- slaed0
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compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
- slaed1
-
compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
- slaed2
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merge the two sets of eigenvalues together into a single sorted set
- slaed3
-
find the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K
- slaed4
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subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
- slaed5
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subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO * Z * transpose(Z)
- slaed6
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compute the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true
- slaed7
-
compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
- slaed8
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merge the two sets of eigenvalues together into a single sorted set
- slaed9
-
find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP
- slaeda
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compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem
- slaein
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use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H
- slaev2
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compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]
- slaexc
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swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation
- slag2
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compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow
- slags2
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compute 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) The rows of the transformed A and B are parallel, where U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ ) Z' denotes the transpose of Z
- slagtf
-
factorize the matrix (T - lambda*I), where T is an n by n tridiagonal matrix and lambda is a scalar, as T - lambda*I = PLU,
- slagtm
-
perform a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1
- slagts
-
may be used to solve one of the systems of equations (T - lambda*I)*x = y or (T - lambda*I)'*x = y,
- slagv2
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compute the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular
- slahqr
-
i an auxiliary routine called by SHSEQR to update the eigenvalues and Schur decomposition already computed by SHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
- slahrd
-
reduce the first NB columns of a real general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero
- slaic1
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applie one step of incremental condition estimation in its simplest version
- slaln2
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solve a system of the form (ca A - w D ) X = s B or (ca A' - w D) X = s B with possible scaling ("s") and perturbation of A
- slals0
-
applie back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach
- slalsa
-
i an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form (The singular vectors are computed as products of simple orthorgonal matrices.)
- slalsd
-
use the singular value decomposition of A to solve the least squares problem of finding X to minimize the Euclidean norm of each column of A*X-B, where A is N-by-N upper bidiagonal, and X and B are N-by-NRHS
- slamch
-
determine single precision machine parameters
- slamrg
-
will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order
- slamsh
-
send multiple shifts through a small (single node) matrix to see how consecutive small subdiagonal elements are modified by subsequent shifts in an effort to maximize the number of bulges that can be sent through
- slangb
-
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
- slange
-
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A
- slangt
-
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A
- slanhs
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return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
- slansb
-
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals
- slansp
-
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form
- slanst
-
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A
- slansy
-
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A
- slantb
-
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
- slantp
-
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
- slantr
-
return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
- slanv2
-
compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form
- slapll
-
two column vectors X and Y, let A = ( X Y )
- slapmt
-
rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
- slapy2
-
return sqrt(x**2+y**2), taking care not to cause unnecessary overflow
- slapy3
-
return sqrt(x**2+y**2+z**2), taking care not to cause unnecessary overflow
- slaqgb
-
equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C
- slaqge
-
equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
- slaqp2
-
compute a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)
- slaqps
-
compute a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas-3