3.1.1 linear-algebra/linear-algebra.asd

Source

linear-algebra.asd.

Parent Component

linear-algebra (system).

ASDF Systems

linear-algebra.

---

3.1.2 linear-algebra/pkgdcl.lisp

Dependency

kernel (module).

Source

linear-algebra.asd.

Parent Component

linear-algebra (system).

Packages

linear-algebra.

---

3.1.3 linear-algebra/kernel/pkgdcl.lisp

Source

linear-algebra.asd.

Parent Component

kernel (module).

Packages

linear-algebra-kernel.

---

3.1.4 linear-algebra/kernel/utility.lisp

Dependency

pkgdcl.lisp (file).

Source

linear-algebra.asd.

Parent Component

kernel (module).

Public Interface

• common-array-element-type (function).
• common-class-of (function).
• complex-equal (function).
• copy-array (generic function).
• number-equal (function).
• specific-array-element-type (function).

Internals

• zero-array (function).
• zero-vector (function).

---

3.1.5 linear-algebra/kernel/permute.lisp

Dependency

pkgdcl.lisp (file).

Source

linear-algebra.asd.

Parent Component

kernel (module).

Public Interface

• left-permute (generic function).
• right-permute (generic function).

---

3.1.6 linear-algebra/kernel/unary-operations.lisp

Dependency

pkgdcl.lisp (file).

Source

linear-algebra.asd.

Parent Component

kernel (module).

Public Interface

• norm-array (generic function).
• norm-vector (generic function).
• sump (generic function).
• sumsq (generic function).
• sumsq-column (function).
• sumsq-row (function).
• sumsq2 (function).
• sumsq3 (function).

Internals

%abs-vector (function).

---

3.1.7 linear-algebra/kernel/binary-operations.lisp

Dependency

pkgdcl.lisp (file).

Source

linear-algebra.asd.

Parent Component

kernel (module).

Public Interface

• add-array (function).
• add-vector (function).
• compatible-dimensions-p (generic function).
• inner-product-vector (function).
• nadd-array (function).
• nadd-vector (function).
• nsubtract-array (function).
• nsubtract-vector (function).
• product-array-array (function).
• product-array-vector (function).
• product-vector-array (function).
• scaled-binary-op (generic function).
• subtract-array (function).
• subtract-vector (function).

Internals

• %array1<-array1-op-array2 (function).
• %array<-array1-op-array2 (function).
• %product-array-array (function).
• %product-array-vector (function).
• %product-vector-array (function).
• %scaled-product-array-array (function).
• %scaled-product-array-vector (function).
• %scaled-product-vector-array (function).
• %vector1<-vector1-op-vector2 (function).
• %vector<-vector1-op-vector2 (function).

---

3.1.8 linear-algebra/kernel/rotation.lisp

Dependency

unary-operations.lisp (file).

Source

linear-algebra.asd.

Parent Component

kernel (module).

Public Interface

• givens-rotation (function).
• householder-reflection (function).
• jacobi-rotation (function).

---

3.1.9 linear-algebra/kernel/gauss.lisp

Dependency

pkgdcl.lisp (file).

Source

linear-algebra.asd.

Parent Component

kernel (module).

Public Interface

• gauss-invert (function).
• gauss-solver (function).

Internals

• column-pivot (function).
• column-pivot-search (function).
• gauss-backsubstitution (function).
• gauss-factorization (function).
• gauss-update (function).
• initialize-pivot-selection-vector (function).
• swap-rows (function).
• unit-pivot-value (function).

---

3.1.10 linear-algebra/kernel/cholesky.lisp

Dependency

unary-operations.lisp (file).

Source

linear-algebra.asd.

Parent Component

kernel (module).

Public Interface

• hermitian-cholesky-decomposition (function).
• hermitian-cholesky-invert (function).
• hermitian-cholesky-solver (function).
• root-free-hermitian-cholesky-decomposition (function).
• root-free-symmetric-cholesky-decomposition (function).
• symmetric-cholesky-decomposition (function).
• symmetric-cholesky-invert (function).
• symmetric-cholesky-solver (function).

---

3.1.11 linear-algebra/kernel/conjugate-gradient.lisp

Dependency

binary-operations.lisp (file).

Source

linear-algebra.asd.

Parent Component

kernel (module).

Public Interface

conjugate-gradient-solver (function).

Internals

• %default-cg-epsilon (function).
• %initialize-cg-residual (function).
• %initialize-cg-solution (function).
• %negative-residual (function).

---

3.1.12 linear-algebra/kernel/tridiagonal.lisp

Dependency

pkgdcl.lisp (file).

Source

linear-algebra.asd.

Parent Component

kernel (module).

Public Interface

tridiagonal-solver (function).

Internals

• tridiagonal-backsubstitution (function).
• tridiagonal-factorization (function).
• tridiagonal-update (function).

---

3.1.13 linear-algebra/interface/fundamental-ops.lisp

Source

linear-algebra.asd.

Parent Component

interface (module).

Public Interface

• add (generic function).
• invert (generic function).
• nadd (generic function).
• ninvert (generic function).
• norm (generic function).
• nscale (generic function).
• nsolve (generic function).
• nsubtract (generic function).
• ntranspose (generic function).
• permute (generic function).
• product (generic function).
• scale (generic function).
• solve (generic function).
• subtract (generic function).
• transpose (generic function).

---

3.1.14 linear-algebra/interface/vector.lisp

Dependency

fundamental-ops.lisp (file).

Source

linear-algebra.asd.

Parent Component

interface (module).

Public Interface

• apply-rotation (generic function).
• copy-vector (generic function).
• dovector (macro).
• make-vector (function).
• map-into-vector (generic function).
• map-vector (generic function).
• napply-rotation (generic function).
• replace-vector (generic function).
• subvector (generic function).
• (setf subvector) (generic function).
• vector-element-type (generic function).
• vector-in-bounds-p (generic function).
• vector-length (generic function).
• vref (generic function).
• (setf vref) (generic function).

---

3.1.15 linear-algebra/interface/matrix.lisp

Dependency

fundamental-ops.lisp (file).

Source

linear-algebra.asd.

Parent Component

interface (module).

Public Interface

• copy-matrix (generic function).
• make-matrix (function).
• matrix-column-dimension (generic function).
• matrix-dimensions (generic function).
• matrix-element-type (generic function).
• matrix-in-bounds-p (generic function).
• matrix-object (class).
• matrix-row-dimension (generic function).
• matrix-validated-range (function).
• matrixp (function).
• mref (generic function).
• (setf mref) (generic function).
• replace-matrix (generic function).
• submatrix (generic function).
• (setf submatrix) (generic function).

Internals

initialize-matrix-contents (generic function).

---

3.1.16 linear-algebra/interface/identity-matrix.lisp

Dependency

matrix.lisp (file).

Source

linear-algebra.asd.

Parent Component

interface (module).

Public Interface

• copy-matrix (method).
• identity-matrix (class).
• identity-matrix-p (function).
• initialize-instance (method).
• matrix-column-dimension (reader method).
• matrix-dimensions (method).
• matrix-element-type (method).
• matrix-in-bounds-p (method).
• matrix-row-dimension (reader method).
• mref (method).

Internals

• contents (reader method).
• size (reader method).

---

3.1.17 linear-algebra/interface/permutation-matrix.lisp

Dependency

matrix.lisp (file).

Source

linear-algebra.asd.

Parent Component

interface (module).

Public Interface

• copy-matrix (method).
• initialize-instance (method).
• matrix-column-dimension (method).
• matrix-dimensions (method).
• matrix-element-type (method).
• matrix-in-bounds-p (method).
• matrix-row-dimension (method).
• mref (method).
• (setf mref) (method).
• permutation-matrix (class).
• permutation-matrix-p (function).
• transpose (method).

Internals

• %initialize-permutation-matrix-with-seq (function).
• contents (reader method).
• (setf contents) (writer method).
• initialize-matrix-contents (method).
• initialize-matrix-contents (method).
• initialize-matrix-contents (method).

---

3.1.18 linear-algebra/sequence/list.lisp

Source

linear-algebra.asd.

Parent Component

sequence (module).

Public Interface

• add (method).
• nadd (method).
• norm (method).
• nscale (method).
• nsubtract (method).
• ntranspose (method).
• permute (method).
• permute (method).
• product (method).
• scale (method).
• subtract (method).
• transpose (method).

Internals

• %norm (method).
• %norm (method).
• %norm (method).
• %norm (method).

---

3.1.19 linear-algebra/sequence/vector.lisp

Source

linear-algebra.asd.

Parent Component

sequence (module).

Public Interface

• add (method).
• nadd (method).
• norm (method).
• nscale (method).
• nsubtract (method).
• ntranspose (method).
• permute (method).
• permute (method).
• product (method).
• scale (method).
• subtract (method).
• transpose (method).

---

3.1.20 linear-algebra/sequence/array.lisp

Source

linear-algebra.asd.

Parent Component

sequence (module).

Public Interface

• add (method).
• compatible-dimensions-p (method).
• invert (method).
• nadd (method).
• ninvert (method).
• norm (method).
• nscale (method).
• nsolve (method).
• nsubtract (method).
• ntranspose (method).
• permute (method).
• permute (method).
• product (method).
• product (method).
• product (method).
• scale (method).
• solve (method).
• subtract (method).
• transpose (method).

---

3.1.21 linear-algebra/data-vector.lisp

Dependency

interface (module).

Source

linear-algebra.asd.

Parent Component

linear-algebra (system).

Public Interface

• add (method).
• add (method).
• add (method).
• apply-rotation (method).
• apply-rotation (method).
• column-vector (function).
• column-vector (class).
• column-vector-p (function).
• copy-vector (method).
• data-vector (class).
• initialize-instance (method).
• map-into-vector (method).
• map-into-vector (method).
• map-vector (method).
• map-vector (method).
• nadd (method).
• nadd (method).
• nadd (method).
• napply-rotation (method).
• napply-rotation (method).
• norm (method).
• nscale (method).
• nsubtract (method).
• nsubtract (method).
• nsubtract (method).
• ntranspose (method).
• ntranspose (method).
• permute (method).
• permute (method).
• permute (method).
• permute (method).
• product (method).
• product (method).
• replace-vector (method).
• row-vector (function).
• row-vector (class).
• row-vector-p (function).
• scale (method).
• subtract (method).
• subtract (method).
• subtract (method).
• subvector (method).
• (setf subvector) (method).
• transpose (method).
• transpose (method).
• vector-element-type (method).
• vector-in-bounds-p (method).
• vector-length (method).
• vref (method).
• (setf vref) (method).

Internals

• %map-data-vector (function).
• %map-into-data-vector (function).
• contents (reader method).
• (setf contents) (writer method).

---

3.1.22 linear-algebra/dense-matrix.lisp

Dependency

data-vector.lisp (file).

Source

linear-algebra.asd.

Parent Component

linear-algebra (system).

Public Interface

• add (method).
• add (method).
• compatible-dimensions-p (method).
• copy-matrix (method).
• dense-matrix (class).
• dense-matrix-p (function).
• initialize-instance (method).
• invert (method).
• matrix-column-dimension (method).
• matrix-dimensions (method).
• matrix-element-type (method).
• matrix-in-bounds-p (method).
• matrix-row-dimension (method).
• mref (method).
• (setf mref) (method).
• nadd (method).
• nadd (method).
• ninvert (method).
• norm (method).
• nscale (method).
• nsolve (method).
• nsolve (method).
• nsubtract (method).
• nsubtract (method).
• ntranspose (method).
• permute (method).
• permute (method).
• product (method).
• product (method).
• product (method).
• product (method).
• product (method).
• product (method).
• replace-matrix (method).
• scale (method).
• solve (method).
• solve (method).
• submatrix (method).
• (setf submatrix) (method).
• subtract (method).
• subtract (method).
• transpose (method).

Internals

• contents (reader method).
• (setf contents) (writer method).
• initialize-matrix-contents (method).
• initialize-matrix-contents (method).
• initialize-matrix-contents (method).
• initialize-matrix-contents (method).

---

3.1.23 linear-algebra/square-matrix.lisp

Dependency

dense-matrix.lisp (file).

Source

linear-algebra.asd.

Parent Component

linear-algebra (system).

Public Interface

• compatible-dimensions-p (method).
• invert (method).
• ninvert (method).
• square-matrix (class).
• square-matrix-p (function).
• submatrix (method).

Internals

initialize-matrix-contents (method).

---

3.1.24 linear-algebra/hermitian-matrix.lisp

Dependency

square-matrix.lisp (file).

Source

linear-algebra.asd.

Parent Component

linear-algebra (system).

Public Interface

• hermitian-matrix (class).
• hermitian-matrix-p (function).
• invert (method).
• (setf mref) (method).
• ninvert (method).
• nsolve (method).
• ntranspose (method).
• permute (method).
• permute (method).
• replace-matrix (method).
• replace-matrix (method).
• solve (method).
• submatrix (method).
• (setf submatrix) (method).
• (setf submatrix) (method).
• transpose (method).

Internals

• %initialize-hermitian-matrix-with-seq (function).
• %replace-hermitian-matrix-off-diagonal (function).
• %replace-hermitian-matrix-on-diagonal (function).
• %setf-hermitian-submatrix-off-diagonal (function).
• %setf-hermitian-submatrix-on-diagonal (function).
• initialize-matrix-contents (method).
• initialize-matrix-contents (method).
• initialize-matrix-contents (method).
• initialize-matrix-contents (method).

---

3.1.25 linear-algebra/symmetric-matrix.lisp

Dependency

square-matrix.lisp (file).

Source

linear-algebra.asd.

Parent Component

linear-algebra (system).

Public Interface

• invert (method).
• (setf mref) (method).
• nadd (method).
• nadd (method).
• ninvert (method).
• nsolve (method).
• nsubtract (method).
• nsubtract (method).
• replace-matrix (method).
• replace-matrix (method).
• solve (method).
• submatrix (method).
• (setf submatrix) (method).
• (setf submatrix) (method).
• symmetric-matrix (class).
• symmetric-matrix-p (function).

Internals

• %initialize-symmetric-matrix-with-seq (function).
• %replace-symmetric-matrix-off-diagonal (function).
• %replace-symmetric-matrix-on-diagonal (function).
• %setf-symmetric-submatrix-off-diagonal (function).
• %setf-symmetric-submatrix-on-diagonal (function).
• initialize-matrix-contents (method).
• initialize-matrix-contents (method).
• initialize-matrix-contents (method).

---

5.1.1 Macros

Macro: dovector ((element vector &optional result) &body body) ¶

Iterate over vector returning result.

Package

linear-algebra.

Source

vector.lisp.

---

5.1.2 Ordinary functions

Function: add-array (array1 array2 scalar1 scalar2) ¶

Array binary addition.

Package

linear-algebra-kernel.

Source

binary-operations.lisp.

Function: add-vector (vector1 vector2 scalar1 scalar2) ¶

Vector binary addition.

Package

linear-algebra-kernel.

Source

binary-operations.lisp.

Function: column-vector (&rest numbers) ¶

Create a column vector from the numbers.

Package

linear-algebra.

Source

data-vector.lisp.

Function: column-vector-p (object) ¶

Return true if object is a column-vector, NIL otherwise.

Package

linear-algebra.

Source

data-vector.lisp.

Function: common-array-element-type (array1 array2) ¶

Return the array type common to both arrays.

Package

linear-algebra-kernel.

Source

utility.lisp.

Function: common-class-of (object1 object2) ¶

Return the common class of the 2 objects or default-class.

Package

linear-algebra-kernel.

Source

utility.lisp.

Function: complex-equal (complex1 complex2 &optional epsilon) ¶

Return true if both numbers are complex and equal.

Package

linear-algebra-kernel.

Source

utility.lisp.

Function: conjugate-gradient-solver (array vector &optional epsilon limit) ¶

Linear system solver using the conjugate gradient method.

Package

linear-algebra-kernel.

Source

conjugate-gradient.lisp.

Function: dense-matrix-p (object) ¶

Return true if object is a dense matrix.

Package

linear-algebra.

Source

dense-matrix.lisp.

Function: gauss-invert (array) ¶

Find A^-1 via Gauss algorithm with partial column pivot search.

Package

linear-algebra-kernel.

Source

gauss.lisp.

Function: gauss-solver (array vector) ¶

Gauss algorithm with column pivot search.

Package

linear-algebra-kernel.

Source

gauss.lisp.

Function: givens-rotation (f g) ¶

Return c,s,r defined from the Givens rotation.

Package

linear-algebra-kernel.

Source

rotation.lisp.

Function: hermitian-cholesky-decomposition (array) ¶

Factor A = LL^T.

Package

linear-algebra-kernel.

Source

cholesky.lisp.

Function: hermitian-cholesky-invert (array) ¶

Invert a positive definite matrices using the root-free Cholesky decomposition.

Package

linear-algebra-kernel.

Source

cholesky.lisp.

Function: hermitian-cholesky-solver (array vector) ¶

Linear system solver for positive definite matrices using the root-free Cholesky decomposition.

Package

linear-algebra-kernel.

Source

cholesky.lisp.

Function: hermitian-matrix-p (object) ¶

Return true if object is a hermitian-matrix, NIL otherwise.

Package

linear-algebra.

Source

hermitian-matrix.lisp.

Function: householder-reflection (alpha vector) ¶

Return Beta, Tau and the Householder vector.

Package

linear-algebra-kernel.

Source

rotation.lisp.

Function: identity-matrix-p (object) ¶

Return true if object is an identity-matrix.

Package

linear-algebra.

Source

identity-matrix.lisp.

Function: inner-product-vector (vector1 vector2 scalar) ¶

Return the vector inner product.

Package

linear-algebra-kernel.

Source

binary-operations.lisp.

Function: jacobi-rotation (x y z) ¶

Return a, b, cos(theta) and sin(theta) terms from the Jacobi rotation.

Package

linear-algebra-kernel.

Source

rotation.lisp.

Function: make-matrix (rows columns &key matrix-type element-type initial-element initial-contents) ¶

Return a new matrix instance.

Package

linear-algebra.

Source

matrix.lisp.

Function: make-vector (size &key vector-type element-type initial-element initial-contents) ¶

Create the data structure to represent a vector.

Package

linear-algebra.

Source

vector.lisp.

Function: matrix-validated-range (matrix start-row start-column &optional end-row end-column) ¶

Returns a validated range of rows and columns for the matrix.

Package

linear-algebra.

Source

matrix.lisp.

Function: matrixp (object) ¶

Return true if object is a matrix, NIL otherwise.

Package

linear-algebra.

Source

matrix.lisp.

Function: nadd-array (array1 array2 scalar1 scalar2) ¶

Destructive array binary addition.

Package

linear-algebra-kernel.

Source

binary-operations.lisp.

Function: nadd-vector (vector1 vector2 scalar1 scalar2) ¶

Destructive vector binary addition.

Package

linear-algebra-kernel.

Source

binary-operations.lisp.

Function: nsubtract-array (array1 array2 scalar1 scalar2) ¶

Destructive array binary subtraction.

Package

linear-algebra-kernel.

Source

binary-operations.lisp.

Function: nsubtract-vector (vector1 vector2 scalar1 scalar2) ¶

Destructive vector binary subtraction.

Package

linear-algebra-kernel.

Source

binary-operations.lisp.

Function: number-equal (number1 number2 &optional epsilon) ¶

Return true if the numbers are equal using the appropriate comparison.

Package

linear-algebra-kernel.

Source

utility.lisp.

Function: permutation-matrix-p (object) ¶

Return true if object is a permutation-matrix.

Package

linear-algebra.

Source

permutation-matrix.lisp.

Function: product-array-array (array1 array2 &optional scalar result) ¶

Return the scaled result of the product of 2 arrays.

Package

linear-algebra-kernel.

Source

binary-operations.lisp.

Function: product-array-vector (array vector &optional scalar result) ¶

Return the result of the array postmultiplied by the vector and scaled.

Package

linear-algebra-kernel.

Source

binary-operations.lisp.

Function: product-vector-array (vector array &optional scalar result) ¶

Return the result of the array premultiplied by the vector and scaled.

Package

linear-algebra-kernel.

Source

binary-operations.lisp.

Function: root-free-hermitian-cholesky-decomposition (array) ¶

Factor A = LDL^t.

Package

linear-algebra-kernel.

Source

cholesky.lisp.

Function: root-free-symmetric-cholesky-decomposition (array) ¶

Factor A = LDL^t.

Package

linear-algebra-kernel.

Source

cholesky.lisp.

Function: row-vector (&rest numbers) ¶

Create a row vector from the numbers.

Package

linear-algebra.

Source

data-vector.lisp.

Function: row-vector-p (object) ¶

Return true if object is a row-vector, NIL otherwise.

Package

linear-algebra.

Source

data-vector.lisp.

Function: specific-array-element-type (array &rest subscripts) ¶

Return the specific type of the element specified by subscripts.

Package

linear-algebra-kernel.

Source

utility.lisp.

Function: square-matrix-p (object) ¶

Return true if OBJECT is a square matrix.

Package

linear-algebra.

Source

square-matrix.lisp.

Function: subtract-array (array1 array2 scalar1 scalar2) ¶

Array binary subtraction.

Package

linear-algebra-kernel.

Source

binary-operations.lisp.

Function: subtract-vector (vector1 vector2 scalar1 scalar2) ¶

Vector binary subtraction.

Package

linear-algebra-kernel.

Source

binary-operations.lisp.

Function: sumsq-column (array column &key scale sumsq start end) ¶

Return the scaling parameter and the sum of the squares of the array column.

Package

linear-algebra-kernel.

Source

unary-operations.lisp.

Function: sumsq-row (array row &key scale sumsq start end) ¶

Return the scaling parameter and the sum of the squares of the array row.

Package

linear-algebra-kernel.

Source

unary-operations.lisp.

Function: sumsq2 (x y) ¶

Return the square root of |x|^2 + |y|^2.

Package

linear-algebra-kernel.

Source

unary-operations.lisp.

Function: sumsq3 (x y z) ¶

Return the square root of |x|^2 + |y|^2 + |z|^2.

Package

linear-algebra-kernel.

Source

unary-operations.lisp.

Function: symmetric-cholesky-decomposition (array) ¶

Factor A = LL^T.

Package

linear-algebra-kernel.

Source

cholesky.lisp.

Function: symmetric-cholesky-invert (array) ¶

Invert a positive definite matrices using the root-free Cholesky decomposition.

Package

linear-algebra-kernel.

Source

cholesky.lisp.

Function: symmetric-cholesky-solver (array vector) ¶

Linear system solver for positive definite matrices using the root-free Cholesky decomposition.

Package

linear-algebra-kernel.

Source

cholesky.lisp.

Function: symmetric-matrix-p (object) ¶

Return true if object is a symmetric-matrix, NIL otherwise.

Package

linear-algebra.

Source

symmetric-matrix.lisp.

Function: tridiagonal-solver (array vector) ¶

Linear equation solver for a tridiagonal matrix.

Package

linear-algebra-kernel.

Source

tridiagonal.lisp.

---

5.1.3 Generic functions

Generic Function: add (vector-or-matrix-1 vector-or-matrix-2 &key scalar1 scalar2) ¶

Vector or matrix binary addition.

Package

linear-algebra.

Source

fundamental-ops.lisp.

Methods

Method: add ((matrix1 dense-matrix) (matrix2 dense-matrix) &key scalar1 scalar2) ¶

Return the addition of the 2 matrices.

Source

dense-matrix.lisp.

Method: add :before ((matrix1 dense-matrix) (matrix2 dense-matrix) &key scalar1 scalar2) ¶

Audit the input data.

Source

dense-matrix.lisp.

Method: add ((vector1 row-vector) (vector2 row-vector) &key scalar1 scalar2) ¶

Return the addition of scalar1*vector1 with scalar2*vector2.

Source

data-vector.lisp.

Method: add ((vector1 column-vector) (vector2 column-vector) &key scalar1 scalar2) ¶

Return the addition of scalar1*vector1 with scalar2*vector2.

Source

data-vector.lisp.

Method: add :before ((vector1 data-vector) (vector2 data-vector) &key scalar1 scalar2) ¶

Verify that the dimensions are equal.

Source

data-vector.lisp.

Method: add ((array1 array) (array2 array) &key scalar1 scalar2) ¶

Return the addition of the 2 arrays.

Source

array.lisp.

Method: add ((vector1 vector) (vector2 vector) &key scalar1 scalar2) ¶

Return the addition of scalar1*vector1 with scalar2*vector2

Source

vector.lisp.

Method: add ((list1 list) (list2 list) &key scalar1 scalar2) ¶

Return the addition of scalar1*list1 with scalar2*list2

Source

list.lisp.

Generic Function: apply-rotation (vector1 vector2 cc ss) ¶

Return the plane rotations of vector1 and vector2 by cc and ss.

Package

linear-algebra.

Source

vector.lisp.

Methods

Method: apply-rotation ((vector1 data-vector) (vector2 data-vector) cc ss) ¶

Return the plane rotations of vector1 and vector2 by cc and ss.

Source

data-vector.lisp.

Method: apply-rotation :before ((vector1 data-vector) (vector2 data-vector) cc ss) ¶

Verify the input to apply-rotation.

Source

data-vector.lisp.

Generic Function: compatible-dimensions-p (operation vector-or-matrix-1 vector-or-matrix-2) ¶

Return true if the vector and matrix dimensions are compatible for the operation.

Package

linear-algebra-kernel.

Source

binary-operations.lisp.

Methods

Method: compatible-dimensions-p ((operation (eql :solve)) (matrix square-matrix) (vector column-vector)) ¶

Return true if the array dimensions are compatible for product.

Source

square-matrix.lisp.

Method: compatible-dimensions-p ((operation (eql :solve)) (matrix dense-matrix) (vector column-vector)) ¶

Return true if the array dimensions are compatible for product.

Source

dense-matrix.lisp.

Method: compatible-dimensions-p ((operation (eql :solve)) (array array) (vector vector)) ¶

Return true if the array dimensions are compatible for product.

Source

array.lisp.

Method: compatible-dimensions-p ((operation (eql :product)) (array1 array) (array2 array)) ¶

Return true if the array dimensions are compatible for product.

Method: compatible-dimensions-p ((operation (eql :add)) (array1 array) (array2 array)) ¶

Return true if the array dimensions are compatible for an addition.

Method: compatible-dimensions-p ((operation (eql :product)) (array array) (vector vector)) ¶

Return true if the array dimensions are compatible for product.

Method: compatible-dimensions-p ((operation (eql :product)) (vector vector) (array array)) ¶

Return true if the array dimensions are compatible for product.

Method: compatible-dimensions-p ((operation (eql :add)) (vector1 vector) (vector2 vector)) ¶

Return true if the vector dimensions are compatible for an addition.

Generic Function: copy-array (array) ¶

Return an element-wise copy of the original array.

Package

linear-algebra-kernel.

Source

utility.lisp.

Methods

Method: copy-array ((original array)) ¶

Return an element-wise copy of the original array.

Method: copy-array ((original vector)) ¶

Return an element-wise copy of the original vector.

Generic Function: copy-matrix (matrix) ¶

Return a copy of the matrix.

Package

linear-algebra.

Source

matrix.lisp.

Methods

Method: copy-matrix ((matrix dense-matrix)) ¶

Return a copy of the dense matrix.

Source

dense-matrix.lisp.

Method: copy-matrix ((matrix permutation-matrix)) ¶

Return a copy of the permutation matrix.

Source

permutation-matrix.lisp.

Method: copy-matrix ((matrix identity-matrix)) ¶

Return a copy of the matrix.

Source

identity-matrix.lisp.

Generic Function: copy-vector (vector) ¶

Return a copy of the vector.

Package

linear-algebra.

Source

vector.lisp.

Methods

Method: copy-vector ((vector data-vector)) ¶

Return a copy of the vector.

Source

data-vector.lisp.

Generic Function: invert (matrix) ¶

Return the invert of the matrix.

Package

linear-algebra.

Source

fundamental-ops.lisp.

Methods

Method: invert ((matrix symmetric-matrix)) ¶

Return the invert of the symmetric matrix.

Source

symmetric-matrix.lisp.

Method: invert ((matrix hermitian-matrix)) ¶

Return the invert of the hermitian matrix.

Source

hermitian-matrix.lisp.

Method: invert ((matrix square-matrix)) ¶

Return the invert of the square matrix.

Source

square-matrix.lisp.

Method: invert ((matrix dense-matrix)) ¶

Return the invert of the dense matrix.

Source

dense-matrix.lisp.

Method: invert ((array array)) ¶

Return the invert of the array.

Source

array.lisp.

Generic Function: left-permute (permutation vector-or-array) ¶

Permute the column vector or rows of the array.

Package

linear-algebra-kernel.

Source

permute.lisp.

Methods

Method: left-permute ((permutation vector) (data array)) ¶

Permute the rows of the array.

Method: left-permute ((permutation vector) (data vector)) ¶

Permute the column vector to create a row vector.

Generic Function: map-into-vector (result-vector function &rest vectors) ¶

Destructively modifies the result vector with the result of applying the function to each element of the vectors.

Package

linear-algebra.

Source

vector.lisp.

Methods

Method: map-into-vector ((result-vector data-vector) (function function) &rest vectors) ¶

Destructively modifies the result vector with the result of applying the function to each element of the vectors.

Source

data-vector.lisp.

Method: map-into-vector :before ((result-vector data-vector) (function function) &rest vectors) ¶

Verify the arguments to map-into-vector.

Source

data-vector.lisp.

Generic Function: map-vector (result-type function first-vector &rest more-vectors) ¶

Calls function on successive sets of vector objects.

Package

linear-algebra.

Source

vector.lisp.

Methods

Method: map-vector (result-type (function function) (first-vector data-vector) &rest more-vectors) ¶

Calls function on successive sets of data vectors.

Source

data-vector.lisp.

Method: map-vector :before (result-type (function function) (first-vector data-vector) &rest more-vectors) ¶

Verify the arguments to map-vector.

Source

data-vector.lisp.

Generic Function: matrix-column-dimension (matrix) ¶

Return the number of columns in MATRIX.

Package

linear-algebra.

Source

matrix.lisp.

Methods

Method: matrix-column-dimension ((matrix dense-matrix)) ¶

Return the number of columns in matrix.

Source

dense-matrix.lisp.

Method: matrix-column-dimension ((matrix permutation-matrix)) ¶

Return the number of columns in matrix.

Source

permutation-matrix.lisp.

Reader Method: matrix-column-dimension ((identity-matrix identity-matrix)) ¶

automatically generated reader method

Source

identity-matrix.lisp.

Target Slot

size.

Generic Function: matrix-dimensions (matrix) ¶

Return the number of rows and columns in MATRIX.

Package

linear-algebra.

Source

matrix.lisp.

Methods

Method: matrix-dimensions ((matrix dense-matrix)) ¶

Return the number of rows and columns in matrix.

Source

dense-matrix.lisp.

Method: matrix-dimensions ((matrix permutation-matrix)) ¶

Return the number of rows and columns in matrix.

Source

permutation-matrix.lisp.

Method: matrix-dimensions ((matrix identity-matrix)) ¶

Return the number of rows and columns in matrix.

Source

identity-matrix.lisp.

Generic Function: matrix-element-type (matrix) ¶

Return the element type of MATRIX.

Package

linear-algebra.

Source

matrix.lisp.

Methods

Method: matrix-element-type ((matrix dense-matrix)) ¶

Return the element type of the matrix.

Source

dense-matrix.lisp.

Method: matrix-element-type ((matrix permutation-matrix)) ¶

Element type of the permutation matrix.

Source

permutation-matrix.lisp.

Method: matrix-element-type ((matrix identity-matrix)) ¶

Return the element type of the identity matrix.

Source

identity-matrix.lisp.

Generic Function: matrix-in-bounds-p (matrix row column) ¶

Return true if ROW and COLUMN do not exceed the dimensions of MATRIX.

Package

linear-algebra.

Source

matrix.lisp.

Methods

Method: matrix-in-bounds-p ((matrix dense-matrix) (row integer) (column integer)) ¶

Return true if row and column do not exceed the dimensions of matrix.

Source

dense-matrix.lisp.

Method: matrix-in-bounds-p ((matrix permutation-matrix) (row integer) (column integer)) ¶

Return true if row and column do not exceed the dimensions of matrix.

Source

permutation-matrix.lisp.

Method: matrix-in-bounds-p ((matrix identity-matrix) (row integer) (column integer)) ¶

Return true if row and column do not exceed the dimensions of matrix.

Source

identity-matrix.lisp.

Generic Function: matrix-row-dimension (matrix) ¶

Return the number of rows in MATRIX.

Package

linear-algebra.

Source

matrix.lisp.

Methods

Method: matrix-row-dimension ((matrix dense-matrix)) ¶

Return the number of rows in matrix.

Source

dense-matrix.lisp.

Method: matrix-row-dimension ((matrix permutation-matrix)) ¶

Return the number of rows in matrix.

Source

permutation-matrix.lisp.

Reader Method: matrix-row-dimension ((identity-matrix identity-matrix)) ¶

automatically generated reader method

Source

identity-matrix.lisp.

Target Slot

size.

Generic Function: mref (matrix row column) ¶

Return the matrix element at ROW,COLUMN.

Package

linear-algebra.

Source

matrix.lisp.

Methods

Method: mref ((matrix dense-matrix) (row integer) (column integer)) ¶

Return the element of matrix at row,column.

Source

dense-matrix.lisp.

Method: mref ((matrix permutation-matrix) (row integer) (column integer)) ¶

Return 1 if a permutation and 0 otherwise.

Source

permutation-matrix.lisp.

Method: mref ((matrix identity-matrix) (row integer) (column integer)) ¶

Return the element of the matrix at row,column.

Source

identity-matrix.lisp.

Generic Function: (setf mref) (matrix row column) ¶

Set the element at row,column of matrix to data.

Package

linear-algebra.

Source

matrix.lisp.

Methods

Method: (setf mref) ((matrix symmetric-matrix) (row integer) (column integer)) ¶

Set the element of matrix at row,column.

Source

symmetric-matrix.lisp.

Method: (setf mref) ((matrix hermitian-matrix) (row integer) (column integer)) ¶

Set the element at row,column of matrix to data.

Source

hermitian-matrix.lisp.

Method: (setf mref) ((matrix dense-matrix) (row integer) (column integer)) ¶

Set the element of matrix at row,column.

Source

dense-matrix.lisp.

Method: (setf mref) ((matrix permutation-matrix) (row integer) (column integer)) ¶

Swap rows of the permutation matrix.

Source

permutation-matrix.lisp.

Generic Function: nadd (vector-or-matrix-1 vector-or-matrix-2 &key scalar1 scalar2) ¶

Destructive vector or matrix addition.

Package

linear-algebra.

Source

fundamental-ops.lisp.

Methods

Method: nadd ((matrix1 symmetric-matrix) (matrix2 symmetric-matrix) &key scalar1 scalar2) ¶

Source

symmetric-matrix.lisp.

Method: nadd ((matrix1 symmetric-matrix) (matrix2 dense-matrix) &key scalar1 scalar2) ¶

Generate an error if a non-symmetric matrix is destructively added to a symmetric matrix.

Source

symmetric-matrix.lisp.

Method: nadd ((matrix1 dense-matrix) (matrix2 dense-matrix) &key scalar1 scalar2) ¶

Return the addition of the 2 matrices.

Source

dense-matrix.lisp.

Method: nadd :before ((matrix1 dense-matrix) (matrix2 dense-matrix) &key scalar1 scalar2) ¶

Audit the input data.

Source

dense-matrix.lisp.

Method: nadd ((vector1 row-vector) (vector2 row-vector) &key scalar1 scalar2) ¶

Return the addition of scalar2*vector2 to scalar1*vector1.

Source

data-vector.lisp.

Method: nadd ((vector1 column-vector) (vector2 column-vector) &key scalar1 scalar2) ¶

Return the addition of scalar2*vector2 to scalar1*vector1.

Source

data-vector.lisp.

Method: nadd :before ((vector1 data-vector) (vector2 data-vector) &key scalar1 scalar2) ¶

Verify that the dimensions are equal.

Source

data-vector.lisp.

Method: nadd ((array1 array) (array2 array) &key scalar1 scalar2) ¶

Destructively add array2 to array1.

Source

array.lisp.

Method: nadd ((vector1 vector) (vector2 vector) &key scalar1 scalar2) ¶

Return the addition of scalar2*vector2 to scalar1*vector1.

Source

vector.lisp.

Method: nadd ((list1 list) (list2 list) &key scalar1 scalar2) ¶

Return the addition of scalar2*list2 to scalar1*list1.

Source

list.lisp.

Generic Function: napply-rotation (vector1 vector2 cc ss) ¶

Return the plane rotations of vector1 and vector2 by cc and ss.

Package

linear-algebra.

Source

vector.lisp.

Methods

Method: napply-rotation ((vector1 data-vector) (vector2 data-vector) cc ss) ¶

Return the plane rotations of vector1 and vector2 by cc and ss.

Source

data-vector.lisp.

Method: napply-rotation :before ((vector1 data-vector) (vector2 data-vector) cc ss) ¶

Verify the input to napply-rotation.

Source

data-vector.lisp.

Generic Function: ninvert (matrix) ¶

Return the invert of the matrix with in-place decomposition.

Package

linear-algebra.

Source

fundamental-ops.lisp.

Methods

Method: ninvert ((matrix symmetric-matrix)) ¶

Return the invert of the symmetric matrix.

Source

symmetric-matrix.lisp.

Method: ninvert ((matrix hermitian-matrix)) ¶

Return the invert of the hermitian matrix.

Source

hermitian-matrix.lisp.

Method: ninvert ((matrix square-matrix)) ¶

Return the invert of the square matrix.

Source

square-matrix.lisp.

Method: ninvert ((matrix dense-matrix)) ¶

Return the invert of the dense matrix.

Source

dense-matrix.lisp.

Method: ninvert ((array array)) ¶

Return the invert of the array.

Source

array.lisp.

Generic Function: norm (vector-or-matrix &optional measure) ¶

Return the norm according to measure.

Package

linear-algebra.

Source

fundamental-ops.lisp.

Methods

Method: norm ((matrix dense-matrix) &optional measure) ¶

Return the norm of the matrix.

Source

dense-matrix.lisp.

Method: norm ((vector data-vector) &optional measure) ¶

Return the p-norm of the vector.

Source

data-vector.lisp.

Method: norm ((data array) &optional measure) ¶

Return the norm of the array.

Source

array.lisp.

Method: norm ((data vector) &optional measure) ¶

Source

vector.lisp.

Method: norm ((data list) &optional measure) ¶

Source

list.lisp.

Generic Function: norm-array (data measure) ¶

Return the norm of the array according to the measure.

Package

linear-algebra-kernel.

Source

unary-operations.lisp.

Methods

Method: norm-array ((data array) (measure (eql :infinity))) ¶

Return the infinity norm of the array.

Method: norm-array ((data array) (measure (eql :frobenius))) ¶

Return the Frobenius norm of the array.

Method: norm-array ((data array) (measure (eql :max))) ¶

Return the max norm of the array.

Method: norm-array ((data array) (measure (eql 1))) ¶

Return the 1 norm of the array.

Generic Function: norm-vector (data measure) ¶

Return the norm of the vector according to the measure.

Package

linear-algebra-kernel.

Source

unary-operations.lisp.

Methods

Method: norm-vector ((data vector) (measure (eql :infinity))) ¶

Return the infinity, or maximum, norm of vector.

Method: norm-vector ((data vector) (measure integer)) ¶

Return the p-norm of the vector.

Method: norm-vector ((data vector) (measure (eql 2))) ¶

Return the Euclidean norm of the vector.

Method: norm-vector ((data vector) (measure (eql 1))) ¶

Return the Taxicab norm of the list.

Generic Function: nscale (scalar vector-or-matrix) ¶

Destructively scale each element by the scalar.

Package

linear-algebra.

Source

fundamental-ops.lisp.

Methods

Method: nscale ((scalar number) (matrix dense-matrix)) ¶

Scale each element of the dense matrix.

Source

dense-matrix.lisp.

Method: nscale ((scalar number) (vector data-vector)) ¶

Return the vector destructively scaled by scalar.

Source

data-vector.lisp.

Method: nscale ((scalar number) (data array)) ¶

Scale each element of the array.

Source

array.lisp.

Method: nscale ((scalar number) (data vector)) ¶

Return the vector destructively scaled by scalar.

Source

vector.lisp.

Method: nscale ((scalar number) (data list)) ¶

Return the list destructively scaled by scalar.

Source

list.lisp.

Generic Function: nsolve (matrix vector) ¶

Return the solution to the system of equations in-place.

Package

linear-algebra.

Source

fundamental-ops.lisp.

Methods

Method: nsolve ((matrix symmetric-matrix) (vector column-vector)) ¶

Return the solution to the system of equations.

Source

symmetric-matrix.lisp.

Method: nsolve ((matrix hermitian-matrix) (vector column-vector)) ¶

Return the solution to the system of equations.

Source

hermitian-matrix.lisp.

Method: nsolve ((matrix dense-matrix) (vector column-vector)) ¶

Return the solution to the system of equations.

Source

dense-matrix.lisp.

Method: nsolve :before ((matrix dense-matrix) (vector column-vector)) ¶

Return the solution to the system of equations.

Source

dense-matrix.lisp.

Method: nsolve ((array array) (vector vector)) ¶

Return the solution to the system of equations.

Source

array.lisp.

Generic Function: nsubtract (vector-or-matrix-1 vector-or-matrix-2 &key scalar1 scalar2) ¶

Destructive vector or matrix subtraction.

Package

linear-algebra.

Source

fundamental-ops.lisp.

Methods

Method: nsubtract ((matrix1 symmetric-matrix) (matrix2 symmetric-matrix) &key scalar1 scalar2) ¶

Source

symmetric-matrix.lisp.

Method: nsubtract ((matrix1 symmetric-matrix) (matrix2 dense-matrix) &key scalar1 scalar2) ¶

Generate an error if a non-symmetric matrix is destructively subtracted to a symmetric matrix.

Source

symmetric-matrix.lisp.

Method: nsubtract ((matrix1 dense-matrix) (matrix2 dense-matrix) &key scalar1 scalar2) ¶

Return the addition of the 2 matrices.

Source

dense-matrix.lisp.

Method: nsubtract :before ((matrix1 dense-matrix) (matrix2 dense-matrix) &key scalar1 scalar2) ¶

Audit the input data.

Source

dense-matrix.lisp.

Method: nsubtract ((vector1 row-vector) (vector2 row-vector) &key scalar1 scalar2) ¶

Return the subraction of scalar2*vector2 from scalar1*vector1.

Source

data-vector.lisp.

Method: nsubtract ((vector1 column-vector) (vector2 column-vector) &key scalar1 scalar2) ¶

Return the subraction of scalar2*vector2 from scalar1*vector1.

Source

data-vector.lisp.

Method: nsubtract :before ((vector1 data-vector) (vector2 data-vector) &key scalar1 scalar2) ¶

Verify that the dimensions are equal.

Source

data-vector.lisp.

Method: nsubtract ((array1 array) (array2 array) &key scalar1 scalar2) ¶

Destructively subtract array2 from array1.

Source

array.lisp.

Method: nsubtract ((vector1 vector) (vector2 vector) &key scalar1 scalar2) ¶

Return the subraction of scalar2*vector2 from scalar1*vector1.

Source

vector.lisp.

Method: nsubtract ((list1 list) (list2 list) &key scalar1 scalar2) ¶

Return the subraction of scalar2*list2 from scalar1*list1.

Source

list.lisp.

Generic Function: ntranspose (vector-or-matrix) ¶

Destructively transpose the vector or matrix.

Package

linear-algebra.

Source

fundamental-ops.lisp.

Methods

Method: ntranspose ((matrix hermitian-matrix)) ¶

The destructive transpose of a Hermitian matrix is itself.

Source

hermitian-matrix.lisp.

Method: ntranspose ((matrix dense-matrix)) ¶

Replace the contents of the dense matrix with the transpose.

Source

dense-matrix.lisp.

Method: ntranspose ((vector row-vector)) ¶

Return a column vector destructively.

Source

data-vector.lisp.

Method: ntranspose ((vector column-vector)) ¶

Return a row vector destructively.

Source

data-vector.lisp.

Method: ntranspose ((data array)) ¶

Replace the contents of the array with the transpose.

Source

array.lisp.

Method: ntranspose ((data vector)) ¶

Return a row vector destructively.

Source

vector.lisp.

Method: ntranspose ((data list)) ¶

Return a row vector destructively.

Source

list.lisp.

Generic Function: permute (vector-or-matrix-1 vector-or-matrix-2) ¶

Permute the vector or matrix.

Package

linear-algebra.

Source

fundamental-ops.lisp.

Methods

Method: permute ((permutation permutation-matrix) (matrix hermitian-matrix)) ¶

Source

hermitian-matrix.lisp.

Method: permute ((matrix hermitian-matrix) (permutation permutation-matrix)) ¶

Source

hermitian-matrix.lisp.

Method: permute ((permutation permutation-matrix) (matrix dense-matrix)) ¶

Source

dense-matrix.lisp.

Method: permute ((matrix dense-matrix) (permutation permutation-matrix)) ¶

Source

dense-matrix.lisp.

Method: permute ((matrix permutation-matrix) (vector column-vector)) ¶

Return the permutation of the column vector.

Source

data-vector.lisp.

Method: permute :before ((matrix permutation-matrix) (vector column-vector)) ¶

Verify that the dimensions are compatible.

Source

data-vector.lisp.

Method: permute ((vector row-vector) (matrix permutation-matrix)) ¶

Return the permutation of the row vector.

Source

data-vector.lisp.

Method: permute :before ((vector row-vector) (matrix permutation-matrix)) ¶

Verify that the dimensions are compatible.

Source

data-vector.lisp.

Method: permute ((matrix permutation-matrix) (data array)) ¶

Source

array.lisp.

Method: permute ((data array) (matrix permutation-matrix)) ¶

Source

array.lisp.

Method: permute ((matrix permutation-matrix) (data vector)) ¶

Return the permutation of the list.

Source

vector.lisp.

Method: permute ((data vector) (matrix permutation-matrix)) ¶

Return the permutation of the list.

Source

vector.lisp.

Method: permute ((matrix permutation-matrix) (data list)) ¶

Return the permutation of the list.

Source

list.lisp.

Method: permute ((data list) (matrix permutation-matrix)) ¶

Return the permutation of the list.

Source

list.lisp.

Generic Function: product (vector-or-matrix-1 vector-or-matrix-2 &optional scalar) ¶

Return the vector-vector, matrix-vector or matrix-matrix product.

Package

linear-algebra.

Source

fundamental-ops.lisp.

Methods

Method: product ((matrix1 dense-matrix) (matrix2 dense-matrix) &optional scalar) ¶

Return the product of the dense matrices.

Source

dense-matrix.lisp.

Method: product :before ((matrix1 dense-matrix) (matrix2 dense-matrix) &optional scalar) ¶

Verify the input.

Source

dense-matrix.lisp.

Method: product ((matrix dense-matrix) (vector column-vector) &optional scalar) ¶

Return a column vector generated by the multiplication of the dense matrix with a column vector.

Source

dense-matrix.lisp.

Method: product :before ((matrix dense-matrix) (vector column-vector) &optional scalar) ¶

Verify the input.

Source

dense-matrix.lisp.

Method: product ((vector row-vector) (matrix dense-matrix) &optional scalar) ¶

Return a row vector generated by the pre-multiplication of a dense matrix by a row vector.

Source

dense-matrix.lisp.

Method: product :before ((vector row-vector) (matrix dense-matrix) &optional scalar) ¶

Verify the inputs.

Source

dense-matrix.lisp.

Method: product ((vector1 row-vector) (vector2 column-vector) &optional scalar) ¶

Return the dot product of vector1 and vector2.

Source

data-vector.lisp.

Method: product :before ((vector1 row-vector) (vector2 column-vector) &optional scalar) ¶

Verify that the dimensions are equal.

Source

data-vector.lisp.

Method: product ((array1 array) (array2 array) &optional scalar) ¶

Return the product of the arrays.

Source

array.lisp.

Method: product ((array array) (vector vector) &optional scalar) ¶

Return a vector generated by the multiplication of the array with a vector.

Source

array.lisp.

Method: product ((vector vector) (array array) &optional scalar) ¶

Return a vector generated by the pre-multiplication of a array by a vector.

Source

array.lisp.

Method: product ((vector1 vector) (vector2 vector) &optional scalar) ¶

Return the dot product of vector1 and vector2.

Source

vector.lisp.

Method: product ((list1 list) (list2 list) &optional scalar) ¶

Return the dot product of list1 and list2.

Source

list.lisp.

Generic Function: replace-matrix (matrix1 matrix2 &key start-row1 end-row1 start-column1 end-column1 start-row2 end-row2 start-column2 end-column2) ¶

Destructively replace elements of matrix1 with matrix2.

Package

linear-algebra.

Source

matrix.lisp.

Methods

Method: replace-matrix ((matrix1 symmetric-matrix) (matrix2 dense-matrix) &key start-row1 end-row1 start-column1 end-column1 start-row2 end-row2 start-column2 end-column2) ¶

Replace the elements of MATRIX1 with MATRIX2.

Source

symmetric-matrix.lisp.

Method: replace-matrix ((matrix1 symmetric-matrix) (matrix2 symmetric-matrix) &key start-row1 end-row1 start-column1 end-column1 start-row2 end-row2 start-column2 end-column2) ¶

Replace the elements of MATRIX1 with MATRIX2.

Source

symmetric-matrix.lisp.

Method: replace-matrix ((matrix1 hermitian-matrix) (matrix2 dense-matrix) &key start-row1 end-row1 start-column1 end-column1 start-row2 end-row2 start-column2 end-column2) ¶

Replace the elements of matrix1 with matrix2.

Source

hermitian-matrix.lisp.

Method: replace-matrix ((matrix1 hermitian-matrix) (matrix2 hermitian-matrix) &key start-row1 end-row1 start-column1 end-column1 start-row2 end-row2 start-column2 end-column2) ¶

Replace the elements of matrix1 with matrix2.

Source

hermitian-matrix.lisp.

Method: replace-matrix ((matrix1 dense-matrix) (matrix2 dense-matrix) &key start-row1 end-row1 start-column1 end-column1 start-row2 end-row2 start-column2 end-column2) ¶

Replace the elements of matrix1 with matrix2.

Source

dense-matrix.lisp.

Generic Function: replace-vector (vector1 vector2 &key start1 end1 start2 end2) ¶

Destructively replace the elements of vector1 with vector2.

Package

linear-algebra.

Source

vector.lisp.

Methods

Method: replace-vector ((vector1 data-vector) (vector2 data-vector) &key start1 end1 start2 end2) ¶

Destructively replace the elements of vector1 with vector2.

Source

data-vector.lisp.

Generic Function: right-permute (vector-or-array permutation) ¶

Permute the row vector or columns of the array.

Package

linear-algebra-kernel.

Source

permute.lisp.

Methods

Method: right-permute ((data array) (permutation vector)) ¶

Permute the columns of the array.

Method: right-permute ((data vector) (permutation vector)) ¶

Permute the row vector to create a column vector.

Generic Function: scale (scalar vector-or-matrix) ¶

Scale each element by the scalar.

Package

linear-algebra.

Source

fundamental-ops.lisp.

Methods

Method: scale ((scalar number) (matrix dense-matrix)) ¶

Scale each element of the dense matrix.

Source

dense-matrix.lisp.

Method: scale ((scalar number) (vector data-vector)) ¶

Return the vector scaled by scalar.

Source

data-vector.lisp.

Method: scale ((scalar number) (data array)) ¶

Scale each element of the array.

Source

array.lisp.

Method: scale ((scalar number) (data vector)) ¶

Return the vector scaled by scalar.

Source

vector.lisp.

Method: scale ((scalar number) (data list)) ¶

Return the list scaled by scalar.

Source

list.lisp.

Generic Function: scaled-binary-op (op scalar1 scalar2) ¶

Compile and return a scaled binary operation.

Package

linear-algebra-kernel.

Source

binary-operations.lisp.

Methods

Method: scaled-binary-op ((op (eql #<function ->)) (scalar1 number) (scalar2 number)) ¶

Return the scaled operation.

Method: scaled-binary-op ((op (eql #<function +>)) (scalar1 number) (scalar2 number)) ¶

Return the scaled operation.

Method: scaled-binary-op ((op (eql #<function ->)) (scalar1 (eql nil)) (scalar2 number)) ¶

Return the scaled operation.

Method: scaled-binary-op ((op (eql #<function +>)) (scalar1 (eql nil)) (scalar2 number)) ¶

Return the scaled operation.

Method: scaled-binary-op ((op (eql #<function ->)) (scalar1 number) (scalar2 (eql nil))) ¶

Return the scaled operation.

Method: scaled-binary-op ((op (eql #<function +>)) (scalar1 number) (scalar2 (eql nil))) ¶

Return the scaled operation.

Method: scaled-binary-op (op (scalar1 (eql nil)) (scalar2 (eql nil))) ¶

Return the operation.

Generic Function: solve (matrix vector) ¶

Return the solution to the system of equations.

Package

linear-algebra.

Source

fundamental-ops.lisp.

Methods

Method: solve ((matrix symmetric-matrix) (vector column-vector)) ¶

Return the solution to the system of equations.

Source

symmetric-matrix.lisp.

Method: solve ((matrix hermitian-matrix) (vector column-vector)) ¶

Return the solution to the system of equations.

Source

hermitian-matrix.lisp.

Method: solve ((matrix dense-matrix) (vector column-vector)) ¶

Return the solution to the system of equations.

Source

dense-matrix.lisp.

Method: solve :before ((matrix dense-matrix) (vector column-vector)) ¶

Return the solution to the system of equations.

Source

dense-matrix.lisp.

Method: solve ((array array) (vector vector)) ¶

Return the solution to the system of equations.

Source

array.lisp.

Generic Function: submatrix (matrix start-row start-column &key end-row end-column) ¶

Return a submatrix of the matrix.

Package

linear-algebra.

Source

matrix.lisp.

Methods

Method: submatrix ((matrix symmetric-matrix) (start-row integer) (start-column integer) &key end-row end-column) ¶

Return a matrix created from the submatrix of matrix.

Source

symmetric-matrix.lisp.

Method: submatrix ((matrix hermitian-matrix) (start-row integer) (start-column integer) &key end-row end-column) ¶

Return a matrix created from the submatrix of matrix.

Source

hermitian-matrix.lisp.

Method: submatrix ((matrix square-matrix) (start-row integer) (start-column integer) &key end-row end-column) ¶

Return a matrix created from the submatrix of matrix.

Source

square-matrix.lisp.

Method: submatrix ((matrix dense-matrix) (start-row integer) (start-column integer) &key end-row end-column) ¶

Return a dense matrix created from the submatrix of a matrix.

Source

dense-matrix.lisp.

Generic Function: (setf submatrix) (matrix start-row start-column &key end-row end-column) ¶

Set the submatrix of the matrix.

Package

linear-algebra.

Source

matrix.lisp.

Methods

Method: (setf submatrix) ((matrix symmetric-matrix) (start-row integer) (start-column integer) &key end-row end-column) ¶

Set a submatrix of MATRIX.

Source

symmetric-matrix.lisp.

Method: (setf submatrix) ((matrix symmetric-matrix) (start-row integer) (start-column integer) &key end-row end-column) ¶

Set a submatrix of the matrix.

Source

symmetric-matrix.lisp.

Method: (setf submatrix) ((matrix hermitian-matrix) (start-row integer) (start-column integer) &key end-row end-column) ¶

Set a submatrix of the matrix.

Source

hermitian-matrix.lisp.

Method: (setf submatrix) ((matrix hermitian-matrix) (start-row integer) (start-column integer) &key end-row end-column) ¶

Set a submatrix of the matrix.

Source

hermitian-matrix.lisp.

Method: (setf submatrix) ((matrix dense-matrix) (start-row integer) (start-column integer) &key end-row end-column) ¶

Set the submatrix of matrix.

Source

dense-matrix.lisp.

Generic Function: subtract (vector-or-matrix-1 vector-or-matrix-2 &key scalar1 scalar2) ¶

Vector or matrix binary subtraction.

Package

linear-algebra.

Source

fundamental-ops.lisp.

Methods

Method: subtract ((matrix1 dense-matrix) (matrix2 dense-matrix) &key scalar1 scalar2) ¶

Return the addition of the 2 matrices.

Source

dense-matrix.lisp.

Method: subtract :before ((matrix1 dense-matrix) (matrix2 dense-matrix) &key scalar1 scalar2) ¶

Audit the input data.

Source

dense-matrix.lisp.

Method: subtract ((vector1 row-vector) (vector2 row-vector) &key scalar1 scalar2) ¶

Return the subraction of scalar2*vector2 from scalar1*vector1.

Source

data-vector.lisp.

Method: subtract ((vector1 column-vector) (vector2 column-vector) &key scalar1 scalar2) ¶

Return the subraction of scalar2*vector2 from scalar1*vector1.

Source

data-vector.lisp.

Method: subtract :before ((vector1 data-vector) (vector2 data-vector) &key scalar1 scalar2) ¶

Verify that the dimensions are equal.

Source

data-vector.lisp.

Method: subtract ((array1 array) (array2 array) &key scalar1 scalar2) ¶

Return the subtraction of the 2 arrays.

Source

array.lisp.

Method: subtract ((vector1 vector) (vector2 vector) &key scalar1 scalar2) ¶

Return the subraction of scalar2*vector2 from scalar1*vector1.

Source

vector.lisp.

Method: subtract ((list1 list) (list2 list) &key scalar1 scalar2) ¶

Return the subraction of scalar2*list2 from scalar1*list1.

Source

list.lisp.

Generic Function: subvector (vector start &optional end) ¶

Return a new vector that is a subvector of the vector.

Package

linear-algebra.

Source

vector.lisp.

Methods

Method: subvector ((vector data-vector) start &optional end) ¶

Return a new data vector that is a subset of vector.

Source

data-vector.lisp.

Generic Function: (setf subvector) (vector start &optional end) ¶

Set the subvector of the vector.

Package

linear-algebra.

Source

vector.lisp.

Methods

Method: (setf subvector) ((vector data-vector) start &optional end) ¶

Set the subvector of the data vector.

Source

data-vector.lisp.

Generic Function: sump (vector-or-array p &optional scale sump) ¶

Return the scaling parameter and the sum of the P powers.

Package

linear-algebra-kernel.

Source

unary-operations.lisp.

Methods

Method: sump ((data array) p &optional scale sump) ¶

Return the scaling parameter and the sum of the P powers of the matrix.

Method: sump ((data vector) p &optional scale sump) ¶

Return the scaling parameter and the sum of the powers of p of the vector.

Method: sump ((data list) (p real) &optional scale sump) ¶

Return the scaling parameter and the sum of the powers of p of the data.

Generic Function: sumsq (vector-or-array &optional scale sumsq) ¶

Return the scaling parameter and the sum of the squares.

Package

linear-algebra-kernel.

Source

unary-operations.lisp.

Methods

Method: sumsq ((data array) &optional scale sumsq) ¶

Return the scaling parameter and the sum of the squares of the array.

Method: sumsq ((data vector) &optional scale sumsq) ¶

Return the scaling parameter and the sum of the squares of the vector.

Method: sumsq ((data list) &optional scale sumsq) ¶

Return the scaling parameter and the sum of the squares of the list.

Generic Function: transpose (vector-or-matrix) ¶

Transpose the vector or matrix.

Package

linear-algebra.

Source

fundamental-ops.lisp.

Methods

Method: transpose ((matrix hermitian-matrix)) ¶

The transpose of a Hermitian matrix is itself.

Source

hermitian-matrix.lisp.

Method: transpose ((matrix dense-matrix)) ¶

Return the transpose of the matrix.

Source

dense-matrix.lisp.

Method: transpose ((vector row-vector)) ¶

Return a column vector.

Source

data-vector.lisp.

Method: transpose ((vector column-vector)) ¶

Return a row vector.

Source

data-vector.lisp.

Method: transpose ((data array)) ¶

Return the transpose of the array.

Source

array.lisp.

Method: transpose ((data vector)) ¶

Return a row vector.

Source

vector.lisp.

Method: transpose ((data list)) ¶

Return a row vector.

Source

list.lisp.

Method: transpose ((matrix permutation-matrix)) ¶

Transpose the permutation matrix.

Source

permutation-matrix.lisp.

Generic Function: vector-element-type (vector) ¶

Return the element type of vector.

Package

linear-algebra.

Source

vector.lisp.

Methods

Method: vector-element-type ((vector data-vector)) ¶

Return the element type of vector.

Source

data-vector.lisp.

Generic Function: vector-in-bounds-p (vector index) ¶

Return true if index does not exceed the dimensions of vector.

Package

linear-algebra.

Source

vector.lisp.

Methods

Method: vector-in-bounds-p ((vector data-vector) (index integer)) ¶

Return true if index does not exceed the dimensions of vector.

Source

data-vector.lisp.

Generic Function: vector-length (vector) ¶

Return the length of the vector.

Package

linear-algebra.

Source

vector.lisp.

Methods

Method: vector-length ((vector data-vector)) ¶

Return the length of the vector.

Source

data-vector.lisp.

Generic Function: vref (vector index) ¶

Return the element of vector at index.

Package

linear-algebra.

Source

vector.lisp.

Methods

Method: vref ((vector data-vector) (index integer)) ¶

Return the element of vector at index.

Source

data-vector.lisp.

Generic Function: (setf vref) (vector index) ¶

Set the element of vector at index to data.

Package

linear-algebra.

Source

vector.lisp.

Methods

Method: (setf vref) ((vector data-vector) (index integer)) ¶

Set the element of vector at index to data.

Source

data-vector.lisp.

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