH-ARRAY-INPUT, it also ensures that OUTPUT-ARRAY contains the contents the memory area pointed to by POINTER when BODY is finished. If OUTPUT-ARRAY is NIL then it is equivalent to WITH-ARRAY-INPUT.

# WITH-ARRAY-OUTPUT (((POINTER &OPTIONAL (COPIED? (GENSYM COPIED?))) ARRAY INTERNAL-TYPE TRANSPOSE?) &BODY BODY)

Ensure that ARRAY is mapped to a corresponding memory area for the duration of BODY (see below for details of semantics). POINTER is bound to the start of the memory address. The representation of values in the memory is determined by INTERNAL-TYPE. When TRANSPOSE?, transpose the array after BODY (only works for matrices, otherwise signal an error).
COPIED? is bound to indicate whether POINTER points to a copy or the actual array contents.
The value of the expression is always the value of BODY.

# WITH-FORTRAN-ATOM ((POINTER VALUE TYPE OUTPUT) &BODY BODY)

Allocate memory for internal TYPE and set it to VALUE for body, which can use POINTER to access it. When OUTPUT is given, the value is assigned to it after BODY. The atom is automatically coerced to the correct type (by FOREIGN-AREF).

# WITH-FORTRAN-CHARACTER ((POINTER CHARACTER) &BODY BODY)

Make character available in an allocated memory area at POINTER for BODY.

# WITH-WORK-AREA ((POINTER INTERNAL-TYPE SIZE) &BODY BODY)

Allocate a work area of SIZE and INTERNAL-TYPE, and bind the POINTER to its start during BODY.

# Undocumented

# DEFINE-FOREIGN-AREF

# DEFINE-MATRIX-SQUARE-ROOT-SCALAR-MULTIPLICATION (TYPE &KEY (MAKE (SYMBOLICATE 'MAKE- TYPE)))

# WITH-PINNED-ARRAY ((POINTER ARRAY) &BODY BODY)

# GENERIC-FUNCTION

# Public

# CHOLESKY (A)

Cholesky factorization.

# HERMITIAN-FACTORIZATION (A)

Compute the hermitian factorization.

# INVERT (A &KEY (TOLERANCE 0) &ALLOW-OTHER-KEYS)

Invert A. The inverse of matrix factorizations are other factorizations when appropriate, otherwise the result is a matrix. Usage note: inverting dense matrices is unnecessary and unwise in most cases, because it is numerically unstable. If you are solving many Ax=b equations with the same A, use a matrix factorization like LU.

# INVERT-XX (XX)

Calculate (X^T X)-1 (which is used for calculating the variance of estimates) and return as a decomposition. Usually XX is a decomposition itself, eg QR returned by least squares. Note: this can be used to generate random draws, etc.

# LEFT-SQUARE-ROOT (A)

Return X such that XX^T=A.

# LOGDET (MATRIX)

Logarithm of the determinant of a matrix. Return -1, 1 or 0 (or equivalent) to correct for the sign, as a second value.

# LU (A)

LU decomposition of A

# MM (A B)

Matrix multiplication of A and B.

# OUTER (A B)

Return the outer product column(a) row(b)^H. If either A or B is T, they are taken to be conjugate transposes of the other argument.

# RIGHT-SQUARE-ROOT (A)

Return Y such that Y^T Y=A.
Efficiency note: decompositions should store the left square root X, and compute Y=X^T on demand, so getting X directly might be more efficient if you don't need X^T.

# SOLVE (A B)

Return X that solves AX=B. When B is a vector, so is X.

# SVD (A &OPTIONAL VECTORS)

Return singular value decomposition A.
VECTORS determines how singular vectors are calculated:
- NIL sets U and VT to NIL
- :ALL makes U and VT square, with dimensions conforming to A
- :THIN makes the larger of U and VT rectangular. This means that not all
of the singular vectors are calculates, and saves computational time when
A is far from square.

# TR (A)

Trace of a square matrix.

# Private

# FORTRAN-ARGUMENT/OUTPUT-INITIALIZER-FORM (ARGUMENT PARAMETERS)

When applicable, return a form that is used to initialize the OUTPUT variable. When NIL is returned, no binding is established.

# MEAN (OBJECT &KEY WEIGHTS)

The mean of elements in OBJECT.

# MEDIAN (OBJECT)

Median of OBJECT.

# PERMUTATIONS (OBJECT)

Return the number of permutations in object (which is usually a matrix factorization, or a pivot index.

# PROCESS-FORM (FORM ENVIRONMENT)

Return a list of argument specifications (atoms are converted into lists).
The code in this file defines a DSL for calling BLAS and LAPACK procedures in FORTRAN, which expect pointers to memory locations. The high-level macros BLAS-CALL and LAPACK-CALL take care of pinning arrays or allocating memory and copying array contents (when applicable), and use PROCESS-FORM to interpret their arguments, which correspond to one or more FORTRAN arguments. These are then expanded into code using WRAP-ARGUMENT.

# VARIANCE (OBJECT &KEY WEIGHTS)

Variance of OBJECT. For samples, normalized by the weight-1 (and thus unbiased if certain assumptions hold, eg weights that count frequencies).

# WRAP-ARGUMENT (ARGUMENT PASS PARAMETERS BODY)

Return BODY wrapped in an environment generated for ARGUMENT in a given PASS.
The code for calling the function is built using nested calls of WRAP-ARGUMENT. The setup is somewhat complicated because some functions require that they are called twice (eg in order to calculate work area size), and we don't necessarily want to allocate and free memory twice. Because of this, expansions take place in 'passes'.
Currently, the following passes are used:
- BINDINGS: establishes the bindings (also empty variables)
- MAIN: for arguments that are the same regardless of what kind of call is made
- QUERY: for querying work area sizes
- CALL: the actual function call
PARAMETERS is used to specify information that is applicable for all arguments (eg a default array element type).

# SLOT-ACCESSOR

# Public

# IPIV (OBJECT)

The Return the pivot indexes of OBJECT.
May only be meaningful with other information. May use the format of LAPACK, counting from 1. Not exported, as external use is discouraged.

# QR (OBJECT)

matrix storing the QR factorization.

# Private

# ARGUMENT-POINTER (OBJECT)

Pointer passed to FORTRAN.

# FACTOR (OBJECT)

see documentation of *SYTRF and *HETRF, storage is
in the half specified by HERMITIAN-ORIENTATION and otherwise
treated as opaque.

# LU-MATRIX (OBJECT)

matrix storing the transpose of the LU factorization.

# TAU (OBJECT)

complex scalar for elementary reflectors (see documentation of xGEQRF).

# SETFTAU (NEW-VALUE OBJECT)

complex scalar for elementary reflectors (see documentation of xGEQRF).

# VARIABLE

# Public

# *LLA-EFFICIENCY-WARNING-ARRAY-CONVERSION*

Toggles whether conversion of array elements to another type when used with foreign functions raises an LLA-EFFICIENCY-WARNING-ARRAY-CONVERSION warning.
Effective only when LLA was loaded & compiled with the appropriate settings in CL-USER::*LLA-CONFIGURATION*. See the documentation on configuration in the README.

# *LLA-EFFICIENCY-WARNING-ARRAY-TYPE*

Toggles whether arrays with types not recognized as LLA types raise an LLA-EFFICIENCY-WARNING-ARRAY-TYPE warning.
Effective only when LLA was loaded & compiled with the appropriate settings in CL-USER::*LLA-CONFIGURATION*. See the documentation on configuration in the README.

# CLASS

# Public

# CHOLESKY (A)

Cholesky factorization a matrix.

# HERMITIAN-FACTORIZATION (A)

Factorization for an indefinite hermitian matrix with
pivoting.

# LU (A)

LU factorization of a matrix with pivoting.

# MATRIX-SQUARE-ROOT

General class for representing XX^T decompositions of matrices, regardless of how they were computed. The convention is to store X, the left square root.

# QR (OBJECT)

QR factorization of a matrix.

# SPECTRAL-FACTORIZATION (A &KEY (ABSTOL 0))

Z W Z^T factorization of a Hermitian matrix, where the columns of Z contain the eigenvectors and W is a diagonal matrix of the eigenvalues. Z is a unitary matrix.

# SVD (A &OPTIONAL VECTORS)

Singular value decomposition. Singular values are in S, in descending order. U and VT may be NIL in case they are not computed.

# Private

# FORTRAN-ARGUMENT

Superclass of all arguments with pointers.

# FORTRAN-ARGUMENT/OUTPUT

Class for arguments that return an output. When FORTRAN-ARGUMENT/OUTPUT-INITIALIZER-FORM returns non-NIL, a local binding of OUTPUT to this form will be wrapped around the relevant BODY. Also see &NEW.

# FORTRAN-ARGUMENT/SIZE

Number of elements in array mapped to a pointer.

# FORTRAN-ARGUMENT/TYPE

For arguments which may have multiple types, mostly arrays or atoms (implemented as single-cell arrays).

# FORTRAN-ATOM

Atoms passed to FORTRAN. Input/output (when OUTPUT is given).

# FORTRAN-CHARACTER

Character passed to FORTRAN. Input only, for specifying triangle orientation, etc.

# FORTRAN-INPUT-ARRAY

Arrays which serve as inputs. See WITH-ARRAY-INPUT for the semantics of the arguments.

# FORTRAN-INPUT-OUTPUT-ARRAY

Input/output array. See WITH-ARRAY-INPUT-OUTPUT for the semantics of the arguments.

# FORTRAN-OUTPUT-ARRAY

Output array. See WITH-ARRAY-OUTPUT for the semantics of the arguments.

# FORTRAN-WORK-AREA

Work area.

# LAPACK-INFO

Information from a LAPACK call. See the LAPACK manual for error codes.

# Undocumented

# LAPACK-WORK-QUERY-AREA

# LAPACK-WORK-QUERY-SIZE

# CONDITION

# Public

# LAPACK-ERROR

The LAPACK procedure returned a nonzero info code.

# LAPACK-FAILURE

Superclass of all LAPACK errors with a positive INFO

# LAPACK-INVALID-ARGUMENT

An argument to a LAPACK procedure had an illegal value. It is very likely that this indicates a bug in LLA and should not happen.

# LLA-EFFICIENCY-WARNING-ARRAY-TYPE

See *LLA-EFFICIENCY-WARNING-ARRAY-TYPE*.

# LLA-INTERNAL-ERROR

Internal error in LLA.

# LLA-UNHANDLED-TYPE

Could not classify object as a numeric type handled by LLA.

# Undocumented

# LAPACK-SINGULAR-MATRIX

# LLA-EFFICIENCY-WARNING

# LLA-EFFICIENCY-WARNING-ARRAY-CONVERSION

# LLA-INCOMPATIBLE-DIMENSIONS

# CONSTANT

# Private

# +FLOAT-TYPES+

List of all internal float types.

# +INTERNAL-TYPES+

List of all internal types.