Table of Contents

System Information

Definition Index

• 3D-MATRICES

  • ORG.SHIRAKUMO.FLARE.MATRIX

  No documentation provided.

  • EXTERNAL STRUCTURE

    MAT2

    Source

    The 2x2 matrix type.

  • EXTERNAL STRUCTURE

    MAT3

    Source

    The 3x3 matrix type.

  • EXTERNAL STRUCTURE

    MAT4

    Source

    The 4x4 matrix type.

  • EXTERNAL STRUCTURE

    MATN

    Source

    The NxM matrix type.

  • EXTERNAL TYPE-DEFINITION

    MAT

    Source

    Supertype for all matrix types.
    
    See MAT2
    See MAT3
    See MAT4
    See MATN

  • EXTERNAL FUNCTION

    M*

    • VAL
    • &REST
    • VALS

    Source

    Computes a matrix multiplication.
    
    If the other operand is a real, the matrix is multiplied with the real element-wise.
    If the other operand is a matrix, they are multiplied as per matrix multiplication.
    Note that the returned matrix may have different size than the input matrices as a result
    of this. The two matrices must agree on the size as per matrix multiplication.
    
    A special provision is made to allow for MAT4*VEC3, which acts as MAT4*(VEC4 X Y Z 1)
    and discarding the W component.

  • EXTERNAL FUNCTION

    M+

    • VAL
    • &REST
    • VALS

    Source

    Computes the element-wise addition of the matrices or reals. Returns a fresh matrix.

  • EXTERNAL FUNCTION

    M-

    • VAL
    • &REST
    • VALS

    Source

    Computes the element-wise subtraction of the matrices or reals. Returns a fresh matrix.

  • EXTERNAL FUNCTION

    M/

    • VAL
    • &REST
    • VALS

    Source

    Computes an element-wise division of the matrix from a real. Returns a fresh matrix.

  • EXTERNAL FUNCTION

    M/=

    • VAL
    • &REST
    • VALS

    Source

    Compares matrices against each other or a real, returning T if they are element-wise equal by /=.

  • EXTERNAL FUNCTION

    M1NORM

    • M

    Source

    Computes the 1 norm of the matrix, namely the maximum of the sums of the columns.

  • EXTERNAL FUNCTION

    M2NORM

    • M

    Source

    Computes the 2 norm of the matrix, namely the square root of the sum of all squared elements.

  • EXTERNAL FUNCTION

    M<

    • VAL
    • &REST
    • VALS

    Source

    Compares matrices against each other or a real, returning T if they are element-wise ordered by <.

  • EXTERNAL FUNCTION

    M<=

    • VAL
    • &REST
    • VALS

    Source

    Compares matrices against each other or a real, returning T if they are element-wise ordered by <=.

  • EXTERNAL FUNCTION

    M=

    • VAL
    • &REST
    • VALS

    Source

    Compares matrices against each other or a real, returning T if they are element-wise equal by =.

  • EXTERNAL FUNCTION

    M>

    • VAL
    • &REST
    • VALS

    Source

    Compares matrices against each other or a real, returning T if they are element-wise ordered by >.

  • EXTERNAL FUNCTION

    M>=

    • VAL
    • &REST
    • VALS

    Source

    Compares matrices against each other or a real, returning T if they are element-wise ordered by >=.

  • EXTERNAL FUNCTION

    MADJ

    • M

    Source

    Computes the adjugate of the matrix.
    
    For MAT2 MAT3 MAT4, inlined variants exist. For MATN, an algorithm based on the cofactors is used.

  • EXTERNAL FUNCTION

    MAPPLY

    • MAT
    • OP

    Source

    Applies the function to each element of the matrix and maps the result of it to a new matrix.

  • EXTERNAL FUNCTION

    MAPPLYF

    • MAT
    • OP

    Source

    Applies the function to each element of the matrix and maps the result of it back into the matrix.

  • EXTERNAL FUNCTION

    MARR

    • MAT

    Source

    Returns the backing array used by the matrix.
    
    This should be a SIMPLE-VECTOR with the elements of type FLOAT-TYPE.
    
    See MARR2
    See MARR3
    See MARR4
    See MARRN

  • EXTERNAL FUNCTION

    MARR2

    • INSTANCE

    Source

    Direct accessor to the backing array of the MAT2.

  • EXTERNAL FUNCTION

    (SETF MARR2)

    • VALUE
    • INSTANCE

    Source

    No documentation provided.
  • EXTERNAL FUNCTION

    MARR3

    • INSTANCE

    Source

    Direct accessor to the backing array of the MAT3o.

  • EXTERNAL FUNCTION

    (SETF MARR3)

    • VALUE
    • INSTANCE

    Source

    No documentation provided.
  • EXTERNAL FUNCTION

    MARR4

    • INSTANCE

    Source

    Direct accessor to the backing array of the MAT4.

  • EXTERNAL FUNCTION

    (SETF MARR4)

    • VALUE
    • INSTANCE

    Source

    No documentation provided.
  • EXTERNAL FUNCTION

    MARRN

    • INSTANCE

    Source

    Direct accessor to the backing array of the MATN.

  • EXTERNAL FUNCTION

    (SETF MARRN)

    • VALUE
    • INSTANCE

    Source

    No documentation provided.
  • EXTERNAL FUNCTION

    MAT

    • &REST
    • VALS

    Source

    Constructs a fitting matrix for the number of elements given.
    
    This only works for square numbers of elements, as otherwise it is not possible
    to guess what dimensions the matrix should have. In the case of a non-square
    number, an error is signalled.
    
    See MAT2
    See MAT3
    See MAT4
    See MATN

  • EXTERNAL FUNCTION

    MAT-P

    • MAT

    Source

    Returns T if the given object is of type MAT.
    
    See MAT2-P
    See MAT3-P
    See MAT4-P
    See MATN-P

  • EXTERNAL FUNCTION

    MAT2

    • &OPTIONAL
    • ELEMENTS

    Source

    Constructs a MAT2 from the given elements.
    
    ELEMENTS can be
      NULL     --- The matrix is initialised with zeroes.
      REAL     --- The matrix is initialised with this number.
      SEQUENCE --- The sequence is mapped into the matrix
                   and the rest are initialised to 0.

  • EXTERNAL FUNCTION

    MAT2-P

    • OBJECT

    Source

    Returns T if the given object is of type MAT2.

  • EXTERNAL FUNCTION

    MAT3

    • &OPTIONAL
    • ELEMENTS

    Source

    Constructs a MAT3 from the given elements.
    
    ELEMENTS can be
      NULL     --- The matrix is initialised with zeroes.
      REAL     --- The matrix is initialised with this number.
      SEQUENCE --- The sequence is mapped into the matrix
                   and the rest are initialised to 0.

  • EXTERNAL FUNCTION

    MAT3-P

    • OBJECT

    Source

    Returns T if the given object is of type MAT3.

  • EXTERNAL FUNCTION

    MAT4

    • &OPTIONAL
    • ELEMENTS

    Source

    Constructs a MAT4 from the given elements.
    
    ELEMENTS can be
      NULL     --- The matrix is initialised with zeroes.
      REAL     --- The matrix is initialised with this number.
      SEQUENCE --- The sequence is mapped into the matrix
                   and the rest are initialised to 0.

  • EXTERNAL FUNCTION

    MAT4-P

    • OBJECT

    Source

    Returns T if the given object is of type MAT4.

  • EXTERNAL FUNCTION

    MATF

    • MAT
    • &REST
    • VALS

    Source

    Maps the VALs into the matrix.
    
    The values will be mapped in row-major order.

  • EXTERNAL FUNCTION

    MATN

    • R
    • C
    • &OPTIONAL
    • ELEMENTS

    Source

    Constructs a MATN of the requested size from the given elements.
    
    ELEMENTS can be
      NULL     --- The matrix is initialised with zeroes.
      REAL     --- The matrix is initialised with this number.
      SEQUENCE --- The sequence is mapped into the matrix
                   and the rest are initialised to 0.
    
    Note that if R and C are both...
      2 - A MAT2 is constructed
      3 - A MAT3 is constructed
      4 - A MAT4 is constructed
    instead of a MATN.

  • EXTERNAL FUNCTION

    MATN-P

    • OBJECT

    Source

    Returns T if the given object is of type MATN.

  • EXTERNAL FUNCTION

    MBLOCK

    • M
    • Y1
    • X1
    • Y2
    • X2

    Source

    Returns the designated sub-matrix as a new matrix.
    Y1, X1 are the upper left corner, inclusive
    Y2, X2 are the lower right corner, exclusive

  • EXTERNAL FUNCTION

    MBOTTOM

    • M
    • N

    Source

    Returns the lowermost N rows as a new matrix.

  • EXTERNAL FUNCTION

    MCOF

    • M

    Source

    Computes the cofactor matrix.
    
    See MCOFACTOR

  • EXTERNAL FUNCTION

    MCOFACTOR

    • M
    • Y
    • X

    Source

    Computes the cofactor at the specified index of the matrix.
    
    This is just the element at the position multiplied by the minor.
    
    See MMINOR

  • EXTERNAL FUNCTION

    MCOL

    • MAT
    • N

    Source

    Accesses the requested column as a vector of the appropriate size.
    
    This only works for MAT2, MAT3, MAT4.

  • EXTERNAL FUNCTION

    (SETF MCOL)

    • VEC
    • MAT
    • N

    Source

    No documentation provided.
  • EXTERNAL FUNCTION

    MCOLS

    • MAT

    Source

    Returns the number of columns the matrix stores.

  • EXTERNAL FUNCTION

    MCOPY

    • M

    Source

    Creates a full copy of the matrix.
    
    See MCOPY2
    See MCOPY3
    See MCOPY4
    See MCOPYN

  • EXTERNAL FUNCTION

    MCOPY2

    • M2

    Source

    Creates a full copy of the MAT2.

  • EXTERNAL FUNCTION

    MCOPY3

    • M3

    Source

    Creates a full copy of the MAT3.

  • EXTERNAL FUNCTION

    MCOPY4

    • M4

    Source

    Creates a full copy of the MAT4.

  • EXTERNAL FUNCTION

    MCOPYN

    • MN

    Source

    Creates a full copy of the MATN.

  • EXTERNAL FUNCTION

    MCREF

    • MAT
    • Y
    • X

    Source

    Returns the element at the given cell in the matrix.
    
    See MCREF2
    See MCREF3
    See MCREF4
    See MCREFN

  • EXTERNAL FUNCTION

    MCREF2

    • MAT
    • Y
    • X

    Source

    Returns the element at the given cell in the MAT2.

  • EXTERNAL FUNCTION

    MCREF3

    • MAT
    • Y
    • X

    Source

    Returns the element at the given cell in the MAT3.

  • EXTERNAL FUNCTION

    MCREF4

    • MAT
    • Y
    • X

    Source

    Returns the element at the given cell in the MAT4.

  • EXTERNAL FUNCTION

    MCREFN

    • MAT
    • Y
    • X

    Source

    Returns the element at the given cell in the MATN.

  • EXTERNAL FUNCTION

    MDET

    • M

    Source

    Computes the determinant of the matrix.
    
    For MAT2 MAT3 MAT4, inlined variants exist. For MATN, an algorithm based on LU factorisation is used.

  • EXTERNAL FUNCTION

    MDIAG

    • M

    Source

    Returns the diagonal values of the matrix as a list.

  • EXTERNAL FUNCTION

    MEIGEN

    • M
    • &OPTIONAL
    • ITERATIONS

    Source

    Computes an approximation of the eigenvalues of the matrix.
    
    An approach based on QR factorisation is used. The number of iterations dictates
    how many times the factorisation is repeated to make the result more accurate.
    Usually something around 50 iterations should give somewhat accurate results, but
    due to floating point limitations that may be off more significantly.
    
    Returns the eigenvalues as a list.

  • EXTERNAL FUNCTION

    MEYE

    • N

    Source

    Constructs a square identity matrix of the requested size.

  • EXTERNAL FUNCTION

    MFRUSTUM

    • LEFT
    • RIGHT
    • BOTTOM
    • TOP
    • NEAR
    • FAR

    Source

    Returns a 3D frustum projection view matrix.
    
    See MPERSPECTIVE

  • EXTERNAL FUNCTION

    MINORM

    • M

    Source

    Computes the infinity norm of the matrix, namely the maximum of the sums of the rows.

  • EXTERNAL FUNCTION

    MINV

    • M

    Source

    Computes the inverses of the matrix.
    
    This is only possible if the determinant is non-zero.
    
    For MAT2 MAT3 MAT4, inlined variants exist. For MATN, an algorithm based on the adjugate is used.
    
    See MINV-AFFINE

  • EXTERNAL FUNCTION

    MINV-AFFINE

    • M
    • &OPTIONAL
    • OUT

    Source

    Computes the inverses of the affine transformation matrix.
    
    If your matrix is only composed of rotation and translation, this will be
    much faster and more numerically stable than minv.
    
    See MINV

  • EXTERNAL FUNCTION

    MIREF

    • MAT
    • I

    Source

    Returns the element at the given index in the matrix.
    
    Elements are stored in row-major format.
    
    See MIREF2
    See MIREF3
    See MIREF4
    See MIREFN

  • EXTERNAL FUNCTION

    MIREF2

    • MAT
    • I

    Source

    Returns the element at the given index in the MAT2.
    
    Elements are stored in row-major format.

  • EXTERNAL FUNCTION

    MIREF3

    • MAT
    • I

    Source

    Returns the element at the given index in the MAT3.
    
    Elements are stored in row-major format.

  • EXTERNAL FUNCTION

    MIREF4

    • MAT
    • I

    Source

    Returns the element at the given index in the MAT4.
    
    Elements are stored in row-major format.

  • EXTERNAL FUNCTION

    MIREFN

    • MAT
    • I

    Source

    Returns the element at the given index in the MATN.
    
    Elements are stored in row-major format.

  • EXTERNAL FUNCTION

    MLEFT

    • M
    • N

    Source

    Returns the leftmost N columns as a new matrix.

  • EXTERNAL FUNCTION

    MLOOKAT

    • EYE
    • TARGET
    • UP

    Source

    Returns a view translation matrix that should "look at" TARGET from EYE where UP is the up vector.

  • EXTERNAL FUNCTION

    MLU

    • M
    • &OPTIONAL
    • PIVOT

    Source

    Computes an LU factorisation of the matrix.
    
    An approach based on Crout is used with on-the-fly pivotisation if requested.
    
    Returns the combined LU matrix, the permutation matrix, and the number of permutations that were done.

  • EXTERNAL FUNCTION

    MMINOR

    • M
    • Y
    • X

    Source

    Computes the minor at the specified index of the matrix.
    
    This basically calculates the determinant of the matrix with the row and
    column of the specified index excluded.

  • EXTERNAL FUNCTION

    MORTHO

    • LEFT
    • RIGHT
    • BOTTOM
    • TOP
    • NEAR
    • FAR

    Source

    Returns a 3D orthographic projection view matrix.

  • EXTERNAL FUNCTION

    MPERSPECTIVE

    • FOVY
    • ASPECT
    • NEAR
    • FAR

    Source

    Returns a 3D perspective projection view matrix.
    
    FOVY       -- The field of view (how "zoomy" it is)
    ASPECT     -- The aspect ratio of the screen
    NEAR / FAR -- The Z near and far clipping planes
    
    See MFRUSTUM

  • EXTERNAL FUNCTION

    MPIVOT

    • M

    Source

    Attempts to do a partial pivotisation.
    
    Returns the pivotised matrix, the permutation matrix, and the number of permutations that were done.

  • EXTERNAL FUNCTION

    MQR

    • MAT

    Source

    Computes the QR factorisation of the matrix.
    
    An approach based on givens rotations is used.
    
    Returns the Q and R matrices, which are fresh.

  • EXTERNAL FUNCTION

    MRAND

    • R
    • C
    • &KEY
    • MIN
    • MAX

    Source

    Constructs a matrix of the requested size where each element is randomized.
    
    MIN and MAX return the inclusive bounds of the numbers in the matrix.

  • EXTERNAL FUNCTION

    MRIGHT

    • M
    • N

    Source

    Returns the rightmost N columns as a new matrix.

  • EXTERNAL FUNCTION

    MROTATION

    • V
    • ANGLE

    Source

    Returns a 3D rotation matrix for the given vector as a MAT4.

  • EXTERNAL FUNCTION

    MROW

    • MAT
    • N

    Source

    Accesses the requested row as a vector of the appropriate size.
    
    This only works for MAT2, MAT3, MAT4.

  • EXTERNAL FUNCTION

    (SETF MROW)

    • VEC
    • MAT
    • N

    Source

    No documentation provided.
  • EXTERNAL FUNCTION

    MROWS

    • MAT

    Source

    Returns the number of rows the matrix stores.

  • EXTERNAL FUNCTION

    MSCALING

    • V

    Source

    Returns a 3D scaling matrix for the given vector as a MAT4.

  • EXTERNAL FUNCTION

    MTOP

    • M
    • N

    Source

    Returns the topmost N rows as a new matrix.

  • EXTERNAL FUNCTION

    MTRACE

    • M

    Source

    Computes the trace of the matrix.
    
    For MAT2 MAT3 MAT4, inlined variants exist. For MATN, a generic sum is used.

  • EXTERNAL FUNCTION

    MTRANSLATION

    • V

    Source

    Returns a 3D translation matrix for the given vector as a MAT4.

  • EXTERNAL FUNCTION

    MTRANSPOSE

    • M

    Source

    Computes the transpose of the matrix.
    
    For MAT2 MAT3 MAT4, inlined variants exist. For MATN, a generic swap is used.

  • EXTERNAL FUNCTION

    MUNIFORM

    • R
    • C
    • ELEMENT

    Source

    Constructs a matrix of the requested size where each element is initialised to the requested element.

  • EXTERNAL FUNCTION

    M~=

    • VAL
    • &REST
    • VALS

    Source

    Compares matrices against each other or a real, returning T if they are element-wise equal by ~=.
    
    See ~=

  • EXTERNAL FUNCTION

    N*M

    • VAL
    • &REST
    • VALS

    Source

    Computes a modifying matrix multiplication, but modifying the right-hand side.
    
    See NM*

  • EXTERNAL FUNCTION

    NM*

    • VAL
    • &REST
    • VALS

    Source

    Computes a modifying matrix multiplication.
    
    If the other operand is a real, the matrix is multiplied with the real element-wise.
    If the other operand is a matrix, they are multiplied as per matrix multiplication.
    Note that this only works for square matrix against square matrix, as otherwise a size
    change would occur, which is not possible to do in a modifying variant. The two matrices
    must agree on the size as per matrix multiplication.
    If the other operand is a vector, the vector is modified.
    
    A special provision is made to allow for MAT4*VEC3, which acts as MAT4*(VEC4 X Y Z 1)
    and discarding the W component.
    
    See N*M

  • EXTERNAL FUNCTION

    NM+

    • VAL
    • &REST
    • VALS

    Source

    Computes the element-wise addition of the matrices or reals. Returns the first matrix, modified.

  • EXTERNAL FUNCTION

    NM-

    • VAL
    • &REST
    • VALS

    Source

    Computes the element-wise subtraction of the matrices or reals. Returns the first matrix, modified.

  • EXTERNAL FUNCTION

    NM/

    • VAL
    • &REST
    • VALS

    Source

    Computes an element-wise division of the matrix from a real. Returns the modified, first matrix.

  • EXTERNAL FUNCTION

    NMLOOKAT

    • M
    • EYE
    • TARGET
    • UP

    Source

    Modifies the matrix to look at TARGET from the EYE.
    
    See MLOOKAT.

  • EXTERNAL FUNCTION

    NMROTATE

    • M
    • V
    • ANGLE

    Source

    Rotates the given matrix around the vector by angle. Returns the modified matrix.

  • EXTERNAL FUNCTION

    NMSCALE

    • M
    • V

    Source

    Scales the given matrix by the vector. Returns the modified matrix.

  • EXTERNAL FUNCTION

    NMSWAP-COL

    • M
    • K
    • L

    Source

    Modifies the matrix by swapping the Kth column with the Lth column.

  • EXTERNAL FUNCTION

    NMSWAP-ROW

    • M
    • K
    • L

    Source

    Modifies the matrix by swapping the Kth row with the Lth row.

  • EXTERNAL FUNCTION

    NMTRANSLATE

    • M
    • V

    Source

    Translates the given matrix by the vector. Returns the modified matrix.

  • EXTERNAL FUNCTION

    NMTRANSPOSE

    • M

    Source

    No documentation provided.
  • EXTERNAL FUNCTION

    WRITE-MATRIX

    • M
    • STREAM
    • &KEY
    • FORMAT

    Source

    Writes the matrix in a certain format, by default a human-readable one.
    
    FORMAT can be one of
      :NICE    - Prints it in a nice representation intended for humans.
      :WOLFRAM - Prints it in the format for Wolfram Alpha, namely {{a,b..},..}
      :ARRAY   - Prints it as a common lisp 2D array.
    
    If the STREAM is NIL, a string of the output is returned. Otherwise the
    matrix itself is returned.

  • EXTERNAL MACRO

    MSETF

    • MAT
    • &REST
    • ELS

    Source

    No documentation provided.
  • EXTERNAL MACRO

    WITH-FAST-MATCASE

    • ACCESSOR
    • MAT
    • &BODY
    • BODY

    Source

    Does an etypecase on MAT and an appropriate WITH-FAST-MATREF on each case.
    
    The body should be an expression of (MAT-TYPE form*). For each
    matrix type /except/ for MATN, the forms will be wrapped in an
    appropriate WITH-FAST-MATREF. This is not done for MATN, as often
    times a different approach to manipulating the matrix than by
    direct reference is preferable for that case.
    
    See WITH-FAST-MATREF

  • EXTERNAL MACRO

    WITH-FAST-MATREF

    • ACCESSOR
    • MAT
    • WIDTH
    • &BODY
    • BODY

    Source

    Allows efficient referencing to matrix elements.
    
    ACCESSOR designates the name of the local macro that will allow
    you to both read and set the matrix element at the given position
    It will take either one or two arguments. If two, they are row and
    column of the cell to dereference, and if one, it is the row-major
    index of the element to dereference.
    
    You must also designate the proper number of columns stored in the
    matrix. This is done because often times when you will want to use
    this macro, you'll already know the number of columns anyway.
    Retrieving it again would be wasteful.
    
    You should use this whenever you need to reference elements in a loop
    or need to do more than one reference overall.

  • EXTERNAL MACRO

    WITH-FAST-MATREFS

    • BINDINGS
    • &BODY
    • BODY

    Source

    Allows efficient referencing of multiple matrices.
    
    Each binding must be of the form that WITH-FAST-MATREF expects.
    
    See WITH-FAST-MATREF