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complib/clags2(3) -- compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0
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CLAGS2 computes 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then ( -CONJG(SNU) CSU ) ( -CONJG(SNV) CSV ) Q = ( CSQ SNQ ) ( -CONJG(SNQ) CSQ ) Z' denotes the conjugate transpose of Z. The rows of the transformed A and B are parallel. Moreover, if the input 2-by-2 matrix A is not zero, then the transformed (1,1) entry of A is not zero. If the input matrices A and B are both not zero, then the transformed (2,2) element of B is not zero, except when the first rows of input A and B are... |
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complib/clagtm(3) -- perform a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of o
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CLAGTM performs a matrix-vector product of the form |
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complib/clahef(3) -- using the Bunch-Kaufman diagonal pivoting method
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CLAHEF computes a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method. The partial factorization has the form: A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: ( 0 U22 ) ( 0 D ) ( U12' U22' ) A = ( L11 0 ) ( D 0 ) ( L11' L21' ) if UPLO = 'L' ( L21 I ) ( 0 A22 ) ( 0 I ) where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. Note that U' denotes the conjugate trans... |
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complib/clahqr(3) -- i an auxiliary routine called by CHSEQR to update the eigenvalues and Schur decomposition already computed by
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CLAHQR is an auxiliary routine called by CHSEQR to update the eigenvalues and Schur decomposition already computed by CHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI. |
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complib/clahrd(3) -- matrix A so that elements below the k-th subdiagonal are zero
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CLAHRD reduces the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero. The reduction is performed by a unitary similarity transformation Q' * A * Q. The routine returns the matrices V and T which determine Q as a block reflector I - V*T*V', and also the matrix Y = A * V * T. This is an auxiliary routine called by CGEHRD. |
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complib/claic1(3) -- applie one step of incremental condition estimation in its simplest version
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CLAIC1 applies one step of incremental condition estimation in its simplest version: Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j lower triangular matrix L, such that twonorm(L*x) = sest Then CLAIC1 computes sestpr, s, c such that the vector [ s*x ] xhat = [ c ] is an approximate singular vector of [ L 0 ] Lhat = [ w' gamma ] in the sense that twonorm(Lhat*xhat) = sestpr. Depending on JOB, an estimate for the largest or smallest singular value is computed. Note that [s ... |
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complib/clangb(3) -- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absol
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CLANGB returns 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. |
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complib/clange(3) -- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absol
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CLANGE returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A. |
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complib/clangt(3) -- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absol
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CLANGT returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A. |
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complib/clanhb(3) -- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absol
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CLANHB returns 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 hermitian band matrix A, with k super-diagonals. |
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complib/clanhe(3) -- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absol
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CLANHE returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A. |
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complib/clanhp(3) -- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absol
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CLANHP returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form. |
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complib/clanhs(3) -- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absol
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CLANHS returns 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. |
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complib/clanht(3) -- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absol
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CLANHT returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix A. |
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complib/clansb(3) -- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absol
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CLANSB returns 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. |
