dblggsylv - Man Page
Name
dblggsylv — Double Precision
— Double Precision routines for standard Sylvester equations.
Synopsis
Functions
subroutine dla_ggcsylv (facta, factb, transa, transb, sgn1, sgn2, m, n, a, lda, b, ldb, c, ldc, d, ldd, qa, ldqa, za, ldza, qb, ldqb, zb, ldzb, e, lde, f, ldf, scale, work, ldwork, info)
Frontend for the solution of Coupled Generalized Sylvester Equations.
subroutine dla_ggcsylv_dual (facta, factb, transa, transb, sgn1, sgn2, m, n, a, lda, b, ldb, c, ldc, d, ldd, qa, ldqa, za, ldza, qb, ldqb, zb, ldzb, e, lde, f, ldf, scale, work, ldwork, info)
Frontend for the solution of the dual Coupled Generalized Sylvester Equations.
subroutine dla_ggsylv (facta, factb, transa, transb, sgn, m, n, a, lda, b, ldb, c, ldc, d, ldd, qa, ldqa, za, ldza, qb, ldqb, zb, ldzb, x, ldx, scale, work, ldwork, info)
Frontend for the solution of Generalized Sylvester Equations.
subroutine dla_ggcsylv_dual_refine (transa, transb, guess, sgn1, sgn2, m, n, a, lda, b, ldb, c, ldc, d, ldd, r, ldr, l, ldl, e, lde, f, ldf, as, ldas, bs, ldbs, cs, ldcs, ds, ldds, q, ldq, z, ldz, u, ldu, v, ldv, maxit, tau, convlog, work, ldwork, info)
Iterative Refinement for the dual Coupled Generalized Sylvester Equations.
subroutine dla_ggcsylv_refine (transa, transb, guess, sgn1, sgn2, m, n, a, lda, b, ldb, c, ldc, d, ldd, r, ldr, l, ldl, e, lde, f, ldf, as, ldas, bs, ldbs, cs, ldcs, ds, ldds, q, ldq, z, ldz, u, ldu, v, ldv, maxit, tau, convlog, work, ldwork, info)
Iterative Refinement for the Coupled Generalized Sylvester Equations.
subroutine dla_ggsylv_refine (transa, transb, guess, sgn, m, n, a, lda, b, ldb, c, ldc, d, ldd, x, ldx, y, ldy, as, ldas, bs, ldbs, cs, ldcs, ds, ldds, q, ldq, z, ldz, u, ldu, v, ldv, maxit, tau, convlog, work, ldwork, info)
Iterative Refinement for the Generalized Sylvester Equations.
Detailed Description
Double Precision routines for standard Sylvester equations.
This subsection contains the solvers for generalized Sylvester equations with general coefficient matrices in double precision arithmetic. The generalized Schur decompositions are computed in double precision with the help of LAPACK.
Function Documentation
subroutine dla_ggcsylv (character, dimension(1) facta, character, dimension(1) factb, character, dimension(1) transa, character, dimension(1) transb, double precision sgn1, double precision sgn2, integer m, integer n, double precision, dimension(lda,*) a, integer lda, double precision, dimension(ldb, *) b, integer ldb, double precision, dimension(ldc, *) c, integer ldc, double precision, dimension(ldd,*) d, integer ldd, double precision, dimension(ldqa, *) qa, integer ldqa, double precision, dimension(ldza, *) za, integer ldza, double precision, dimension(ldqb, *) qb, integer ldqb, double precision, dimension(ldzb, *) zb, integer ldzb, double precision, dimension(lde, *) e, integer lde, double precision, dimension(ldf,*) f, integer ldf, double precision scale, double precision, dimension(*) work, integer ldwork, integer info)
Frontend for the solution of Coupled Generalized Sylvester Equations.
Purpose:
DLA_GGCSYLV solves a coupled generalized Sylvester equation of the following forms op1(A) * R + SGN1 * L * op2(B) = SCALE * E (1) op1(C) * R + SGN2 * L * op2(D) = SCALE * F where (A,C) is a M-by-M matrix pencil and (B,D) is a N-by-N matrix pencil. The right hand side (E,F) and the solution (R,L) are M-by-N matrix pencils. The pencils (A,C) and (B,D) can be either given as general unreduced matrices or in terms of their generalized Schur decomposition. If they are given as general matrices their generalized Schur decomposition will be computed.
- Parameters
FACTA
FACTA is CHARACTER Specifies how the matrix pencil (A,C) is given. == 'N': The matrix pencil (A,C) is given as a general matrices and its Schur decomposition A = QA*S*ZA**T, C = QA*R*ZA**T will be computed. == 'F': The matrix pencil (A,C) is already in generalized Schur form and S, R, QA, and ZA are given.
FACTB
FACTB is CHARACTER Specifies how the matrix pencil (B,D) is given. == 'N': The matrix pencil (B,D) is given as a general matrices and its Schur decomposition B = QB*U*ZB**T, D = QB*V*ZB**T will be computed. == 'F': The matrix pencil (B,D) is already in generalized Schur form and U, V, QB, and ZB are given.
TRANSA
TRANSA is CHARACTER Specifies the form of the system of equations with respect to A and C : == 'N': op1(A) = A == 'T': op1(A) = A**T
TRANSB
TRANSB is CHARACTER Specifies the form of the system of equations with respect to B and D: == 'N': op2(B) = B, == 'T': op2(B) = B**T
SGN1
SGN1 is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between in the first equation.
SGN2
SGN2 is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between in the second equation.
M
M is INTEGER The order of the matrices A and C. M >= 0.
N
N is INTEGER The order of the matrices B and D. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,M) If FACT == 'N', the matrix A is a general matrix and it is overwritten with the (quasi-) upper triangular factor S of the Schur decomposition of (A,C). If FACT == 'F', the matrix A contains its (quasi-) upper triangular matrix S of the Schur decomposition of (A,C).
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
B
B is DOUBLE PRECISION array, dimension (LDB,N) If FACT == 'N', the matrix B is a general matrix and it is overwritten with the (quasi-) upper triangular factor U of the Schur decomposition of (B,D). If FACT == 'F', the matrix B contains its (quasi-) upper triangular matrix U of the Schur decomposition of (B,D).
LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
C
C is DOUBLE PRECISION array, dimension (LDC,M) If FACT == 'N', the matrix C is a general matrix and it is overwritten with the upper triangular factor R of the Schur decomposition of (A,C). If FACT == 'F', the matrix C contains its upper triangular matrix R of the Schur decomposition of (A,C).
LDC
LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).
D
D is DOUBLE PRECISION array, dimension (LDD,N) If FACT == 'N', the matrix D is a general matrix and it is overwritten with the upper triangular factor V of the Schur decomposition of (B,D). If FACT == 'F', the matrix D contains its upper triangular matrix V of the Schur decomposition of (B,D).
LDD
LDD is INTEGER The leading dimension of the array D. LDD >= max(1,N).
QA
QA is DOUBLE PRECISION array, dimension (LDQA,M) If FACT == 'N', the matrix QA is an empty M-by-M matrix on input and contains the left Schur vectors of (A,C) on output. If FACT == 'F', the matrix QA contains the left Schur vectors of (A,C).
LDQA
LDQA is INTEGER The leading dimension of the array QA. LDQA >= max(1,M).
ZA
ZA is DOUBLE PRECISION array, dimension (LDZA,M) If FACT == 'N', the matrix ZA is an empty M-by-M matrix on input and contains the right Schur vectors of (A,C) on output. If FACT == 'F', the matrix ZA contains the right Schur vectors of (A,C).
LDZA
LDZA is INTEGER The leading dimension of the array ZA. LDZA >= max(1,M).
QB
QB is DOUBLE PRECISION array, dimension (LDQB,N) If FACT == 'N', the matrix QB is an empty N-by-N matrix on input and contains the left Schur vectors of (B,D) on output. If FACT == 'F', the matrix QB contains the left Schur vectors of (B,D).
LDQB
LDQB is INTEGER The leading dimension of the array QB. LDQB >= max(1,N).
ZB
ZB is DOUBLE PRECISION array, dimension (LDZB,N) If FACT == 'N', the matrix ZB is an empty N-by-N matrix on input and contains the right Schur vectors of (B,D) on output. If FACT == 'F', the matrix ZB contains the right Schur vectors of (B,D).
LDZB
LDZB is INTEGER The leading dimension of the array ZB. LDZB >= max(1,N).
E
E is DOUBLE PRECISION array, dimension (LDE,N) On input, the matrix E contains the right hand side E. On output, the matrix E contains the solution R.
LDE
LDE is INTEGER The leading dimension of the array E. LDE >= max(1,M).
F
F is DOUBLE PRECISION array, dimension (LDF,N) On input, the matrix F contains the right hand side F. On output, the matrix F contains the solution L.
LDF
LDF is INTEGER The leading dimension of the array F. LDF >= max(1,M).
SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LDWORK)) Workspace for the algorithm. The optmimal workspace is returned in LDWORK, if LDWORK == -1 on input. In this case no computations are performed.
LDWORK
LDWORK is INTEGER If LDWORK == -1 on input the subroutine will return the required size of the workspace in LDWORK on exit. No computations are performed and none of the arrays are referenced.
INFO
INFO is INTEGER == 0: successful exit = 1: DGGES failed = 2: DLA_SORT_GEV failed = 3: Inner solver failed < 0: if INFO = -i, the i-th argument had an illegal value
- See also
DLA_TGCSYLV_DAG
DLA_TGCSYLV_LEVEL3
DLA_TGCSYLV_L3_2S
DLA_TGCSYLV_L2_UNOPT
DLA_TGCSYLV_L2
DLA_TGCSYLV_L2_REORDER
DLA_TGCSYLV_L2_LOCAL_COPY_32
DLA_TGCSYLV_L2_LOCAL_COPY_64
DLA_TGCSYLV_L2_LOCAL_COPY_96
DLA_TGCSYLV_L2_LOCAL_COPY_128
DLA_TGCSYLV_L2_LOCAL_COPY
- Author
Martin Koehler, MPI Magdeburg
- Date
Januar 2023
Definition at line 310 of file dla_ggcsylv.f90.
subroutine dla_ggcsylv_dual (character, dimension(1) facta, character, dimension(1) factb, character, dimension(1) transa, character, dimension(1) transb, double precision sgn1, double precision sgn2, integer m, integer n, double precision, dimension(lda,*) a, integer lda, double precision, dimension(ldb, *) b, integer ldb, double precision, dimension(ldc, *) c, integer ldc, double precision, dimension(ldd,*) d, integer ldd, double precision, dimension(ldqa, *) qa, integer ldqa, double precision, dimension(ldza, *) za, integer ldza, double precision, dimension(ldqb, *) qb, integer ldqb, double precision, dimension(ldzb, *) zb, integer ldzb, double precision, dimension(lde, *) e, integer lde, double precision, dimension(ldf,*) f, integer ldf, double precision scale, double precision, dimension(*) work, integer ldwork, integer info)
Frontend for the solution of the dual Coupled Generalized Sylvester Equations.
Purpose:
DLA_GGCSYLV_DUAL_L3 solves a generalized coupled Sylvester equation of the following form op1(A)**T * R + op1(C)**T * L = SCALE * E (1) SGN1 * R * op2(B)**T + SGN2 * L * op2(D)** T = SCALE * F where A and C are M-by-M matrices and B and D are N-by-N matrices. The right hand sides E, F and the solutions R, L are M-by-N matrices. The equation (1) is the dual to the generalized coupled Sylvester equation op1(A) * R + SGN1 * L * op2(B) = SCALE * E (2) op1(C) * R + SGN2 * L * op2(D) = SCALE * F The equation (1) is the dual one to equation (2) with respect to the underlying linear system. Let Z be the matrix formed by rewriting (2) into its Kronecker form. This yields | kron(I, op1(A)) SGN1*kron(op2(B)**T, I) | | Vec R | | Vec E | Z X = | |*| | = | | | kron(I, op1(C)) SGN2*kron(op2(D)**T, I) | | Vec L | | Vec F | Regarding Z**T one obtains | kron(I, op1(A)**T ) kron(I, op1(C)**T) | | Vec R | | Vec E | Z**T X = | |*| | = | | | SGN1*kron(op2(B), I) SGN2*kron(op2(D), I) | | Vec L | | Vec F | which belongs to the Sylvester equation (1). For this reason the parameters TRANSA and TRANSB are expressed in terms of the Sylvester equation (2).
- Parameters
FACTA
FACTA is CHARACTER Specifies how the matrix pencil (A,C) is given. == 'N': The matrix pencil (A,C) is given as a general matrices and its Schur decomposition A = QA*S*ZA**T, C = QA*R*ZA**T will be computed. == 'F': The matrix pencil (A,C) is already in generalized Schur form and S, R, QA, and ZA are given.
FACTB
FACTB is CHARACTER Specifies how the matrix pencil (B,D) is given. == 'N': The matrix pencil (B,D) is given as a general matrices and its Schur decomposition B = QB*U*ZB**T, D = QB*V*ZB**T will be computed. == 'F': The matrix pencil (B,D) is already in generalized Schur form and U, V, QB, and ZB are given.
TRANSA
TRANSA is CHARACTER Specifies the form of the system of equations with respect to A and C : == 'N': op1(A) = A == 'T': op1(A) = A**T
TRANSB
TRANSB is CHARACTER Specifies the form of the system of equations with respect to B and D: == 'N': op2(B) = B, == 'T': op2(B) = B**T
SGN1
SGN1 is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between in the first equation.
SGN2
SGN2 is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between in the second equation.
M
M is INTEGER The order of the matrices A and C. M >= 0.
N
N is INTEGER The order of the matrices B and D. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,M) If FACT == 'N', the matrix A is a general matrix and it is overwritten with the (quasi-) upper triangular factor S of the Schur decomposition of (A,C). If FACT == 'F', the matrix A contains its (quasi-) upper triangular matrix S of the Schur decomposition of (A,C).
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
B
B is DOUBLE PRECISION array, dimension (LDB,N) If FACT == 'N', the matrix B is a general matrix and it is overwritten with the (quasi-) upper triangular factor U of the Schur decomposition of (B,D). If FACT == 'F', the matrix B contains its (quasi-) upper triangular matrix U of the Schur decomposition of (B,D).
LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
C
C is DOUBLE PRECISION array, dimension (LDC,M) If FACT == 'N', the matrix C is a general matrix and it is overwritten with the upper triangular factor R of the Schur decomposition of (A,C). If FACT == 'F', the matrix C contains its upper triangular matrix R of the Schur decomposition of (A,C).
LDC
LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).
D
D is DOUBLE PRECISION array, dimension (LDD,N) If FACT == 'N', the matrix D is a general matrix and it is overwritten with the upper triangular factor V of the Schur decomposition of (B,D). If FACT == 'F', the matrix D contains its upper triangular matrix V of the Schur decomposition of (B,D).
LDD
LDD is INTEGER The leading dimension of the array D. LDD >= max(1,N).
QA
QA is DOUBLE PRECISION array, dimension (LDQA,M) If FACT == 'N', the matrix QA is an empty M-by-M matrix on input and contains the left Schur vectors of (A,C) on output. If FACT == 'F', the matrix QA contains the left Schur vectors of (A,C).
LDQA
LDQA is INTEGER The leading dimension of the array QA. LDQA >= max(1,M).
ZA
ZA is DOUBLE PRECISION array, dimension (LDZA,M) If FACT == 'N', the matrix ZA is an empty M-by-M matrix on input and contains the right Schur vectors of (A,C) on output. If FACT == 'F', the matrix ZA contains the right Schur vectors of (A,C).
LDZA
LDZA is INTEGER The leading dimension of the array ZA. LDZA >= max(1,M).
QB
QB is DOUBLE PRECISION array, dimension (LDQB,N) If FACT == 'N', the matrix QB is an empty N-by-N matrix on input and contains the left Schur vectors of (B,D) on output. If FACT == 'F', the matrix QB contains the left Schur vectors of (B,D).
LDQB
LDQB is INTEGER The leading dimension of the array QB. LDQB >= max(1,N).
ZB
ZB is DOUBLE PRECISION array, dimension (LDZB,N) If FACT == 'N', the matrix ZB is an empty N-by-N matrix on input and contains the right Schur vectors of (B,D) on output. If FACT == 'F', the matrix ZB contains the right Schur vectors of (B,D).
LDZB
LDZB is INTEGER The leading dimension of the array ZB. LDZB >= max(1,N).
E
E is DOUBLE PRECISION array, dimension (LDE,N) On input, the matrix E contains the right hand side E. On output, the matrix E contains the solution R.
LDE
LDE is INTEGER The leading dimension of the array E. LDE >= max(1,M).
F
F is DOUBLE PRECISION array, dimension (LDF,N) On input, the matrix F contains the right hand side F. On output, the matrix F contains the solution L.
LDF
LDF is INTEGER The leading dimension of the array F. LDF >= max(1,M).
SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LDWORK)) Workspace for the algorithm. The optmimal workspace is returned in LDWORK, if LDWORK == -1 on input. In this case no computations are performed.
LDWORK
LDWORK is INTEGER If LDWORK == -1 on input, the subroutine will return the required size of the workspace in LDWORK on exit. No computations are performed and none of the arrays are referenced.
INFO
INFO is INTEGER == 0: successful exit = 1: DGGES failed = 2: DLA_SORT_GEV failed = 3: Inner solver failed < 0: if INFO = -i, the i-th argument had an illegal value
- See also
DLA_TGCSYLV_DUAL_DAG
DLA_TGCSYLV_DUAL_LEVEL3
DLA_TGCSYLV_DUAL_L3_2S
DLA_TGCSYLV_DUAL_L2
DLA_TGCSYLV_DUAL_L2_LOCAL_COPY_32
DLA_TGCSYLV_DUAL_L2_LOCAL_COPY_64
DLA_TGCSYLV_DUAL_L2_LOCAL_COPY_96
DLA_TGCSYLV_DUAL_L2_LOCAL_COPY_128
DLA_TGCSYLV_DUAL_L2_LOCAL_COPY
- Author
Martin Koehler, MPI Magdeburg
- Date
Januar 2023
Definition at line 326 of file dla_ggcsylv_dual.f90.
subroutine dla_ggcsylv_dual_refine (character, dimension(1) transa, character, dimension(1) transb, character, dimension(1) guess, double precision sgn1, double precision sgn2, integer m, integer n, double precision, dimension(lda, *) a, integer lda, double precision, dimension(ldb, *) b, integer ldb, double precision, dimension(ldc, *) c, integer ldc, double precision, dimension(ldd, *) d, integer ldd, double precision, dimension(ldr, *) r, integer ldr, double precision, dimension(ldl, *) l, integer ldl, double precision, dimension ( lde , * ) e, integer lde, double precision, dimension( ldf, *) f, integer ldf, double precision, dimension(ldas, *) as, integer ldas, double precision, dimension(ldbs,*) bs, integer ldbs, double precision, dimension(ldcs, *) cs, integer ldcs, double precision, dimension(ldds, *) ds, integer ldds, double precision, dimension(ldq, *) q, integer ldq, double precision, dimension(ldz, *) z, integer ldz, double precision, dimension(ldu, *) u, integer ldu, double precision, dimension(ldv, *) v, integer ldv, integer maxit, double precision tau, double precision, dimension(*) convlog, double precision, dimension(*) work, integer ldwork, integer info)
Iterative Refinement for the dual Coupled Generalized Sylvester Equations.
Purpose:
DLA_GGCSYLV_DUAL_REFINE solves a coupled generalized Sylvester equation of the following forms op1(A)**T * R + op1(C)**T * L = SCALE * E (1) SGN1 * R * op2(B)**T + SGN2 * L * op2(D)** T = SCALE * F where A and C are M-by-M matrices and B and D are N-by-N matrices. The right hand sides E, F and the solutions R, L are M-by-N matrices. The equation (1) is the dual to the generalized coupled Sylvester equation op1(A) * R + SGN1 * L * op2(B) = SCALE * E (2) op1(C) * R + SGN2 * L * op2(D) = SCALE * F The equation (1) is the dual one to equation (2) with respect to the underlying linear system. Let Z be the matrix formed by rewriting (2) into its Kronecker form. This yields | kron(I, op1(A)) SGN1*kron(op2(B)**T, I) | | Vec R | | Vec E | Z X = | |*| | = | | | kron(I, op1(C)) SGN2*kron(op2(D)**T, I) | | Vec L | | Vec F | Regarding Z**T one obtains | kron(I, op1(A)**T ) kron(I, op1(C)**T) | | Vec R | | Vec E | Z**T X = | |*| | = | | | SGN1*kron(op2(B), I) SGN2*kron(op2(D), I) | | Vec L | | Vec F | which belongs to the Sylvester equation (1). For this reason the parameters TRANSA and TRANSB are expressed in terms of the Sylvester equation (2). The pencils (A,C) and (B,D) need to be given in the original form as well as in their generalized Schur decomposition since both are required in the iterative refinement procedure.
- Parameters
TRANSA
TRANSA is CHARACTER Specifies the form of the system of equations with respect to A and C : == 'N': op1(A) = A == 'T': op1(A) = A**T
TRANSB
TRANSB is CHARACTER Specifies the form of the system of equations with respect to B and D: == 'N': op2(B) = B, == 'T': op2(B) = B**T
GUESS
GUESS is CHARACTER Specifies whether (R,L) contains an initial guess or nor not. = 'I': (R, L) contains an initial guess = 'N': No initial guess, (R,L) is set to zero at the begin of the iteration.
SGN1
SGN1 is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between in the first equation.
SGN2
SGN2 is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between in the second equation.
M
M is INTEGER The order of the matrices A and C. M >= 0.
N
N is INTEGER The order of the matrices B and D. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,M) The array A contains the original matrix A defining the equation.
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
B
B is DOUBLE PRECISION array, dimension (LDB,N) The array B contains the original matrix B defining the equation.
LDB
LDB is INTEGER The leading dimension of the array A. LDB >= max(1,N).
C
C is DOUBLE PRECISION array, dimension (LDC,M) The array C contains the original matrix C defining the equation.
LDC
LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).
D
D is DOUBLE PRECISION array, dimension (LDD,N) The array D contains the original matrix D defining the equation.
LDD
LDD is INTEGER The leading dimension of the array D. LDD >= max(1,N).
R
R is DOUBLE PRECISION array, dimension (LDR,N) On input, the array R contains the initial guess R0 for the first solution matrix. On output, the array R contains the refine solution matrix R.
LDR
LDR is INTEGER The leading dimension of the array R. LDR >= max(1,M).
L
L is DOUBLE PRECISION array, dimension (LDL,N) On input, the array L contains the initial guess for the second solution matrix. On output, the array L contains the solution L.
LDL
LDL is INTEGER The leading dimension of the array L. LDF >= max(1,M).
E
E is DOUBLE PRECISION array, dimension (LDE,N) On input, the array E contains the right hand side E.
LDE
LDE is INTEGER The leading dimension of the array E. LDE >= max(1,M).
F
F is DOUBLE PRECISION array, dimension (LDF,N) On input, the array F contains the right hand side F.
LDF
LDF is INTEGER The leading dimension of the array F. LDF >= max(1,M).
AS
AS is DOUBLE PRECISION array, dimension (LDAS,M) The array AS contains the generalized Schur decomposition of the A.
LDAS
LDAS is INTEGER The leading dimension of the array AS. LDAS >= max(1,M).
BS
BS is DOUBLE PRECISION array, dimension (LDBS,N) The array BS contains the generalized Schur decomposition of the B.
LDBS
LDBS is INTEGER The leading dimension of the array BS. LDBS >= max(1,N).
CS
CS is DOUBLE PRECISION array, dimension (LDCS,M) The array CS contains the generalized Schur decomposition of the C.
LDCS
LDCS is INTEGER The leading dimension of the array CS. LDCS >= max(1,M).
DS
DS is DOUBLE PRECISION array, dimension (LDDS,N) The array DS contains the generalized Schur decomposition of the D.
LDDS
LDDS is INTEGER The leading dimension of the array DS. LDDS >= max(1,N).
Q
Q is DOUBLE PRECISION array, dimension (LDQ,M) The array Q contains the left generalized Schur vectors for (A,C) as returned by DGGES.
LDQ
LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,M).
Z
Z is DOUBLE PRECISION array, dimension (LDZ,M) The array Z contains the right generalized Schur vectors for (A,C) as returned by DGGES.
LDZ
LDZ is INTEGER The leading dimension of the array Z. LDZ >= max(1,M).
U
U is DOUBLE PRECISION array, dimension (LDU,N) The array U contains the left generalized Schur vectors for (B,D) as returned by DGGES.
LDU
LDU is INTEGER The leading dimension of the array U. LDU >= max(1,N).
V
V is DOUBLE PRECISION array, dimension (LDV,N) The array V contains the right generalized Schur vectors for (B,D) as returned by DGGES.
LDV
LDV is INTEGER The leading dimension of the array V. LDV >= max(1,N).
MAXIT
MAXIT is INTEGER On input, MAXIT contains the maximum number of iteration that are performed, 2 <= MAXIT <= 100 On exit, MAXIT contains the number of iteration steps taken by the algorithm.
TAU
TAU is DOUBLE PRECISION On input, TAU contains the additional security factor for the stopping criterion, typical values are 0.1 On exit, TAU contains the last relative residual when the stopping criterion got valid.
CONVLOG
CONVLOG is DOUBLE PRECISION array, dimension (MAXIT) The CONVLOG array contains the convergence history of the iterative refinement. CONVLOG(I) contains the maximum relative residual of both equations before it is solved for the I-th time.
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LDWORK)) Workspace for the algorithm. The optmimal workspace is returned in LDWORK, if LDWORK == -1 on input. In this case no computations are performed.
LDWORK
LDWORK is INTEGER If LDWORK == -1 the subroutine will return the required size of the workspace in LDWORK on exit. No computations are performed and none of the arrays are referenced.
INFO
INFO is INTEGER == 0: Success > 0: Iteration failed in step INFO < 0: if INFO = -i, the i-th argument had an illegal value = -50: Some of the internal settings like NB,... are incorrect.
- See also
DLA_TGCSYLV_DUAL_DAG
DLA_TGCSYLV_DUAL_LEVEL3
DLA_TGCSYLV_DUAL_L3_2S
DLA_TGCSYLV_DUAL_L2
DLA_TGCSYLV_DUAL_L2_LOCAL_COPY_32
DLA_TGCSYLV_DUAL_L2_LOCAL_COPY_64
DLA_TGCSYLV_DUAL_L2_LOCAL_COPY_96
DLA_TGCSYLV_DUAL_L2_LOCAL_COPY_128
DLA_TGCSYLV_DUAL_L2_LOCAL_COPY
- Author
Martin Koehler, MPI Magdeburg
- Date
Januar 2023
Definition at line 399 of file dla_ggcsylv_dual_refine.f90.
subroutine dla_ggcsylv_refine (character, dimension(1) transa, character, dimension(1) transb, character, dimension(1) guess, double precision sgn1, double precision sgn2, integer m, integer n, double precision, dimension(lda, *) a, integer lda, double precision, dimension(ldb, *) b, integer ldb, double precision, dimension(ldc, *) c, integer ldc, double precision, dimension(ldd, *) d, integer ldd, double precision, dimension(ldr, *) r, integer ldr, double precision, dimension(ldl, *) l, integer ldl, double precision, dimension ( lde , * ) e, integer lde, double precision, dimension( ldf, *) f, integer ldf, double precision, dimension(ldas, *) as, integer ldas, double precision, dimension(ldbs,*) bs, integer ldbs, double precision, dimension(ldcs, *) cs, integer ldcs, double precision, dimension(ldds, *) ds, integer ldds, double precision, dimension(ldq, *) q, integer ldq, double precision, dimension(ldz, *) z, integer ldz, double precision, dimension(ldu, *) u, integer ldu, double precision, dimension(ldv, *) v, integer ldv, integer maxit, double precision tau, double precision, dimension(*) convlog, double precision, dimension(*) work, integer ldwork, integer info)
Iterative Refinement for the Coupled Generalized Sylvester Equations.
Purpose:
DLA_GGCSYLV_REFINE solves a coupled generalized Sylvester equation of the following forms op1(A) * R + SGN1 * L * op2(B) = E (1) op1(C) * R + SGN2 * L * op2(D) = F with iterative refinement, Thereby (A,C) is a M-by-M matrix pencil and (B,D) is a N-by-N matrix pencil. The right hand side (E,F) and the solution (R,L) are M-by-N matrices. The pencils (A,C) and (B,D) need to be given in the original form as well as in their generalized Schur decomposition since both are required in the iterative refinement procedure.
- Parameters
TRANSA
TRANSA is CHARACTER Specifies the form of the system of equations with respect to A and C : == 'N': op1(A) = A == 'T': op1(A) = A**T
TRANSB
TRANSB is CHARACTER Specifies the form of the system of equations with respect to B and D: == 'N': op2(B) = B, == 'T': op2(B) = B**T
GUESS
GUESS is CHARACTER Specifies whether (R,L) contains an initial guess or nor not. = 'I': (R, L) contains an initial guess = 'N': No initial guess, (R,L) is set to zero at the begin of the iteration.
SGN1
SGN1 is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between in the first equation.
SGN2
SGN2 is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between in the second equation.
M
M is INTEGER The order of the matrices A and C. M >= 0.
N
N is INTEGER The order of the matrices B and D. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,M) The array A contains the original matrix A defining the equation.
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
B
B is DOUBLE PRECISION array, dimension (LDB,N) The array B contains the original matrix B defining the equation.
LDB
LDB is INTEGER The leading dimension of the array A. LDB >= max(1,N).
C
C is DOUBLE PRECISION array, dimension (LDC,M) The array C contains the original matrix C defining the equation.
LDC
LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).
D
D is DOUBLE PRECISION array, dimension (LDD,N) The array D contains the original matrix D defining the equation.
LDD
LDD is INTEGER The leading dimension of the array D. LDD >= max(1,N).
R
R is DOUBLE PRECISION array, dimension (LDR,N) On input, the array R contains the initial guess R0 for the first solution matrix. On output, the array R contains the refine solution matrix R.
LDR
LDR is INTEGER The leading dimension of the array R. LDR >= max(1,M).
L
L is DOUBLE PRECISION array, dimension (LDL,N) On input, the array L contains the initial guess for the second solution matrix. On output, the array L contains the solution L.
LDL
LDL is INTEGER The leading dimension of the array L. LDF >= max(1,M).
E
E is DOUBLE PRECISION array, dimension (LDE,N) On input, the array E contains the right hand side E.
LDE
LDE is INTEGER The leading dimension of the array E. LDE >= max(1,M).
F
F is DOUBLE PRECISION array, dimension (LDF,N) On input, the array F contains the right hand side F.
LDF
LDF is INTEGER The leading dimension of the array F. LDF >= max(1,M).
AS
AS is DOUBLE PRECISION array, dimension (LDAS,M) The array AS contains the generalized Schur decomposition of the A.
LDAS
LDAS is INTEGER The leading dimension of the array AS. LDAS >= max(1,M).
BS
BS is DOUBLE PRECISION array, dimension (LDBS,N) The array BS contains the generalized Schur decomposition of the B.
LDBS
LDBS is INTEGER The leading dimension of the array BS. LDBS >= max(1,N).
CS
CS is DOUBLE PRECISION array, dimension (LDCS,M) The array CS contains the generalized Schur decomposition of the C.
LDCS
LDCS is INTEGER The leading dimension of the array CS. LDCS >= max(1,M).
DS
DS is DOUBLE PRECISION array, dimension (LDDS,N) The array DS contains the generalized Schur decomposition of the D.
LDDS
LDDS is INTEGER The leading dimension of the array DS. LDDS >= max(1,N).
Q
Q is DOUBLE PRECISION array, dimension (LDQ,M) The array Q contains the left generalized Schur vectors for (A,C) as returned by DGGES.
LDQ
LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,M).
Z
Z is DOUBLE PRECISION array, dimension (LDZ,M) The array Z contains the right generalized Schur vectors for (A,C) as returned by DGGES.
LDZ
LDZ is INTEGER The leading dimension of the array Z. LDZ >= max(1,M).
U
U is DOUBLE PRECISION array, dimension (LDU,N) The array U contains the left generalized Schur vectors for (B,D) as returned by DGGES.
LDU
LDU is INTEGER The leading dimension of the array U. LDU >= max(1,N).
V
V is DOUBLE PRECISION array, dimension (LDV,N) The array V contains the right generalized Schur vectors for (B,D) as returned by DGGES.
LDV
LDV is INTEGER The leading dimension of the array V. LDV >= max(1,N).
MAXIT
MAXIT is INTEGER On input, MAXIT contains the maximum number of iteration that are performed, 2 <= MAXIT <= 100 On exit, MAXIT contains the number of iteration steps taken by the algorithm.
TAU
TAU is DOUBLE PRECISION On input, TAU contains the additional security factor for the stopping criterion, typical values are 0.1 On exit, TAU contains the last relative residual when the stopping criterion got valid.
CONVLOG
CONVLOG is DOUBLE PRECISION array, dimension (MAXIT) The CONVLOG array contains the convergence history of the iterative refinement. CONVLOG(I) contains the maximum relative residual of both equations before it is solved for the I-th time.
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LDWORK)) Workspace for the algorithm. The optmimal workspace is returned in LDWORK, if LDWORK == -1 on input. In this case no computations are performed.
LDWORK
LDWORK is INTEGER If LDWORK == -1 the subroutine will return the required size of the workspace in LDWORK on exit. No computations are performed and none of the arrays are referenced.
INFO
INFO is INTEGER == 0: Success > 0: Iteration failed in step INFO < 0: if INFO = -i, the i-th argument had an illegal value = -50: Some of the internal settings like NB,... are incorrect.
- See also
DLA_TGCSYLV_DAG
DLA_TGCSYLV_LEVEL3
DLA_TGCSYLV_L3_2S
DLA_TGCSYLV_L2_UNOPT
DLA_TGCSYLV_L2
DLA_TGCSYLV_L2_REORDER
DLA_TGCSYLV_L2_LOCAL_COPY_32
DLA_TGCSYLV_L2_LOCAL_COPY_64
DLA_TGCSYLV_L2_LOCAL_COPY_96
DLA_TGCSYLV_L2_LOCAL_COPY_128
DLA_TGCSYLV_L2_LOCAL_COPY
- Author
Martin Koehler, MPI Magdeburg
- Date
Januar 2023
Definition at line 381 of file dla_ggcsylv_refine.f90.
subroutine dla_ggsylv (character, dimension(1) facta, character, dimension(1) factb, character, dimension(1) transa, character, dimension(1) transb, double precision sgn, integer m, integer n, double precision, dimension(lda,*) a, integer lda, double precision, dimension(ldb, *) b, integer ldb, double precision, dimension(ldc, *) c, integer ldc, double precision, dimension(ldd,*) d, integer ldd, double precision, dimension(ldqa, *) qa, integer ldqa, double precision, dimension(ldza, *) za, integer ldza, double precision, dimension(ldqb, *) qb, integer ldqb, double precision, dimension(ldzb, *) zb, integer ldzb, double precision, dimension(ldx, *) x, integer ldx, double precision scale, double precision, dimension(*) work, integer ldwork, integer info)
Frontend for the solution of Generalized Sylvester Equations.
Purpose:
DLA_GGSYLV solves a generalized Sylvester equation of the following forms op1(A) * X * op2(B) + op1(C) * X * op2(D) = SCALE * Y (1) or op1(A) * X * op2(B) - op1(C) * X * op2(D) = SCALE * Y (2) where (A,C) is a M-by-M matrix pencil and (B,D) is a N-by-N matrix pencil. The right hand side Y and the solution X M-by-N matrices. The pencils (A,C) and (B,D) can be either given as general unreduced matrices or in terms of their generalized Schur decomposition. If they are given as general matrices their generalized Schur decomposition will be computed.
- Parameters
FACTA
FACTA is CHARACTER Specifies how the matrix pencil (A,C) is given. == 'N': The matrix pencil (A,C) is given as a general matrices and its Schur decomposition A = QA*S*ZA**T, C = QA*R*ZA**T will be computed. == 'F': The matrix pencil (A,C) is already in generalized Schur form and S, R, QA, and ZA are given.
FACTB
FACTB is CHARACTER Specifies how the matrix pencil (B,D) is given. == 'N': The matrix pencil (B,D) is given as a general matrices and its Schur decomposition B = QB*U*ZB**T, D = QB*V*ZB**T will be computed. == 'F': The matrix pencil (B,D) is already in generalized Schur form and U, V, QB, and ZB are given.
TRANSA
TRANSA is CHARACTER Specifies the form of the system of equations with respect to A and C : == 'N': op1(A) = A == 'T': op1(A) = A**T
TRANSB
TRANSB is CHARACTER Specifies the form of the system of equations with respect to B and D: == 'N': op2(B) = B, == 'T': op2(B) = B**T
SGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between the two parts of the Sylvester equation. = 1 : Solve Equation (1) == -1: Solve Equation (2)
M
M is INTEGER The order of the matrices A and C. M >= 0.
N
N is INTEGER The order of the matrices B and D. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,M) If FACT == 'N', the matrix A is a general matrix and it is overwritten with the (quasi-) upper triangular factor S of the Schur decomposition of (A,C). If FACT == 'F', the matrix A contains its (quasi-) upper triangular matrix S of the Schur decomposition of (A,C).
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
B
B is DOUBLE PRECISION array, dimension (LDB,N) If FACT == 'N', the matrix B is a general matrix and it is overwritten with the (quasi-) upper triangular factor U of the Schur decomposition of (B,D). If FACT == 'F', the matrix B contains its (quasi-) upper triangular matrix U of the Schur decomposition of (B,D).
LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
C
C is DOUBLE PRECISION array, dimension (LDC,M) If FACT == 'N', the matrix C is a general matrix and it is overwritten with the upper triangular factor R of the Schur decomposition of (A,C). If FACT == 'F', the matrix C contains its upper triangular matrix R of the Schur decomposition of (A,C).
LDC
LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).
D
D is DOUBLE PRECISION array, dimension (LDD,N) If FACT == 'N', the matrix D is a general matrix and it is overwritten with the upper triangular factor V of the Schur decomposition of (B,D). If FACT == 'F', the matrix D contains its upper triangular matrix V of the Schur decomposition of (B,D).
LDD
LDD is INTEGER The leading dimension of the array D. LDD >= max(1,N).
QA
QA is DOUBLE PRECISION array, dimension (LDQA,M) If FACT == 'N', the matrix QA is an empty M-by-M matrix on input and contains the left Schur vectors of (A,C) on output. If FACT == 'F', the matrix QA contains the left Schur vectors of (A,C).
LDQA
LDQA is INTEGER The leading dimension of the array QA. LDQA >= max(1,M).
ZA
ZA is DOUBLE PRECISION array, dimension (LDZA,M) If FACT == 'N', the matrix ZA is an empty M-by-M matrix on input and contains the right Schur vectors of (A,C) on output. If FACT == 'F', the matrix ZA contains the right Schur vectors of (A,C).
LDZA
LDZA is INTEGER The leading dimension of the array ZA. LDZA >= max(1,M).
QB
QB is DOUBLE PRECISION array, dimension (LDQB,N) If FACT == 'N', the matrix QB is an empty N-by-N matrix on input and contains the left Schur vectors of (B,D) on output. If FACT == 'F', the matrix QB contains the left Schur vectors of (B,D).
LDQB
LDQB is INTEGER The leading dimension of the array QB. LDQB >= max(1,N).
ZB
ZB is DOUBLE PRECISION array, dimension (LDZB,N) If FACT == 'N', the matrix ZB is an empty N-by-N matrix on input and contains the right Schur vectors of (B,D) on output. If FACT == 'F', the matrix ZB contains the right Schur vectors of (B,D).
LDZB
LDZB is INTEGER The leading dimension of the array ZB. LDZB >= max(1,N).
X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2) Right hand side Y and the solution X are M-by-N matrices.
LDX
LDX is INTEGER The leading dimension of the array X. LDX >= max(1,M).
SCALE
SCALE is DOUBLE PRECISION SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LDWORK)) Workspace for the algorithm. The optmimal workspace is given either by \ref mepack_memory_frontend or a previous call to the this routine with LDWORK === -1.
LDWORK
LDWORK is INTEGER Size of the workspace for the algorithm. This can be determined by a call \ref mepack_memory_frontend . Alternatively, if LDWORK == -1 on input, the subroutine will return the required size of the workspace in LDWORK without performing any computations.
INFO
INFO is INTEGER == 0: successful exit = 1: DGGES failed = 2: DLA_SORT_GEV failed = 3: Inner solver failed < 0: if INFO = -i, the i-th argument had an illegal value
- See also
DLA_TGSYLV_DAG
DLA_TGSYLV_L3_COLWISE
DLA_TGSYLV_L3_2S
DLA_TGSYLV_L2_REORDER
DLA_TGSYLV_L2
DLA_TGSYLV_L2_COLWISE
DLA_TGSYLV_L2_LOCAL_COPY_32
DLA_TGSYLV_L2_LOCAL_COPY_64
DLA_TGSYLV_L2_LOCAL_COPY_96
DLA_TGSYLV_L2_LOCAL_COPY_128
DLA_TGSYLV_L2_LOCAL_COPY
DLA_TGSYLV_GARDINER_LAUB
- Author
Martin Koehler, MPI Magdeburg
- Date
Januar 2023
Definition at line 299 of file dla_ggsylv.f90.
subroutine dla_ggsylv_refine (character, dimension(1) transa, character, dimension(1) transb, character, dimension(1) guess, double precision sgn, integer m, integer n, double precision, dimension(lda, *) a, integer lda, double precision, dimension(ldb, *) b, integer ldb, double precision, dimension(ldc, *) c, integer ldc, double precision, dimension(ldd, *) d, integer ldd, double precision, dimension ( ldx , * ) x, integer ldx, double precision, dimension (ldy, *) y, integer ldy, double precision, dimension(ldas, *) as, integer ldas, double precision, dimension(ldbs,*) bs, integer ldbs, double precision, dimension(ldcs, *) cs, integer ldcs, double precision, dimension(ldds, *) ds, integer ldds, double precision, dimension(ldq, *) q, integer ldq, double precision, dimension(ldz, *) z, integer ldz, double precision, dimension(ldu, *) u, integer ldu, double precision, dimension(ldv, *) v, integer ldv, integer maxit, double precision tau, double precision, dimension(*) convlog, double precision, dimension(*) work, integer ldwork, integer info)
Iterative Refinement for the Generalized Sylvester Equations.
Purpose:
DLA_GGSYLV_REFINE solves a generalized Sylvester equation of the following forms op1(A) * X * op2(B) + SGN * op1(C) * X * op2(D) = Y (1) with iterative refinement, Thereby (A,C) is a M-by-M matrix pencil and (B,D) is a N-by-N matrix pencil. The right hand side Y and the solution X are M-by-N matrices. The pencils (A,C) and (B,D) need to be given in the original form as well as in their generalized Schur decomposition since both are required in the iterative refinement procedure.
- Parameters
TRANSA
TRANSA is CHARACTER Specifies the form of the system of equations with respect to A and C : == 'N': op1(A) = A == 'T': op1(A) = A**T
TRANSB
TRANSB is CHARACTER Specifies the form of the system of equations with respect to B and D: == 'N': op2(B) = B, == 'T': op2(B) = B**T
GUESS
GUESS is CHARACTER Specifies whether X contains an initial guess or nor not. = 'I': X contains an initial guess = 'N': No initial guess, X is set to zero at the begin of the iteration.
SGN
SGN is DOUBLE PRECISION, allowed values: +/-1 Specifies the sign between in the first equation.
M
M is INTEGER The order of the matrices A and C. M >= 0.
N
N is INTEGER The order of the matrices B and D. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,M) The array A contains the original matrix A defining the eqaution.
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
B
B is DOUBLE PRECISION array, dimension (LDB,N) The array B contains the original matrix B defining the eqaution.
LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
C
C is DOUBLE PRECISION array, dimension (LDC,M) The array C contains the original matrix C defining the eqaution.
LDC
LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).
D
D is DOUBLE PRECISION array, dimension (LDD,N) The array D contains the original matrix D defining the eqaution.
LDD
LDD is INTEGER The leading dimension of the array D. LDD >= max(1,N).
X
X is DOUBLE PRECISION array, dimension (LDX,N) On input, the array X contains the initial guess, if GUESS = 'I'. On output, the array X contains the solution X.
LDX
LDX is INTEGER The leading dimension of the array X. LDX >= max(1,M).
Y
Y is DOUBLE PRECISION array, dimension (LDY,N) On input, the array Y contains the right hand side Y. The array stays unchanged during the iteration.
LDY
LDY is INTEGER The leading dimension of the array Y. LDY >= max(1,M).
AS
AS is DOUBLE PRECISION array, dimension (LDAS,M) The array AS contains the generalized Schur decomposition of the A.
LDAS
LDAS is INTEGER The leading dimension of the array AS. LDAS >= max(1,M).
BS
BS is DOUBLE PRECISION array, dimension (LDBS,N) The array BS contains the generalized Schur decomposition of the B.
LDBS
LDBS is INTEGER The leading dimension of the array BS. LDBS >= max(1,N).
CS
CS is DOUBLE PRECISION array, dimension (LDCS,M) The array CS contains the generalized Schur decomposition of the C.
LDCS
LDCS is INTEGER The leading dimension of the array CS. LDCS >= max(1,M).
DS
DS is DOUBLE PRECISION array, dimension (LDDS,N) The array DS contains the generalized Schur decomposition of the D.
LDDS
LDDS is INTEGER The leading dimension of the array DS. LDDS >= max(1,N).
Q
Q is DOUBLE PRECISION array, dimension (LDQ,M) The array Q contains the left generalized Schur vectors for (A,C) as returned by DGGES.
LDQ
LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,M).
Z
Z is DOUBLE PRECISION array, dimension (LDZ,M) The array Z contains the right generalized Schur vectors for (A,C) as returned by DGGES.
LDZ
LDZ is INTEGER The leading dimension of the array Z. LDZ >= max(1,M).
U
U is DOUBLE PRECISION array, dimension (LDU,N) The array U contains the left generalized Schur vectors for (B,D) as returned by DGGES.
LDU
LDU is INTEGER The leading dimension of the array U. LDU >= max(1,N).
V
V is DOUBLE PRECISION array, dimension (LDV,N) The array V contains the right generalized Schur vectors for (B,D) as returned by DGGES.
LDV
LDV is INTEGER The leading dimension of the array V. LDV >= max(1,N).
MAXIT
MAXIT is INTEGER On input, MAXIT contains the maximum number of iteration that are performed, 2 <= MAXIT <= 100 On exit, MAXIT contains the number of iteration steps taken by the algorithm.
TAU
TAU is DOUBLE PRECISION On input, TAU contains the additional security factor for the stopping criterion, typical values are 0.1 On exit, TAU contains the last relative residual when the stopping criterion got valid.
CONVLOG
CONVLOG is DOUBLE PRECISION array, dimension (MAXIT) The CONVLOG array contains the convergence history of the iterative refinement. CONVLOG(I) contains the maximum relative residual before it is solved for the I-th time.
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LDWORK)) Workspace for the algorithm. The optmimal workspace is returned in LDWORK, if LDWORK == -1 on input. In this case no computations are performed.
LDWORK
LDWORK is INTEGER If LDWORK == -1 the subroutine will return the required size of the workspace in LDWORK on exit. No computations are performed and none of the arrays are referenced.
INFO
INFO is INTEGER == 0: Success > 0: Iteration failed in step INFO < 0: if INFO = -i, the i-th argument had an illegal value = -50: Some of the internal settings like NB,... are incorrect.
- See also
DLA_TGSYLV_DAG
DLA_TGSYLV_LEVEL3
DLA_TGSYLV_L3_2S
DLA_TGSYLV_L2_UNOPT
DLA_TGSYLV_L2
DLA_TGSYLV_L2_REORDER
DLA_TGSYLV_L2_LOCAL_COPY_32
DLA_TGSYLV_L2_LOCAL_COPY_64
DLA_TGSYLV_L2_LOCAL_COPY_96
DLA_TGSYLV_L2_LOCAL_COPY_128
DLA_TGSYLV_L2_LOCAL_COPY
DLA_TGSYLV_GARDINER_LAUB
- Author
Martin Koehler, MPI Magdeburg
- Date
Januar 2023
Definition at line 349 of file dla_ggsylv_refine.f90.
Author
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