trsyl - trsyl: Sylvester equation

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Thu Aug 7 2025 17:26:25 trsyl(3)

subroutinectrsyl(charactertrana,charactertranb,integerisgn,integerm,integern,complex,dimension(lda,*)a,integerlda,complex,dimension(ldb,*)b,integerldb,complex,dimension(ldc,*)c,integerldc,realscale,integerinfo)CTRSYLPurpose: CTRSYL solves the complex Sylvester matrix equation: op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C, where op(A) = A or A**H, and A and B are both upper triangular. A is M-by-M and B is N-by-N; the right hand side C and the solution X are M-by-N; and scale is an output scale factor, set <= 1 to avoid overflow in X. ParametersTRANA TRANA is CHARACTER*1 Specifies the option op(A): = 'N': op(A) = A (No transpose) = 'C': op(A) = A**H (Conjugate transpose) TRANB TRANB is CHARACTER*1 Specifies the option op(B): = 'N': op(B) = B (No transpose) = 'C': op(B) = B**H (Conjugate transpose) ISGN ISGN is INTEGER Specifies the sign in the equation: = +1: solve op(A)*X + X*op(B) = scale*C = -1: solve op(A)*X - X*op(B) = scale*C M M is INTEGER The order of the matrix A, and the number of rows in the matrices X and C. M >= 0. N N is INTEGER The order of the matrix B, and the number of columns in the matrices X and C. N >= 0. A A is COMPLEX array, dimension (LDA,M) The upper triangular matrix A. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). B B is COMPLEX array, dimension (LDB,N) The upper triangular matrix B. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). C C is COMPLEX array, dimension (LDC,N) On entry, the M-by-N right hand side matrix C. On exit, C is overwritten by the solution matrix X. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M) SCALE SCALE is REAL The scale factor, scale, set <= 1 to avoid overflow in X. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value = 1: A and B have common or very close eigenvalues; perturbed values were used to solve the equation (but the matrices A and B are unchanged). Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinedtrsyl(charactertrana,charactertranb,integerisgn,integerm,integern,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(ldb,*)b,integerldb,doubleprecision,dimension(ldc,*)c,integerldc,doubleprecisionscale,integerinfo)DTRSYLPurpose: DTRSYL solves the real Sylvester matrix equation: op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C, where op(A) = A or A**T, and A and B are both upper quasi- triangular. A is M-by-M and B is N-by-N; the right hand side C and the solution X are M-by-N; and scale is an output scale factor, set <= 1 to avoid overflow in X. A and B must be in Schur canonical form (as returned by DHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign. ParametersTRANA TRANA is CHARACTER*1 Specifies the option op(A): = 'N': op(A) = A (No transpose) = 'T': op(A) = A**T (Transpose) = 'C': op(A) = A**H (Conjugate transpose = Transpose) TRANB TRANB is CHARACTER*1 Specifies the option op(B): = 'N': op(B) = B (No transpose) = 'T': op(B) = B**T (Transpose) = 'C': op(B) = B**H (Conjugate transpose = Transpose) ISGN ISGN is INTEGER Specifies the sign in the equation: = +1: solve op(A)*X + X*op(B) = scale*C = -1: solve op(A)*X - X*op(B) = scale*C M M is INTEGER The order of the matrix A, and the number of rows in the matrices X and C. M >= 0. N N is INTEGER The order of the matrix B, and the number of columns in the matrices X and C. N >= 0. A A is DOUBLE PRECISION array, dimension (LDA,M) The upper quasi-triangular matrix A, in Schur canonical form. 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 upper quasi-triangular matrix B, in Schur canonical form. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). C C is DOUBLE PRECISION array, dimension (LDC,N) On entry, the M-by-N right hand side matrix C. On exit, C is overwritten by the solution matrix X. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M) SCALE SCALE is DOUBLE PRECISION The scale factor, scale, set <= 1 to avoid overflow in X. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value = 1: A and B have common or very close eigenvalues; perturbed values were used to solve the equation (but the matrices A and B are unchanged). Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinestrsyl(charactertrana,charactertranb,integerisgn,integerm,integern,real,dimension(lda,*)a,integerlda,real,dimension(ldb,*)b,integerldb,real,dimension(ldc,*)c,integerldc,realscale,integerinfo)STRSYLPurpose: STRSYL solves the real Sylvester matrix equation: op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C, where op(A) = A or A**T, and A and B are both upper quasi- triangular. A is M-by-M and B is N-by-N; the right hand side C and the solution X are M-by-N; and scale is an output scale factor, set <= 1 to avoid overflow in X. A and B must be in Schur canonical form (as returned by SHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign. ParametersTRANA TRANA is CHARACTER*1 Specifies the option op(A): = 'N': op(A) = A (No transpose) = 'T': op(A) = A**T (Transpose) = 'C': op(A) = A**H (Conjugate transpose = Transpose) TRANB TRANB is CHARACTER*1 Specifies the option op(B): = 'N': op(B) = B (No transpose) = 'T': op(B) = B**T (Transpose) = 'C': op(B) = B**H (Conjugate transpose = Transpose) ISGN ISGN is INTEGER Specifies the sign in the equation: = +1: solve op(A)*X + X*op(B) = scale*C = -1: solve op(A)*X - X*op(B) = scale*C M M is INTEGER The order of the matrix A, and the number of rows in the matrices X and C. M >= 0. N N is INTEGER The order of the matrix B, and the number of columns in the matrices X and C. N >= 0. A A is REAL array, dimension (LDA,M) The upper quasi-triangular matrix A, in Schur canonical form. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). B B is REAL array, dimension (LDB,N) The upper quasi-triangular matrix B, in Schur canonical form. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). C C is REAL array, dimension (LDC,N) On entry, the M-by-N right hand side matrix C. On exit, C is overwritten by the solution matrix X. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M) SCALE SCALE is REAL The scale factor, scale, set <= 1 to avoid overflow in X. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value = 1: A and B have common or very close eigenvalues; perturbed values were used to solve the equation (but the matrices A and B are unchanged). Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutineztrsyl(charactertrana,charactertranb,integerisgn,integerm,integern,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(ldb,*)b,integerldb,complex*16,dimension(ldc,*)c,integerldc,doubleprecisionscale,integerinfo)ZTRSYLPurpose: ZTRSYL solves the complex Sylvester matrix equation: op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C, where op(A) = A or A**H, and A and B are both upper triangular. A is M-by-M and B is N-by-N; the right hand side C and the solution X are M-by-N; and scale is an output scale factor, set <= 1 to avoid overflow in X. ParametersTRANA TRANA is CHARACTER*1 Specifies the option op(A): = 'N': op(A) = A (No transpose) = 'C': op(A) = A**H (Conjugate transpose) TRANB TRANB is CHARACTER*1 Specifies the option op(B): = 'N': op(B) = B (No transpose) = 'C': op(B) = B**H (Conjugate transpose) ISGN ISGN is INTEGER Specifies the sign in the equation: = +1: solve op(A)*X + X*op(B) = scale*C = -1: solve op(A)*X - X*op(B) = scale*C M M is INTEGER The order of the matrix A, and the number of rows in the matrices X and C. M >= 0. N N is INTEGER The order of the matrix B, and the number of columns in the matrices X and C. N >= 0. A A is COMPLEX*16 array, dimension (LDA,M) The upper triangular matrix A. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). B B is COMPLEX*16 array, dimension (LDB,N) The upper triangular matrix B. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). C C is COMPLEX*16 array, dimension (LDC,N) On entry, the M-by-N right hand side matrix C. On exit, C is overwritten by the solution matrix X. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M) SCALE SCALE is DOUBLE PRECISION The scale factor, scale, set <= 1 to avoid overflow in X. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value = 1: A and B have common or very close eigenvalues; perturbed values were used to solve the equation (but the matrices A and B are unchanged). Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.

trsyl - trsyl: Sylvester equation

Functions subroutine ctrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info) CTRSYL subroutine dtrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info) DTRSYL subroutine strsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info) STRSYL subroutine ztrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info) ZTRSYL