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complib/chgeqz(3) -- w(i) B ) = 0 If JOB='S', then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both u
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CHGEQZ implements a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation A are then ALPHA(1),...,ALPHA(N), and of B are BETA(1),...,BETA(N). If JOB='S' and COMPQ and COMPZ are 'V' or 'I', then the unitary transformations used to reduce (A,B) are accumulated into the arrays Q and Z s.t.: Q(in) A(in) Z(in)* = Q(out) A(out) Z(out)* Q(in) B(in) Z(in)* = Q(out) B(out) Z(out)* Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Genera... |
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complib/CHICO(3) -- CHICO factors a complex Hermitian matrix by elimination with symmetric pivoting and estimates the condition of
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On Entry A COMPLEX(LDA, N) the Hermitian matrix to be factored. Only the diagonal and upper triangle are used. LDA INTEGER the leading dimension of the array A . N INTEGER the order of the matrix A . Output A a block diagonal matrix and the multipliers which were used to obtain it. The factorization can be written A = U*D*CTRANS(U) where U is a product of permutation and unit upper triangular matrices , CTRANS(U) is the conjugate transpose of U , and D is block diagonal with 1 by 1 and 2 by 2 bl... |
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complib/CHIDI(3) -- CHIDI computes the determinant, inertia and inverse of a complex Hermitian matrix using the factors from CHIFA
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On Entry A COMPLEX(LDA,N) the output from CHIFA. LDA INTEGER the leading dimension of the array A. N INTEGER the order of the matrix A. KVPT INTEGER(N) the pivot vector from CHIFA. WORK COMPLEX(N) work vector. Contents destroyed. JOB INTEGER JOB has the decimal expansion ABC where if C .NE. 0, the inverse is computed, if B .NE. 0, the determinant is computed, if A .NE. 0, the inertia is computed. For example, JOB = 111 gives all three. On Return Variables not requested by JOB are not used. A con... |
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complib/CHIFA(3) -- CHIFA factors a complex Hermitian matrix by elimination with symmetric pivoting. To solve A*X = B , follow CHI
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On Entry A COMPLEX(LDA,N) the Hermitian matrix to be factored. Only the diagonal and upper triangle are used. LDA INTEGER the leading dimension of the array A . N INTEGER the order of the matrix A . On Return A a block diagonal matrix and the multipliers which were used to obtain it. The factorization can be written A = U*D*CTRANS(U) where U is a product of permutation and unit upper triangular matrices , CTRANS(U) is the conjugate transpose of U , and D is block diagonal with 1 by 1 and 2 by 2 ... |
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complib/CHISL(3) -- CHISL solves the complex Hermitian system A * X = B using the factors computed by CHIFA.
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On Entry A COMPLEX(LDA,N) the output from CHIFA. LDA INTEGER the leading dimension of the array A . N INTEGER the order of the matrix A . KVPT INTEGER(N) the pivot vector from CHIFA. B COMPLEX(N) the right hand side vector. On Return B the solution vector X . Error Condition A division by zero may occur if CHICO has set RCOND .EQ. 0.0 or CHIFA has set INFO .NE. 0 . To compute INVERSE(A) * C where C is a matrix with P columns CALL CHIFA(A,LDA,N,KVPT,INFO) IF (INFO .NE. 0) GO TO ... DO 10 J = 1, p... |
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ftn/chmod(3) -- change mode of a file
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This function changes the filesystem mode of file name. Mode can be any specification recognized by chmod(1). Name must be a single pathname. The normal returned value is 0. Any other value will be a system error number. |
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complib/CHPCO(3) -- CHPCO factors a complex Hermitian matrix stored in packed form by elimination with symmetric pivoting and esti
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On Entry AP COMPLEX (N*(N+1)/2) the packed form of a Hermitian matrix A . The columns of the upper triangle are stored sequentially in a one-dimensional array of length N*(N+1)/2 . See comments below for details. N INTEGER the order of the matrix A . Output AP a block diagonal matrix and the multipliers which were used to obtain it stored in packed form. The factorization can be written A = U*D*CTRANS(U) where U is a product of permutation and unit upper triangular matrices , CTRANS(U) is the co... |
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complib/chpcon(3) -- estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization
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CHPCON estimates the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). |
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complib/CHPDI(3) -- CHPDI computes the determinant, inertia and inverse of a complex Hermitian matrix using the factors from CHPFA
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On Entry AP COMPLEX (N*(N+1)/2) the output from CHPFA. N INTEGER the order of the matrix A. KVPT INTEGER(N) the pivot vector from CHPFA. WORK COMPLEX(N) work vector. Contents ignored. JOB INTEGER JOB has the decimal expansion ABC where if C .NE. 0, the inverse is computed, if B .NE. 0, the determinant is computed, if A .NE. 0, the inertia is computed. For example, JOB = 111 gives all three. On Return Variables not requested by JOB are not used. AP contains the upper triangle of the inverse of th... |
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complib/chpev(3) -- compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage
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CHPEV computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage. |
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complib/chpevd(3) -- compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
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CHPEVD computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm. The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal o... |
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complib/chpevx(3) -- compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
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CHPEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage. Eigenvalues/vectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. |
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complib/CHPFA(3) -- CHPFA factors a complex Hermitian matrix stored in packed form by elimination with symmetric pivoting. To solv
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On Entry AP COMPLEX (N*(N+1)/2) the packed form of a Hermitian matrix A . The columns of the upper triangle are stored sequentially in a one-dimensional array of length N*(N+1)/2 . See comments below for details. N INTEGER the order of the matrix A . Output AP A block diagonal matrix and the multipliers which were used to obtain it stored in packed form. The factorization can be written A = U*D*CTRANS(U) where U is a product of permutation and unit upper triangular matrices , CTRANS(U) is the co... |
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complib/chpgst(3) -- reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage
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CHPGST reduces a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage. If ITYPE = 1, the problem is A*x = lambda*B*x, and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L. B must have been previously factorized as U**H*U or L*L**H by CPPTRF.... |
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complib/chpgv(3) -- a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x
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CHPGV computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be Hermitian, stored in packed format, and B is also positive definite. |
