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complib/zlaesy(3) -- compute the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the mat
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ZLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value. RT1 is the eigenvalue of larger absolute value, and RT2 of smaller absolute value. If the eigenvectors are computed, then on return ( CS1, SN1 ) is the unit eigenvector for RT1, hence [ CS1 SN1 ] . [ A B ] . [ CS1 -SN1 ] = [ RT1 0 ] [ -SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ]... |
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complib/zlaev2(3) -- compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]
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ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]. On return, RT1 is the eigenvalue of larger absolute value, RT2 is the eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right eigenvector for RT1, giving the decomposition [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ] [- SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ]. |
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complib/zlags2(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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ZLAGS2 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/zlagtm(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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ZLAGTM performs a matrix-vector product of the form |
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complib/zlahef(3) -- using the Bunch-Kaufman diagonal pivoting method
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ZLAHEF 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/zlahqr(3) -- i an auxiliary routine called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by
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ZLAHQR is an auxiliary routine called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by ZHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI. |
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complib/zlahrd(3) -- matrix A so that elements below the k-th subdiagonal are zero
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ZLAHRD 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 ZGEHRD. |
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complib/zlaic1(3) -- applie one step of incremental condition estimation in its simplest version
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ZLAIC1 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 ZLAIC1 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/zlangb(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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ZLANGB 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/zlange(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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ZLANGE 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/zlangt(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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ZLANGT 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/zlanhb(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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ZLANHB 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/zlanhe(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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ZLANHE 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/zlanhp(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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ZLANHP 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/zlanhs(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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ZLANHS 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. |
