hbgst - {hb,sb}gst: reduction to standard form, banded

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Sun Jul 20 2025 01:40:05 hbgst(3)

subroutinechbgst(charactervect,characteruplo,integern,integerka,integerkb,complex,dimension(ldab,*)ab,integerldab,complex,dimension(ldbb,*)bb,integerldbb,complex,dimension(ldx,*)x,integerldx,complex,dimension(*)work,real,dimension(*)rwork,integerinfo)CHBGSTPurpose: CHBGST reduces a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, such that C has the same bandwidth as A. B must have been previously factorized as S**H*S by CPBSTF, using a split Cholesky factorization. A is overwritten by C = X**H*A*X, where X = S**(-1)*Q and Q is a unitary matrix chosen to preserve the bandwidth of A. ParametersVECT VECT is CHARACTER*1 = 'N': do not form the transformation matrix X; = 'V': form X. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrices A and B. N >= 0. KA KA is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0. KB KB is INTEGER The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 0. AB AB is COMPLEX array, dimension (LDAB,N) On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first ka+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). On exit, the transformed matrix X**H*A*X, stored in the same format as A. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KA+1. BB BB is COMPLEX array, dimension (LDBB,N) The banded factor S from the split Cholesky factorization of B, as returned by CPBSTF, stored in the first kb+1 rows of the array. LDBB LDBB is INTEGER The leading dimension of the array BB. LDBB >= KB+1. X X is COMPLEX array, dimension (LDX,N) If VECT = 'V', the n-by-n matrix X. If VECT = 'N', the array X is not referenced. LDX LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise. WORK WORK is COMPLEX array, dimension (N) RWORK RWORK is REAL array, dimension (N) 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. subroutinedsbgst(charactervect,characteruplo,integern,integerka,integerkb,doubleprecision,dimension(ldab,*)ab,integerldab,doubleprecision,dimension(ldbb,*)bb,integerldbb,doubleprecision,dimension(ldx,*)x,integerldx,doubleprecision,dimension(*)work,integerinfo)DSBGSTPurpose: DSBGST reduces a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, such that C has the same bandwidth as A. B must have been previously factorized as S**T*S by DPBSTF, using a split Cholesky factorization. A is overwritten by C = X**T*A*X, where X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the bandwidth of A. ParametersVECT VECT is CHARACTER*1 = 'N': do not form the transformation matrix X; = 'V': form X. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrices A and B. N >= 0. KA KA is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0. KB KB is INTEGER The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 0. AB AB is DOUBLE PRECISION array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first ka+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). On exit, the transformed matrix X**T*A*X, stored in the same format as A. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KA+1. BB BB is DOUBLE PRECISION array, dimension (LDBB,N) The banded factor S from the split Cholesky factorization of B, as returned by DPBSTF, stored in the first KB+1 rows of the array. LDBB LDBB is INTEGER The leading dimension of the array BB. LDBB >= KB+1. X X is DOUBLE PRECISION array, dimension (LDX,N) If VECT = 'V', the n-by-n matrix X. If VECT = 'N', the array X is not referenced. LDX LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise. WORK WORK is DOUBLE PRECISION array, dimension (2*N) 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. subroutinessbgst(charactervect,characteruplo,integern,integerka,integerkb,real,dimension(ldab,*)ab,integerldab,real,dimension(ldbb,*)bb,integerldbb,real,dimension(ldx,*)x,integerldx,real,dimension(*)work,integerinfo)SSBGSTPurpose: SSBGST reduces a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, such that C has the same bandwidth as A. B must have been previously factorized as S**T*S by SPBSTF, using a split Cholesky factorization. A is overwritten by C = X**T*A*X, where X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the bandwidth of A. ParametersVECT VECT is CHARACTER*1 = 'N': do not form the transformation matrix X; = 'V': form X. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrices A and B. N >= 0. KA KA is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0. KB KB is INTEGER The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 0. AB AB is REAL array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first ka+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). On exit, the transformed matrix X**T*A*X, stored in the same format as A. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KA+1. BB BB is REAL array, dimension (LDBB,N) The banded factor S from the split Cholesky factorization of B, as returned by SPBSTF, stored in the first KB+1 rows of the array. LDBB LDBB is INTEGER The leading dimension of the array BB. LDBB >= KB+1. X X is REAL array, dimension (LDX,N) If VECT = 'V', the n-by-n matrix X. If VECT = 'N', the array X is not referenced. LDX LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise. WORK WORK is REAL array, dimension (2*N) 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. subroutinezhbgst(charactervect,characteruplo,integern,integerka,integerkb,complex*16,dimension(ldab,*)ab,integerldab,complex*16,dimension(ldbb,*)bb,integerldbb,complex*16,dimension(ldx,*)x,integerldx,complex*16,dimension(*)work,doubleprecision,dimension(*)rwork,integerinfo)ZHBGSTPurpose: ZHBGST reduces a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, such that C has the same bandwidth as A. B must have been previously factorized as S**H*S by ZPBSTF, using a split Cholesky factorization. A is overwritten by C = X**H*A*X, where X = S**(-1)*Q and Q is a unitary matrix chosen to preserve the bandwidth of A. ParametersVECT VECT is CHARACTER*1 = 'N': do not form the transformation matrix X; = 'V': form X. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrices A and B. N >= 0. KA KA is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0. KB KB is INTEGER The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 0. AB AB is COMPLEX*16 array, dimension (LDAB,N) On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first ka+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). On exit, the transformed matrix X**H*A*X, stored in the same format as A. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KA+1. BB BB is COMPLEX*16 array, dimension (LDBB,N) The banded factor S from the split Cholesky factorization of B, as returned by ZPBSTF, stored in the first kb+1 rows of the array. LDBB LDBB is INTEGER The leading dimension of the array BB. LDBB >= KB+1. X X is COMPLEX*16 array, dimension (LDX,N) If VECT = 'V', the n-by-n matrix X. If VECT = 'N', the array X is not referenced. LDX LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise. WORK WORK is COMPLEX*16 array, dimension (N) RWORK RWORK is DOUBLE PRECISION array, dimension (N) 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.

hbgst - {hb,sb}gst: reduction to standard form, banded

Functions subroutine chbgst (vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx, work, rwork, info) CHBGST subroutine dsbgst (vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx, work, info) DSBGST subroutine ssbgst (vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx, work, info) SSBGST subroutine zhbgst (vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx, work, rwork, info) ZHBGST