unmtr - {un,or}mtr: multiply by Q from hetrd

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

subroutinecunmtr(characterside,characteruplo,charactertrans,integerm,integern,complex,dimension(lda,*)a,integerlda,complex,dimension(*)tau,complex,dimension(ldc,*)c,integerldc,complex,dimension(*)work,integerlwork,integerinfo)CUNMTRPurpose: CUNMTR overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H where Q is a complex unitary matrix of order nq, with nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of nq-1 elementary reflectors, as returned by CHETRD: if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A contains elementary reflectors from CHETRD; = 'L': Lower triangle of A contains elementary reflectors from CHETRD. TRANS TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Conjugate transpose, apply Q**H. M M is INTEGER The number of rows of the matrix C. M >= 0. N N is INTEGER The number of columns of the matrix C. N >= 0. A A is COMPLEX array, dimension (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which define the elementary reflectors, as returned by CHETRD. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. TAU TAU is COMPLEX array, dimension (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CHETRD. C C is COMPLEX array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK LWORK is INTEGER The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = 'L', and LWORK >=M*NB if SIDE = 'R', where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 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. subroutinedormtr(characterside,characteruplo,charactertrans,integerm,integern,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(*)tau,doubleprecision,dimension(ldc,*)c,integerldc,doubleprecision,dimension(*)work,integerlwork,integerinfo)DORMTRPurpose: DORMTR overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix of order nq, with nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of nq-1 elementary reflectors, as returned by DSYTRD: if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A contains elementary reflectors from DSYTRD; = 'L': Lower triangle of A contains elementary reflectors from DSYTRD. TRANS TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T. M M is INTEGER The number of rows of the matrix C. M >= 0. N N is INTEGER The number of columns of the matrix C. N >= 0. A A is DOUBLE PRECISION array, dimension (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which define the elementary reflectors, as returned by DSYTRD. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. TAU TAU is DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DSYTRD. C C is DOUBLE PRECISION array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK LWORK is INTEGER The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 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. subroutinesormtr(characterside,characteruplo,charactertrans,integerm,integern,real,dimension(lda,*)a,integerlda,real,dimension(*)tau,real,dimension(ldc,*)c,integerldc,real,dimension(*)work,integerlwork,integerinfo)SORMTRPurpose: SORMTR overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix of order nq, with nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of nq-1 elementary reflectors, as returned by SSYTRD: if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A contains elementary reflectors from SSYTRD; = 'L': Lower triangle of A contains elementary reflectors from SSYTRD. TRANS TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T. M M is INTEGER The number of rows of the matrix C. M >= 0. N N is INTEGER The number of columns of the matrix C. N >= 0. A A is REAL array, dimension (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which define the elementary reflectors, as returned by SSYTRD. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. TAU TAU is REAL array, dimension (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSYTRD. C C is REAL array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK LWORK is INTEGER The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 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. subroutinezunmtr(characterside,characteruplo,charactertrans,integerm,integern,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(*)tau,complex*16,dimension(ldc,*)c,integerldc,complex*16,dimension(*)work,integerlwork,integerinfo)ZUNMTRPurpose: ZUNMTR overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H where Q is a complex unitary matrix of order nq, with nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of nq-1 elementary reflectors, as returned by ZHETRD: if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A contains elementary reflectors from ZHETRD; = 'L': Lower triangle of A contains elementary reflectors from ZHETRD. TRANS TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Conjugate transpose, apply Q**H. M M is INTEGER The number of rows of the matrix C. M >= 0. N N is INTEGER The number of columns of the matrix C. N >= 0. A A is COMPLEX*16 array, dimension (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which define the elementary reflectors, as returned by ZHETRD. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. TAU TAU is COMPLEX*16 array, dimension (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZHETRD. C C is COMPLEX*16 array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK LWORK is INTEGER The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = 'L', and LWORK >=M*NB if SIDE = 'R', where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 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.

unmtr - {un,or}mtr: multiply by Q from hetrd

Functions subroutine cunmtr (side, uplo, trans, m, n, a, lda, tau, c, ldc, work, lwork, info) CUNMTR subroutine dormtr (side, uplo, trans, m, n, a, lda, tau, c, ldc, work, lwork, info) DORMTR subroutine sormtr (side, uplo, trans, m, n, a, lda, tau, c, ldc, work, lwork, info) SORMTR subroutine zunmtr (side, uplo, trans, m, n, a, lda, tau, c, ldc, work, lwork, info) ZUNMTR