tpmlqt - tpmlqt: applies Q

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

subroutinectpmlqt(characterside,charactertrans,integerm,integern,integerk,integerl,integermb,complex,dimension(ldv,*)v,integerldv,complex,dimension(ldt,*)t,integerldt,complex,dimension(lda,*)a,integerlda,complex,dimension(ldb,*)b,integerldb,complex,dimension(*)work,integerinfo)CTPMLQTPurpose: CTPMLQT applies a complex unitary matrix Q obtained from a 'triangular-pentagonal' complex block reflector H to a general complex matrix C, which consists of two blocks A and B. ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right. 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 B. M >= 0. N N is INTEGER The number of columns of the matrix B. N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. L L is INTEGER The order of the trapezoidal part of V. K >= L >= 0. See Further Details. MB MB is INTEGER The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in CTPLQT. V V is COMPLEX array, dimension (LDV,K) The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CTPLQT in B. See Further Details. LDV LDV is INTEGER The leading dimension of the array V. LDV >= K. T T is COMPLEX array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by CTPLQT, stored as a MB-by-K matrix. LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. A A is COMPLEX array, dimension (LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R' On entry, the K-by-N or M-by-K matrix A. On exit, A is overwritten by the corresponding block of Q*C or Q**H*C or C*Q or C*Q**H. See Further Details. LDA LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,K); If SIDE = 'R', LDA >= max(1,M). B B is COMPLEX array, dimension (LDB,N) On entry, the M-by-N matrix B. On exit, B is overwritten by the corresponding block of Q*C or Q**H*C or C*Q or C*Q**H. See Further Details. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M). WORK WORK is COMPLEX array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'. 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. FurtherDetails: The columns of the pentagonal matrix V contain the elementary reflectors H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a trapezoidal block V2: V = [V1] [V2]. The size of the trapezoidal block V2 is determined by the parameter L, where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L rows of a K-by-K upper triangular matrix. If L=K, V2 is lower triangular; if L=0, there is no trapezoidal block, hence V = V1 is rectangular. If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is K-by-M. [B] If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is K-by-N. The complex unitary matrix Q is formed from V and T. If TRANS='N' and SIDE='L', C is on exit replaced with Q * C. If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C. If TRANS='N' and SIDE='R', C is on exit replaced with C * Q. If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H. subroutinedtpmlqt(characterside,charactertrans,integerm,integern,integerk,integerl,integermb,doubleprecision,dimension(ldv,*)v,integerldv,doubleprecision,dimension(ldt,*)t,integerldt,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(ldb,*)b,integerldb,doubleprecision,dimension(*)work,integerinfo)DTPMLQTPurpose: DTPMQRT applies a real orthogonal matrix Q obtained from a 'triangular-pentagonal' real block reflector H to a general real matrix C, which consists of two blocks A and B. ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right. 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 B. M >= 0. N N is INTEGER The number of columns of the matrix B. N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. L L is INTEGER The order of the trapezoidal part of V. K >= L >= 0. See Further Details. MB MB is INTEGER The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in DTPLQT. V V is DOUBLE PRECISION array, dimension (LDV,K) The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DTPLQT in B. See Further Details. LDV LDV is INTEGER The leading dimension of the array V. LDV >= K. T T is DOUBLE PRECISION array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by DTPLQT, stored as a MB-by-K matrix. LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. A A is DOUBLE PRECISION array, dimension (LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R' On entry, the K-by-N or M-by-K matrix A. On exit, A is overwritten by the corresponding block of Q*C or Q**T*C or C*Q or C*Q**T. See Further Details. LDA LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,K); If SIDE = 'R', LDA >= max(1,M). B B is DOUBLE PRECISION array, dimension (LDB,N) On entry, the M-by-N matrix B. On exit, B is overwritten by the corresponding block of Q*C or Q**T*C or C*Q or C*Q**T. See Further Details. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M). WORK WORK is DOUBLE PRECISION array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'. 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. FurtherDetails: The columns of the pentagonal matrix V contain the elementary reflectors H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a trapezoidal block V2: V = [V1] [V2]. The size of the trapezoidal block V2 is determined by the parameter L, where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L rows of a K-by-K upper triangular matrix. If L=K, V2 is lower triangular; if L=0, there is no trapezoidal block, hence V = V1 is rectangular. If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is K-by-M. [B] If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is K-by-N. The real orthogonal matrix Q is formed from V and T. If TRANS='N' and SIDE='L', C is on exit replaced with Q * C. If TRANS='T' and SIDE='L', C is on exit replaced with Q**T * C. If TRANS='N' and SIDE='R', C is on exit replaced with C * Q. If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T. subroutinestpmlqt(characterside,charactertrans,integerm,integern,integerk,integerl,integermb,real,dimension(ldv,*)v,integerldv,real,dimension(ldt,*)t,integerldt,real,dimension(lda,*)a,integerlda,real,dimension(ldb,*)b,integerldb,real,dimension(*)work,integerinfo)STPMLQTPurpose: STPMLQT applies a real orthogonal matrix Q obtained from a 'triangular-pentagonal' real block reflector H to a general real matrix C, which consists of two blocks A and B. ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right. 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 B. M >= 0. N N is INTEGER The number of columns of the matrix B. N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. L L is INTEGER The order of the trapezoidal part of V. K >= L >= 0. See Further Details. MB MB is INTEGER The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in STPLQT. V V is REAL array, dimension (LDV,K) The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by STPLQT in B. See Further Details. LDV LDV is INTEGER The leading dimension of the array V. LDV >= K. T T is REAL array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by STPLQT, stored as a MB-by-K matrix. LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. A A is REAL array, dimension (LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R' On entry, the K-by-N or M-by-K matrix A. On exit, A is overwritten by the corresponding block of Q*C or Q**T*C or C*Q or C*Q**T. See Further Details. LDA LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,K); If SIDE = 'R', LDA >= max(1,M). B B is REAL array, dimension (LDB,N) On entry, the M-by-N matrix B. On exit, B is overwritten by the corresponding block of Q*C or Q**T*C or C*Q or C*Q**T. See Further Details. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M). WORK WORK is REAL array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'. 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. FurtherDetails: The columns of the pentagonal matrix V contain the elementary reflectors H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a trapezoidal block V2: V = [V1] [V2]. The size of the trapezoidal block V2 is determined by the parameter L, where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L rows of a K-by-K upper triangular matrix. If L=K, V2 is lower triangular; if L=0, there is no trapezoidal block, hence V = V1 is rectangular. If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is K-by-M. [B] If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is K-by-N. The real orthogonal matrix Q is formed from V and T. If TRANS='N' and SIDE='L', C is on exit replaced with Q * C. If TRANS='T' and SIDE='L', C is on exit replaced with Q**T * C. If TRANS='N' and SIDE='R', C is on exit replaced with C * Q. If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T. subroutineztpmlqt(characterside,charactertrans,integerm,integern,integerk,integerl,integermb,complex*16,dimension(ldv,*)v,integerldv,complex*16,dimension(ldt,*)t,integerldt,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(ldb,*)b,integerldb,complex*16,dimension(*)work,integerinfo)ZTPMLQTPurpose: ZTPMLQT applies a complex unitary matrix Q obtained from a 'triangular-pentagonal' complex block reflector H to a general complex matrix C, which consists of two blocks A and B. ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right. 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 B. M >= 0. N N is INTEGER The number of columns of the matrix B. N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. L L is INTEGER The order of the trapezoidal part of V. K >= L >= 0. See Further Details. MB MB is INTEGER The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in ZTPLQT. V V is COMPLEX*16 array, dimension (LDV,K) The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZTPLQT in B. See Further Details. LDV LDV is INTEGER The leading dimension of the array V. LDV >= K. T T is COMPLEX*16 array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by ZTPLQT, stored as a MB-by-K matrix. LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. A A is COMPLEX*16 array, dimension (LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R' On entry, the K-by-N or M-by-K matrix A. On exit, A is overwritten by the corresponding block of Q*C or Q**H*C or C*Q or C*Q**H. See Further Details. LDA LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,K); If SIDE = 'R', LDA >= max(1,M). B B is COMPLEX*16 array, dimension (LDB,N) On entry, the M-by-N matrix B. On exit, B is overwritten by the corresponding block of Q*C or Q**H*C or C*Q or C*Q**H. See Further Details. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M). WORK WORK is COMPLEX*16 array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'. 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. FurtherDetails: The columns of the pentagonal matrix V contain the elementary reflectors H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a trapezoidal block V2: V = [V1] [V2]. The size of the trapezoidal block V2 is determined by the parameter L, where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L rows of a K-by-K upper triangular matrix. If L=K, V2 is lower triangular; if L=0, there is no trapezoidal block, hence V = V1 is rectangular. If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is K-by-M. [B] If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is K-by-N. The complex unitary matrix Q is formed from V and T. If TRANS='N' and SIDE='L', C is on exit replaced with Q * C. If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C. If TRANS='N' and SIDE='R', C is on exit replaced with C * Q. If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.

tpmlqt - tpmlqt: applies Q

Functions subroutine ctpmlqt (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info) CTPMLQT subroutine dtpmlqt (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info) DTPMLQT subroutine stpmlqt (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info) STPMLQT subroutine ztpmlqt (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info) ZTPMLQT