upgtr - {up,op}gtr: generate Q from hetrd

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

subroutinecupgtr(characteruplo,integern,complex,dimension(*)ap,complex,dimension(*)tau,complex,dimension(ldq,*)q,integerldq,complex,dimension(*)work,integerinfo)CUPGTRPurpose: CUPGTR generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by CHPTRD using packed storage: if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). ParametersUPLO UPLO is CHARACTER*1 = 'U': Upper triangular packed storage used in previous call to CHPTRD; = 'L': Lower triangular packed storage used in previous call to CHPTRD. N N is INTEGER The order of the matrix Q. N >= 0. AP AP is COMPLEX array, dimension (N*(N+1)/2) The vectors which define the elementary reflectors, as returned by CHPTRD. TAU TAU is COMPLEX array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CHPTRD. Q Q is COMPLEX array, dimension (LDQ,N) The N-by-N unitary matrix Q. LDQ LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N). WORK WORK is COMPLEX array, dimension (N-1) 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. subroutinedopgtr(characteruplo,integern,doubleprecision,dimension(*)ap,doubleprecision,dimension(*)tau,doubleprecision,dimension(ldq,*)q,integerldq,doubleprecision,dimension(*)work,integerinfo)DOPGTRPurpose: DOPGTR generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by DSPTRD using packed storage: if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). ParametersUPLO UPLO is CHARACTER*1 = 'U': Upper triangular packed storage used in previous call to DSPTRD; = 'L': Lower triangular packed storage used in previous call to DSPTRD. N N is INTEGER The order of the matrix Q. N >= 0. AP AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) The vectors which define the elementary reflectors, as returned by DSPTRD. TAU TAU is DOUBLE PRECISION array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DSPTRD. Q Q is DOUBLE PRECISION array, dimension (LDQ,N) The N-by-N orthogonal matrix Q. LDQ LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N). WORK WORK is DOUBLE PRECISION array, dimension (N-1) 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. subroutinesopgtr(characteruplo,integern,real,dimension(*)ap,real,dimension(*)tau,real,dimension(ldq,*)q,integerldq,real,dimension(*)work,integerinfo)SOPGTRPurpose: SOPGTR generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by SSPTRD using packed storage: if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). ParametersUPLO UPLO is CHARACTER*1 = 'U': Upper triangular packed storage used in previous call to SSPTRD; = 'L': Lower triangular packed storage used in previous call to SSPTRD. N N is INTEGER The order of the matrix Q. N >= 0. AP AP is REAL array, dimension (N*(N+1)/2) The vectors which define the elementary reflectors, as returned by SSPTRD. TAU TAU is REAL array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSPTRD. Q Q is REAL array, dimension (LDQ,N) The N-by-N orthogonal matrix Q. LDQ LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N). WORK WORK is REAL array, dimension (N-1) 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. subroutinezupgtr(characteruplo,integern,complex*16,dimension(*)ap,complex*16,dimension(*)tau,complex*16,dimension(ldq,*)q,integerldq,complex*16,dimension(*)work,integerinfo)ZUPGTRPurpose: ZUPGTR generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by ZHPTRD using packed storage: if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). ParametersUPLO UPLO is CHARACTER*1 = 'U': Upper triangular packed storage used in previous call to ZHPTRD; = 'L': Lower triangular packed storage used in previous call to ZHPTRD. N N is INTEGER The order of the matrix Q. N >= 0. AP AP is COMPLEX*16 array, dimension (N*(N+1)/2) The vectors which define the elementary reflectors, as returned by ZHPTRD. TAU TAU is COMPLEX*16 array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZHPTRD. Q Q is COMPLEX*16 array, dimension (LDQ,N) The N-by-N unitary matrix Q. LDQ LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N). WORK WORK is COMPLEX*16 array, dimension (N-1) 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.

upgtr - {up,op}gtr: generate Q from hetrd

Functions subroutine cupgtr (uplo, n, ap, tau, q, ldq, work, info) CUPGTR subroutine dopgtr (uplo, n, ap, tau, q, ldq, work, info) DOPGTR subroutine sopgtr (uplo, n, ap, tau, q, ldq, work, info) SOPGTR subroutine zupgtr (uplo, n, ap, tau, q, ldq, work, info) ZUPGTR