ggbal - ggbal: balance matrix

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subroutinecggbal(characterjob,integern,complex,dimension(lda,*)a,integerlda,complex,dimension(ldb,*)b,integerldb,integerilo,integerihi,real,dimension(*)lscale,real,dimension(*)rscale,real,dimension(*)work,integerinfo)CGGBALPurpose: CGGBAL balances a pair of general complex matrices (A,B). This involves, first, permuting A and B by similarity transformations to isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N elements on the diagonal; and second, applying a diagonal similarity transformation to rows and columns ILO to IHI to make the rows and columns as close in norm as possible. Both steps are optional. Balancing may reduce the 1-norm of the matrices, and improve the accuracy of the computed eigenvalues and/or eigenvectors in the generalized eigenvalue problem A*x = lambda*B*x. ParametersJOB JOB is CHARACTER*1 Specifies the operations to be performed on A and B: = 'N': none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0 and RSCALE(I) = 1.0 for i=1,...,N; = 'P': permute only; = 'S': scale only; = 'B': both permute and scale. N N is INTEGER The order of the matrices A and B. N >= 0. A A is COMPLEX array, dimension (LDA,N) On entry, the input matrix A. On exit, A is overwritten by the balanced matrix. If JOB = 'N', A is not referenced. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). B B is COMPLEX array, dimension (LDB,N) On entry, the input matrix B. On exit, B is overwritten by the balanced matrix. If JOB = 'N', B is not referenced. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). ILO ILO is INTEGER IHI IHI is INTEGER ILO and IHI are set to integers such that on exit A(i,j) = 0 and B(i,j) = 0 if i > j and j = 1,...,ILO-1 or i = IHI+1,...,N. If JOB = 'N' or 'S', ILO = 1 and IHI = N. LSCALE LSCALE is REAL array, dimension (N) Details of the permutations and scaling factors applied to the left side of A and B. If P(j) is the index of the row interchanged with row j, and D(j) is the scaling factor applied to row j, then LSCALE(j) = P(j) for J = 1,...,ILO-1 = D(j) for J = ILO,...,IHI = P(j) for J = IHI+1,...,N. The order in which the interchanges are made is N to IHI+1, then 1 to ILO-1. RSCALE RSCALE is REAL array, dimension (N) Details of the permutations and scaling factors applied to the right side of A and B. If P(j) is the index of the column interchanged with column j, and D(j) is the scaling factor applied to column j, then RSCALE(j) = P(j) for J = 1,...,ILO-1 = D(j) for J = ILO,...,IHI = P(j) for J = IHI+1,...,N. The order in which the interchanges are made is N to IHI+1, then 1 to ILO-1. WORK WORK is REAL array, dimension (lwork) lwork must be at least max(1,6*N) when JOB = 'S' or 'B', and at least 1 when JOB = 'N' or 'P'. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. FurtherDetails: See R.C. WARD, Balancing the generalized eigenvalue problem, SIAM J. Sci. Stat. Comp. 2 (1981), 141-152. subroutinedggbal(characterjob,integern,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(ldb,*)b,integerldb,integerilo,integerihi,doubleprecision,dimension(*)lscale,doubleprecision,dimension(*)rscale,doubleprecision,dimension(*)work,integerinfo)DGGBALPurpose: DGGBAL balances a pair of general real matrices (A,B). This involves, first, permuting A and B by similarity transformations to isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N elements on the diagonal; and second, applying a diagonal similarity transformation to rows and columns ILO to IHI to make the rows and columns as close in norm as possible. Both steps are optional. Balancing may reduce the 1-norm of the matrices, and improve the accuracy of the computed eigenvalues and/or eigenvectors in the generalized eigenvalue problem A*x = lambda*B*x. ParametersJOB JOB is CHARACTER*1 Specifies the operations to be performed on A and B: = 'N': none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0 and RSCALE(I) = 1.0 for i = 1,...,N. = 'P': permute only; = 'S': scale only; = 'B': both permute and scale. N N is INTEGER The order of the matrices A and B. N >= 0. A A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the input matrix A. On exit, A is overwritten by the balanced matrix. If JOB = 'N', A is not referenced. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). B B is DOUBLE PRECISION array, dimension (LDB,N) On entry, the input matrix B. On exit, B is overwritten by the balanced matrix. If JOB = 'N', B is not referenced. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). ILO ILO is INTEGER IHI IHI is INTEGER ILO and IHI are set to integers such that on exit A(i,j) = 0 and B(i,j) = 0 if i > j and j = 1,...,ILO-1 or i = IHI+1,...,N. If JOB = 'N' or 'S', ILO = 1 and IHI = N. LSCALE LSCALE is DOUBLE PRECISION array, dimension (N) Details of the permutations and scaling factors applied to the left side of A and B. If P(j) is the index of the row interchanged with row j, and D(j) is the scaling factor applied to row j, then LSCALE(j) = P(j) for J = 1,...,ILO-1 = D(j) for J = ILO,...,IHI = P(j) for J = IHI+1,...,N. The order in which the interchanges are made is N to IHI+1, then 1 to ILO-1. RSCALE RSCALE is DOUBLE PRECISION array, dimension (N) Details of the permutations and scaling factors applied to the right side of A and B. If P(j) is the index of the column interchanged with column j, and D(j) is the scaling factor applied to column j, then LSCALE(j) = P(j) for J = 1,...,ILO-1 = D(j) for J = ILO,...,IHI = P(j) for J = IHI+1,...,N. The order in which the interchanges are made is N to IHI+1, then 1 to ILO-1. WORK WORK is DOUBLE PRECISION array, dimension (lwork) lwork must be at least max(1,6*N) when JOB = 'S' or 'B', and at least 1 when JOB = 'N' or 'P'. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. FurtherDetails: See R.C. WARD, Balancing the generalized eigenvalue problem, SIAM J. Sci. Stat. Comp. 2 (1981), 141-152. subroutinesggbal(characterjob,integern,real,dimension(lda,*)a,integerlda,real,dimension(ldb,*)b,integerldb,integerilo,integerihi,real,dimension(*)lscale,real,dimension(*)rscale,real,dimension(*)work,integerinfo)SGGBALPurpose: SGGBAL balances a pair of general real matrices (A,B). This involves, first, permuting A and B by similarity transformations to isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N elements on the diagonal; and second, applying a diagonal similarity transformation to rows and columns ILO to IHI to make the rows and columns as close in norm as possible. Both steps are optional. Balancing may reduce the 1-norm of the matrices, and improve the accuracy of the computed eigenvalues and/or eigenvectors in the generalized eigenvalue problem A*x = lambda*B*x. ParametersJOB JOB is CHARACTER*1 Specifies the operations to be performed on A and B: = 'N': none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0 and RSCALE(I) = 1.0 for i = 1,...,N. = 'P': permute only; = 'S': scale only; = 'B': both permute and scale. N N is INTEGER The order of the matrices A and B. N >= 0. A A is REAL array, dimension (LDA,N) On entry, the input matrix A. On exit, A is overwritten by the balanced matrix. If JOB = 'N', A is not referenced. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). B B is REAL array, dimension (LDB,N) On entry, the input matrix B. On exit, B is overwritten by the balanced matrix. If JOB = 'N', B is not referenced. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). ILO ILO is INTEGER IHI IHI is INTEGER ILO and IHI are set to integers such that on exit A(i,j) = 0 and B(i,j) = 0 if i > j and j = 1,...,ILO-1 or i = IHI+1,...,N. If JOB = 'N' or 'S', ILO = 1 and IHI = N. LSCALE LSCALE is REAL array, dimension (N) Details of the permutations and scaling factors applied to the left side of A and B. If P(j) is the index of the row interchanged with row j, and D(j) is the scaling factor applied to row j, then LSCALE(j) = P(j) for J = 1,...,ILO-1 = D(j) for J = ILO,...,IHI = P(j) for J = IHI+1,...,N. The order in which the interchanges are made is N to IHI+1, then 1 to ILO-1. RSCALE RSCALE is REAL array, dimension (N) Details of the permutations and scaling factors applied to the right side of A and B. If P(j) is the index of the column interchanged with column j, and D(j) is the scaling factor applied to column j, then LSCALE(j) = P(j) for J = 1,...,ILO-1 = D(j) for J = ILO,...,IHI = P(j) for J = IHI+1,...,N. The order in which the interchanges are made is N to IHI+1, then 1 to ILO-1. WORK WORK is REAL array, dimension (lwork) lwork must be at least max(1,6*N) when JOB = 'S' or 'B', and at least 1 when JOB = 'N' or 'P'. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. FurtherDetails: See R.C. WARD, Balancing the generalized eigenvalue problem, SIAM J. Sci. Stat. Comp. 2 (1981), 141-152. subroutinezggbal(characterjob,integern,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(ldb,*)b,integerldb,integerilo,integerihi,doubleprecision,dimension(*)lscale,doubleprecision,dimension(*)rscale,doubleprecision,dimension(*)work,integerinfo)ZGGBALPurpose: ZGGBAL balances a pair of general complex matrices (A,B). This involves, first, permuting A and B by similarity transformations to isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N elements on the diagonal; and second, applying a diagonal similarity transformation to rows and columns ILO to IHI to make the rows and columns as close in norm as possible. Both steps are optional. Balancing may reduce the 1-norm of the matrices, and improve the accuracy of the computed eigenvalues and/or eigenvectors in the generalized eigenvalue problem A*x = lambda*B*x. ParametersJOB JOB is CHARACTER*1 Specifies the operations to be performed on A and B: = 'N': none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0 and RSCALE(I) = 1.0 for i=1,...,N; = 'P': permute only; = 'S': scale only; = 'B': both permute and scale. N N is INTEGER The order of the matrices A and B. N >= 0. A A is COMPLEX*16 array, dimension (LDA,N) On entry, the input matrix A. On exit, A is overwritten by the balanced matrix. If JOB = 'N', A is not referenced. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). B B is COMPLEX*16 array, dimension (LDB,N) On entry, the input matrix B. On exit, B is overwritten by the balanced matrix. If JOB = 'N', B is not referenced. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). ILO ILO is INTEGER IHI IHI is INTEGER ILO and IHI are set to integers such that on exit A(i,j) = 0 and B(i,j) = 0 if i > j and j = 1,...,ILO-1 or i = IHI+1,...,N. If JOB = 'N' or 'S', ILO = 1 and IHI = N. LSCALE LSCALE is DOUBLE PRECISION array, dimension (N) Details of the permutations and scaling factors applied to the left side of A and B. If P(j) is the index of the row interchanged with row j, and D(j) is the scaling factor applied to row j, then LSCALE(j) = P(j) for J = 1,...,ILO-1 = D(j) for J = ILO,...,IHI = P(j) for J = IHI+1,...,N. The order in which the interchanges are made is N to IHI+1, then 1 to ILO-1. RSCALE RSCALE is DOUBLE PRECISION array, dimension (N) Details of the permutations and scaling factors applied to the right side of A and B. If P(j) is the index of the column interchanged with column j, and D(j) is the scaling factor applied to column j, then RSCALE(j) = P(j) for J = 1,...,ILO-1 = D(j) for J = ILO,...,IHI = P(j) for J = IHI+1,...,N. The order in which the interchanges are made is N to IHI+1, then 1 to ILO-1. WORK WORK is DOUBLE PRECISION array, dimension (lwork) lwork must be at least max(1,6*N) when JOB = 'S' or 'B', and at least 1 when JOB = 'N' or 'P'. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. FurtherDetails: See R.C. WARD, Balancing the generalized eigenvalue problem, SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.

ggbal - ggbal: balance matrix

Functions subroutine cggbal (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info) CGGBAL subroutine dggbal (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info) DGGBAL subroutine sggbal (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info) SGGBAL subroutine zggbal (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info) ZGGBAL