FunctionLAPACKdsyrkLibrary "FunctionLAPACKdsyrk"
subroutine part of LAPACK: Linear Algebra Package,
performs one of the symmetric rank k operations
.
C := alpha*A*A**T + beta*C, or C := alpha*A**T*A + beta*C,
.
where alpha and beta are scalars, C is an n by n symmetric matrix
and A is an n by k matrix in the first case and a k by n matrix
in the second case.
.
reference:
netlib.org
dsyrk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
performs one of the symmetric rank k operations
.
C := alpha*A*A**T + beta*C, or C := alpha*A**T*A + beta*C,
.
where alpha and beta are scalars, C is an n by n symmetric matrix
and A is an n by k matrix in the first case and a k by n matrix
in the second case.
.
Parameters:
uplo : string specifies whether the upper or lower triangular part of
the array C is to be referenced as follows:
UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced.
.
trans : string specifies the operation to be performed as follows:
TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C.
TRANS = 'T' or 't' C := alpha*A**T*A + beta*C.
TRANS = 'C' or 'c' C := alpha*A**T*A + beta*C.
.
n : int specifies the order of the matrix C. N must be at least zero.
k : int On entry with:
TRANS = 'N' or 'n', K specifies the number of columns of the matrix A.
TRANS = 'T' or 't' or 'C' or 'c', K specifies the number of rows of the matrix A.
K must be at least zero.
.
alpha : float scalar.
a : matrix matrix A.
lda : int specifies the first dimension of A.
beta : float scalar.
c : matrix matrix C, is overwritten by the lower triangular part of the updated matrix.
ldc : int specifies the first dimension of C
Returns: void, C is overwritten by the lower triangular part of the updated matrix.
Solution
FunctionLAPACKdtrsmLibrary "FunctionLAPACKdtrsm"
subroutine in the LAPACK:linear algebra package, used to solve one of the following matrix equations:
op( A )*X = alpha*B, or X*op( A ) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or
non-unit, upper or lower triangular matrix and op( A ) is one of
op( A ) = A or op( A ) = A**T.
The matrix X is overwritten on B.
reference:
netlib.org
dtrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
solves one of the matrix equations
op( A )*X = alpha*B, or X*op( A ) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or
non-unit, upper or lower triangular matrix and op( A ) is one of
op( A ) = A or op( A ) = A**T.
The matrix X is overwritten on B.
Parameters:
side : string , On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows:
SIDE = 'L' or 'l' op( A )*X = alpha*B.
SIDE = 'R' or 'r' X*op( A ) = alpha*B.
uplo : string , specifies whether the matrix A is an upper or lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
transa : string , specifies the form of op( A ) to be used in the matrix multiplication as follows:
TRANSA = 'N' or 'n' op( A ) = A.
TRANSA = 'T' or 't' op( A ) = A**T.
TRANSA = 'C' or 'c' op( A ) = A**T.
diag : string , specifies whether or not A is unit triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit triangular.
m : int , the number of rows of B. M must be at least zero.
n : int , the number of columns of B. N must be at least zero.
alpha : float , specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.
a : matrix, Triangular matrix.
lda : int , specifies the first dimension of A.
b : matrix, right-hand side matrix B, and on exit is overwritten by the solution matrix X.
ldb : int , specifies the first dimension of B.
Returns: void, modifies matrix b.
usage:
dtrsm ('L', 'U', 'N', 'N', 5, 3, 1.0, a, 7, b, 6)
FunctionMatrixSolveLibrary "FunctionMatrixSolve"
Matrix Equation solution for Ax = B, finds the value of x.
solve(A, B) Solves Matrix Equation for Ax = B, finds value for x.
Parameters:
A : matrix, Square matrix with data values.
B : matrix, One column matrix with data values.
Returns: matrix with X, x = A^-1 b, assuming A is square and has full rank
introcs.cs.princeton.edu
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