vectors clabrd clabrd (3p) - reduce the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form by a unitary transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A clacgv clacgv (3p) - conjugate a complex vector of length N clacon clacon (3p) - estimate the 1-norm of a square, complex matrix A clacpy clacpy (3p) - copie all or part of a two-dimensional matrix A to another matrix B clacrm clacrm (3p) - perform a very simple matrix-matrix multiplication clacrt clacrt (3p) - applie a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex cladiv cladiv (3p) - := X / Y, where X and Y are complex claed0 claed0 (3p) - the divide and conquer method, CLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix claed7 claed7 (3p) - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix claed8 claed8 (3p) - merge the two sets of eigenvalues together into a single sorted set claein claein (3p) - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H claesy claesy (3p) - compute 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 claev2 claev2 (3p) - compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ] clags2 clags2 (3p) - 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 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 ) where U = ( CSU SNU ), V = ( CSV SNV ), clahef clahef (3p) - compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method clahqr clahqr (3p) - i 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 clahrd clahrd (3p) - reduce 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 claic1 claic1 (3p) - applie one step of incremental condition estimation in its simplest version clangb clangb (3p) - 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 clange clange (3p) - return 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 clangt clangt (3p) - return 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 clanhb clanhb (3p) - 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 hermitian band matrix A, with k super-diagonals clanhe clanhe (3p) - return 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 clanhp clanhp (3p) - return 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 clanhs clanhs (3p) - 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 clanht clanht (3p) - return 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 clansb clansb (3p) - 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 clansp clansp (3p) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form clansy clansy (3p) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A clantb clantb (3p) - 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 clantp clantp (3p) - 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 clantr clantr (3p) - 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 clapll clapll (3p) - two column vectors X and Y, let A = ( X Y ) clapmt clapmt (3p) - 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 claqgb claqgb (3p) - 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 claqge claqge (3p) - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C claqhb claqhb (3p) - equilibrate a symmetric band matrix A using the scaling factors in the vector S claqhe claqhe (3p) - equilibrate a Hermitian matrix A using the scaling factors in the vector S claqhp claqhp (3p) - equilibrate a Hermitian matrix A using the scaling factors in the vector S claqsb claqsb (3p) - equilibrate a symmetric band matrix A using the scaling factors in the vector S claqsp claqsp (3p) - equilibrate a symmetric matrix A using the scaling factors in the vector S claqsy claqsy (3p) - equilibrate a symmetric matrix A using the scaling factors in the vector S clar2v clar2v (3p) - applie a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices, clarf clarf (3p) - applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right clarfb clarfb (3p) - applie a complex block reflector H or its transpose H' to a complex M-by-N matrix C, from either the left or the right clarfg clarfg (3p) - generate a complex elementary reflector H of order n, such that H' * ( alpha ) = ( beta ), H' * H = I clarft clarft (3p) - form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors clarfx clarfx (3p) - applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right clargv clargv (3p) - generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y clarnv clarnv (3p) - return a vector of n random complex numbers from a uniform or normal distribution clartg clartg (3p) - generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ] clartv clartv (3p) - applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y clascl clascl (3p) - multiply the M by N complex matrix A by the real scalar CTO/CFROM claset claset (3p) - initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals clasr clasr (3p) - perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) where A is an m by n complex matrix and P is an orthogonal matrix, classq classq (3p) - return the values scl and ssq such that ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, claswp claswp (3p) - perform a series of row interchanges on the matrix A clasyf clasyf (3p) - compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method clatbs clatbs (3p) - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b, clatps clatps (3p) - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b, clatrd clatrd (3p) - reduce NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A clatrs clatrs (3p) - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b, clatzm clatzm (3p) - applie a Householder matrix generated by CTZRQF to a matrix clauu2 clauu2 (3p) - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A clauum clauum (3p) - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A cosqb cosqb (3p) - synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 * N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. cosqf cosqf (3p) - compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 * N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. cosqi cosqi (3p) - initialize the array xWSAVE, which is used in both xCOSQF and xCOSQB. costi costi (3p) - initialize the array xWSAVE, which is used in xCOST. cpbco cpbco (3p) - compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then xPBFA is slightly faster. It is typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. cpbcon cpbcon (3p) - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF cpbdi cpbdi (3p) - compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA. cpbequ cpbequ (3p) - compute row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm) cpbfa cpbfa (3p) - compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to xPBFA with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. cpbrfs cpbrfs (3p) - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution cpbsl cpbsl (3p) - section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA, and vectors b and x. cpbstf cpbstf (3p) - compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A cpbsv cpbsv (3p) - compute the solution to a complex system of linear equations A * X = B, cpbsvx cpbsvx (3p) - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B, cpbtf2 c